I received this message today from a student I taught for 3 years back in Oregon.

I wanted to thank you. Even though you are not my teacher anymore, you still help me all the time. You wrote in my yearbook to remember that I am good at math, and I always go back to that and it actually helps me when I am stressed about algebra. Whenever I think about it, I feel as though I can push through and actually do it. I am doing pretty well in it so far and I owe part of that to you.

Sometimes teaching is the best job in the world.

A journal on Teaching Math and my only hope for Professional Development

## Sunday, December 30, 2012

## Wednesday, December 19, 2012

### Common Core vs. Regents?

This being my first year teaching in New York, navigating the Regents has been a challenge. I feel so torn in different directions that I've ended up in a state of complete and utter indecision. Especially about geometry. Here are the facts:

- I'm teaching at a private school so technically, we don't have to do the Regents but our parents want us to offer Regents prep courses.
- The private school has its own curriculum imported from its California model that isn't correlated either to New York State or to the Common Core.
- We are restricted to 50 total sessions with the students per year rather than the 150 classroom hours you normally get at public school. If we need to go over 50, the parents have to pay more so we try very hard not to do that.
- I love all the ideas the blogging community has for geometry, but everyone seems to be pushing Common Core and the geometry Regents exam doesn't seem to be there yet.
- I have my own inclinations for teaching geometry that I'm having trouble shoving to the side to adhere to any standards.
- Two months ago my boss asked me to look at our boxed curriculum from California and compare it to the New York State Standards and the Regents exam and make sure they were aligned. I discovered that they couldn't be more different and she has asked me to come up with a Regents friendly curriculum map.

I LOVE the way Drawing on Math has organized her geometry class, but I'm really torn. I was also very inclined to do parallel lines and transverals right at the beginning but a Regents aligned textbook, AMSCO-Geometry, puts it more than half-way through the course. Why did they make this decision? Is there some profound reason students should do congruent triangles and transformations first? They've split up all the points of concurrency in triangles into different chapters too, whereas I was inclined to put them all together. Which way is best? A lot of the organization seems strange to me, but I've only learned geometry through teaching it over the past two years (I was skipped through it in High School and my college didn't offer any college level geometry courses) and I'm unsure whether or not to trust myself on what seems logical to me vs. how the book organizes material.

In the same Drawing on Math post, she also mentions scrapping most of the logic unit and only teaching converses. But the NYS standards have LOTS of logic material including converses, negations, contrapositives, direct and indirect proofs, truth tables and Law of Detachment. BUT, combing through old Regents exams reveals that they only ever seem to ask questions about negations, and the Common Core doesn't have much logic at all... Yet I love teaching it and when I got to college and took college level math courses, the fact that I'd been skipped through geometry became a real handicap in the more advanced proof based classes because I'd never been exposed to logic before. So I'm inclined to teach logic because knowing just high school level geo-logic would have really helped me.

*BUT*we only have 50 sessions and I can't waste time on material not on the Regents exam.*BUT*everyone's saying the Common Core is better anyway so shouldn't I align our curriculum to the Common core and not to a standardized test?*BUT*our kids*need*to pass the Regents because our parents care about it so much.
My heart tells me that I should just teach it in a way that feels right to me and if the kids really internalize the material they will pass the Regents. Yet the Regents has

[12/20/12 edited to add the following paragraph] I'm still struggling with the geo curriculum and I decided to trust the book and do triangles before parallel lines and transverals but I'm running into difficulties. If you don't do parallel lines and transversals first, then you can't do the proof that there are 180 degrees in a triangle (or at least you can't do my favorite one) and trying to do all the triangle stuff without this is pretty crippling. In fact talking about angles at all becomes a little sticky. We're supposed to do exterior angles in the triangle unit, but how do you prove any of the exterior angle theorems without knowing there are 180 degrees in a triangle? And what about AAS triangle congruence? They've thrown that in much later in the course 3 units after doing all the other triangle congruence theorems. I wish textbooks provided a justification for how they organize their content because I always start by trying to follow a book (they know best right? Tons of experts and trials in classrooms and thousands of dollars.) and then

*such*specific types of questions covering specific topics that I'm worried if I don't teach them with the Regents in mind, they'll get to the exam and it will use vocabulary they're not used to and ask types of questions we haven't covered. I wish the State would just trust me a little. I can help the students navigate this material but I want to let them enjoy it and I want to let them explore and I feel like I can't do that with this ticking bomb hanging over my head. I guess I just have to try something and hope. Teaching is about experimenting however nervous this makes me. I hate the idea of an experiment failing at the detriment to a student's enjoyment of math. But we learn by making mistakes right?[12/20/12 edited to add the following paragraph] I'm still struggling with the geo curriculum and I decided to trust the book and do triangles before parallel lines and transverals but I'm running into difficulties. If you don't do parallel lines and transversals first, then you can't do the proof that there are 180 degrees in a triangle (or at least you can't do my favorite one) and trying to do all the triangle stuff without this is pretty crippling. In fact talking about angles at all becomes a little sticky. We're supposed to do exterior angles in the triangle unit, but how do you prove any of the exterior angle theorems without knowing there are 180 degrees in a triangle? And what about AAS triangle congruence? They've thrown that in much later in the course 3 units after doing all the other triangle congruence theorems. I wish textbooks provided a justification for how they organize their content because I always start by trying to follow a book (they know best right? Tons of experts and trials in classrooms and thousands of dollars.) and then

*always*scrap the book a quarter of the way in because their sequencing just doesn't make sense to me. I wish I could squelch my internal sense of logic and just trust a textbook... my life would be so much easier.## Sunday, December 9, 2012

### Where are the history teacher bloggers?

I have a confession to make. I majored in history. I loved doing research and piecing together an argument out of scraps. I loved analyzing bias and wondering about how people's perceptions of history, true or false, shape how they act. But teaching history was a whole different world. The litany of timelines, facts, dates, and vocab words I was supposed to shove into students' heads while the clock was ticking left me with a sense of hopelessness. I switched to teaching math. In college I'd always taken a math class on the side because compared to studying history where nothing can be certain, the logical certainty of math kept my head from exploding.

My boss asked me recently, because of my history background, to help reshape the 8th grade history curriculum for our school. We needed to take their curriculum that had been designed for California state standards and adapt it to fit into New York State standards. Whenever I'm about to plan a lesson for math I consult my friendly math blogging community. Sometimes I search specific blogs, sometimes I just google "system of equations activity" and scroll through the first few entries until I find one published by a blogger. I've used curricula published by textbooks and by for-profit internet companies and visited the teacher stores and bought the workbooks. None of the published material out there can even come close to matching the creativity of what math bloggers produce. The lessons published by math teacher bloggers are adaptable, easy to implement, enjoyable and thought provoking. I've been relying on this wonderful community for the last three years and I can't imagine teaching without it. So when I needed to help develop curriculum for history, with joy I started googling to find fellow history teachers who could help me with this project. Crickets. Silence. Page after page of historical info sites, or lessons published by for-profit companies. Museum published curricula or government sponsored curricula abounded. PBS has a wealth of nice lesson plans. But where are the bloggers? Maybe they're out there but they're much harder to find than their math teacher counterparts. In fact, even while math teacher blogging is rich and prolific, none of the math teachers I've run across in real life know about this community and while I give them lists of my favorite blogs and tell them that it really is worth their time, none of them have followed up.

Reading math teacher blogs has revolutionized the way I think about teaching. It has made me humble and insecure at times (because I feel like there's no way I'll be as awesome as the teachers I read about,) but that has pushed me to try more ideas, to keep pushing myself, to try to come up with lessons worthy enough to share. When I feel overwhelmed or terrified by the responsibilities I've assumed the blogging community shows me others who push through difficulties with humor and humility and this gives me strength. I guess I'm just trying to give a post Thanksgiving thanks. My two month foray into history has made me so appreciative that there are math teachers out there taking care of each other. I'm not a very good blogger yet, but I will keep striving to give back to this community that has given me so much.

My boss asked me recently, because of my history background, to help reshape the 8th grade history curriculum for our school. We needed to take their curriculum that had been designed for California state standards and adapt it to fit into New York State standards. Whenever I'm about to plan a lesson for math I consult my friendly math blogging community. Sometimes I search specific blogs, sometimes I just google "system of equations activity" and scroll through the first few entries until I find one published by a blogger. I've used curricula published by textbooks and by for-profit internet companies and visited the teacher stores and bought the workbooks. None of the published material out there can even come close to matching the creativity of what math bloggers produce. The lessons published by math teacher bloggers are adaptable, easy to implement, enjoyable and thought provoking. I've been relying on this wonderful community for the last three years and I can't imagine teaching without it. So when I needed to help develop curriculum for history, with joy I started googling to find fellow history teachers who could help me with this project. Crickets. Silence. Page after page of historical info sites, or lessons published by for-profit companies. Museum published curricula or government sponsored curricula abounded. PBS has a wealth of nice lesson plans. But where are the bloggers? Maybe they're out there but they're much harder to find than their math teacher counterparts. In fact, even while math teacher blogging is rich and prolific, none of the math teachers I've run across in real life know about this community and while I give them lists of my favorite blogs and tell them that it really is worth their time, none of them have followed up.

Reading math teacher blogs has revolutionized the way I think about teaching. It has made me humble and insecure at times (because I feel like there's no way I'll be as awesome as the teachers I read about,) but that has pushed me to try more ideas, to keep pushing myself, to try to come up with lessons worthy enough to share. When I feel overwhelmed or terrified by the responsibilities I've assumed the blogging community shows me others who push through difficulties with humor and humility and this gives me strength. I guess I'm just trying to give a post Thanksgiving thanks. My two month foray into history has made me so appreciative that there are math teachers out there taking care of each other. I'm not a very good blogger yet, but I will keep striving to give back to this community that has given me so much.

## Wednesday, November 21, 2012

### The Math Teacher Anthem

We had a workshop yesterday where each teacher at our school showcased a lesson to all the students and the other teachers. In the morning, the two music teachers had an awesome song writing workshop. Our kids busted out the most heartfelt, funny, tuneful ballads. The other math and science teacher, the history teacher and I got together in group to write a song which none of us had ever done before. It turned into more of a poem and most of the clever bits were thought up by the history teacher, but I'm proud to say that the original idea and some of couplets were mine. I think that this may need to be the official math teacher anthem:

Doesn't matter if its black or light

Fill my cup and you fill my life

Sandy knocked out gasoline

But please don't limit my caffeine

Cup of Joe

Sweet and low

Paper work stacking up

Please oh god just fill my cup

You can keep your weak green tea

I think that Dunkin' runs on me

Thoughts are sluggish, head aches

Pump me up till fingers shake

We only had about 10 minutes to write, so I don't think it's done yet. We need a few more couplets (is that the proper literary term? I'm not sure...) Any suggestions?

## Sunday, November 18, 2012

### Equations of Vertical, Horizontal, Parallel and Perpendicular Lines

My new school is one-on-one instruction. Just a teacher and a student. In some ways this is AMAZING. We can cover so much material, I can gear my explanations specifically to that student and take their learning styles into account, I can really see if they get it or if they're just faking it so as not to stand out. It is not amazing in terms of games though. None of my old games will really work. A lot of them are team based, or competition based or communication/discussion based. I can play some of the competition games with the student, but any of the games that are based on knowledge or practice are not too much fun because I'll always either beat the student or the student will know I'm going easy on them. One of my boys got very upset with me when he realized I was "letting" him win. I don't enjoy games where winning is based on chance (i.e. board games where you roll a die and answer the problem you land on.) Or where math is just a hurdle to play the game, not the focus of it.

I've been writing a lesson plan on equations of horizontal, vertical, parallel and perpendicular lines and I came up with a game that I think will be good. Winning takes strategy combined with luck and the strategy is independent of, yet still related to knowledge of the material. This means that hopefully, the student will have a chance of beating me while still practicing equation writing skills. I have NO idea if this game will work, but I thought I'd share it. Horizontal, Vertical, Parallel and Perpendicular Lines Game

I've been writing a lesson plan on equations of horizontal, vertical, parallel and perpendicular lines and I came up with a game that I think will be good. Winning takes strategy combined with luck and the strategy is independent of, yet still related to knowledge of the material. This means that hopefully, the student will have a chance of beating me while still practicing equation writing skills. I have NO idea if this game will work, but I thought I'd share it. Horizontal, Vertical, Parallel and Perpendicular Lines Game

Labels:
algebra,
equation of lines game,
horizontal lines,
parallel lines,
perpendicular lines,
vertical lines

## Thursday, November 8, 2012

### Standards and Pre-Algebra

My husband moved us out to NY so that he could get a physics PhD (I know, I couldn't bring him over to the much more beautiful and elegant world of math.) He has an Iranian classmate that we've started hanging out with. The other night he invited us over for dinner with his roommates and friends all of whom are Iranian and all of whom are either studying physics, mechanical engineering or computer science. Because most of them have TA-ships and are teaching undergraduate courses, when they found out I was a math teacher they all turned to me and asked a ton of questions along the vein of "why don't American undergrads know any math?! What DO they learn in high school?" My husband's friend had been struggling with his undergrads in a physics lab because they couldn't make a simple algebraic substitution (I can't remember what the problem was, but something like if a=b/c and d=2a, then d=2(b/c). Of course instead of a, b, c, and d they had maybe q with subscripts.) I asked him if maybe the subscripts had confused them, and he said he went back to simple a, b, c and d variables and they were still stumped. It took him 2 hours to explain this substitution to these students. He said they had no sense of variable at all. They could solve equations by rote, and they had bits and pieces of algebraic techniques, but no logical understanding of what algebra is and why they need to know it for physics. The other Iranian PhD students chimed in with their own anecdotes of students who have come to college to study the hard sciences with very little mathematical aptitude. They spent a while discussing how the Iranian education system is much more rigorous compared to what we have in the US.

This is not a low ranked college. The students who come to Stony Brook University should know their algebra, especially those who want to study the hard sciences and math because it has very competitive science and math departments. And New York has the Regents. How can students who passed the grueling Algebra 1, Geometry and Algebra 2/trig Regents exams not know simple substitutions (and not be able to grasp them even when a physics TA comes over and personally explains the process for over an hour?) With such a small sample and only anecdotes from overworked TAs who aren't trained to teach math this is not a fair base from which to judge the New York high school math curriculum, but I'm feeling a little judgy at the moment especially after wrestling with the New York math standards and the regents for the first time this year.

Pre-algebra was a sacred class for me at my old school because it creates the base the rest of students' algebra understandings must rest on. For this reason I went really slowly and carefully in my pre-algebra class and made sure students were really understanding the jump from concrete to abstract mathematics. I strongly believe that pre-algebra should spend as much time as possible on cementing the ideas of what variables are, how to write expressions, and how equations and formulas are linked to variables and expressions. These are DIFFICULT ideas. Students need time to process them. They need the freedom to explore them in their own ways. They need to see how variables aren't just unknown numbers- that they're so much richer and more flexible than number- that's why they're so useful in algebra. Students should spend time observing patterns in variables (specifically, combining like terms and the exponent rules are a great way to do this) and how we can generalize number patterns using variables in simple and elegant ways. I believe this is what pre-algebra is for. It's NOT for statistics! It's NOT for quadratics and FOIL. It's NOT for re-drilling fractions, decimals, ratios and percents again for the 50th time. The New York (and Oregon for that matter) standards cram so much into each school year that students don't cement their knowledge or have time to make meaningful connections. This means that each topic appears in the math standards for at least four years in a row because students have to constantly review stuff they should have learned last year but only "covered" because there wasn't time to go into it in depth. (i.e. adding and subtracting fractions appears from 5th-9th grades.) Each topic gets "covered" each year but not taught each year. So quick students have to relearn the same content year after year, while students who struggle never properly learn it at all.

I know this argument doesn't necessarily have traction. Students need to review no matter how deeply you taught the material the year before, but I do know that I spent a month on developing variable sense and then another month showing students the usefulness of variables and expressions in writing out general number patterns placing specific emphasis on exponent rules and geometric patterns at my previous school and when the students needed the exponent rules again in algebra 1, we only needed a half-hour review and ALL my students were fluid with using them in very complex situations. I'm getting algebra 2, pre-calc, and calc students now who don't understand their exponent rules and their eyes glaze over every time I try to show them the logic behind the rules because to them, they're just a random assortment of letters to be memorized when needed and forgotten the rest of the time. You can't learn differentiation in calc without being able to turn roots and rationals into exponential expressions instead. This inability to understand that this one seemingly random technique (exponent rules) is rooted deeply in mathematical logic and needs to be understood logically because it is a foundational piece of the structure of algebra I believe is a symptom of the standards push for breadth over depth. Students have memorized math techniques as a history student memorizes dates. They may sort of have a sense of order, but no sense of significance.

Variable sense is important and deserves time. If given time in pre-algebra, students will be much more successful in their higher math classes. It does not deserve a week a year spread over 4 years. So to answer the question posed by our Iranian friends on what is wrong with American education, I think it's the standards. And more specifically, that no one seems to know what should be shoved into pre-algebra so they make it a hodgepodge of random techniques they think will be useful for algebra 1 rather than spending that year to really develop variable sense. And I am a part of the problem too because I'm correlating my lesson plans to NY state standards so that my students will be able to pass the Regents. I'm scared of going off in the direction I feel is right because it doesn't cover the "standards" I'm supposed to cover. I think pre-algebra is the problem and I wish I could go shake the people who put "determine if a relation is a function" and "describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations)" on the PRE-ALGEBRA standards. There's a reason we have a whole year of highschool geometry and two years of algebra. Give them time to get used to the idea of variable BEFORE rushing them into function translations!

This is not a low ranked college. The students who come to Stony Brook University should know their algebra, especially those who want to study the hard sciences and math because it has very competitive science and math departments. And New York has the Regents. How can students who passed the grueling Algebra 1, Geometry and Algebra 2/trig Regents exams not know simple substitutions (and not be able to grasp them even when a physics TA comes over and personally explains the process for over an hour?) With such a small sample and only anecdotes from overworked TAs who aren't trained to teach math this is not a fair base from which to judge the New York high school math curriculum, but I'm feeling a little judgy at the moment especially after wrestling with the New York math standards and the regents for the first time this year.

Pre-algebra was a sacred class for me at my old school because it creates the base the rest of students' algebra understandings must rest on. For this reason I went really slowly and carefully in my pre-algebra class and made sure students were really understanding the jump from concrete to abstract mathematics. I strongly believe that pre-algebra should spend as much time as possible on cementing the ideas of what variables are, how to write expressions, and how equations and formulas are linked to variables and expressions. These are DIFFICULT ideas. Students need time to process them. They need the freedom to explore them in their own ways. They need to see how variables aren't just unknown numbers- that they're so much richer and more flexible than number- that's why they're so useful in algebra. Students should spend time observing patterns in variables (specifically, combining like terms and the exponent rules are a great way to do this) and how we can generalize number patterns using variables in simple and elegant ways. I believe this is what pre-algebra is for. It's NOT for statistics! It's NOT for quadratics and FOIL. It's NOT for re-drilling fractions, decimals, ratios and percents again for the 50th time. The New York (and Oregon for that matter) standards cram so much into each school year that students don't cement their knowledge or have time to make meaningful connections. This means that each topic appears in the math standards for at least four years in a row because students have to constantly review stuff they should have learned last year but only "covered" because there wasn't time to go into it in depth. (i.e. adding and subtracting fractions appears from 5th-9th grades.) Each topic gets "covered" each year but not taught each year. So quick students have to relearn the same content year after year, while students who struggle never properly learn it at all.

I know this argument doesn't necessarily have traction. Students need to review no matter how deeply you taught the material the year before, but I do know that I spent a month on developing variable sense and then another month showing students the usefulness of variables and expressions in writing out general number patterns placing specific emphasis on exponent rules and geometric patterns at my previous school and when the students needed the exponent rules again in algebra 1, we only needed a half-hour review and ALL my students were fluid with using them in very complex situations. I'm getting algebra 2, pre-calc, and calc students now who don't understand their exponent rules and their eyes glaze over every time I try to show them the logic behind the rules because to them, they're just a random assortment of letters to be memorized when needed and forgotten the rest of the time. You can't learn differentiation in calc without being able to turn roots and rationals into exponential expressions instead. This inability to understand that this one seemingly random technique (exponent rules) is rooted deeply in mathematical logic and needs to be understood logically because it is a foundational piece of the structure of algebra I believe is a symptom of the standards push for breadth over depth. Students have memorized math techniques as a history student memorizes dates. They may sort of have a sense of order, but no sense of significance.

Variable sense is important and deserves time. If given time in pre-algebra, students will be much more successful in their higher math classes. It does not deserve a week a year spread over 4 years. So to answer the question posed by our Iranian friends on what is wrong with American education, I think it's the standards. And more specifically, that no one seems to know what should be shoved into pre-algebra so they make it a hodgepodge of random techniques they think will be useful for algebra 1 rather than spending that year to really develop variable sense. And I am a part of the problem too because I'm correlating my lesson plans to NY state standards so that my students will be able to pass the Regents. I'm scared of going off in the direction I feel is right because it doesn't cover the "standards" I'm supposed to cover. I think pre-algebra is the problem and I wish I could go shake the people who put "determine if a relation is a function" and "describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations)" on the PRE-ALGEBRA standards. There's a reason we have a whole year of highschool geometry and two years of algebra. Give them time to get used to the idea of variable BEFORE rushing them into function translations!

## Tuesday, November 6, 2012

### Lesson Planning In New York

The move from Oregon to New York has been jarring in many ways but I found a little piece of the west cost right here on Long Island and I don't intend to ever leave it. I got a job at this quirky private school that originated in California and is now branching out to the East Coast. I'd fantasized that changing schools would mean my work load would be a little less for a few different reasons. Being the only math and science teacher for a whole school meant a MILLION preps (well between 8 and 15 to be specific) and that made the work week busy. Also, because I'm crazy and there was nothing in place when I arrived, I'd created the entire 7-12th grade curriculum single-handedly for my old school which made weekends and summers

He, he he ... he

Well, my new school specializes in teaching one-to-one. We serve students who have severe anxiety, depression, drug problems, learning disabilities, who are extremely gifted or who are professional athletes, actors or musicians. Basically, we work with anyone who doesn't quite fit into a traditional school schedule or system. I love the idea of being able to work with these students who have been so poorly served by the public (or even private) school systems but one-to-one means I have to create a separate curriculum

Hmmmmm. Are all teachers this masochistic? Most of the blogger teachers out there seem to be. Guess I'm in good company. Because of Hurricane Sandy we haven't had school for a week and a half and rather than using this time to relax, reflect, volunteer or work on human being type things, I've lesson planned so obsessively that I have developed severe eye strain. The best (or worst?) part of it all is that I'm not going to stop. I know my lesson planning is crazy, but I love finally having things written down and organized the way I want them to be. This is why I haven't blogged in so long. No time to blog when you're torturing yourself with word formatting! Here are some examples of my obsession. I want to put them all up on scribd eventually because I'd like to know if these lessons are actually feasible or useful. These lessons do cram in A LOT more material than I would normally ever try to cover at my old school. This new school restricts us to 25 sessions per student per semester- so we have to pack a lot into each lesson.

Unfortunately, Scribd can't quite get the formatting right (and I futzed with in in word for forever to get it to come out the way I wanted! :) But it at least gives you an idea of what I've been pouring all my free time into. Pre-Alg Lesson 12

*really*busy. Moving schools meant maybe I'd have the normal burden of 2-4 preps and also I dreamed that I'd be moving into a more established school that had a curriculum in place.He, he he ... he

Well, my new school specializes in teaching one-to-one. We serve students who have severe anxiety, depression, drug problems, learning disabilities, who are extremely gifted or who are professional athletes, actors or musicians. Basically, we work with anyone who doesn't quite fit into a traditional school schedule or system. I love the idea of being able to work with these students who have been so poorly served by the public (or even private) school systems but one-to-one means I have to create a separate curriculum

*for each student*. And I'm still me. So even while my new school does have a curriculum, I have to rewrite it all for myself. Also, I set myself an ambitious goal last year. I really wanted to make for real lesson plans. Plans where all my examples, notes, games, warm-ups, worksheets, and homework sheets were in the same document with time windows, standards and everything. Being a forth year teacher means I can do this now, right? I'm done with survival mode. It's time to get serious and professional.Hmmmmm. Are all teachers this masochistic? Most of the blogger teachers out there seem to be. Guess I'm in good company. Because of Hurricane Sandy we haven't had school for a week and a half and rather than using this time to relax, reflect, volunteer or work on human being type things, I've lesson planned so obsessively that I have developed severe eye strain. The best (or worst?) part of it all is that I'm not going to stop. I know my lesson planning is crazy, but I love finally having things written down and organized the way I want them to be. This is why I haven't blogged in so long. No time to blog when you're torturing yourself with word formatting! Here are some examples of my obsession. I want to put them all up on scribd eventually because I'd like to know if these lessons are actually feasible or useful. These lessons do cram in A LOT more material than I would normally ever try to cover at my old school. This new school restricts us to 25 sessions per student per semester- so we have to pack a lot into each lesson.

Unfortunately, Scribd can't quite get the formatting right (and I futzed with in in word for forever to get it to come out the way I wanted! :) But it at least gives you an idea of what I've been pouring all my free time into. Pre-Alg Lesson 12

## Friday, August 10, 2012

### Teaching Coma

So after my accident with the rental car, I woke up the next morning with a concussion that stranded me in NY for an extra week and a half. I couldn't sit up or read- it was maybe the most boring week of my life. I did get the job though! So I will not be unemployed, YAY!

I feel like I've been in a coma all summer. It started with my concussion and after that, I just haven't been able to think school or math at all. The last three years have been so intense and not knowing if I'd have a new job or not made staying motivated really hard. I've been so isolated though that I NEED to get out there and keep working on professional development. I especially MUST learn geogebra. I'm going to follow Bowman in Arabia's tutorial on geogebra because I think it's a really cool program, I've just been too busy slash scared to learn it.

My new boss gave me my first homework assignment. She asked me to create a rubric spanning all the content students should cover in my classes. She thinks it would be a nice, tangible way for students to keep track of their learning throughout the course of the year. Students would all start in the lowest categories and then move up through to the higher categories as they advance. Here's the start on my Algebra 1 rubric. I think it's a pretty neat idea. This is the only school related thing I've worked on ALL summer. You'd think I'd be relaxed but I think not working has been even more stressful than working... maybe that's why I became a teacher- there's always something to do :). Algebra 1 Semester 1 Rubric

The formatting got a little messed up. I don't know how useful having this will be, but it's a nice project to keep me busy. I've organized it carefully. Let me know if you have any suggestions.

I feel like I've been in a coma all summer. It started with my concussion and after that, I just haven't been able to think school or math at all. The last three years have been so intense and not knowing if I'd have a new job or not made staying motivated really hard. I've been so isolated though that I NEED to get out there and keep working on professional development. I especially MUST learn geogebra. I'm going to follow Bowman in Arabia's tutorial on geogebra because I think it's a really cool program, I've just been too busy slash scared to learn it.

My new boss gave me my first homework assignment. She asked me to create a rubric spanning all the content students should cover in my classes. She thinks it would be a nice, tangible way for students to keep track of their learning throughout the course of the year. Students would all start in the lowest categories and then move up through to the higher categories as they advance. Here's the start on my Algebra 1 rubric. I think it's a pretty neat idea. This is the only school related thing I've worked on ALL summer. You'd think I'd be relaxed but I think not working has been even more stressful than working... maybe that's why I became a teacher- there's always something to do :). Algebra 1 Semester 1 Rubric

The formatting got a little messed up. I don't know how useful having this will be, but it's a nice project to keep me busy. I've organized it carefully. Let me know if you have any suggestions.

## Wednesday, June 27, 2012

### Interview

I've been so quiet because I've been in the process of leaving my old job to move all the way across the country to New York. The prospect of the move was terrifying and leaving my kids has been so much more heart rending than I ever imagined. Also, getting a license in New York so far hasn't been a picnic. But I did get a job interview! I got called for a job interview and I flew across the country and spent too many hundreds of dollars. Today was the interview and this morning, I decided to stop by the mall to pick up some new interview clothes because all my old ones are too big and too frumpy. I arrived at the mall at around 10:30 and the interview wasn't until 2. No problem. No rush. I got the clothes and headed back out to my car around 11:15. Yay. Plenty of time for a coffee and a long relaxing lunch. I duck into my rental car which is a little lower to the ground than my own wonderful Prius and BANG. I slammed my head on the door frame. Still, I'm thinking I'm fine, just a little dizzy and my head really hurt so I sat for a minute with my head in my hands waiting for the headache to subside. I opened my eyes and there's blood pooling in my lap, all over my hands and car keys. I looked up into the mirror and the right side of my head is dripping. I stepped out of the car and headed for the nearest store hoping to find a bathroom. A lady opened the door for me, but NO ONE else commented, as I walked, covered in BLOOD through the store to the bathroom. The lady who opened the door for me even asked a store clerk for me where the bathroom was and the store clerk just matter-of-factly told me that the bathroom was in the back of the store. Does someone dripping blood walk through their store hourly!? I went to the bathroom and rinsed my hands and face first, found that the cut wasn't that bad, waited for it to stop bleeding, walked back out to my car to get my interview clothes, walked back into the store with my clothes still bloody and changed in the bathroom. All without comment from any store personnel. I had to rinse my hair out in the bathroom sink because it was caked but all in all I was fine. Just a little shaken. I'm afraid it wasn't my best interview performance. But I made it. The cut was right next to my eyebrow and it hadn't really swollen up yet because I iced it right away so the interview people didn't even notice it. I don't think I'll get the job because I was still so shaken that I tripped over my own tongue, but boy do I deserve it after that!

## Sunday, April 22, 2012

### Hiring the new me

In my last post, I mentioned all the craziness that has been going on recently. On Thursday, we had our exhibition night, which was the culmination of a huge, all school physics project we've been working on for 2 and a half months as a school, but I and the other math and science teacher have been planning all year. It turned out really beautifully, but boy was it a lot of work. We gave each separate grade level a different engineering challenge.

(1) The 4th/5th graders had to design and build an electromagnetic crane to move nails from one bucket to another. The group that moved the most nails in a minute would be the winner.

(2) The 6th/7th graders were asked to design a generator. The one that could produce the most voltage was the winner.

(3) The 8th/9th graders designed trebuchets to hit a target

(4) the 10th-12th graders had to build adjustable launching devices to hit a target that wouldn't be announced until competition day.

We had competition day a week and a half ago and the last week and half has been spent making tri-boards, decorating the school and making documentaries of the development process (each group had to video the whole building/competition process). We premiered our videos and showed off the tri-boards and engineering devices to over 200 parents and community members on Thursday night.

Now that the event we've been working on all year is over, I feel pretty deflated. Throughout this project, we've been interviewing people to take over my job because my husband got accepted to a graduate school in New York and we're moving. Watching the students take such pride and ownership in their own learning makes me so nervous to start over somewhere else because where else would I have such amazing students. I'm so in love with my school and my students and my job that I just can't believe I won't be back next year. It's time to move on. I'm exhausted. 15 preps my first year, 14 my second and 9 this year. Along with planning 3 of these all school projects a year. I've been working 10+ hours a day 7 days a week all year round. Every once in a while I get half a Sunday off. This past summer I took a week! I only worked a few hours a day during spring break which is a new record. So the work is getting less and if I were to stay next year, it's the first year so far where my curriculum is already in place and I wouldn't have had to start over from scratch in several of my classes. But now instead I'm moving to start all over again somewhere else. I'm not sure I should even look for another job because I'm so tired, but at the same time, I know I have a lot of experience now, and I don't know what else I would do with myself if I weren't teaching. Half of me is excited to move on and to maybe have some down time, and half of me is sure I won't be able to find another job and even if I did it would take forever to feel good at it and maybe I won't ever feel as part of a purposeful educational community as I do now.

Anyway, enough complaining. What will happen will happen. I wanted to post because I've been finding the process of replacing myself fascinating and horrifying at the same time. First of all, the horrifying part: I'm surprisingly resentful of replacement mes. I shouldn't feel resentful at all because I desperately want to find someone who will do a good job and will help the students that I care so much about succeed, but at the same time a small, mean, evil part of me doesn't want my students to love my replacement as much as they love me. I know I've done a poor job in a lot of ways because I've had so much on my plate and just couldn't keep up. What if my replacement shows students what real math teaching should be? So much of my curriculum is ramshackle because I had to throw it together so fast. If the new person can build on what I've done, the students will have truly high quality math instruction that will totally overshadow what I've accomplished. What an awful, selfish feeling. I've got to squish it. I've got to be warm, welcoming, friendly and helpful to my replacement. I want them to succeed, I really do! For my students to succeed they need a good teacher. And this replacement teacher needs my help because when I arrived the school had NOTHING. I didn't even know what level my students were in, let alone if they'd actually learned anything in their previous levels. I will not leave the school in that state again. I'm handing everything I've made over.

Now for the fascinating part. I've noticed a few things about the resume, cover letter, interview process that is very revealing about the hiring process.

(1) I read through the whole resume, cover letter and recommendations. Maybe they say most people hiring just glance at them, but I've been reading them all the way through, which makes me hope that other educators who are hiring really do consider these documents carefully.

(2) BUT, these documents are flat. Even good ones (and a lot of them aren't very good. I think formatting is important to highlight essential information, but many of the resumes we've gotten are devoid of formatting- no bold text or underlined text, no dividers. They use bullet points and that's it. It makes it more difficult to find what I'm interested in finding.) Even really well written cover letters sound stale. They're often so full of I will statements and I believe statements but I don't know if the person will actually

(3) So personal impressions are the most important. This is bad for me because I'm an awkward interviewer. I'm hopelessly shy when I first meet people. When I'm comfortable, I'm quite gregarious but until I'm comfortable I freeze up and can't make interesting or witty comments. But while personal impressions are important, interviewers who are too smooth are harder to trust. Our hiring committee has gravitated towards favoring the less polished/more honest candidates. They still need to seem professional, enthusiastic and driven, but they don't need to answer every question the way we want them to. Instead, we need to feel that they're genuinely interested in teaching at our school.

(4) Strangely enough, the above has been more important even than experience. At least at our school, we need really determined, driven and passionate educators. Experience comes in time, but there's no replacement for a true love of teaching. This is nice to realize because when I was first looking for a teaching job, it felt hopeless because everyone seemed to want 3+ years of experience. The truth is if the hiring committee personally likes a candidate, that seems to outweigh experience.

(5) Transcripts are important! A lot of people talk big. They have good ideas but little follow through. Be it fair or not, transcripts seem to reveal the true dedication someone has for learning, and a passion for learning is essential in being a good teacher. Candidates that have weak grades to begin with but get stronger over time show dedication. Candidates that have a lot of As and Bs are appealing and are probably hard workers. Candidates that have As and Cs make us nervous because it seems to say that they're very smart but not necessarily hard working. Candidates with Cs and Bs all the way through with little improvement are not in a good position.

(6) Letters of recommendation aren't very helpful. They're all the same. They're all dripping with positivity which makes them hard to trust. I remember thinking about letters of recommendation written for me by professors that they were pretty biased and contained little useful information. And thinking of letters I've written myself for students I realize how I never really said what I thought. Some students really deserved glowing letters and I tried to make them glowing. Other students didn't deserve glowing letters, but I still tried to cast that student in the best light possible. No one wants to be the reason someone doesn't get their dream job. So all the recommendation letters are the same. When interviewing my potential replacement, I want to see how that person has learned to live with their faults, their mistakes, their inadequacies. Are they still trying to overcome their weaknesses? Do they have a good picture of where their teaching needs work? Are they constantly reflecting or are they content with where they are? When interviewees admitted their weaknesses, we as a hiring committee usually felt more favorably towards that candidate.

In my small fraction of the world, this is what I've observed. I'm sure each hiring committee is different, but I'll try to keep all this in mind as I think about getting a new job of my own.

(1) The 4th/5th graders had to design and build an electromagnetic crane to move nails from one bucket to another. The group that moved the most nails in a minute would be the winner.

(2) The 6th/7th graders were asked to design a generator. The one that could produce the most voltage was the winner.

(3) The 8th/9th graders designed trebuchets to hit a target

(4) the 10th-12th graders had to build adjustable launching devices to hit a target that wouldn't be announced until competition day.

We had competition day a week and a half ago and the last week and half has been spent making tri-boards, decorating the school and making documentaries of the development process (each group had to video the whole building/competition process). We premiered our videos and showed off the tri-boards and engineering devices to over 200 parents and community members on Thursday night.

Now that the event we've been working on all year is over, I feel pretty deflated. Throughout this project, we've been interviewing people to take over my job because my husband got accepted to a graduate school in New York and we're moving. Watching the students take such pride and ownership in their own learning makes me so nervous to start over somewhere else because where else would I have such amazing students. I'm so in love with my school and my students and my job that I just can't believe I won't be back next year. It's time to move on. I'm exhausted. 15 preps my first year, 14 my second and 9 this year. Along with planning 3 of these all school projects a year. I've been working 10+ hours a day 7 days a week all year round. Every once in a while I get half a Sunday off. This past summer I took a week! I only worked a few hours a day during spring break which is a new record. So the work is getting less and if I were to stay next year, it's the first year so far where my curriculum is already in place and I wouldn't have had to start over from scratch in several of my classes. But now instead I'm moving to start all over again somewhere else. I'm not sure I should even look for another job because I'm so tired, but at the same time, I know I have a lot of experience now, and I don't know what else I would do with myself if I weren't teaching. Half of me is excited to move on and to maybe have some down time, and half of me is sure I won't be able to find another job and even if I did it would take forever to feel good at it and maybe I won't ever feel as part of a purposeful educational community as I do now.

Anyway, enough complaining. What will happen will happen. I wanted to post because I've been finding the process of replacing myself fascinating and horrifying at the same time. First of all, the horrifying part: I'm surprisingly resentful of replacement mes. I shouldn't feel resentful at all because I desperately want to find someone who will do a good job and will help the students that I care so much about succeed, but at the same time a small, mean, evil part of me doesn't want my students to love my replacement as much as they love me. I know I've done a poor job in a lot of ways because I've had so much on my plate and just couldn't keep up. What if my replacement shows students what real math teaching should be? So much of my curriculum is ramshackle because I had to throw it together so fast. If the new person can build on what I've done, the students will have truly high quality math instruction that will totally overshadow what I've accomplished. What an awful, selfish feeling. I've got to squish it. I've got to be warm, welcoming, friendly and helpful to my replacement. I want them to succeed, I really do! For my students to succeed they need a good teacher. And this replacement teacher needs my help because when I arrived the school had NOTHING. I didn't even know what level my students were in, let alone if they'd actually learned anything in their previous levels. I will not leave the school in that state again. I'm handing everything I've made over.

Now for the fascinating part. I've noticed a few things about the resume, cover letter, interview process that is very revealing about the hiring process.

(1) I read through the whole resume, cover letter and recommendations. Maybe they say most people hiring just glance at them, but I've been reading them all the way through, which makes me hope that other educators who are hiring really do consider these documents carefully.

(2) BUT, these documents are flat. Even good ones (and a lot of them aren't very good. I think formatting is important to highlight essential information, but many of the resumes we've gotten are devoid of formatting- no bold text or underlined text, no dividers. They use bullet points and that's it. It makes it more difficult to find what I'm interested in finding.) Even really well written cover letters sound stale. They're often so full of I will statements and I believe statements but I don't know if the person will actually

*do*the stuff they're advocating.(3) So personal impressions are the most important. This is bad for me because I'm an awkward interviewer. I'm hopelessly shy when I first meet people. When I'm comfortable, I'm quite gregarious but until I'm comfortable I freeze up and can't make interesting or witty comments. But while personal impressions are important, interviewers who are too smooth are harder to trust. Our hiring committee has gravitated towards favoring the less polished/more honest candidates. They still need to seem professional, enthusiastic and driven, but they don't need to answer every question the way we want them to. Instead, we need to feel that they're genuinely interested in teaching at our school.

(4) Strangely enough, the above has been more important even than experience. At least at our school, we need really determined, driven and passionate educators. Experience comes in time, but there's no replacement for a true love of teaching. This is nice to realize because when I was first looking for a teaching job, it felt hopeless because everyone seemed to want 3+ years of experience. The truth is if the hiring committee personally likes a candidate, that seems to outweigh experience.

(5) Transcripts are important! A lot of people talk big. They have good ideas but little follow through. Be it fair or not, transcripts seem to reveal the true dedication someone has for learning, and a passion for learning is essential in being a good teacher. Candidates that have weak grades to begin with but get stronger over time show dedication. Candidates that have a lot of As and Bs are appealing and are probably hard workers. Candidates that have As and Cs make us nervous because it seems to say that they're very smart but not necessarily hard working. Candidates with Cs and Bs all the way through with little improvement are not in a good position.

(6) Letters of recommendation aren't very helpful. They're all the same. They're all dripping with positivity which makes them hard to trust. I remember thinking about letters of recommendation written for me by professors that they were pretty biased and contained little useful information. And thinking of letters I've written myself for students I realize how I never really said what I thought. Some students really deserved glowing letters and I tried to make them glowing. Other students didn't deserve glowing letters, but I still tried to cast that student in the best light possible. No one wants to be the reason someone doesn't get their dream job. So all the recommendation letters are the same. When interviewing my potential replacement, I want to see how that person has learned to live with their faults, their mistakes, their inadequacies. Are they still trying to overcome their weaknesses? Do they have a good picture of where their teaching needs work? Are they constantly reflecting or are they content with where they are? When interviewees admitted their weaknesses, we as a hiring committee usually felt more favorably towards that candidate.

In my small fraction of the world, this is what I've observed. I'm sure each hiring committee is different, but I'll try to keep all this in mind as I think about getting a new job of my own.

## Saturday, April 7, 2012

### Can't Keep Up

I have loved blogging so far. It's only been a few months, but it has given me a space to reflect that I haven't had before. Unfortunately, time is always an issue and work has eaten me alive. Over the last few weeks I've desperately wanted to share a few things but I haven't had time to write a post. Among these is:

(1) what I did for Pi day because we had a few really amazing activities. We made mathscots (like mascots, heh heh). Enough said I think. Here's our wall of mathscots:

(2) I've wanted to discuss how my students did on their most recent state tests (every one of my high school students passed, only half of my 8th graders did. I think I know why my 8th graders didn't do so well, and I don't think it's my fault, but I have to plan an emergency 3 weeks of test prep material thus contributing to my lack of time to blog.

(3) I've really wanted to share and get advice on several lesson plans including my feeble attempts to teach the FTC for the first time.

(4) And finally, I've really wanted to share about this amazing all school science project we've been working on for two months. The whole school is grouped into four large, multi age teams and each grade level in each team has an engineering challenge they must complete. Then they will complete with other age levels in other teams in a grand competition. The large multi-age teams will have to make documentaries of the entire process and present these documentaries to 200-300 community members on Exhibition night. Our kids are building large generators, trebuchets, catapults, and balistas.

Unfortunately, as cool as the exhibition is, it leaves me with less than no time for outside activities like blogging.

On top of this all, my husband has been accepted into a PhD program in Stony Brook, New York so I'm going to have to leave my job and move across the country. Listening to all these reports of teachers losing their jobs right now, it's really scary to leave a job that I'm so secure in for the unknown. Plus the New York education department might feel like an anvil falling on my head compared to how lax the Oregon Department of Education is. No one here is looking over my shoulder. My impression of education in New York is that teachers are watched a lot more carefully and that they run a much tighter ship over there. I'm terrified. What will I do if I'm not a teacher? If I can't find a job? My whole identity is wrapped up in my profession.

I hope I can write a real post soon because I'm desperate for advice on some of my lesson plans, but for now, this will have to do. If anyone has any advice about getting a job in New York, I'm all ears. I'm frantically trying to pull together my resume and cover letter, but I'm so used to easy going Oregon.

(1) what I did for Pi day because we had a few really amazing activities. We made mathscots (like mascots, heh heh). Enough said I think. Here's our wall of mathscots:

(2) I've wanted to discuss how my students did on their most recent state tests (every one of my high school students passed, only half of my 8th graders did. I think I know why my 8th graders didn't do so well, and I don't think it's my fault, but I have to plan an emergency 3 weeks of test prep material thus contributing to my lack of time to blog.

(3) I've really wanted to share and get advice on several lesson plans including my feeble attempts to teach the FTC for the first time.

(4) And finally, I've really wanted to share about this amazing all school science project we've been working on for two months. The whole school is grouped into four large, multi age teams and each grade level in each team has an engineering challenge they must complete. Then they will complete with other age levels in other teams in a grand competition. The large multi-age teams will have to make documentaries of the entire process and present these documentaries to 200-300 community members on Exhibition night. Our kids are building large generators, trebuchets, catapults, and balistas.

Unfortunately, as cool as the exhibition is, it leaves me with less than no time for outside activities like blogging.

On top of this all, my husband has been accepted into a PhD program in Stony Brook, New York so I'm going to have to leave my job and move across the country. Listening to all these reports of teachers losing their jobs right now, it's really scary to leave a job that I'm so secure in for the unknown. Plus the New York education department might feel like an anvil falling on my head compared to how lax the Oregon Department of Education is. No one here is looking over my shoulder. My impression of education in New York is that teachers are watched a lot more carefully and that they run a much tighter ship over there. I'm terrified. What will I do if I'm not a teacher? If I can't find a job? My whole identity is wrapped up in my profession.

I hope I can write a real post soon because I'm desperate for advice on some of my lesson plans, but for now, this will have to do. If anyone has any advice about getting a job in New York, I'm all ears. I'm frantically trying to pull together my resume and cover letter, but I'm so used to easy going Oregon.

## Saturday, March 17, 2012

### 1 year anniversary

I've been sick with a flu type virus for the last week and a half or so. I've been in a torpor- not reading blog posts, not thinking about teaching, barely dragging myself to school and home and sometimes not even managing that. Sadly this sick torpor couldn't have come at a worse time. I spent days planning a spectacular pi-day (but it was supposed to extend over the week with various competitions) and I've been absent for most of it. My husband and I were supposed to have a getaway weekend this weekend that we've been planning for a year, a YEAR! And now all I can do at this awesome resort is whimper and sniffle. Finally, this week marked the first anniversary of the earthquake and tsunami in Japan. If I hadn't been in a congestion induced coma I would have thought to do something at school about this. Fortunately my boss thought of it first and sent us all packing yesterday on a field trip to visit a local university that had a talk about the earthquake and tsunami. It was kind of a terrible talk, but it inspired me to share some of my thoughts about this anniversary. I wish I'd been able to get my act together to talk with my students about this stuff, but maybe it's better I talk about it somewhere than nowhere.

You may wonder why I would talk to my students about this at all. My school was established on the philosophies of Japanese education 15 years ago and all our students study Japanese for two hours a day- so the earthquake and tsunami already would have caused (excuse me but I must) waves at my school. But a year ago I was sitting in my classroom on a grading day when I heard the news that an earthquake, then tsunami had struck Tohoku, Japan- a region I lived in for two years. I don't know how explain my connection to the region or it's people in a non cheesy way- but I studied abroad in Morioka, Iwate when I was 19 and fell in love with my host family and the region. For the last 8 years my host family and I have written letters to each other monthly- have bi-monthly phone calls and send each other goodies from our respective countries. I was so torn when I left Morioka as a student that as soon as I graduated with my MAT, I applied and was accepted into the JET Programme (a program to bring native English speakers into Japanese schools) and I requested to be placed in Iwate near my host family. For a year I worked in a town an hour away from Morioka and took a bus into Morioka every weekend to see my host family. They took me on trips throughout Japan, took care of me when I was sick, and christened me with their last name because they said I was their American daughter. They're alright- this is not a build up to a "now they're gone and I'm heart broken" story. But I had a very difficult weekend a year ago when I saw video after video of the town my host-sister lived and worked in being swept away. When I finally made contact with my host parents 3 days after the tsunami hit- my host sister still hadn't been located. You'll never guess what my host mom kept telling me throughout this phone call and subsequent phone calls throughout the week as her daughter remained missing- "thank you so much for caring from so far away." While her daughter was missing and her prefecture was in ruins (no power, water or food), my host mom was thanking me for caring. The speaker we went to see for our field-trip yesterday went to Japan for a few weeks last summer to help with clean-up and he characterized the Japanese people he met as "respectful". He had no experience with Japan before he went on this relief effort, and he's right, they are respectful, but this is such a small word to characterize how the Japanese have responded to such a massive cataclysm.

About 5 or 6 days after the tsunami hit I received word from my host mother that my host sister was ok. She is also a teacher and she was at school with her students when the earthquake hit. The school was up pretty high on a cliff overlooking the water, and because of its altitude, it had been designated as the place the towns people should flee to in the event of a tsunami. The teachers of the school, when they saw the swelling water, decided that their students weren't high enough and they collected all the students in the field and evacuated the students into the hills while the towns people came in behind them fleeing to the school. The teachers were wise and the towns people (including many parents of the students) were all killed when water flooded the school. My students knew about my connections with Tohoku and after the tsunami, we spent months raising money for the students of my host-sister's school. Every student in our school wrote two letters, (there are 88 of us and 160 of them) decorated manila envelopes, and collected toys to put in the envelopes for students of the school. The money we raised went to buying games and gym equipment for the students at the school now living in shelters. Last summer my husband and I went to Japan to visit my host family and personally delivered the letters and gym equipment to my host sister's principle. I'm glad we did something, but I'm so sad we didn't do more. As we drove around in Japan this past summer visiting my host family, the country seemed almost unchanged from my previous visits. The Japanese people I met were still very respectful and polite, they still were or pretended to be impressed by my Japanese, they laughed and joked and worked as hard as ever. They spoke very matter-of-factly about the earthquake and tsunami, often without discernible bitterness. I felt like a clown- bringing these letters and these donations to a school as a great charitable act. It was such a small thing compared to the mountains each individual Japanese person has moved to push themselves and their country forward. Underneath their smiles, politeness, respect, and humor lay deep wells of emotion that they control and harness for collective good. There's a word for this in Japanese- "gaman"- it loosely translates to perseverance- but it is closer to the word "stoic" I think. I don't really know how to put it in words- but I know most of the people I saw while I was on my trip were suffering deep personal losses. Their whole worlds had been turned upside down. They lost homes, parents, children, spouses and in some cases- their entire neighborhood or town had been washed away. But they hadn't fallen to pieces. They hadn't turned to bitterness, over indulgence, listlessness, cynicism, or regret. I'm sure they felt many of these things but they didn't show any of it. They rebuilt, they welcomed tourists, they thanked us whole heartedly for the small support we were able to offer. They gave us tea and let us take pictures of their ruined lives. There are many things about Japanese culture and society that I disagreed with, or made me feel uncomfortable- of course there were, I am from entirely opposite cultural values- but I'm proud that my host family always said I have a Japanese heart because I can't think of a better heart to have.

I haven't really shared these pictures with anyone, but I think I want to now. These are pictures my husband and I took when we were vising my host family this past summer. Maybe you noticed above, but I feel pretty sheepish for even having taken these pictures. It seemed like such an awful thing to do-fat American tourist snapping shots of ruined Japanese towns while Japanese residents watch on from shelters. I felt compelled to take these pictures though because I was representing my school and I knew my students back home would want a share of my experiences because they had worked so hard to produce the letters and toys that I was delivering. I did not end up sharing these pictures with my students though. There never seemed like a good time to do it and it all just seemed too sad to bring up again.

Here's a view of where the town my host sister lived in used to be:

You may wonder why I would talk to my students about this at all. My school was established on the philosophies of Japanese education 15 years ago and all our students study Japanese for two hours a day- so the earthquake and tsunami already would have caused (excuse me but I must) waves at my school. But a year ago I was sitting in my classroom on a grading day when I heard the news that an earthquake, then tsunami had struck Tohoku, Japan- a region I lived in for two years. I don't know how explain my connection to the region or it's people in a non cheesy way- but I studied abroad in Morioka, Iwate when I was 19 and fell in love with my host family and the region. For the last 8 years my host family and I have written letters to each other monthly- have bi-monthly phone calls and send each other goodies from our respective countries. I was so torn when I left Morioka as a student that as soon as I graduated with my MAT, I applied and was accepted into the JET Programme (a program to bring native English speakers into Japanese schools) and I requested to be placed in Iwate near my host family. For a year I worked in a town an hour away from Morioka and took a bus into Morioka every weekend to see my host family. They took me on trips throughout Japan, took care of me when I was sick, and christened me with their last name because they said I was their American daughter. They're alright- this is not a build up to a "now they're gone and I'm heart broken" story. But I had a very difficult weekend a year ago when I saw video after video of the town my host-sister lived and worked in being swept away. When I finally made contact with my host parents 3 days after the tsunami hit- my host sister still hadn't been located. You'll never guess what my host mom kept telling me throughout this phone call and subsequent phone calls throughout the week as her daughter remained missing- "thank you so much for caring from so far away." While her daughter was missing and her prefecture was in ruins (no power, water or food), my host mom was thanking me for caring. The speaker we went to see for our field-trip yesterday went to Japan for a few weeks last summer to help with clean-up and he characterized the Japanese people he met as "respectful". He had no experience with Japan before he went on this relief effort, and he's right, they are respectful, but this is such a small word to characterize how the Japanese have responded to such a massive cataclysm.

About 5 or 6 days after the tsunami hit I received word from my host mother that my host sister was ok. She is also a teacher and she was at school with her students when the earthquake hit. The school was up pretty high on a cliff overlooking the water, and because of its altitude, it had been designated as the place the towns people should flee to in the event of a tsunami. The teachers of the school, when they saw the swelling water, decided that their students weren't high enough and they collected all the students in the field and evacuated the students into the hills while the towns people came in behind them fleeing to the school. The teachers were wise and the towns people (including many parents of the students) were all killed when water flooded the school. My students knew about my connections with Tohoku and after the tsunami, we spent months raising money for the students of my host-sister's school. Every student in our school wrote two letters, (there are 88 of us and 160 of them) decorated manila envelopes, and collected toys to put in the envelopes for students of the school. The money we raised went to buying games and gym equipment for the students at the school now living in shelters. Last summer my husband and I went to Japan to visit my host family and personally delivered the letters and gym equipment to my host sister's principle. I'm glad we did something, but I'm so sad we didn't do more. As we drove around in Japan this past summer visiting my host family, the country seemed almost unchanged from my previous visits. The Japanese people I met were still very respectful and polite, they still were or pretended to be impressed by my Japanese, they laughed and joked and worked as hard as ever. They spoke very matter-of-factly about the earthquake and tsunami, often without discernible bitterness. I felt like a clown- bringing these letters and these donations to a school as a great charitable act. It was such a small thing compared to the mountains each individual Japanese person has moved to push themselves and their country forward. Underneath their smiles, politeness, respect, and humor lay deep wells of emotion that they control and harness for collective good. There's a word for this in Japanese- "gaman"- it loosely translates to perseverance- but it is closer to the word "stoic" I think. I don't really know how to put it in words- but I know most of the people I saw while I was on my trip were suffering deep personal losses. Their whole worlds had been turned upside down. They lost homes, parents, children, spouses and in some cases- their entire neighborhood or town had been washed away. But they hadn't fallen to pieces. They hadn't turned to bitterness, over indulgence, listlessness, cynicism, or regret. I'm sure they felt many of these things but they didn't show any of it. They rebuilt, they welcomed tourists, they thanked us whole heartedly for the small support we were able to offer. They gave us tea and let us take pictures of their ruined lives. There are many things about Japanese culture and society that I disagreed with, or made me feel uncomfortable- of course there were, I am from entirely opposite cultural values- but I'm proud that my host family always said I have a Japanese heart because I can't think of a better heart to have.

I haven't really shared these pictures with anyone, but I think I want to now. These are pictures my husband and I took when we were vising my host family this past summer. Maybe you noticed above, but I feel pretty sheepish for even having taken these pictures. It seemed like such an awful thing to do-fat American tourist snapping shots of ruined Japanese towns while Japanese residents watch on from shelters. I felt compelled to take these pictures though because I was representing my school and I knew my students back home would want a share of my experiences because they had worked so hard to produce the letters and toys that I was delivering. I did not end up sharing these pictures with my students though. There never seemed like a good time to do it and it all just seemed too sad to bring up again.

Here's a view of where the town my host sister lived in used to be:

Here are some various sights throughout the town. The "OK" spray painted onto buildings meant that it's OK for the buildings to be demolished- anything inside that was salvageable has been taken out already.

This is one of the most striking sights to me. The boat is upside-down on a tsunami wall. These walls were designed to withstand tsunamis produced by earthquakes up to 8.5 in magnitude.

This is my host sister's car sitting outside the school where many of the towns people died.

Here's the school itself that was hit by the tsunami. When we first pulled in this mural- of children playing in the sea- was the first thing we saw:

Here are a few pictures around the school.

Here's a view from the school out to the ocean

Finally, here's a picture from the new, temporary school. They're using an old office building to house two displaced schools. They won't be able to rebuild new schools for about 10 years according to my host sister.

## Friday, March 9, 2012

### Don't Break the Quotient Rule or Our Friendly Giant will Stick You Between His Couch Cushions that Never get Vacuumed!

I've been meaning to put these up for a while. My pre-algebra students finished their exponents brochures (description here) and they're kind of awesome so I thought I would post them. Unfortunately, they did not do as well on the test following the brochures as I would have liked (80% average which is ok, but I wanted better). I think they performed poorly because even though the brochures helped them cement the basic rules, it didn't help them review how to tackle the different types of problems they might see. I was trying to avoid doing a drill and kill review worksheet by doing a project instead, but since the test had drill and kill problems, the only way to really prepare them for the test was with a worksheet. So we're going to spend another few days reviewing exponents and we'll have a retake in a week.

I already started the review. With our first extra day on exponents, I made a fake test for them that I had "taken" by compiling all the mistakes they made on their first test. I showed them how I grade tests and then asked them to grade "my" test without an answer key. I tried to make it a little bit fun in that I said I would award a prize to the student who's final grade was closest to the grade I would have given this test. Every single student graded the test to within two or three points of the grade I would have given it. They also found all the mistakes and discussed how frustrating it was when I didn't show my work or circle my answer. It actually turned into a pretty fun activity because they got to scold me and they were having great discussions about which errors constituted arithmetic errors (which is only -1/2 a point) and which errors constituted understanding errors (which is -1 point). So clearly they know the material well enough to recognize good work from bad work. I just need to get them to recognize their own good work and bad work. When I was wondering aloud about how the same student who got a 65% on his own test could have identified and corrected 100% of my mistakes the very next day, one of our Japanese teachers mentioned that it's easier to understand a language that you're studying than it is to speak it. So I need to give them more speaking practice? Maybe I've been focusing too much on error correction. I decided to make one of my teaching goals this year to help kids learn to recognize their own errors and I guess I went a little overboard. I have a nice, long drill and kill practice test lined up for them next.

Anyway, without further ado, here are my students' "exponent planet" brochures.

Front of brochure

Inside of brochure

And just one more because I can't resist the math puns this student used

I already started the review. With our first extra day on exponents, I made a fake test for them that I had "taken" by compiling all the mistakes they made on their first test. I showed them how I grade tests and then asked them to grade "my" test without an answer key. I tried to make it a little bit fun in that I said I would award a prize to the student who's final grade was closest to the grade I would have given this test. Every single student graded the test to within two or three points of the grade I would have given it. They also found all the mistakes and discussed how frustrating it was when I didn't show my work or circle my answer. It actually turned into a pretty fun activity because they got to scold me and they were having great discussions about which errors constituted arithmetic errors (which is only -1/2 a point) and which errors constituted understanding errors (which is -1 point). So clearly they know the material well enough to recognize good work from bad work. I just need to get them to recognize their own good work and bad work. When I was wondering aloud about how the same student who got a 65% on his own test could have identified and corrected 100% of my mistakes the very next day, one of our Japanese teachers mentioned that it's easier to understand a language that you're studying than it is to speak it. So I need to give them more speaking practice? Maybe I've been focusing too much on error correction. I decided to make one of my teaching goals this year to help kids learn to recognize their own errors and I guess I went a little overboard. I have a nice, long drill and kill practice test lined up for them next.

Anyway, without further ado, here are my students' "exponent planet" brochures.

Front of brochure

Inside of brochure

Here's another one

Front

Inside (The pictures are adorable)

Labels:
error correction,
exponent rules,
exponents,
pre-algebra

## Thursday, March 1, 2012

### Systems of Equations Scavenger Hunt

My algebra 1 students are coming to the end of their unit on systems of equations. So far, they've done so much better with it than my students last year that I've been completely blown away. They even had very little difficulty with the word problems which still has me reeling. I set up a ladder game type activity where they did problems in pairs and then came to check answers with me before getting a new problem to work on. I told them I'd award jolly ranchers (I know, I know. Bribery is not the solution to student engagement, but it just works so well...) to pairs that got the answer on the very first try. I thought I wouldn't really be handing out any candy because they would struggle so much with the word problems that they'd never be able to get the right answers the first time. I went broke. They tore through my stash of candies. All students got through the 4 problems that were part of the game and about half got through the additional 9 problems that were on the homework

So this week I've been trying to come up with a summative assessment that really challenges my students. I'm a little bit bored of tests and I want to try something related to the real world. I spent an hour earlier this week trolling around the internet hoping to find some good, real world application, performance assessment type activity, or worksheet or project but I didn't see anything I liked. There are some activities out there on supply and demand, but my students I think are more intrinsically motivated to do math than to learn about economics, so a supply and demand activity that's unconnected to their direct experience seems contrived, and less engaging to my students than pure math would be. Maybe I could fabricate some scenario when they'd be interested in figuring out a supply and demand problem? I think that this would be a really cool way to go with a summative assessment for this unit, but I can't think of anything practical, doable and a manageable amount of prep. I played with the idea of a Settler's of Catan type game (where students trade for resources to build stuff) but this is WAY more prep than I can manage right now. I'm really torn because after reading so many blogs and articles that stress the importance of showing students how their math knowledge can be used practically in the real world, I really want to plan projects and simulations into my classes but I just don't know how to make it genuine. I could try something like what dy/dan does and find a cool and interesting real life example, but I haven't found one yet and I don't have the time to keep looking. I played with other ideas like taking a map of a town or city and plotting the paths of cars and seeing where cars may crash or where the road would be the most worn down. This seemed doable, but again, contrived and impractical.

Because I ran out of time to work on this, I made a game that's maybe a bit of a compromise. I made a map of our school and superimposed a coordinate grid on it. I'll hide envelopes in 9 different locations throughout the school. Each envelope will have copies of problems in them. I'll hand each pair of students a system of equations problem and they need to solve it, graph the solution on their map, and go to that location to find another problem. That problem will send them somewhere else in the school. This is just a variation of a test, but at least it gets the kids moving around and potentially gives them a spacial understanding of what systems of equations mean. It only took me about three or four hours to prep this game (uggg...). And it's not really what I wanted, but I think it will be pretty fun.

Here's the map. I'm especially proud of this. It will be really useful to have when we're doing any graphing activity in any of my math classes.

System of Equations Scavenger Hunt Map of SJS With Cartesian Grid

Here are the scavenger hunt problems I'll hide in different places around the school:

System of Equations Scavenger Hunt Cards

Here is the worksheets students will fill out as they go around the school

System of Equations Scavenger Hunt Handout

Finally, here's the answer key. Of course, none of this is of any use to someone who doesn't work at my school and it won't be of any use to me when I leave this school (which is probably going to be soon), but I did put a lot of time and thought into it so I felt the need to share.

System of Equations Scavenger Hunt Key

*all in the space of one class period*!So this week I've been trying to come up with a summative assessment that really challenges my students. I'm a little bit bored of tests and I want to try something related to the real world. I spent an hour earlier this week trolling around the internet hoping to find some good, real world application, performance assessment type activity, or worksheet or project but I didn't see anything I liked. There are some activities out there on supply and demand, but my students I think are more intrinsically motivated to do math than to learn about economics, so a supply and demand activity that's unconnected to their direct experience seems contrived, and less engaging to my students than pure math would be. Maybe I could fabricate some scenario when they'd be interested in figuring out a supply and demand problem? I think that this would be a really cool way to go with a summative assessment for this unit, but I can't think of anything practical, doable and a manageable amount of prep. I played with the idea of a Settler's of Catan type game (where students trade for resources to build stuff) but this is WAY more prep than I can manage right now. I'm really torn because after reading so many blogs and articles that stress the importance of showing students how their math knowledge can be used practically in the real world, I really want to plan projects and simulations into my classes but I just don't know how to make it genuine. I could try something like what dy/dan does and find a cool and interesting real life example, but I haven't found one yet and I don't have the time to keep looking. I played with other ideas like taking a map of a town or city and plotting the paths of cars and seeing where cars may crash or where the road would be the most worn down. This seemed doable, but again, contrived and impractical.

Because I ran out of time to work on this, I made a game that's maybe a bit of a compromise. I made a map of our school and superimposed a coordinate grid on it. I'll hide envelopes in 9 different locations throughout the school. Each envelope will have copies of problems in them. I'll hand each pair of students a system of equations problem and they need to solve it, graph the solution on their map, and go to that location to find another problem. That problem will send them somewhere else in the school. This is just a variation of a test, but at least it gets the kids moving around and potentially gives them a spacial understanding of what systems of equations mean. It only took me about three or four hours to prep this game (uggg...). And it's not really what I wanted, but I think it will be pretty fun.

Here's the map. I'm especially proud of this. It will be really useful to have when we're doing any graphing activity in any of my math classes.

System of Equations Scavenger Hunt Map of SJS With Cartesian Grid

Here are the scavenger hunt problems I'll hide in different places around the school:

System of Equations Scavenger Hunt Cards

Here is the worksheets students will fill out as they go around the school

System of Equations Scavenger Hunt Handout

Finally, here's the answer key. Of course, none of this is of any use to someone who doesn't work at my school and it won't be of any use to me when I leave this school (which is probably going to be soon), but I did put a lot of time and thought into it so I felt the need to share.

System of Equations Scavenger Hunt Key

## Saturday, February 25, 2012

### Don't Break the Product Rule or you'll be Slathered in Butter and Grilled!

My Pre-algebra class is reaching the end of their exponent unit. I blogged about this unit before, but it was one of my first posts so I'm sorry about the roughness (I was also a little scribd happy because I was excited by how easy it was to throw documents right into my post. It's magical!) I still feel like this unit is really important because really internalizing the exponent rules makes for a much smoother transition into algebra 2 and beyond, but after reading around a lot on other people's blogs, I'm not sure that stomping along through all the rules in order is the best way to teach them. I also am aware that in the real world students will never have to simplify these ridiculous exponent problems. Though I still think that understanding these rules is necessary in creating a foundation for high school math and is a good way to introduce the logical system of math, I'm a little uncomfortable with how hard it is to tie them to the real world. I ended the unit with exponential growth and decay and scientific notation which use the exponent rules in context, but I still wish I had a more concrete way to make these rules relevant to students.

I've been trying to think of a way to review what we learned throughout the whole unit. Last year, I had the students just do a poster project where they had to neatly and creatively demonstrate all the rules, but I think that was just a desperate attempt on my part to have them review the material without adding a whole bunch more prep work on my part because I was swamped. This year I created this review activity for them:

Exponent Unit 'Going on Vacation' Review Project After reading around so many blogs and seeing what the larger teaching community is doing, I've realized that even the activities I'm most proud of are lacking the real world context that has been stressed by so many other bloggers. I've stressed teaching the logic of mathematics to my students because that is what is beautiful about math to me, but my students probably need more context driven activities and examples. The problem is that my education in mathematics has been entirely traditional (i.e. contextless) and I don't think about applications and I don't interpret the "real world" through math. I don't know how to see math in the world around me. Yet I guess, just as we tend to repeat our parent's mistakes, it's so easy to teach the way I was taught and to focus strictly on logic. I've realized that this is a grave deficiency in my teaching that I need to learn to correct, but changing the way I think about mathematics is going take a lot of time. At least I'm pretty good at making fun and silly math assignments, even if they're not tied to context. Two months ago when I came up with the idea for this project I was pretty proud of it. Now I realize that it doesn't give students any deeper insights into math. It will be silly and engaging I think, but I need to do better.

I've been trying to think of a way to review what we learned throughout the whole unit. Last year, I had the students just do a poster project where they had to neatly and creatively demonstrate all the rules, but I think that was just a desperate attempt on my part to have them review the material without adding a whole bunch more prep work on my part because I was swamped. This year I created this review activity for them:

Exponent Unit 'Going on Vacation' Review Project After reading around so many blogs and seeing what the larger teaching community is doing, I've realized that even the activities I'm most proud of are lacking the real world context that has been stressed by so many other bloggers. I've stressed teaching the logic of mathematics to my students because that is what is beautiful about math to me, but my students probably need more context driven activities and examples. The problem is that my education in mathematics has been entirely traditional (i.e. contextless) and I don't think about applications and I don't interpret the "real world" through math. I don't know how to see math in the world around me. Yet I guess, just as we tend to repeat our parent's mistakes, it's so easy to teach the way I was taught and to focus strictly on logic. I've realized that this is a grave deficiency in my teaching that I need to learn to correct, but changing the way I think about mathematics is going take a lot of time. At least I'm pretty good at making fun and silly math assignments, even if they're not tied to context. Two months ago when I came up with the idea for this project I was pretty proud of it. Now I realize that it doesn't give students any deeper insights into math. It will be silly and engaging I think, but I need to do better.

Labels:
contectualizing math,
exponent rules,
pre-algebra

## Sunday, February 19, 2012

### Gifted and Talented

I was listening again to an old Radiolab episode and though I know it's a bit out of date and the conversation about this episode has probably long dried up, it just bothered me so much that I felt like I needed to rant about it somewhere. My husband says that's what blogs are for, so here's the episode:

## Thursday, February 16, 2012

### Perfect Squares and Perfect Cubes

My algebra 2 students are starting their unit on radicals. This unit includes a review of square root arithmetic, the quadratic formula, higher order roots and fractional exponents. It's kind of a dry unit. I was trying to think of a way to spice it up and also, I was thinking about how in years past, my high school students have not been able to recognize perfect squares or perfect cubes at all because elementary schools around here don't emphasize the multiplication tables. Then I remembered a comment on a blog (I think it was f(t) but I can't find the actual comment) from a guy who said he got students to recognize perfect squares by coding the alphabet with perfect squares from 1^2 through 26^2 and putting messages up on his board in code. I thought this was a pretty awesome idea, so I went through and coded messages for my students for each day of the unit. Because they're in algebra 2 though, I went beyond perfect squares and made more interesting codes. I'm just awarding candy to those who solve the codes, but I'm also thinking about making it a competition. The person who decodes the most messages correctly gets some prize. I did my first one yesterday and my second today and so far, my students are really into it. I thought I'd share the coded messages here for anyone who was interested. I got all the messages by googling around for math jokes or math quotes.

Day 1:

Day 2:

Day 3:

Day 4:

Day 5:

Day 6:

Day 7:

Day 8:

Day 9:

I hope my students learn to recognize perfect squares and perfect cubes after doing these codes. At the very least they're fun and they don't take away any class time because I'll pass them out on slips of paper at the end of class and students will have to decode in their own time.

If you want an answer key, just leave me a comment.

Day 1:

“169-1-400-64 81-361
324-1-16-81-9-1-144”

Day 2:

81-400
81-361 196-225-400 400-64-25
100-225-4 225-36 169-1-400-64-25-169-1-400-81-9-1-196-361 400-225
16-225

9-225-324-324-25-9-400 1-324-81-400-64-169-25-400-81-9. 81-400
81-361 400-64-25 100-225-4
225-36 4-1-196-121

1-9-9-225-441-196-400-1-196-400-361

Day 3:

676
196-676-49-361-484-196-676-49-324-676-169 324-64 676
529-484-25-324-576-484 441-144-81
49-36-81-169-324-169-400
576-144-441-441-484-484
324-169-49-144
49-361-484-144-81-484-196-64

Day 4:

676-289-64-361-49-144-16-361-64-4 64-324
1-16-64-169-36 676-1-121-16 361-196
4-196-400-169-361 400-225 361-196
361-484-16-169-361-576 484-64-361-49-196-400-361 361-676-100-64-169-36 196-25-25
576-196-400-289 324-49-196-16-324

Day 5:

4-144-1-9-121
64-225-144-25-361
324-25-361-441-144-400
36-324-225-169 49-225-16 16-81-484-81-16-81-196-49 400-64-25
441-196-81-484-25-324-361-25
4-625 676-25-324-225

Day 6:

441-324-25-484 144-36-49
144-441 441-144-36-81 121-484-144-121-225-484 361-676-25-484 49-81-144-36-625-225-484 16-324-49-361
441-81-676-576-49-324-144-169-64

Day 7:

3375-1728-64
2197-1-8000-512-125-2197-1-8000-729-27-729-1-2744-6859 2477-125-10648-125-5832 64-729-125
8000-512-125-15625
1000-9261-6859-8000
1728-3375-6859-125
6859-3375-2197-125 3375-216 8000-512-125-729-5832 216-9261-2744-27-8000-729-3375-2744-6859

Day 8:

8191-2-2187-256-32-8192-2-2187-512-8-729 512-729
27-243-9-19683-512-3-128
2187-256-32 8192-9-729-2187 9-4-19683-512-9-6561-729 2187-256-512-3-128 512-3
2197-256-32
4096-32-2-729-2187
9-4-19683-512-9-3561-729
59049-2-531441

Day 9:

3
1296-7776-3-7776-256-7776-256-27-256-3-625 27-3-625
64-3-49-243 64-256-1296 64-243-3-81
256-625 3-625 3125-49-243-625 3-625-81
64-256-1296 4-243-243-7776 256-625
256-27-243 3-625-81 64-243
343-256-25-25 1296-3-16807 7776-64-3-7776 3125-625 3-49-243-216-3-16-243 64-243
4-243-243-25-1296 4-256-625-243

I hope my students learn to recognize perfect squares and perfect cubes after doing these codes. At the very least they're fun and they don't take away any class time because I'll pass them out on slips of paper at the end of class and students will have to decode in their own time.

If you want an answer key, just leave me a comment.

Labels:
algebra 2,
perfect cubes,
perfect squares,
radicals,
roots

## Saturday, February 11, 2012

### Parallel Lines and Transversals

I wanted to share this document I made because I used this lesson on Tuesday with my geometry class and it worked really nicely. I did it with them on a doc camera and shared their answers over the doc camera as well. We all really enjoyed especially the last problem which was written about a student. He really enjoyed the problem even though it poked fun at him. I did a terrible job after this lesson though with reinforcing all the angle relationships and their names. I just went over all the vocab- alternate interior/exterior etc. and had them do problems out of the book. In my defense, I just didn't have time to do anything more exciting. But at least we had a good intro to the topic I think.

The pictures came from world.mitrasites.com and bookbuilder.cast.org. By the way, I'm still pretty new to this so is it best to cite pictures as I did above, in fine print below the picture, or should I try to restrict myself to only using pictures I myself have taken?

Parallel Lines and Transversals Worksheet

The pictures came from world.mitrasites.com and bookbuilder.cast.org. By the way, I'm still pretty new to this so is it best to cite pictures as I did above, in fine print below the picture, or should I try to restrict myself to only using pictures I myself have taken?

Parallel Lines and Transversals Worksheet

## Tuesday, February 7, 2012

### Quadratic Functions Performance Assessment

My algebra 2 students just turned in a performance assessment over graphing quadratic functions and it turned out really nicely, so I thought I would share it.

First, I asked students to graph several functions I'd put together. When graphed they form a man with wings. I then asked them to make their own picture out of functions. They then traded papers and tried to graph each other's pictures. Finally, they colored in their pictures and we had an art show.

This project helped them reinforce function transformation rules, especially vertical dilation and some students even created their own functions that we hadn't studied to help them create their picture. (One student taught himself how to flip an absolute value graph on its side and shift it, then another student had to figure out what he'd done to graph it.) The best part of the project was when a student thanked me for having fun homework. And of course today was a lot of fun when we got to hang up their pictures, admire them, vote on the best one and eat candy. The whole project took two and a half periods and I think a lot of learning got done.

Here's my original hand out:

*Oops, there's a typo. Function 11 should be p(x)=x^2+(y-5)^2. The squared should be on the outside of the parentheses. I throw these sheets together too quickly...

Quadratic Functions Performance Assessment Here are pictures of the students admiring each other's work and voting on the best piece of art:

Here are the pictures they created:

I do have more than 7 students, but two were absent today (I know, 9 students is still an awesome student teacher ratio.)

Here's the third place winner

Here's second place:

And here's first place

First, I asked students to graph several functions I'd put together. When graphed they form a man with wings. I then asked them to make their own picture out of functions. They then traded papers and tried to graph each other's pictures. Finally, they colored in their pictures and we had an art show.

This project helped them reinforce function transformation rules, especially vertical dilation and some students even created their own functions that we hadn't studied to help them create their picture. (One student taught himself how to flip an absolute value graph on its side and shift it, then another student had to figure out what he'd done to graph it.) The best part of the project was when a student thanked me for having fun homework. And of course today was a lot of fun when we got to hang up their pictures, admire them, vote on the best one and eat candy. The whole project took two and a half periods and I think a lot of learning got done.

Here's my original hand out:

*Oops, there's a typo. Function 11 should be p(x)=x^2+(y-5)^2. The squared should be on the outside of the parentheses. I throw these sheets together too quickly...

Quadratic Functions Performance Assessment Here are pictures of the students admiring each other's work and voting on the best piece of art:

Here are the pictures they created:

I do have more than 7 students, but two were absent today (I know, 9 students is still an awesome student teacher ratio.)

Here's the third place winner

Here's second place:

And here's first place

Labels:
algebra 2,
picture project,
quadratic functions

Subscribe to:
Posts (Atom)