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.
Sunday, December 9, 2012
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
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 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
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!
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