Sunday, February 23, 2014


Right now, I'm making lesson plans for my first period algebra 1 class.  Here is the first slide I decided to add to my presentation for tomorrow.

"Right now...

  • 4 of you have As
  • 2 of you have Cs
  • 9 of you have Fs
It's really easy for me to tell though without looking at my gradebook who is passing and who is not: those who are here everyday are passing.  Those of you who are absent two or more times a week are failing."

What do I do?  I can't teach students who don't show up.  When I make this announcement, most likely at least half my class will be absent and won't even hear the message I'm trying to convey.

Update: 3/8
The Monday after writing the above post I decided to try a new grading system in my class to see if that could help with attendance. I had been assigning homework and calling it homework, but I had been giving the students time to complete it in class.  Only if they didn't finish it in class would they need to do it at home.  I did this because I didn't want students to feel pressured to get the work done quickly- when I assign only classwork the slower and more careful students tend to get stressed out.  The problem though was that students were not using class time well.  When I asked them to work they said they would finish it at home, and then of course it (and the student) never came back.

I thought that maybe if I made their grade entirely based on them showing up and using class time well, then I would have more luck with both attendance and with comprehension.  Miraculously all the students did show up on Monday and I told my students that attendance was our biggest problem.  That those who were failing were failing because they weren't here.  I explained that I was going to make their grade based entirely on if they came to class, took notes and if they completed the work asked of them during class.  Immediately, I saw relief wash through the classroom.  I think because for the first time all year, they realized that they could pass.  That they could do what I was asking them to do.  The late homework, missed lessons and poor classwork completion had been weighing on them and had been causing them to avoid class.  It was easy for them to not show up because this class is first period and at our school, only freshmen and sophomores have to come to first period.  So my freshmen were hanging out with their Junior and Senior friends instead of coming to class.

They want to do well and only their guilt and lack of confidence had been keeping them away from class.  They constantly tell me that they like me as a teacher which is why I was so baffled by their poor attendance.  Maybe the fact that they do seem to like me contributed to them not wanting to face me when they thought they'd let me down.

Since changing my grading system two weeks ago, my attendance has sky rocketed.  They're all completing class work, asking questions and performing well on quizzes.  They still definitely lack initiative.  Since I require them to turn in an exit ticket to receive credit for the day's work, the end of class has gotten awfully chaotic as students frantically try to get my help because they don't trust their own abilities.  But they're trying and showing up now.  We can work on initiative later.  

I am torn about this no- homework system.  I have been following the homework vs. no homework debate and I'm more on the side of assigning homework because I've seen students grow so much from wresting with problems when they have no one around to help them.  They take better notes, ask better questions, and demonstrate much more mastery over the material than when I don't assign homework.  This experiment has reinforced my belief that homework does significantly contribute to learning because my other algebra 1 class to whom I still assign homework are demonstrating much more confidence with the material and are growing more rapidly.  Both my first and fifth period Algebra 1 classes are composed of low-income students who have failed algebra at least once before.  But my fifth period class has time earlier in the day (usually during lunch) to complete their homework so their homework turn in rate is good, their attendance is good and their learning is evident.  But clearly when students can't do homework and the not doing it wears down their self confidence and causes them to avoid class, the homework needs to be nixed because it's doing much more harm than good.

I guess this just reinforces my belief that there are no absolutes in education.  Every thing about teaching needs to be modified depending on the composition of students sitting in your classroom.  When students do homework it's good for them, but when they can't do it and are still expected to do it, it's bad for them.

Sunday, February 9, 2014

Asking for help

I seek help on-line constantly when it comes to lesson planning.  I've grown used to the idea that anything I can think of, someone out there in the blogosphere has probably already perfected and I love that I can see kernels of lessons I've just dreamed come alive in others' hands.  This doesn't even include the gazillions of ideas I've never thought of that are about a hundred times better than anything I can dream.

But when it comes to actually teaching- implementing the lessons, getting my kids excited, supporting their growth, encouraging them to persevere, I've never received much help (administrators never pop in.  I've been formally observed only once and that was by a coworker) and I feel like at this stage, I don't need much help.  I have a thriving community of students coming during lunch to do math because they enjoy it, and I've watched the most recalcitrant math students slowly gain confidence and enthusiasm and I feel like this is what I'm good at.  I'm good at patiently coaxing students into learning that they can learn math and over time, that they enjoy learning it.

But this semester I have the most stubbornly anti math student I've ever taught.  For three weeks, she was an angel in my advisory and a demon in my math classroom.  She refuses to accept help saying that she doesn't need it, she'll do it at home.  Then she proceeds to do nothing at all through the whole 80 minute block.  When I try to help her she slides under her desk, covers her paper, refuses to look at the problem, gets up and walks away, or starts ranting about the uselessness of math.  She's a wonderful student in advisory so I know she's bright and capable, but she refuses to cooperate in math (especially whenever division becomes involved.  She says she never learned it and she never wants to learn it.)  She slept through all of my math classes two weeks ago and refused to stir when I tried to rouse her.  She got a 30% on her first test and even though I discussed with her the consequences of her actions through all of advisory that day she slept through math again the next day. I asked her if she wants to fail? It means she'll have to do it all again next year.  She replied she doesn't but she can BS her way through the other tests.  I said that learning to read is tedious, but once you do learn, it's magical what you can discover and that math is the same way.  She replied that reading is vital but math is superfluous.  I said that everyone needs help to learn math because it's several thousand years of accumulated knowledge that we're trying to impart in a few short years and that all I would like is for her to let me help her.  Right now I don't even care about notes or homework or tests.  I would just like her to allow me to talk to her about math without arguing.  She wouldn't budge.

I thought that I'd have to just wait her out.  I'd need to stop nagging her and let her come around on her own.  Maybe over time she'd start to feel left out.  Or she'd realize that she couldn't BS her way on her own and she didn't want to fail.  She was so obstinate that maybe just the fact that I was pushing was making her push against me and if I stopped pushing she'd stop fighting.  I was worried though that she would get so far behind by the time she came round that it would be too late to learn what she needed to learn since she was already so far behind.

So I turned to our vice principle, explained what was going on and what I'd tried and he said he'd talk to her.  The next day she took notes, completed her homework and asked for help.  I asked him what he said and he told me he'd talked about how many thousands of years of knowledge we were trying to teach her in a tiny span of time and that she could not learn without my help.  He said that this will be maybe the only time in her life where she had a teacher who was willing to give her extra time, extra help and who really cared about her and if she waited, she would never get the help she needed.  It was almost exactly the same logic I'd tried on her.  Her efforts have continued through the week.

I guess this just reinforces my belief that if I ever get to a place where I think I've figured it out- that means I've grown too complacent.  Teaching will always and forever be something I'll need help with and that's the way it's supposed to be because it's a collaborative endeavor.  I hope I'm always humble enough to ask for the help I need.

Saturday, February 1, 2014

Angleatron Failure and Distance Formula Game Success

I taught the lesson on angleatrons that I previously posted about and it was not very successful at all.  I'm reluctant to write about my failures because I'm already the type of person who doubts everything I do and even my most successful lessons leave me feeling like I'm not the teacher I wish I was.  This is also why I'm a terrible blogger.  In my most insecure moments, I can't help but compare my teaching to these fantastic teachers I so admire and aspire to me more like.  I hope the fact that I am constantly striving to be better makes me a better teacher, but it also makes me very uncomfortable in my own skin much of the time.

The lesson was unsuccessful for several reasons beyond my control.  My speakers broke partway through showing the video so the students couldn't hear Vi Hart's narrations.  I then tried to paraphrase what she was doing with paper folding but students grew bored watching a soundless video.  This made me rush through the video to move on to the activity, but then students were confused about how to do the paper folding.  Their confusion reinforced my reasoning behind doing the activity because if students couldn't grasp the idea that the corner of their paper can be used as a 90 degree angle, then they really did need to practice basic angle drawings.  About half the class did take off doing drawings and folding angles.  A couple of them produced really beautiful designs and I think all of them did grasp what 90 degree and 45 degree angles are supposed to look like.  The other half of the class adamantly refused to draw, or refused to draw precisely (sloppily drawing 90 degree angles that looked more like they were 100 degrees because they refused to use the corner of their papers to guide their drawings.)  Their reluctance and difficulty only convinced me that they did need to practice, but the activity didn't work for the students who needed the practice.

I did try some other games this past week and they were much more successful.  For me, the simpler the game, the easier it is for me to pull off because I have a very minimalist classroom (I have to buy all my own supplies, the students have tiny desks and we don't have a white board, only a smart board which allows only one student to write on it at a time.)  I came up with a game to practice the distance formula which worked beautifully mostly because it was so simple.  First, I had to bribe the students to play because playing games involves more thinking than taking notes and they actually wanted me to keep lecturing so that they could passively copy/ sleep.  Then I asked them to group into threes and told them they were competing against their group members to convince them to work with people other than their best friends.  Finally, I just displayed four numbers on the smart board.  The students could rearrange the numbers into two ordered pairs however they wanted and could add negatives if they wanted.  The person in their group that was able to organize the ordered pairs in such a way as to maximize distance won and earned a candy.  I started with 0,0, 4, 12.  Then gave them 2,3,4,5.  Then started giving them bigger numbers.  At first the students just paired the first two digits and the last two digits and used the distance formula.  But after a round or two they started figuring out how to add negatives and rearrange the bigger numbers with smaller numbers to get larger distances.  They also were doing a good job of checking each other's work because they only earned candy if they did the calculations correctly.  By the end of the game, every student had figured out how to maximize distance and they were all tying and I was going bankrupt on Jolly Ranchers.  My favorite part was when one person in a group announced their largest distance was 13.2 and students from a different group came over and clustered around asking the person from the first group how they'd gotten such a big distance. I think the game worked very nicely because it was simple, strategic, competitive but not so competitive that students who were "losing" became disheartened.  By the end everyone was winning.

I didn't like the game because I don't like the distance formula.  I would much rather students use the Pythagorean theorem enough that they could then extrapolate the distance formula by picturing triangles on the coordinate plane without needing to graph.  Unfortunately I just didn't have the time to reinforce this method of calculating distance so I caved and taught them the distance formula (but at least I did show them how it came from the Pythagorean theorem, though half my class fell asleep or glazed over when I tried to show the derivation to them.  I've tried having them do the derivation themselves but their algebra skills are too weak.)  At least though, they did do some critical thinking in terms of figuring out how to maximize distance.  That was the saving grace of this game.

Saturday, January 25, 2014


I inherited a geometry class last semester that was already two months into the curriculum and it was very frustrating that their basic sense of shape hadn't been strengthened.  I was supposed to start with congruent triangles, but many of them didn't even know what a right angle was supposed to look like.  It was too late to go back and work on basic drawing skills but I've been thinking about how to help students with little practical drawing experience succeed in geometry.  Gone are the days when all students had formal art classes and without these classes, their visualization and drawing skills are so weak that geometry can be really challenging and frustrating.

With the new semester, I'm starting over with a new class and I'm working on building more drawing and visualization into my curriculum.  I've just written up a lesson tied to Vi Hart's angleatron video. I want my students to be able to do rough sketches of all the basic angles so that their drawings, when we get to triangles and polygons can be at least a little bit accurate.

First I'll show my students the video and have them try to explain how the different angleatrons were formed.

Then I'll have the students make the different angleatrons, name their vertices, sides and the angles themselves.

Then I want my students to try making 3 different geometric patterns using their angleatrons like Vi Hart did.
Finally, they'll each pick the pattern they like the best and we'll make a class quilt out of their different patterns.

I'm a little nervous because a lot of my students really hate drawing, but I hope the structure of this activity and Vi Hart's beautiful examples will help.

Here's the lesson sheet I'm planning to use:

Sunday, December 1, 2013

Article on "Math People"

Soo.... I wrote an article for Quartz magazine on why so many people identify themselves as "math people" or "non math people" and what we can do about it.  It's the first time I've ever been officially published and I'm both terrified and excited.  The magazine editors came up with the article title and the subheadings but the rest is mostly my work.  Here it is.

I don't know how many people will read it, but so far it's been well worth the two weeks I stressed over it because of some of the wonderful responses I've gotten from former students.  I have to share them.  If the article was terrible, it was worth writing just to get these wonderful words of encouragement from my students.

Student 1: Congratulations on having your article published! I miss having you as my teacher so much! You were the best teacher I have ever had <3

Student 2: You are so brilliant! I am so lucky I had you as my teacher. Not only were you a good teacher, but a super-cool one. I miss you!

Student 3 (this is the one that made me cry): I want to thank you for writing that article. I have been so scared to take another math class because of the last one I took. It was Math 110; basic college Algebra. I failed the class. I went to the math lab regularly, I participated in study groups, office hours, the works. I tried hard, but the teacher just could not explain things in a way that I could understand well and remember. After that class, I decided that I could not ever have a career in the math/science field despite my love for them because I just was not a "math person." A few weeks ago I was reading a Biology/Science textbook and realized that those were the only textbooks I had ever read for fun. I always have. But right then I nearly started crying thinking about how I just did not have the math skills to ever pursue it. Your article has given me hope... I now have the courage to try again. Thank you so much. I am so grateful for the time I had as your student. I know that all of your former students feel the same way. We love you. You are the best. Don't believe anyone who tells you otherwise

Saturday, November 30, 2013

Why teach Algebra

I've been thinking about a response to the article published in the New York Times, "Is Algebra Necessary?"  for over a year.  I've started maybe 10 different draft posts and scrapped them.  I've been following the follow-up debates in blogs (see Wiggins' post on algebra 1 as a poorly designed course and Honner's response to Wiggins) and thinking about related articles like "Wrong Answer: The Case Against Algebra II" and "The Mathematician's Lament".

I've been so torn about how to respond because as a math teacher, of course I believe teaching math is vital.  I became a teacher because I wanted to save the world and martyr myself with 80 hour work weeks and panicked sweats every Sunday night.  And reading these articles seems to trivialize what I have poured sweat, tears and many many gallons of coffee into.  Yet I see their side of things.  I hate the idea of algebra 1 being the barrier between a talented artist and a career in art.  I am now teaching students in algebra 1 who have failed it two or three times before and it broke my heart yesterday when I handed back a  homework assignment I had given a 7/10 to a student and her face lit up as she said that she'd never gotten a passing score on a math assignment.

Also, I've never used math in "the real world".  I'm not an engineer, an economist, a physicist or a banker.  I don't know how math gets used out there so who am I to tell students year after year that they're going to need these skills when I don't know that they will.  The argument that math sharpens general cognitive skills and teaches students problem solving strategies that will be useful later in life, especially as it's backed up by research, holds water but that doesn't help us algebra teachers argue for teaching algebra.  Why not teach statistics?  Or a formal logic class?  Should we defend the traditional math sequence, or should we branch out and give students who are failing at algebra alternative math options?

But the other day I was talking with my husband and I realized why I love math, not why I teach it or how I use it, but why I love it.  And I think the reason for my love is also the reason it needs to be taught.  I am decidedly introverted, perhaps the queen of introverts.  I can't handle phones- it's very very difficult for me to talk on the phone with those I love and even harder with those I don't know.  I need to see eyes, to gauge reactions, to be able to comment on surroundings or engage my conversation partner in a task that removes the focus of conversation off of me.  I've found the adult world intimidating and overwhelming and need frequent breaks from it.  I like playing board games to escape because they have defined protocols.  I know exactly what the object of the game is and how to get there.  I can enjoy socializing while playing because of the game's comforting structure.

The world is overwhelming for anyone- even those not so introverted as I am.  There are complex political systems to understand, the natural world can be scary and confusing, bad things happen to good people inexplicably, we are born with deficiencies and insecurities that make socializing difficult or awkward.  School is for this- to help our young students learn that knowledge will conquer their confusions and difficulties.   When they understand how something works, they aren't as afraid of it and they know how to navigate it.   Or when they understand how something works, they won't make a mess of it because of overconfidence or arrogance.  Understanding our history and political systems is vital but impossible.  We give our students the best analysis tools we can and hope that time and a love of learning will help guide them in making wise decisions for themselves.  Learning science is fascinating and practical, but requires lots of field trips, labs, props and math to even begin understanding the basics of how our world works.  Math is the only field where understanding can be created by the student with nothing more than a pencil, a paper and a system of logical rules- just like a board game.  Yet unlike a board game, math helps us untangle the mysteries of how the world around us works.  It gives us a sense of order and control over our own minds and our own environments.  Isn't our job as educators to help students make sense of the world around them and to help them feel in control of their own lives?  Math is instrumental in accomplishing these two goals but especially for helping students realize what their minds are capable of and that they don't have to go outside to conquer a small piece of their universe.

So this is why we need algebra and not just statistics or logic.  Algebra is about finding the unknowns.  It's about looking at how the complex variables in our lives that affect each other and us. It has the further advantage of being the bedrock of higher level math so that if a student chose to pursue advanced math, she could.  It's got an easily understood framework of logic so that when the basic properties of algebra are mastered, all the other results are easily provable by a 14 year old with a pencil.  But most importantly, mastering algebra - especially because it can be such a difficult transition for many students- makes a student feel powerful and in control of her mind and world.  Isn't this how we want students to feel when they go out to help shape our society?

Sunday, November 17, 2013

Congruent Triangles Review Game

I played a review game with my geometry class a few weeks ago that they loved so I thought I'd share it.  I think I stole this idea from a blog, but I can't for the life of me remember which blog, so if it's yours let me know.

I stole the problems from the Pearson Geometry Common Core Edition. 

I printed the document below double sided but didn't staple it.  Then I shuffled the pages and made 8 or so copies of all of them for the 8 groups in my class.  The groups needed to start with the page that has "RP" at the top and do the proof.  Then they hunt for the answer in the sheaf of papers.  When they find the answer, they grade their proof against the answer key, turn the answer key over and work the problem on the back of the answer key.  Then they hunt out the answer key to the new problem.

If they keep track of the order in which they did the problems, they can write down all the letters from the upper right hand corners of the problems, unscramble them and a message appears.

I had students for the first time actually paying close attention to every step of the proof, asking great questions about why different steps appeared, if they were necessary, and if/how order in the proof matters.  They also really loved working out the code.

I know it's just drill and kill two-column proofing, but it did a nice job of getting my students to compare different proving methods and getting them to analyze their own work.

Here it is: