In response to Justin’s Day 44/Something’s Gotta Give

Justin – you know I love and admire your daily posts, not to mention your artwork.  This started as a comment on your blog, but then I started to ramble, and felt the need to expound in unfettered detail, yet again.

I teach an off-track Geometry class comprised of juniors; they are already on a 3-term cycle, and if they are taking Geometry in the fall, it means they failed either a term of Algebra sometime during that 3-term cycle, or failed the first term of Geometry last spring.  And the class takes place early in the morning.  They are not the easiest bunch of kids to motivate.

I have discovered that while the students are working to make sense visually of Geometry, many of them not only can’t solve equations, but lack basic arithmetic skills.   And if they have made it to their junior year with such low levels of mathematical achievement, you can imagine (a) what their academic self-esteem looks like and (b) how much time they have spent sitting in some form of a tortured state in math classes.  The upside to teaching in this class  – and this will sound odd, I know – is that the school has low expectations and does not truly plan for these students to take the NYS Regents exam (which does suck in a very real sense, I am aware) so I can take my time, do exploratory, hands-on activities, and take a day every two weeks to do some differentiated skill practice.   If I can get some of these kids to feel a modicum of mathematical accomplishment this term, I will have my own sense of efficacy.   I have had several of them in the first term of three term Algebra, and can see that they are trying, really trying.  They do not like repeating classes over and over again.    But the task is Sisyphean for all of us.  I use groups, manipulatives, graphic organizers, iPads – anything I can think of to engage and enthuse.  And I am seeing a very wide range of success and motivation.  I’m not sure where to go with this class; it is very much a case of me doing a LOT of the heavy lifting.  I would love to completely transform the classroom into a community of learners in which the students were motivating themselves and each other – you know, the stuff of those inspirational teacher movies.   I’ll keep trying, but I feel like the whole thing needs to be stood on its head.

Which brings me to the second part of the title: Something’s Gotta Give.  I read Paul Lockhart’s A Mathematician’s Lament last spring, and took a huge gulp/cringed when I read this line: “All metaphor aside, geometry class is by far the most mentally and emotionally destructive component of the entire K-12 mathematics curriculum.”  I was forced to take a long, painful look in the mirror as Lockhart described with convincing arguments and accurate detail what goes on in most high school geometry classrooms, including mine.  Why do I love 2 column proofs?  What purpose is there in writing out Angle Addition sentences? Or proving all right angles congruent?  I began to relax some of my strictures if students could convince me of their understanding without rewriting definitions verbatim.  If my current Geometry students (or any, for that matter) can describe to me in words, or perhaps pictures, why two triangles are congruent, or how they know which angle of a triangle is the largest, that, to me, is evidence of learning and understanding; I don’t need it in 2 columns with numbered steps.

Required HW "Proof Booklets"

Required HW “Proof Booklets”


If I told you what was behind those textbooks, you probably wouldn’t believe me.

Then last week I read three things.  The first thing was Dan Meyer’s column on Lifeless Geometry Proof which linked to Ben Orlin’s hilarious column on Proofs that 2 Column Proofs are Terrible.  Not only did these reinforce what I had already been thinking about, but they sparked a debate in my office (aka The Bat Cave)  about why we should spend at least six straight weeks in the fall term, and probably another six in the spring, teaching two column proofs. My dear friend and cave buddy, Al, is about to earn his masters degree in Math and is a Math for America fellow.  Even though this debate began because he was moaning over the geometry papers he had to grade, he amazingly stuck fast to the position that this was the curriculum we had to teach, so what choice did we have?  I thought, all we have is choice.

The other thing I read was sent to me by my amazing progeny, Geo, currently an art student at MICA.  It was an article from Wired magazine about schools that allowed students to direct their own education.  I’m not sure I am ready to go that far, but it echoed a presentation I heard this summer by Bruce Dixon, founder of the Anytime Anywhere Learning Foundation on Reimagining Education.  The future of education will be – needs to be – something that looks VERY different from what we are used to.  I have taught high need students for all eight years of my teaching career and I know that traditional classrooms don’t do the trick.  Yes, poverty is the enemy, yes, families need to do more work, but still.  Things will have to change in a big way, and I’m kind of itching to be part of that change.

I know that students like my classes because ‘they’re not like all the other math classes’.  There are definitely days of direct instruction – notes, guided examples, independent practice – but we also have estimation, individual and group whiteboards, patty paper, legos, Mathalicious, MathMunch, and Solve-Crumple-Toss (considered ground-breaking in my school).  But I know it’s not enough, not when I look at Sharenza in my Geometry class who has made a 180 degree turn-around from the disdainful, angry student I had two years ago but still can’t add and subtract, not when Stephan in Discrete Math who, for all his concentration and extra-help, still struggles with graphing a line.  I try hard to imagine this bright educational future when I teach in an 80-year-old building with few upgrades, and an unsynched iPad cart (with less than a full class set of tablets) because there is only one MacBook in the school with which to synch all the departmental carts, and an office in a once-boys’ bathroom.

Exhausting work, this is.  But I feel compelled.  Compelled because of the kids, because of the #MTBoS, of the folks I met at Exeter and Twitter Math Camp last summer, those who have become people I like to banter with, and those who have become friends.  Compelled because, honestly, maybe it’s a diversion from facing mid-life and scary health issues.  Or maybe just because when Paul Lockhart took aim, I became determined that my beloved geometry would not destroy any more students, but rather recruit more true believers in the beauty of math.  The Geometer



  1. jdmahlstedt

    Well said!!! I too teach students whose math skills are below that of their peers and motivating them st times is definitely tough! Like you, I know that things have to change, and like you, I’m also incredibly excited to be part of that change! Lockhart’s book got me fired up this past summer and I’m glad it did the same for you too! Keep on doing what you’re doing! It sounds like you’re making a tremendous impact on your students!

    • Wendy Menard

      Thanks for reading. I vacillate between wanting to change the world and wanting to put my feet up at the end of those never-ending days! But it is exciting to think about changing things. As far as a tremendous impact – well, I’m not so sure, but I hope I’m helping some of them. Ironically, I went on this evening, curious because a friend of mine mentioned she was getting written up. I found this comment, which I loved despite its negativity, and which cracked me up.
      “She gives a lot of work sometimes and makes us do retarded activities she calls exploration. She has guaranteed us that we will ALL get 90 and above on the geo regents. I guess she’s a good teacher. sometimes unclear. She does her dumb today in history shit which is funny bc she says she don’t wanna waste time and yet she does on that. Gives a lot of quizzes. Usually every week. Just do all your work. Get good grades on quiz/tests they are above all since they are 80% of your grade.”
      [Note: The grading policy is departmental, and I have never given quizzes every week.]

  2. @JustinAion

    I’ve been spending a ton of time thinking about this stuff and trying to figure out WHY I’m teaching the topics that I am. Since I don’t have access to a curriculum (and actually don’t have any idea what one looks like) I’ve been following what the other teachers do, which means I’m following the book.

    I hate this.

    But, I don’t have enough confidence in my own teaching abilities to be able to develop my own sequence and scope and the current sequence and scope seem VERY haphazard to me.

    The only reason I haven’t skipped two-column proofs altogether is because they are on the graduation exams for the state.

    It may seem like I have my stuff together, but I honestly have no idea what I’m doing in the grand scheme. Day to day, I’m awesome, but more than that, I can’t help but think “Why the hell do I need to teach them this??”

    And If I’m thinking it, the kids certainly are. If they ever ask, I’ll be up the river.

    • Wendy Menard

      Justin – I’d be happy to share my curriculum with you, or help you find a more creative scope and sequence than just following the textbook. I’ve actually managed to open a dialogue with my AP about limiting 2-column proofs in the curriculum in the future. How big a part are they on the state exams? The NYS Regents only has one proof on it, usually. The big idea, in my view, is being able to deductively use logic to draw conclusions (even in NYS, students are allowed to write paragraphs, flow-charts, or 2-column proofs, although most teachers have been using this last option for years and don’t want to change). In any case, I would do as much hands-on/exploratory stuff as you can get away with while covering the required curriculum.

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