# A High School Math-Science Journal

In my first year of teaching, fresh from my haze from history grad school, I remember approaching the history and English department chairs about creating a high school level journal for those subjects. I mean, our school has a literary magazine, and also even a publication for works in foreign languages (seriously!). But nothing for amazing critical analyses and interpretations in English and history. I figured having something like this might encourage students to revise already excellent work for publication, and also make the audience of their paper be an audience of more than one. I even contacted the literary magazine student editors to see if they would feel like the journal would encroach on their domain (they said no). For reasons that are still quite beyond my understanding (because I still think it’s an amazing idea), both department heads rebuffed my idea. (Also, if they said yes, they would have gotten an enthusiastic first year teacher who would have taken on all this work!)

And so, I let this idea pass. One of many that I have, think are awesome, and then languish and die, either due to my own laziness or due to external circumstances beyond my control.

Until last year. When I was thinking: I’m a math teacher. Why not start a math and science journal? It’s so obvious that I don’t know why the idea didn’t hit me over the head years ago. So I found a science teacher compatriot who I knew would be interested, and we came up with an initial plan. And at the end of last year, we presented it to some students who we thought might have been interested (as this was something that is something that has to be for them, by them… if they don’t want it, there’s not point in doing it… it’s not about us…). They were, and we were officially off to the races.

We shared with the students the following document we made, with a brief outline of one vision for the journal. But with the understanding that this was their thing so their ideas reign supreme. This was, in some sense, a mock-up that the science teacher and I made to show them one possibility. The one thing that the science teacher and I were really aiming for in our mock-up was that the journal shouldn’t just be for superstar students. We wanted to come up with an journal that has a low barrier of entry for students submitting to the journal, and that if a student has interest or a passion for math or science, that’s really all they need to get started. To do this, original and deep research wasn’t really the primary focus of the journal. So here’s our brief proposal:

The additional benefit of having this journal is hopefully it will cause curricular changes. Teachers will hopefully feel moved to create assignments that go “outside of the box” — and that could result in things being submitted. Students who express an interest in some math-y or science-y idea (like why is 0/0 undefined… something that came up in calculus this week) could have a teacher say “hey, that’s great… why don’t you look it up and do a 3 minute presentation on what you find tomorrow?” … and if they do a good job, encourage them to write it up for the journal. Or a teacher might assign a group project on nuclear disasters, and encourages the students who do extraordinary work to submit their project to the journal. (Which can be showcased by teachers the following year!) Or a student who notices a neat pattern, or comes up with an innovative explanation for something, or who wants to try to create their own sudoku puzzle, or decides to research fractions that satisfy $\frac{1}{a}+\frac{1}{b}=\frac{2}{a+b}$. Or whatever. Knowing there is a publication you can direct the student to, as a way to say “hey, you’re doing something awesome… seriously… so awesome I think you kind of have to share it with others!” is going to be so cool for teachers. (As a random aside, I was thinking I could enlist the help of the art and photography teachers, because of the overlap between math and art… They might make an assignment based around something mathematical/geometrical, which students can submit…)

I honestly have no idea how this is going to turn out. What’s going to happen. How the word is going to get out. If anything will be submitted. If kids get excited about it. Lots of questions. But I have a deep feeling that the answers will come and good things are going to happen with this.

I’m soliciting in the comments any thoughts you might have about this. If your school does a math journal, a science journal, or a math-science journal, what does it look like? What works and what doesn’t? Do you have a website/sample we could look at? If you don’t have one, and you are inspired and think of awesome things kids could put in there (e.g. kids submitting their own puzzles! kids writing book reviews of popular math/science books, or biographies of mathematicians/scientists! getting kids to create photographs or computer images of science or data visualization or just making geometrical graphing designs! trust me — brainstorming this is super fun!) I’d love to share any and all ideas with the kids involved with this project at my school.

# Students communicating mathematics has opened my eyes to mathematical ugliness (and what that means to me)

This year, as I have been in the past few years, I’ve been attempting to incorporate more writing in my math classes [note: Shelli found a post from 2009 I wrote on this endeavor]. It’s been extraordinarily enlightening, because what this has done is show me two things: (1) kids don’t know how to explain their reasoning in clear ways, and (2) I’m usually extraordinarily wrong when I think my kids understand something, and the extent to which I am wrong makes me cringe.

(wow, been too busy to shave, have we Mr. Shah?)

For the first point, I don’t actually do much. I ask them to write, they write, I comment. And we discuss (more at the start of the year, but I always let this go and I forget to talk about it a lot). In Algebra II, they get one or two writing questions on every assessment. And each quarter they had problem sets where they had to write out their thought processes/solutions comprehensively and clearly. Even though I didn’t actually do anything systematic and formal in terms of teaching them to write (mainly I just had them write), I can say that I’ve seen a huge huge improvement in their explanatory skills from the beginning of the year. What I used to get just didn’t make sense, honestly. A random string of words that made sense in their heads, but not to anyone reading them. But now I get much more comprehensive explanations, which usually include words, diagrams, graphs, examples. They aren’t usually amazing, but they’re not ready to be amazing.

For the second point, I realized that the types of questions that we tend to ask (you know, those more routine questions that all textbooks ask) don’t always let me know if a student understands what they’re doing. It just lets me know they can do a procedure. So, for example, if I asked students to graph $y < 2x+3$, I would bet my Algebra II kids would be able to. But if I showed them the question and the solution, and ask them to explain what the solution to that question means, I would expect that only half or two thirds of the class would get it right. (Hint: The solution is the set of all points (x,y) which make the inequality a true statement.) They can do the procedure, but they don’t know what the solution means? That’s what I’ve found. And you know what? Before asking students to write in the classroom, I had deceived myself into conflating students being able to answer $y < 2x+3$ with a full understanding of 2-D linear inequalities. [1]

Before having students write, I actually believed that if I asked that question (“What does this solution mean?”), almost all the students would be able to answer it. (“Like, duh, of course they can!”) But since asking students to explain themselves, explain mathematics, I’ve uncovered the nasty underbelly to what students truly understand. The horror! The horror! But now that I recognize this seedy underworld of misconceptions or no-conceptions, I’ve finally been able to get beyond the despair that I originally had. Because now I know I have a place to work from.

The counterside to this point is that when kids do understand something, they kill it.

This simple question I made for my calculus students early in the year, and this student response, says it all. I have no concern about this kid understanding relative maxs and mins. No traditional question would have let me see how well this student knew what was up.

For me the obvious corollary is that: we need to start rethinking what our assessments ought to look like. If we want kids to truly understand concepts deeply, why don’t we actually make assessments that require students to demonstrate deep understanding of concepts? I am coming to the realization that the more we keep giving the same-old-same-old-assessments, the more we are reinforcing the message (implicitly) that we don’t reallyreally care to know about their thinking. We are telling our kids (implicitly) that we are content if they show their algebraic steps. But as I’ve noted, my big realization is that students performing those algebraic steps don’t necessarily mean that the student knows what they’re doing, or what the big picture is.

I don’t know have an example of what I think a truly ideal assessment might look like, but I do know it isn’t anything like I gave when I started off teaching five years ago (has it really been five years? why am I not better at this?), and I do know that each year I am slowly inching towards something better. Right now, my assessments are fairly traditional, but with each year, they are getting less so.

Sorry if I’ve posted something like this before. I have a feeling I have. But it’s what’s been going through my head recently, and I wanted to get it out there before I lost it.

[1] Another good illustration might be having students solve $-3x<6$. Sure, they can get $x>-2$. But does doing that really mean they understand that whole “if you divide by a negative in an inequality, you switch the direction of the inequality” rule that has been pounded in them since seventh grade? Nope. The traditional questions don’t tend to check if the kids know why they’re doing what they’re doing.

# Absolute Value

So I taught absolute value equations in Algebra II. And so far I think things have gone fairly well. I read Kate Nowak’s post on how she did absolute values, and I thought I would change my more traditional introduction to them… but I didn’t. I realized that the way Kate was motivating it (with the distance on the numberline model) was great, but I felt I could still get deep conceptual understanding with the traditional way she eschewed in her post.

So I stuck with that.

I used exit cards to see how they could do… and they were okay.

But after learning how to solve $|2x-3|=5$ or $|2x-3|=-10$, I asked kids to solve things like $2-5|5x+6|=5$ or something similar. Many students said on their home enjoyment:

$2-5(5x+6)=5$ or $2-5(5x+6)=-5$.

It is unsurprising to me, and yet, it makes me want to throw up. Because what’s coming more and more into focus, and I’m sure you’re going to hear me complain about this more and more in the coming months, is how reliant students are on “coming up with rules” and “applying rules” — without thinking. They desperately want unthinking rules. And this year, because I can’t handle throwing up all the time, I’m vowing to really not give rules to them.

I really got to the heart of this “I LIKE PROCEDURES” thing with them with a true-false activity that I did, using my poor man clickers. I think this exercise highlighted how dependent my kids are on procedures and coming up with simple rules that help them in the short term… but that can hurt them in the long term… It’s a bunch of True-False questions. And when we talked about each one of them, my class saw concretely how reliant they were on misconceptions and false rules. EVERY SINGLE QUESTION led to a great short discussion.

So here they are, for you to use. Sadly, I don’t have the blank slides to share with you, because my school laptop is not with me at home now.

These were great for asking “so who wants to justify their answer?”

# And So It Begins…

The year in full swing, and it feels like I’ve been teaching for days upon days, even though it has only been two days, so I suppose I should have said “day upon day.” It shocks me (BZZZ!) that a person can go from lazing about, jaunting off for coffee, picking up a book and reading it through in a day, watching an entire season of real housewives of (insertanycityhereandit’sprollytrueforme), going to the restroom whenever you please… to being trapped in a building (no AC!) with a hierarchy, having to answer to a lot of someone elses, having inhaled and not having the opportunity to exhale until hours later. And then you remember: oh yeah, I have to plan for the next day.

So it’s like I’ve never left. And I love it. There are things I cringe at, but heck if seeing my kids and my colleague friends, and getting to think about how I can do what I do but less sucky: it’s thrilling. I suspect this glow will be gone in a week, so don’t worry: my normal self will return soon enough.

Glow Self:

I just wanted to talk about the first two days of Algebra II. I usually start out the year with a honest but (upon reflection when I looked at it a few days ago) boring exhortation about mathematics and why it’s useful, beautiful, interesting. Then I talk a bit about the course expectations. And then we jump straight into talking about sets. I did it this way because I wanted to dive right in and show them what I valued: doing math. This wasn’t going to be a class where we get derailed with non-math things.

Well, I was unsatisfied with that, because it was boring. A boring set of slides with me speaking (albeit with a wildly inflecting voice, which can make anything less boring), followed by possibly the most boring topic: union and intersection of sets. It also was me lecturing about sets.

This year I vowed to take risks in how I teach. Less lecturing. Less partner work. More group work. More deep thinking and problem solving. And since I made a post saying some of the things I wanted to try, I decided to scrap everything and start anew.

I looked through the Park School of Baltimore’s curriculum and found a perfect thing to transition us into sets: mathematical symbols.

So on the first day, I sat kids down in their seats, I explained how they were to move their chairs to get in their groups. I asked them how they were feeling, I told them my goal was to make them feel good about math. Then, suddenly, I asked students to get in their groups. I projected the first page of the Park School packet that I photocopied. We did one part of one problem together (I had kids read the problem aloud and work in their groups to come up with the answer). Then I set them free, after handing out the packet, with only the following instructions.

Then they started (some faster than others) and I went to the following SmartBoard page [update: here if you want to download it]…

… and started the participation quiz (what I’m calling “groupwork feedback”). [To understand what comes next, you have to read the link above.] I didn’t explain anything. I just typed and dragged and typed and typed and walked around. Kids would ask me questions, and I would just shrug. They stopped asking me questions and started relying on each other and their brains. I didn’t stop groups which were off task. One group of four broke up into two groups of two, and then rejoined. I just kept on filling in the grid, not talking about it.

Honestly, the idea that I would have to be filling in this grid scared me. I didn’t know if I was going to be able to do it. I didn’t know if I would have the heart to put “off task” if a group were off task. I didn’t know if I could keep up, or if I could hear the kids talking, or keep track of everything. But it was easier than I thought. Students worked for about 30 minutes. I think that’s the right amount of time, because I wouldn’t have gotten a critical mass of feedback if they had worked any less.

Then I stopped them. What I noticed after doing it in two classes is that engaging in this type of observations of groups is super interesting and helpful for me. I had a good sense of which groups knew how to do groupwork already and which groups didn’t. I heard some great conversations, really great conversations, about some rich problems (“does it mean that the only way to get an odd number is with …”). I saw group dynamics at work (especially the difficulties that present themselves with groups of 4). I also saw that one of my two classes already has a good handle on how to work in groups, and the other is going to need some time and coaching.

We spent 12 minutes talking about the results. We talked about if “I don’t know” is a good or bad thing to have on that chart (it depends…) and finally I asked groups to look at this thing that I whipped up (not great, but I needed something) and to classify themselves, and to think of some ways they could improve and think of some things they did well. And we went around and had each group explain.

Although terrifying, I’m glad I did it on the first day. It was scary to try something new (new problems! groupwork feedback!). I feel confident that I showed my kids what I hope to value in the classroom this year. Communication. True thinking. Independence. Collaboration in the learning process. (I don’t see the last two things as contradictory.)

That was the first day. Today (the second day) I saw only one of my classes. And what I did in it didn’t unfold nearly as well, in my opinion. I wanted kids to present their solutions. The night before I had them do a few more problems on their own, so I gave groups 8 minutes at the start of class to talk through their work, telling ‘em that they were going to be asked to explain.

Then I had individual students come up and explain their work for some of the problems (after a short discussion on how it’s great to not get something and to have misconceptions / confusions, because that’s where we learn, and a discussion on how to be a good audience for the explainers).

They put their work up under the document projector. And talked. But what I learned is: I need to work on having students be effective presenters. And how to encourage the audience engage with the presenters more. And how to balance me intervening versus letting the student go on. (It’s hard for me to let go of the “explain” part of class.) So now I know I have to work on this. (Luckily I was meeting with my teacher friend mentor for lunch, who does a lot of modeling work in her classroom, and she had a lot of good things to suggest. )

So there we are. I’m trying to be very intentional (thanks @bowmanimal for the word) in how I start the year. I also printed out “exit slips” for my classes tomorrow because my goal is to get formative feedback at least once a week in each class. And I tried to do “What’s the Question?” (known in my class as “Que es la Pregunta?”) in Calculus to activate prior knowledge on rational functions. However it kinda totally fell flat. It did what it should have, but it wasn’t as enjoyable/fun as I hoped. I think I might need to rethink how I set it up.

And there you are. Some words on the first couple days of school.

# Math Taboo

I participated in a great twitter conversation the other day where we brainstormed a few strategies to help make our courses more accessible to English Language Learners (we used the hashtag #ELLmath, the approximate transcript is here if you are interested). It was a great start to what needs to be a running dialogue for me, as I teach almost 100% students for whom English is not their first language. If anyone has any ideas about #ELLmath, I would love to hear them in the comments. The conversation reminded me of a little idea I had last year, playing the game Math Taboo to help students expand “definitions” to actual understandings of concepts. Now, I’m sure other people do this, and a quick Google search leads me to believe it’s not all that novel, but while discussing #ELLmath, it struck me as a particularly good exercise for ELL students.

The idea of the real game is to get your partner to guess a word by describing without using any of the five taboo words, which are usually the first words that anyone would go to in a description. So the obvious math equivalent is to pick a term that you are throwing around in your class and get students to describe it without using their go-to math descriptors.

We played during beginning-of-the-year-review as a class, with the word to guess already known to everyone, and I gave students a chance to take a stab at verbalizing a definition without using the taboo words, one at a time until we got an acceptable description. However, this could easily be adapted to be a much more interactive activity (though its creation might take just a bit of time).

#### So why play this?

Whenever working one on one with students, I found myself trying to diagnose why they were not understanding a problem. I would ask them things like, “Well, what is a derivative anyway?” and they would often answer with something that I found acceptable, but perhaps could have been just something that they had figured out should be said as the “correct” answer. Even if they weren’t saying book definitions (which would actually be easier to deal with), many times they were using my informal definitions – words that they had internalized about the concept that might not actually display a deep understanding, but that I had been mistakenly accepting as evidence of learning. Definitions are important, but assuming that those are indicators of deep understanding is, of course, very problematic, no matter where those definitions come from.

So, this Taboo game serves a two-fold purpose: learning for the students (by forcing them to think deeply about a mathematical concept; by having them trade in math jargon for conceptual understanding; and by hearing classmates describe something in more accessible vernacular) and learning for me (by seeing how well students actually understand a concept; and by seeing what language students use to talk math in the hopes that my mathematical narrative can better reflect theirs in the future).

#### Alternative game: In how few words can you express this definition?

I have never tried this game I’m about to describe, but the idea is to start out with a long definition from a math textbook and see how few words you can use to express the same idea. Delving into the Twitter world this summer I have realized how wordy I am, and the process of editing my tweets down has made me realize how many words I use that are unnecessary. Twitter forces me to think about what is the core of my idea, which led me to think up this exercise. This could be done competitively (give groups 5 minutes to brainstorm), or you could do it countdown style, trying to lower the number of words by one each time. This could get students to really consider what is important about a mathematical concept and to get them to realize that the thing itself is more important the words you use to express it.

# Make it Better: Memory Modeling

“A monk weighing 170 lbs begins a fast to protest a war. His weight after t days is given by W = 170e^(-0.008t). When the war ends 20 days later, how much does the monk weigh? At what rate is the monk losing weight after 20 days (before any food is consumed)?” <– That’s an actual problem from our Calculus book, which I find very amusing. Though it doesn’t really fit Dan Meyer’s definition of psuedocontext, I just get a kick out my mental picture of a monk sitting in a dark room taking a break from protesting the war to scribble away on a notepad trying to make predictions with an exponential model… There are so many word problems that force “real-life” situations into the convenient framework of whatever math topic is being presented in that section. I guess these are supposed to demonstrate to students how useful and relevant math is, but I think we all know that students just find them to be tricky and unyielding disguises to math that they generally know how to do.

There was one word problem that fit an exponential decay model to someone forgetting information, so I decided that instead of just doing the word problem, we would test the model by recreating the experiment. The day after we had a midterm exam, instead of handing back their corrected test, I put them in groups and gave them the following list of 50 three-letter syllables that I generated with a random number generator:

SOQ XAC DOB NEB BAR JYS ZYW GEK TUD ZEM GAK KUR BEN XOQ DUX BYR NIT WAP ZIJ HOG HIQ DUW CUD SAM BIM LIH JEV VEZ QEM GUL ZIQ SEQ JYV GUT XYM XAX BIQ DOJ ROM ZIV QEW JEH CYS ZEM FOM KEG DUC GYK WYQ POD

I gave them 15 minutes to memorize as many as they could and then tested them by having them write down all that they remembered. Then, I handed out the midterms and we started going over them. About 5 minutes later, I had them write down as many of the syllables as they could again. Then, we went over a few problems on the midterm… then another memory test…. then more midterm… then another memory test. They had absolutely no idea why we were doing this, so each time they groaned and complained. And they groaned even more when I opened class the next day with another trial. And then again two days after that… And then a last time a week and a half later. All without studying the list after the original 15 minutes.

Finally, I revealed the purpose of the whole experiment. We collected data and used GeoGebra to fit various models to their data. There were four different mathematical models to choose from that I found from various psychological studies (which I had loaded into a GeoGebra file with sliders so that they could move the various models around to fit their data). Each student picked the one that they thought fit their data best (a function to calculate how many words they would remember over time), took the derivative of that to calculate their “forgetting function” (a function that tells them how fast they are forgetting words at any given time), and then used both to calculate how many words they will remember in a few weeks and how fast they will be forgetting them at the point.

We graphed all of their functions on the same axes (y-axis = number of words remembered, x-axis = time in hours) to analyze which model was best and analyze how their memories compared to their classmates. The results are below. The different colors correspond to the model that each student chose.

#### CLASS 2 -

Now, the clean final result of that graph hides how messy the model fitting part was. Though some students’ data fit well, some didn’t, at all, which was actually really nice. They really struggled trying to fit the model and hopefully realized that a lot of these models that we are dealing with in cooked textbook problems aren’t as powerful as they purport to be. If I could do it again, I would have them use more mathematically sound ways of fitting the models than just eyeballing it (I hadn’t really considered this and realize now that, though it would be an investment in time, it would make the whole thing much better).

But besides doing some authentic math that was individually tailored to each student, my favorite part of the experiment was the followup meta-cognitive discussion. We ended up having a really great conversation on how best to memorize these random things, which then led to a great discussion about how to learn and study best (especially how you should go about studying math). We talked about how some people put the words in context by using a story, some people made patterns by grouping similar items together, and the ones that didn’t do very well talked about how they just tried to memorize these random unconnected things by rote memorization. Many also noticed that throughout the closely connected trials on the first day, their number memorized actually went up, so we talked about how assessment can actually help you learn something too (in addition, of course, to regular practice).

Make it Better.

I have one simple question this time: the thing that I really didn’t like about this experiment was that it was entirely teacher centered. They were in the dark about what was going on (for experimental purposes) until the day that we collected data, fit models and did some quick calculations. How can I make this more student-centered and add elements of inquiry? I have a few ideas, but I wanted to see what other people thought.

#### Files:

from @bowmanimal

# Email breakdown 2010-2011

Last year I had archived 2,270 emails to and from (and about) students. (I make a separate folder for each student and file everything related to that student.) The breakdown from the data last year was here.

This year, the total comes to 3,364 emails. The reason for the increase is probably due to the reassessments in calculus… students had to send me an email justifying their request for a reassessment.

The student with whom I had the least communication to/from/about had 16 emails. The student with the most had 192 emails. Each student on average has 71 emails.

# Edublog Nominations

Here are my 2010 Edublog Award Nominations…  (my 2009 nominations are here)

Best individual blog: Shawn Cornally’s Think Thank Thunk

Shawn’s blog arrived on the scene in Februrary 2010, and has quickly won over the math teacher blog community. He’s a staple read. Why? Clearly he’s a compelling writer, with posts chock full of quotations inspiring enough to lift and emblazon on classroom banners. But it’s more than that — than the inspiration dripping from every post for the readers to hold out our cupped hands and collect. It’s that Shawn arrived on the scene with a simple philosophy about the classroom, and built a whole curricular and assessment-based regime around it. The philosophy is this: LET KIDS LEARN! GIVE THEM FREEDOM AND THEY WILL LEARN TO THRIVE. This philosophy lends itself perfectly to Standards Based Grading, and his work, coupled with Dan Meyer, Matt Townsley, and others, have led to a wholesale shift in the math edublog community. At the very least, spearheaded by Shawn, Standards Based Grading led to serious, questioning, and respectful conversations around the nature of assessments. And for some of us, it has led to a wholesale reorientation of how we view the classroom and how we think about learning. Did I mention that Shawn only started blogging in February 2010? His blog is a Tour de Force.

Best individual tweeter: David Cox / @dcox21

Reason: He’s always there, and his snarkiness is always on, ready to go! If you need any convincing, check out any of these “Favorite Tweet” posts. He also tweets about teaching.

Best new blog: Shawn Cornally’s Think Thank Thunk

Reasons: listed above

Best resource sharing blog: Mimi’s I Hope This Old Train Breaks Down

Reasons:  I don’t think Mimi gets the recognition she deserves. She has created countless amazing resources for her classroom, and shares them. These worksheets and activities are inspiring enough that… well, let me put it this way… she teaches Geometry, and I dread the day that I have to teach Geometry, but knowing I have Mimi’s stuff at hand makes me think teaching it could almost be fun.

Best teacher blog: Kate Nowak’s f(t)

Reasons: Kate is our Fairy Blogmother. Her blog doesn’t have a singlular focus, but that’s part of its charm. Kate blogs about whatever, and not knowing what’s coming next is part of the appeal. One post might be on special right triangles in dollar bills, and the next her trying to work through the muck and mire of Standards Based Grading. Kate also spends time drawing new people into the blogging community, and she even wrote a post on how to start a math teacher blog that I dare say spawned quite a few new faces in our expanding circle. Her blog is a perennial staple, read and admired by all.

Best use of a PLN: Riley Lark and his Conference on Soft Skills

Reason: Riley Lark created what I think is the first Virtual Conference for the online math teacher community. In general most of the posts that we write, and read, deal with curriculum — and how we get our kids to know it, and how we know they know it. Riley saw a gap in the conversations. We don’t talk about those other things we do as teachers to be effective: those things we do to connect with students so they know we’re there for them, and we want them to be there for us. The relationship building that goes on in the classroom… we all do it tacitly. He asked us to make explicit what we do implicitly. This conference started with 5 “speakers” and blossomed into 17 “speakers,” each writing with our own voice. Riley called upon our PLN and our PLN responded.

Reason: He’s part of the first generation of math teacher bloggers. His cause celebres have changed, but his overarching goal is the same: to get others to think about ways to engage students in the classroom. From focusing on design, to focusing on assessing, to focusing on his What Can You Do With This (WCYDWT) series, to focusing on pseudocontext, Dan has asked provocative questions since 2006. He asks teachers to re-look at what we’re teaching, and asks us to pique the curiosity of our students. Specifically, his mantra (though he has never put it this way) is don’t put the cart before the horse. Don’t teach the concept and the method of solution, without motivating the need for the concept. Grab your students’s curiosity by showing them they need a concept, so they want to learn the concept. And let me tell you, it is easier said than done… but Dan makes it look effortless. He has inspired the second wave of math teacher bloggers, which have since inspired the third wave. Yes, in online terms, 2006 – present is a lifetime.

My Algebra II kids don’t like to read the textbook. Heck, neither do my calculus students. This isn’t surprising. It’s extra work and it’s hard. My class also makes it hard for them, because I do not use the textbook as a skeletal structure for the course. I teach mainly out of my own materials, and use the book more as a supplement.

But that doesn’t mean that I don’t want them reading math. Kids are never taught to “read” a math textbook. If they ever do approach a math textbook, they approach it like a history book. The read it linearly. They also read it passively. Their eyes glaze over. They read words, but they don’t try to connect the words to the equations or pictures. They don’t read with a pencil in their hands. They hope for some Divine Knowledge to descend upon them simply by having the book open and their eyes on it.

That doesn’t work. We all know this. Reading math is an active thing.

And so recently I’ve started talking with my class about it. To start this process/discussion, one that I hope continues, I gave my students a worksheet to fill out (see above). I love the honesty with which they responded.

For question A, some representative responses:

“I read what was assigned to me but did not read anything extra.”
“I find that textbook reading is pretty boring, so I don’t do it unless I have to.”
“I did not because I had assumed I wouldn’t learn things I needed. All I would do was look at examples.”
“No, I find it difficult to understand math when reading it in paragraphs; it makes more sense to me with a teacher.”
“I did not generally read my math textbooks. I did, however, always look over the example problems.”

Some responses for Question B:

1. The writing can be confusing, wordy, and not thorough
2. The book is BORING
3.  Small print
4. Too many words for math
5. Outdated examples

Some responses for Question C

1. Everything is all in one place
2. Have a glossary
3. Can read at own pace; refer pack to the text when I get stuck
4. Sidenotes! Diagrams! Pictures
5. Real life examples
6. Definitions clear
7. Key terms are highlighted
8. Wide range of example problems with step by step instructions
9. Colors!

I hope to do more as we go along. I might have them learn on their own, using the textbook (and the online video help) a whole section or two. There’s no reason they can’t learn to use the book to be independent learners. I will give them class time and photocopies of the section they need to learn, and they will have to figure things out by the end of the class for a 3 question quiz.

I also hope that by the end of the year, we can use their critique of math textbooks for them to write their own textbook. Okay, okay, not quite. That’s way too ambitious for me. Two years ago I had my Algebra II kids write really comprehensive Study Guides for the final exam. This year I might ask my kids to pick some of the hardest material and create their own “textbook” for it. They’ll get to write it in pairs, and then they can share their finished product with the rest of the class. That will probably happen in the 3rd for 4th quarter.

Anyway, I thought I’d share. Since I like to emphasize the importance of mathematical communication to my kids (though I don’t do it nearly enough), I thought I’d talk about this one additional component in addition to getting students to talk and write math… READING MATH!

# WELCOME TO THE INTERNETS, a series of tubes

Kate “I’m not snarky” Nowak and Sean “the squirm” Sweeney are working on putting together a…

“Welcome to the internet, math teachers”

page on the internet. As much as I like them, I feel like this project needs a new working title. Because that’s just sad.  In the meanwhile, you should fill out their survey here.

Full confession: I haven’t filled it out yet. But I’m going to, today. So there. THERE. I PUT YOU IN YOUR PLACE FOR CALLING ME A HYPOCRITE.