Putting it all together

On Friday I left home after the first two periods, sick. That’s not the bad news — I mean, we all get sick sometimes. The bad news is that I had already planned on leaving after the first two periods, to go to a wedding. I had to miss my friend’s wedding, to be sick at home. But I guess if there was a perfect time to be sick, it’s the day that I had already prepped sub plans.

I’m going to share ’em with you, because they worked really well.

The year is coming to a close, and I wanted my calculus classes to pause for a moment and take stock of what we’ve accomplished. I also wanted them to try to fit it all together in one large conceptual framework.

So I decided to ask ’em to — on giant yellow poster paper, with markers — create a concept map in groups of 3.

I didn’t know what to expect. I hadn’t done this before. I did offer a prize to the best map (bag o’ candy).

I came to school on Monday, and was really impressed. The maps were colorful, comprehensive, and fun. I can only imagine the conversations that students had when drawing them (“remember when we did …”; “what was that thing we did with…”; “look at this!”).

A funny thing happened by accident. When I broke the kids into groups, I gave ’em group names (“The Polynomials,” “The Concavities,” “The Tangents,” and “The Anti-Derivatives”). There were just cutsie names, no thought behind ’em.  I meant for each group to make a concept map for all of calculus. In fact, each group ended up making a concept map for their group name.

I’ll admit my initial reaction was disappointment, because they missed the “this is the entirety of calculus all together” aspect of what I was goin’ for. But then I looked at all four maps together — and they formed a pretty awesomely comprehensive map for the entire course.

Brainstorming Some Extensions/Changes

1. Use this as a 35 minute final exam review activity for a class — where each group takes a cluster of topics and connects them. Hang these up during review days for students to look at and refer to. (I might do this for Algebra II.)

2. If a course is broken into, say, 12 large conceptual units, ask groups to design one concept map for 4 random units they draw out of a hat — making connections among ’em. Then (somehow — this I haven’t figured out totally), have the class use these smaller concept maps to generate a giant map for the entire year.

3. Have students do this at the end of each unit, so they can visually see what they’ve learned and how everything relates to each other. (Possible studying technique for students who are detail oriented and can’t see the larger picture or how things relate.)

Their Homework

After this exercise, I gave my kids homework. I gave ’em a writing assignment, promising them I wouldn’t read ’em until after their final grades were entered. I do this for all my classes as they wind down.

For homework I’m going to ask each of you to write a letter from yourselves now to yourselves at the beginning of the year, telling yourself what you wish you had known about how to succeed in this particular Calculus class.

Something like:

Dear Sam from the Past,

Wow, what a long year. I can’t believe it is finally winding down. You might think it’s weird that I’m writing to you from the future, but I am. (The future is amazing.) Here are some important things to know so you can be successful in Calculus, and in life. Don’t wear Green. Mr. Shah hates Green. […]

You can talk about my quirks as a teacher (like “Mr. Shah does/doesn’t give a lot of partial credit” or “Mr. Shah doesn’t like when you use pen in class”), math things you wish you knew beforehand (like “you should make sure to really know your exponent rules” or “you should really be comfortable with fractions”), and any other general advice (like “trust me, doing your homework every day is key” or “Mr. Shah knows what he’s talking about so do everything he says without question” and “I found that cramming the night before did/didn’t work”).

You can and should also say whatever you want about the class — if you found it rewarding, if it’s really tough to visualize things, if meeting with me helps, if it’s impossible to do well, whatever. I won’t read them until after your final grades are calculated. Feel free to be funny — like if you look at yourself at the beginning of the year, and you hate that sweater you wore every day, warn yourself not to wear that sweater because it’s stupid. Or if you stole a teacher’s cupcakes, and you want to warn your previous self not to be so selfish, you can do that too. Don’t stress yourself out if you’re not funny.

I use these to create “Advice from Students Past” packets to give to my students next year (here too) — advice which might resonate with ’em on how to succeed. It also gives me some insight into my own teaching and my own class from my students’ perspectives.

So that was all from last Friday, a day I missed.



  1. I thought about having my calc student create a prezi tying together different topics from the course as a final project/final exam review. The problem came with inserting equations as image files…our school has a proxy server that doesn’t play well with others. I thought it was a cool idea, though! Thanks for sharing yours.

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