How I Teach New Concepts: A Prequel

Thanks to some comments on my post about how I like to teach, I decided to expound.

My new love is concept attainment.

I'll use my parallelogram unit as an example since I referenced it in the post above.

I started out with a Powerpoint slide in two columns.

The left column contains examples, the right column contains non-examples. As I clicked through, a shape appeared in each column. Students had to compare/contrast the two figures and decide what the example had that the non-example did not. After each pair, I instructed the students to modify or add to their guess so that it would apply to every pair.

By the end, they should have around 4 different properties of parallelograms without me ever saying a word. Well, maybe some leading questions. But we never mention the word parallelogram.

Then using rulers and protractors, we dove in to this investigation. Students measured pieces of parallelograms to find properties of a parallelogram, some of which are the same as what they deduced from the Powerpoint slides.

By the end of the period, students collaborated in teams to write a pretty well all-encompassing definition of a parallelogram. The 'actual learning' is that they've brainstormed, compared/contrasted, modified, and deduced these things all on their own. They've discovered the hidden secrets of the parallelogram! And they're much more likely to remember what they've found on their own as opposed to what they read or heard me say.

For those of you that are curious, the next day we did a parallelogram sort. Students measured pieces of other quadrilaterals to decide what properties apply to all, some, or none. Once they cut out and sorted the properties into four piles, they converted that information into this nifty checklist.

Finally from there, I threw the handout of problems referenced in my post. Using only the properties they discovered, they began to solve problems. We had not solved any problems at all. So in my mind, this was a "problem of a type learners had never seen, and related to a concept that had never been taught". I guess what I should have mentioned is that we did lay a foundation of properties before throwing those problems to students. But, in no teaching strategy that I know of, do we ever toss brand new information out to students without a lifeline.

We want to provide opportunities that are challenging but doable.Say it with me: scaffolding. I believe this strategy achieved that for me. I made sure my students could swim and and had their life preserver, then I threw them overboard.

And they're swimming.

And they just keep swimming, just keep swimming. Just keep swimming, swimming, swimming. What do we dooooooooooooo? We swim, swim.

Ah-hem. Pardon me.

I have some life preservers to fetch.


  1. Wow, you have some great ideas and methodolgies. I just stumbled upon your blog after doing a Google search for "best math blogs", and yours was on page #1 :) I am slowly starting to read through your posts...

    I must say that even though you are a "newbie" in terms of years in the classroom, you can take it from a veteran of 25+ years that it's refreshing to see a passionate teacher such as yourself continuing to come up with fresh ideas on how best to educate students in math....

    I hope to post more substantially after digesting your other posts. I just set up Rick's Algeblog at www.algeblog.com. A blog dedicated to Math Teaching, Education, Music, Drama, Sports, Internet Marketing, eBay Sellers, The Beatles,...and anything else that may come to mind! Hopefully I will be able to add something substantial to the math-blogging world myself:)

    Keep up your spirited work, it looks like you're doing just fine, and I am sure your students love your classes...and isn't that what it's all about, having kids excited about math?


  2. Rick,

    Thanks so much for reading and posting such positive commentary! Glad to know we are adding another blogger to the math blogosphere. Please please please check the "Blogroll" tab at the top for a ton of other great blogs to peruse and digest.

    Thanks for the encouragement.


  3. I'm so glad that you blogged about this! I read about it in one of your recent posts and meant to ask you about it but haven't had a chance. I am good with examples but need work on non-examples! Thanks!

  4. Not gonna lie, my coach helps me with the nonexamples but it gets easier as you go. It's actually kind of my favorite part.