# Math Practice 3: Higher Level Questions and the Mistake Game

After a bit of frustration with Math Pratice 3: Construct viable arguments and critique the reasoning of others, a colleague sent me this link to “The Mistake Game”. So I thought I’d try it to see if it helps students critique the reasoning of others. All students want to be smart and making a mistake is scary!

But first I wanted to teach higher level questioning skills. So I started by showing them this graphic of Depth of Knowledge:

Then we brainstormed questions they’ve been asked on tests or assignments in any of their classes that relate to different depths of knowledge.

Then we played a couple games: 20 questions and The Great Brain. Really this only takes about 10 minutes max so it is worth the time.

20 Questions:

• One student is a secret celebrity
• The rest of the class asks questions that have a “yes” or “no” answer – but only 20 – to try to figure out who the celebrity is.

The Great Brain:

• Three students are one entity known as The Great Brain who can answer any question you could possibly ever want to know like “Why is the sky blue?”
• The students answer in order, one word at a time, which turns out to be funny, full of gibberish and a lot of fun.
• Make sure to preface that the questions are “school appropriate.”

So, as a recap, the 20 Question questions are “low level” depth of knowledge – not a lot of thought needed to answer them, not much brain activity, just recall. The Great Brain questions are only fun if they are “higher level” and require more than one word answer. They mostly start with “How…”, “Why…”, and “Explain….” The Great Brain questions are the ones we are going to use in the mistake game.

We played the mistake game and I offered some extra credit for the students who could ask higher level questions. They did great! It took a little time and was a little scary – but very worthwhile.

Test corrections became Mistake game #2 and was awesome! First, the students asked to “do that mistake thing again because it was fun.” So after our unit test, we played again.

I handed back their tests and assigned 1 problem per group to present – and to pick a mistake that someone in their group made on the test. Instead of students hiding their tests from each other, they actually brought them out, picked apart their work together and shared their mistakes. I found myself walking around the room saying, “Oh, yeah, that’s a good mistake! Quite a few people made the same one.” A good mistake!

Best.Test.Corrections.Ever! No one had to stay after class and ask for extra help. They got it. They asked great questions. Everyone was happy with their mistakes.

Time to put Math Practice 3 into practice (outside of the mistake game): a partner test.

I hoped they would start to critique each other after this game while they worked on this one real world problem. As I walked around, I heard them critiquing each other and not just accepting the other students’ ideas. Were they just showing off for me when I was in hearing range? Did I need my teacher team to come and observe? Well, fortunately the school district Principals decided to walk through our classes that day – and suddenly in walked 8 outside observers! Yay! (really who says “Yay” when a bunch of administrators suddenly descend on your classroom?) But yay! The observers were able to confirm that yes, indeed, the students were actually explaining well and asking questions! Yay for math practice 3!

Now to keep it going….for a short review next week I will have students in groups choose a small object from their backpack and create 2 low level and 2 high level questions.

AND now in class, I won’t accept anything other than a high level question – no more “I don’t get it” for my students!