High Level Thinking in Math

When differentiating for my most brilliant mathematicians, there are two traps I fell into:

• Just making it harder. (Use more numbers or more steps.)
• Turning it into an art project. (Design a bedroom!)

On Bloom’s Taxonomy, my math tasks always maxed out at Apply or would leap away to a fluffy creative task. I think that Analyze is the key level on Bloom’s. So how do we get there in math?

We Use Math, We Don’t Do Math

The key is to understand that math is different from the other topics we teach. Math is just a tool. It helps people make decisions in other fields. People use math to make choices. No one just does math professionally. So this is our cute mnemonic: use math, don’t do math.

• As a teacher, I used math to decide which topics needed to be re-taught.
• As a small business owner, I use math constantly. It helps me decide if I can hire someone or if I should expand my product offerings.
• Economists use math to decide how to advise the president.
• A social scientist will use math to draw conclusions about the effects of population change.
• A game programmer uses math to make a player’s movements feel realistic.

No one just sits there and performs calculations! No one just does math. They use it. And often they use math to help make a decision.

Using Math To Make Decisions

When we’re making decisions, we’re inherently at the Analyze and Evaluate levels of Bloom’s Taxonomy.

• We have to compare and contrast choices (Analyze).
• We have to pick from a set of not perfect options (Evaluate).

So once we have a student who can do calculations correctly (they Remember and Understand the steps), we need to make the task about a tricky choice in another field.

• If students can calculate a discount percentage, we need to ask them to use that skill to make a decision. A product is discounted. But is it the right choice? The discount is just one factor in the decision.
• My students can multiply decimals. Great. Now let’s have them pick which hourly job is best for them. The wage will be just one factor to consider. (I wrote the hourly job task up here.)
• When my class knows how to read a bar graph, let’s have them analyze bad graphs to choose which is the least reliable – even though the data is correct. (And I wrote about the bad graphs task here).

In each case, the math skill becomes a tool to make a decision. And the decision has no right answer. The math is just one factor. You might ignore it completely! In this way, we’re making math into a fuzzy problem.