A few years ago, I was inspired by this Ted Talk by Dan Meyer in which he argues that math teachers need to be less helpful:
Specifically, two of the examples he gives (beginning at 4:26 and 6:43) have influenced my practice a lot. Instead of working through an example with the class and then having students work through several similar problems, I now try to pose a question (like how long will it take for the bucket to fill with water?) and have students formulate the mathematical part(s) of the problem. As a teacher at an International Baccalaureate school, this fits really nicely with MYP math criterion D, Applying mathematics in real-world contexts, which requires that students
- identify relevant elements of authentic real-life situations
- select appropriate mathematical strategies when solving authentic real-life situations
- apply the selected mathematical strategies successfully to reach a solution
- justify the degree of accuracy of a solution
- justify whether a solution makes sense in the context of the authentic real-life situation.
Recently, however, I have started using this approach more widely. When I assess criterion A, Knowing and understanding, I have to give students an opportunity to apply what they know in an unfamiliar situation. Students don’t like seeing an unfamiliar problem on a test and many will panic in that high-stakes setting. So, lately, my goal has been to make each lesson about unfamiliar situations. In so doing, students get used to seeing problems that are unfamiliar and have a variety of strategies to try. For example, a student recently asked me what to do when an exponent is raised to an exponent, I think it was:
Rather than telling him to multiply the exponents, I told him to try writing out the long form and he was able to do this:
From there, he could see that:
With only a prompt from me, he was able to answer his own question.
Some of my most-used prompts are:
- what skills do you have that might be useful in this situation?
- if you saw this question with simpler (smaller) numbers, what would you do?
- what different ways could you write that expression (or equation or fraction or radical) that could help you solve the problem?
Because students get used to these prompts throughout the unit, they have something familiar to draw on when they are faced with unfamiliar questions on the test. Moreover, students become more independent as mathematicians.