Over the past two weeks, I’ve been working with both students and teachers on algebra tasks. One of the things we have been doing is writing rules for different geometric patterns.
For me, identifying key questions that will guide students towards meeting the learning target for the day is one of the most important things I do when planning a lesson.
I find that it can be easy to do really cool activities that get students engaged and have great potential but if the questions we ask don’t pull out the mathematics, kids get excited about math class but don’t learn much. The questions asked as the students work need to guide them to see the connections and pull the mathematics out of the situation (which may be obvious to us but not to them).
I think sometimes the resistance to inquiry based approaches is because if students aren’t carefully guided to see the mathematical connections, it’s no better (and maybe even worse) than simply telling them a procedure and having them practice a bunch of problems.
When working on my algebra lesson, I went to researcher Mark Driscoll’s book, Fostering Algebraic Thinking: A guide for teachers, Grades 6-10. In it, there are various questions that can be used to foster different types of algebraic reasoning. Below are some of the questions he suggests using when students are engaged in writing rules to represent functions:
Questions for building rules to represent functions
- How are things changing?
- Is there information here that lets me predict what’s going to happen?
- What steps am I doing over and over?
- How can I describe the steps without using specific inputs?
- What if I do the same thing with different numbers? What still holds true? What changes?
- Can I write down a rule that will do this job once and for all?
- Why does the rule work the way it does?
- Does my rule work for all cases?
- Now that I have an equation, how do the numbers in the equation relate to the problem context?
I used these questions to help assist small groups when they were stuck as well as to guide the whole class discussion. They helped students see the connection between the pattern they were drawing and the algebraic rule that could be written to describe it.
Want to know more? Check out: Fostering Algebraic Thinking: A guide for teachers, Grades 6-10 by Mark Driscoll