Memo #4 Algebraic Thinking

Algebraic thinking is a difficult topic to nail down. Some suggest that it's the ability to do and undo mathematics fluidly, building upon rules and patterns in order to logically work through an algebraic problem. Students who possess algebraic thinking also may have acquired the ability to look at the bigger picture and think abstractly about a given problem. While not all students are currently thinking algebraically, it's important for teachers to recognize it's a valuable skill worth developing within our students.

One way teachers may foster algebraic thinking is by taking into account that there is more than one way of thinking about a problem, and certainly more than one strategy to solve it. To incorporate this idea into our practice, we might allow students to demonstrate their ideas to each other, or even the class. This helps students develop a meta-cognition when solving math as they have to explain their answers, and additionally it benefits the class, as individual students may have their own solving strategy validated, or see a connection to a new way of thinking about it. These connections across curriculum are vital, as we have learned from Hiebert and Carpenter. In my placement I have seen my teacher strive for students to voice their thoughts in an attempt to foster critical thought and meta-cognition as suggested, but it is hardly successful. The students even worked on a problem similar to the problem Driscoll posed about trolls, but unfortunately none of the students used algebra, or backwards thinking in order to solve. They picked random numbers and tried again and again until they got the right answer. Even when prompted to describe how exactly they gauged what theyr next guess would be. It magically just comes to them they say.

This leads us to a more important point, being the kinds of questions we ask and the ways in which we prompt for critical thinking. It is a difficult skill to master, but one that is worth paying close attention to. We can often do thi through eliciting algebraic thinking, incorporating wait time, clarifying, encouraging student exploration, as well as various other strategies. The important part is that students have an opportunity to really think, and reflect upon their thinking when building their math skills.