How can educators connect math lessons with the problem-solving skills of computational thinking?
The 2006 article Computational Thinking, by Jeanette Wing, was an influential contribution to my awareness of computational thinking (CT) as a fundamental skill for all students. Today, most states have some set of Digital Literacy and Computer Science standards for K-12, and particular standards targeting CT.
As a mathematics teacher, the processes involved in CT seemed natural. But, were my students really aware of when they were using decomposition or abstraction? Probably not.
I needed to better connect what we were doing in the mathematics classroom with the problem-solving skills that Jeanette Wing described. Since my teaching beliefs include developing problem solvers and critical thinkers, CT needs to be a part of my students’ thinking processes. Students needed to understand where they would apply a particular CT skill or practice, reflect on how it helped to solve the problem, and discuss their thinking with their peers.
Often found in computer sciences, computational thinking is a set of behaviors or problem-solving heuristics used to solve problems in any discipline. Some core practices or thinking skills in CT are abstraction, pattern recognition, algorithmic thinking, decomposition, data practices, and debugging.
In my high school mathematics classroom at North Salem Central School District, uncovering CT started with this recognition of “every day” problem-solving heuristics. It had become part of the district’s set of initiatives. Partnering with Digital Promise in creating a CT K-12 pathway was essential for our district’s understanding of where CT was already occurring in our classrooms and how we could uncover it within all disciplines.
These CT behaviors may prompt a student to say “I think I can”:
An example I use to capture some of the CT practices in my classroom is the Peg Puzzle activity, which I call Leap Frog. It is a classic logic problem applicable in grade 8-12 mathematics.
Figure 1: Peg Puzzle. A wooden block with 11 holes drilled into it. Five green golf Ts on the left, five red golf Ts from the right with the center hole empty. Photo credit: Ellen Falk.
The objective of Leap Frog is to switch the five red pegs (right) with the five green pegs (left) in the fewest number of moves possible. The initial state always has an empty space in the middle. Each peg can move to an empty space by hopping over one peg or by moving to an empty adjacent space. You cannot hop over more than one peg at a time or hop to an empty space that is not adjacent. Students are typically placed in pairs to discuss strategies and to facilitate the counting of the moves.
The peg problem provides rich opportunities to call out CT practices and behaviors, and also an opportunity for students to experience productive struggle and exhibit perseverance in mathematics. Unlike solving a linear equation that follows a particular algorithm, and a solution within a short amount of time, this puzzle allows students the opportunity to work with something unfamiliar, which equalizes opportunity in the classroom. The focus is on the thinking process, and a perfect segue to launch a student’s experience in CT.
As I have extended my teaching experience, I find myself structuring many of my lessons and problems with CT practices at the forefront. As student experience expands with these practices, I see less of the need for the “nudge” and more of the student taking ownership and calling on their own understanding. While it is not always possible to modify what you have to fit a particular CT practice, many resources are available, not just in math or computer science.
Through all my work and experience, I realized a crucial instructional shift: understanding computational thinking as an essential add-in to teaching practices and not an add-on, like many initiatives feel these days. I’ve also recognized that CT has many touch points to other initiatives such as Habits of Mind and Making Thinking Visible. Whether it is a problem in Calculus or determining divisors of a number, CT has empowered my students to be successfully armed with strategies and behaviors to solve challenging and complex problems.
Want to know more about CT Pathways? Find more resources here:
This material is based upon work supported by the National Science Foundation under Grant No. 1837386. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
