By Kathy Liu Sun
If you feel like screaming after helping your children with their math homework, you’re not alone. Across the United States there’s mounting frustration towards the Common Core State Standards for mathematics.
What many parents and teachers are experiencing is not the intent of the standards.
The key idea of Common Core is for students to come up with the solutions on their own, and not be prescriptively told how to solve the problem. The goal is for students to be able to think flexibly. Students should have the opportunity to explore, test strategies, and make sense of answers when solving problems.
In my research and work with math teachers, I’ve observed that educators are trying to fit the standards into an old system of teaching math. We used to learn math by memorizing a “rule” and then repeating it to solve a series of similar problems. Teachers would stand at the board and model how to follow this algorithm. Students would then practice the algorithm over and over.
Under the guise of Common Core, rather than learning one rule, students are now memorizing and executing three or more different rules for the same set of problems.
To better understand this, let’s look at an example of subtraction.
In the past, many of us learned subtraction by following the traditional algorithm, which involved stacking two numbers and some form of “borrowing” over digits.
Traditional Subtraction Algorithm: 31 – 18
Many schools have misinterpreted the Common Core by requiring students to solve subtraction problems by memorizing the traditional algorithm, the “counting up” method and the “counting down” method, which are described below.
Subtraction Problem: 31- 18 Counting Up: begin from the number being taken away, how many do I need to count up to reach the starting amount?
Start at 18. Count up by 2 to get to 20.From 20. Count up 11 to get to 31.
I counted up by 2 and 11 for a total of 13.
The answer is 13.
Counting Down: begin with the starting amount, how many do I need to count down to reach the amount taken away?
Start at 31. Count down by 1 to get to 30.
From 30. Count down 10 to get to 20.
From 20. Count down 2 to get to 18.
I counted up by 1 , 10, and 2 for a total of 13.
The answer is 13.
The reality is that various strategies will emerge from children’s own sense making. In the case of subtraction, without being told a method, children will naturally come up with the “counting up” and “counting down” methods.
There’s a large body of research that shows the benefits of children coming up with their own strategies in both the elementary and secondary levels. These studies paint rich pictures of students engaging deeply in mathematical problem solving and achieving at higher rates than students in rule-driven classrooms. Students also enjoy math more when they have the freedom to explore ideas and experiment in math class.
So how can we help to align what’s happening with what’s intended?
Let students do the thinking. Parents and teachers can often fall into a habit of doing all of the thinking and simply telling students how to solve the problem. Instead, the reverse should happen. Students should have the opportunity to pursue their strategies and experiment, rather than blindly follow the teacher’s formula. There seems to be a popular misconception that young children are not developmentally ready to explain their understanding. Research has shown that, if given the chance, young children can explain, represent, and debate their mathematical thinking.
Increase Teacher and Parent Support. Simply adopting a new curriculum is not sufficient to change instruction. We need to provide learning opportunities for teachers and parents to engage in mathematics in new ways. This is particularly true with those who grew up viewing math as a set of rules and procedures. If you don’t understand a way of solving a math problem, it’s perfectly ok. This is a great opportunity to model for your children how to problem solve by experimenting with different strategies – draw pictures, act out the word problems, or use objects to model the problem.
Provide more Open-Ended Math Problems. We cannot apply Common Core ideas to traditional procedural tasks. Open-ended math tasks allow for multiple starting points and strategies or what many call “low-floor, high ceiling tasks.” All students can start these tasks, and the math can be extended to high levels.
Math is much more than following a set of prescribed rules. If we align our instruction to better support student exploration and sense making, we can alleviate some of the frustration associated with Common Core, and perhaps, infuse some fun while doing math.