Recognizing Students’ Creative Solutions
When I was working as a math resource teacher in the mid-1970s, a student named Craig showed me an interesting algorithm for computing subtraction problems. Craig, a second grader, developed a system on his own that involved using negative integers and expanded notation.
Illustration 1
Craig's Method
In the mid-1970s primary grade students were not “supposed” to be solving subtraction problems that required regrouping, let alone using negative integers. (Negative numbers are all around us; we live in a credit card/debit society!)
About ten years after this, another child in the second grade, my son, came up with a similar algorithm for computing subtraction problems again utilizing the concept of negative numbers.
Illustarion 2
Coskun's Method
The methods these two second graders utilized made me question instructional practices that led some educators to tell students that their methods were wrong or “…not the way we solve these problems.” In college after reading Thomas Kuhn’s book on paradigm shifts and Max Wertheimer’s book entitled Productive Thinking, it seemed to me that creative ways to solve problems were ideas to applaud not discourage. When students develop pedagogically sound, insightful solutions utilizing conceptual constructs, shouldn’t we encourage them and give them credit for their discoveries and problem-solving ingenuity?
We now recognize that second grade students are ready for regrouping, but unfortunately many public schools still do not introduce negative numbers until much later than second grade. Young students enjoy experimenting with positive and negative numbers, and by second grade some students use them without direct instruction. In summary, teachers should be flexible and recognize the validity of student-invented algorithms when they are conceptually sound and reflect good thought process.
