Jacobs and Philipp (2010) explore the possibilities of support that teachers can provide to students during problem solving. They discussed four basic types of support:
- support that focuses on the teacher’s mathematical thinking,
- support that focuses on the child’s mathematical thinking,
- support that focuses on the child’s affect, and
- support that includes general teaching moves.
When working with students on an individual basis, support that focuses on that student’s thinking is best. Teachers must adjust their instructional behavior to fit every individual student’s needs. In the example of Rex, this teacher said she would use what she learned about Rex’s thinking on the first two problems to help him solve the third, more challenging, one. Rex liked to use his fingers instead of the manipulatives that were available, so teachers should not push for use of one manipulative over another. In addition, children often think about math differently than adults do, and many can offer new ideas to the table. Provided the opportunity, teachers can learn from their students all the time.
That is not to say that the other three types are not appropriate. In a class discussion or lecture-type class, support that focuses on the teacher’s thinking is more suitable, since the teacher is providing content and modeling processes for the students. Students’ affect should always be taken into account, especially for struggling students; and general teaching moves are useful ‘go-to’ tools in everyday instruction.
This article would have major effectiveness in a traditional classroom. In this type of classroom, all students follow along with the teacher at the same pace, and individual needs are rarely attended to. Usually, problem solving is nonexistent because there is only one or two ‘right’ ways to solve a problem, and these ways are presented by the teacher. The students’ job is to remember how the teacher solved it and perform the same procedure on a similar problem in assessment. Rather, problem solving itself includes the task of figuring out on one’s own the method of solving the problem, and then carrying out that method.
Once the algorithm for completing a task is known, the problem is no longer a ‘problem’ even if the answer is still unknown (Harvey, 2010b, p. 3).
Teachers could, and will, benefit from concentrating on students’ mathematical thinking when instructing their classes. By calling for more student involvement and keeping their classes stimulating, engaging, and fun, teachers can get to know their students and how they think mathematically.
- Jacobs, V. R., & Philipp, R. A. (). Supporting children's problem solving. Teaching Children Mathematics, 17(2), 98–105.