Implementing theoretical intervention principles in teaching mathematics to struggling students to promote problem-solving skills

ABSTRACT

A teacher–researcher searched for and defined theoretical principles in the literature that could be used as a basis for teaching high-school students who were struggling in mathematics (in a regular-level mathematics classroom) and could offer a framework to design tasks to encourage a problem-solving, thinking classroom. After identifying 13 principles, she refined them to a list of nine. Over the duration of the academic year, she designed lessons for two high-school classes (one Grade 11 and one Grade 12; 300 lessons in total) according to the principles to promote her class’s group problem-solving skills, carefully documented them all, and then analysed her findings. The principles identified pertain mainly to awareness of how to promote active thinking and meta-cognition, explicit heuristic strategies for problem-solving, and using worked examples. All these to allow students (not only struggling) to build a general schema for approaching problem-solving with increasing efficiency. Two authentic class scenarios demonstrate how specific principles were applied and their effect on problem-solving efficiency in the classes. The findings suggest that introducing these principles into the class culture can offer a significant way to improve group problem-solving skills and, in particular, involve struggling students in the class discussions.

KEYWORDS:

• Intervention principles for teaching mathematics
• heuristic strategies
• worked examples
• struggling high-school students
• group problem-solving
• learning difficulties

Acknowledgements

Many thanks to Professor Boris Koichu for guiding me in this study.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 In this article, words in brackets are additions to students’ remarks that I inserted in order to improve clarity.

2 A problem involving a cube on the corners of which the Hebrew word hadas is written, with the letters of which the word is composed, H.D.S. (heh, dalet, and samekh in Hebrew letters), written twice on the six corners.

3 Explanations of the students’ remarks appear in brackets.