Abstract:

Students find it hard to choose appropriate algebraic operations for problem solving, and lack the ability to view algebraic expressions logically. They thus approach problems technically, and this is manifest in several ways: the time needed for solution, a multiplicity of calculation mistakes, and difficulties in finding the solution.

The current study deals with the effect of teaching combining knowledge, skills, and “algebraic structures” on students’ mental flexibility, understanding, efficiency in problem solving, and achievements. The study aimed to examine the effect of such instruction upon students’ performance in equation solving. The research questions inspected whether such an instruction can improve students’ ability to recognize “algebraic structures” as well as their achievements in equation solving. The research population included 23 tenth-graders studying at the 4-point matriculation level. The students first answered a pretest, after which they were exposed to an instruction unit prepared especially for the purpose of the present study, and were then tested post-teaching. Moreover, students chosen according to test results were interviewed. The study was conducted at the school in which the researcher works. The school’s name, as well as the participants’ names, have remained anonymous.

The current study sought to innovate regarding the effect of delivering an instruction unit to students upon their ability to recognize algebraic structures and upon their achievements. Based on the findings, it appears that before their exposure to the instruction unit, only a third of the students turned to a solution using structure sense. The remaining students either turned to complicated solutions or failed to solve the equation altogether. This small percentage indicates a limited ability to both consider the equation before turning to solve it, and take into account different ways for solution. Following exposure to the instruction unit, a large percentage of the students turned to use structure sense and the average success rates have increased. Already at the pre-teaching stage, a correlation was observed between the successfulness of the solution and the use of structure sense or lack thereof. The instruction unit prepared for the study presents a difference and a deviation from the standard curriculum and, based on the study’s findings, has proven efficient. Once the students were exposed to the problem’s structure in an organized, experiential manner, based on discussions and on an understanding of the material covered, they learned to think and inspect the problem’s structure before turning to solve it, and could thus find the most efficient way for solution.

The study’s contribution is seen in the fact that delivering an instruction unit which focuses on algebraic structures can improve both the students’ ability to use structure sense and their success in problem solving. According to the findings, it is recommended to combine algebraic structure instruction in the curriculum and to dedicate some time to teach structure sense strategies in terms of math teaching. Teachers should be trained to encourage the developing of understanding-based solution strategies, rather than to encourage memorizing.

Keywords:

Equation solution, algebraic structures, structure sense.