One of the major aims of STEM education is the development of mathematical thinking. The common misconception is that "doing mathematics" is the same as getting involved in "mathematical thinking". Rallying to such argument, many would agree that mathematics should be taught as a thinking activity. Thus, this study endeavours to review the effects of a problemsolving heuristic application technique on learners' mathematical thinking development. This twophase study analysed the data utilising a descriptive design (N=660) and experimental design (N=54). In the first phase, 660 High School Leavers, with 93% obtaining an A grade in the Math National Examination, ages 18-19, registered with a college to undergo a two-year Diploma engineering program were administered a Mathematical Thinking Test. Then, fifty-four of these students participated in a seven-week Pre-Post experimental design to investigate the impact of heuristics application on their development of mathematical thinking. These student's post-test score was also compared with a batch of one hundred and twenty third-year university students (N=120) majoring in STEM related courses where all these students have taken at least five university level related math courses. Firstly, the results indicate that the high school leavers grades obtained in the national Examination was not translated into their Mathematical Thinking prowess. Secondly, the results depicted a significant increase in the mathematical Thinking posttest score among the students who underwent a seven-week pre-post problem solving heuristic treatment. Thirdly, the students involved in the heuristic application treatment performed better than the third-year students in the Mathematical Thinking test. It is vital that the heuristic method of teaching mathematics be employed to enhance student's development of mathematical thinking, especially for STEM students.
This paper investigates the nature of the interaction between the teacher and students as they worked on different mathematics activities in a single classroom over a 10-month period. Sociocultural theories and the Vygotskian zone of proximal development provide the main framework for examining the teaching and learning processes and explaining the incorporation of a four-phase lesson plan as increasing participation of the teacher and students in the teaching and learning process. Drawing on the analyses of discourse from videotaped lessons and the interviews with the teacher and students, five different types of interactions that emphasized mathematical sense-making and justification of ideas and arguments were identified. Excerpts from transcriptions of such interactions are provided to illustrate the learning practices, either academic or non-academic, that students developed in response to these interactions.
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