Lesson study for mathematics problem-solving heuristics through collaborative teacher reflection

¶ … Lesson Plan Study: Act it Out

The teaching and study of mathematics can present special challenges and complications to many instructors and learners, and a variety of methodologies exist for mathematics education that are meant to simplify and ease this process. Many of these are heuristic methodologies meant to make certain abstract concepts and functions more concrete. The Act-it-Out heuristic has been demonstrated as a successful and efficient method of mathematics instruction in a variety of age groups and math levels, as this brief review demonstrates.

Act-it-Out involves using physical objects, truly anything that is handy, to represent specific items or quantities that can the be moved around, combined, etc., to illustrate the movement of abstract mathematical quantities either individually or with groups of learners (Masters 2003). This technique has been in sue for some time, and is well-represented in both empirical literature and in anecdotal evidence from generations of educators, and all of this evidence indicates that students struggling with concepts from basic math functions such as addition and multiplication to more complex algebraic concepts can be assisted by this method (Harcourt Brace 1999; SGMB 1978). Confidence levels in math subjects and skills were measurably improved, and recent research has even demonstrated that the tool can be adapted to university-level mathematics and instill long-term learning and ability with such complex applications as differential equations (SGMB 1978; Kwon 2010; Fletcher & Lu 2009). Attitudes towards learning and engagement with material has also been observed in students ranging from primary school to university (Masters 2003; Fletcher & Lu 2009).

The revolutionized learning process that has come with the increased presence of technology in the classroom, emphasizing independence in learning due to the increased potential for direct instructor monitoring of each individual student's progress, does not impede but rather supports the Act-it-Out heuristic. Some research has found that heuristic learning processes can be seen as aligned with and enhancing of adaptive expertise and learning strategies, rather than merely routine and more passively learned knowledge; an increased or enhanced use of adaptive strategies on the part of the learner leads to greater overall skill levels and longer learning retention at all phases of learning (Verschaffel et al. 2009). This is analysis is supported by larger perspectives and frameworks of mathematics education and learning strategies, which call for increased direct engagement of the learner in the learning process as well as a new and emphasized approach to the practicalities and applicability of math skills learned during standard education, as such skills are increasingly necessary to obtain adequate levels of higher education in-demand professions (Sriraman 2010).