The use of Bayesian inference to identify problem-solving strategies employed in selected Geometry and Algebra problems

Higher-Order Thinking Skills (HOTS) are at the centre of a new awareness for an education system adapted to 21st century job demands. While the term HOTS is widely used, it remains rather vague and disconnected from the STEM (science, technology, engineering, mathematics) Education content itself. Even in good curricula, such as Singapore’s MProSE, there is little explicit mention of HOTS. A coherent framework is needed to bind the psychology of HOTS problems, STEM knowledge and mathematical problem-solving frameworks (e.g., Polya, Schoenfeld), before students can actually benefit from those separate knowledge areas. I propose to study stable patterns in problems posed across various math subjects (algebra, geometry, analysis, etc) and investigate how much and deep have they so far, if any, implemented Bayesian inference. Broad problem classes will first be identified and indexed, and prototypes within these classes will then be identified. Secondly, relevant problem-solving heuristics will be enumerated for each prototype. Finally, the stability of the patterns across the math subject will be analysed for their usefulness in exploiting HOTS .
Basically, the dissertation work will be interested in looking at what’s been done in the area of Bayesian inference for maths problem-solving strategies deployed in self-study products.

The strategies to do statistics on would read something like:

Given a prototype problem P (e.g. prove the two given triangles are congruent), exploit the …
​- axioms of the relevant theory,
– definitions (e.g. congruent triangles),
– premises of the problem,
– useful relationships from a given list, and
– useful theorems from a given list.

This exploitation mechanism is meant to see which combinations and orderings are typically used for solving a prototype problem, say for middle school (IGCSE), late high school (A Levels) or undergraduate level.

Since this dissertation intends to explore what’s out there first then exploit an optimal structure of an AL based learning, the title can also read like “Statistics on Problem-Solving Strategies in Geometry and Algebra for Bayesian Supported Decisions and Inference Networks”.

This work is not intending to touch on the pupils’ psychology because, doubtfully enough, the scope of the dissertation would allow that. Mainly, the work is into the extent to which the problems themselves can achieve the prescribed learning outcomes and how it can be improved via textual analysis and other research means.

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