The student-directed versus teacher-directed learning debate is an ancient one; indeed, the polemic goes back to Plato. In her doctoral research (
The Effects of a 15-minute Direct Instruction Intervention in the Regular Mathematics Class on Students’ Mathematical Self-efficacy and Achievement) the author carried out a comprehensive review of the relevant research and literature, and reached the inescapable conclusion that some skills were better acquired through one approach and some through the other. When it came to the employment and cultivation of higher order skills where reasoning and reflection were required it was clear that a student-directed approach to learning was better suited. But when it came to the acquisition of basic skills the empirical evidence unequivocally showed that a teacher-directed approach was best suited.
It is well accepted that problem solving skills operate from a knowledge base that has been acquired through practice; in fact, genuine competence in both problem solving and basic skills
only comes with practice. Significantly though, it is actually when the base knowledge in a discipline is being acquired that the foundations for effective problem solving are being laid. Because the essential knowledge required for automaticity is stored in students' long term memory, it is best retained when explicitly taught and practiced repeatedly. This automaticity originating from practice empowers students to maximise their mental capacity by concentrating exclusively on the more complex task of problem solving.
It is also well accepted that to perform a task competently one requires not only the requisite skills, but also the self-belief in one's ability to implement performance. In the learning process this is termed
self-efficacy, and when laying the foundational skills in mathematics, or for that matter any academic discipline, it is important that student self-efficacy be accomodated. Students with low self-efficacy in a particular skill area are reluctant to engage in tasks where those skills are required, and if they do, they are more likely to quit when encountering difficulty.
Students engaged in the learning process automatically monitor their progress, and for this reason the capacity to self-evaluate progress is an integral and ongoing component of the JEMM program. Because JEMM tasks gradually increase in difficulty, students have clear criteria by which they can independently assess their performance and gauge their progress. As they progress they acquire more skills and become more proficient at the self-evaluation process.
JEMM lessons were deliberately designed not to be seen as tests, but this is precisely what is happening on a daily basis; without being conscious of it, students are willingly engaging in ongoing assessment. As such the lessons serve as a powerful diagnostic tool clearly mapping students' progress, identifying precisely where and when they are experiencing difficulty. The students' responses provide teachers with reliable diagnostic information similar to that which could only be acquired from a formal test situation. Because students receive daily feedback on their performance they are acutely and immediately aware of their progress, which strengthens their self-efficacy, sustains their motivation and enhances their academic achievement.
source: JEMM =
Junior Elementary Maths Mastery, page x
