Submitted by: Low Kok Soon
In the primary problem-solving lesson video, the setting is discussion in groups, ie, cooperative learning among 3-4 students. I noticed that in the course of the ‘discussion’ pupils were observed to be sharing and justifying their strategies with their peers. However, some seem lost which is not surprising as it happens in a lot of cooperative learning settings. The higher ability ones usually dominate leaving the lower ability ones playing a shadowing role. That set me thinking; perhaps we should arm these lower ability students with certain skills so that they could participate more proactively and will not feel left out.
Kramarski, Mevarech and Arami (2002) cited various studies in their literature review that run a common thread of training students who work in small groups (defined as 4-6 students) to reason mathematically by formulating and answering a series of self-addressed metacognitive questions. Such techniques are called cooperative-metacognitive approach. The rationale is two-fold, supported by theories and research. First, cognitive theories of learning emphasize the important role of elaboration in constructing new knowledge. Second, the well established research on cooperative learning argues that it has the potential for children to improve their mathematical problem solving abilities as it provides them a natural setting for them to supply explanations and elaborate their reasoning. More importantly, the researchers reported positive effects of such instruction on students’ achievement and seem to benefit lower achievers even more. The lower and higher achievers in the cooperative-metacognitive experimental group outperformed their counterparts in the cooperative-only control group , and Effect-Size for lower achievers (ES=1.93) was reported as higher than that for higher achievers (ES=1.06).
With these as a background, my research proposal stimulated by the video would be to investigate whether metacognitive instruction embedded in cooperative mathematics classrooms would exert positive effects on students’ mathematical problem solving ability. The main research question, in particular, relates to the effects of such cooperative-metacognitive instruction on lower and higher achievers. To go about doing this research, I could do anpre-post test experimental-control study on 4 groups of 3 pupils working in groups. Two groups (one higher achiever group, one lower achiever group) will be in experimental groups receiving metacognitive instruction embedded in cooperative learning settings treatment while the other 2 groups (same makeup as above) as control groups will receive only cooperative settings. The experimental groups receive the treatment using methodology such as IMPROVE^ method (Mevarech, et al, 1997) which train students to activate metacognitive processes in small groups and students are taught to formulate and answer four kinds of self-addressed metacognitive questions: comprehension, connection, strategic and reflection questions. The cooperative-only groups will not receive training on metacognitive but employ the usual discuss in groups strategy till a consensus is reached, and asking for teacher help when they encounter diffculties. The details surrounding the statistical tests on their pre-post tessts will be omitted for this discussion.
Such research on cooperative-metacognitive approach will shape instructional practice (perhaps making every student go through metacognitive training as a life-skill and not just in maths?) and further generate useful knowledge for researchers to investigate further for two reasons. First, if we could leverage on such cooperative settings early on in the school days, as they would in the working world anyway, the higher achievers will soar even higher and the lower achievers will benefit more, learnt to be more self-confident and be more motivated to learn (eg the N(T) students?). Second, it benefits the learning environment as it will become more conducive and engender us a step closer to the Thinking Schools Learning Nation vision painted by the ministry.
In conclusion, it may be instructive for the lifelong learner to start learning explicitly how to think, as what Edward de Bono (1993) championed in his Six Thinking Hats theory, one of which is the Green Hat which is thinking about thinking and control of the thinking process.
(number of words excluding title: 644 )
In the primary problem-solving lesson video, the setting is discussion in groups, ie, cooperative learning among 3-4 students. I noticed that in the course of the ‘discussion’ pupils were observed to be sharing and justifying their strategies with their peers. However, some seem lost which is not surprising as it happens in a lot of cooperative learning settings. The higher ability ones usually dominate leaving the lower ability ones playing a shadowing role. That set me thinking; perhaps we should arm these lower ability students with certain skills so that they could participate more proactively and will not feel left out.
Kramarski, Mevarech and Arami (2002) cited various studies in their literature review that run a common thread of training students who work in small groups (defined as 4-6 students) to reason mathematically by formulating and answering a series of self-addressed metacognitive questions. Such techniques are called cooperative-metacognitive approach. The rationale is two-fold, supported by theories and research. First, cognitive theories of learning emphasize the important role of elaboration in constructing new knowledge. Second, the well established research on cooperative learning argues that it has the potential for children to improve their mathematical problem solving abilities as it provides them a natural setting for them to supply explanations and elaborate their reasoning. More importantly, the researchers reported positive effects of such instruction on students’ achievement and seem to benefit lower achievers even more. The lower and higher achievers in the cooperative-metacognitive experimental group outperformed their counterparts in the cooperative-only control group , and Effect-Size for lower achievers (ES=1.93) was reported as higher than that for higher achievers (ES=1.06).
With these as a background, my research proposal stimulated by the video would be to investigate whether metacognitive instruction embedded in cooperative mathematics classrooms would exert positive effects on students’ mathematical problem solving ability. The main research question, in particular, relates to the effects of such cooperative-metacognitive instruction on lower and higher achievers. To go about doing this research, I could do anpre-post test experimental-control study on 4 groups of 3 pupils working in groups. Two groups (one higher achiever group, one lower achiever group) will be in experimental groups receiving metacognitive instruction embedded in cooperative learning settings treatment while the other 2 groups (same makeup as above) as control groups will receive only cooperative settings. The experimental groups receive the treatment using methodology such as IMPROVE^ method (Mevarech, et al, 1997) which train students to activate metacognitive processes in small groups and students are taught to formulate and answer four kinds of self-addressed metacognitive questions: comprehension, connection, strategic and reflection questions. The cooperative-only groups will not receive training on metacognitive but employ the usual discuss in groups strategy till a consensus is reached, and asking for teacher help when they encounter diffculties. The details surrounding the statistical tests on their pre-post tessts will be omitted for this discussion.
Such research on cooperative-metacognitive approach will shape instructional practice (perhaps making every student go through metacognitive training as a life-skill and not just in maths?) and further generate useful knowledge for researchers to investigate further for two reasons. First, if we could leverage on such cooperative settings early on in the school days, as they would in the working world anyway, the higher achievers will soar even higher and the lower achievers will benefit more, learnt to be more self-confident and be more motivated to learn (eg the N(T) students?). Second, it benefits the learning environment as it will become more conducive and engender us a step closer to the Thinking Schools Learning Nation vision painted by the ministry.
In conclusion, it may be instructive for the lifelong learner to start learning explicitly how to think, as what Edward de Bono (1993) championed in his Six Thinking Hats theory, one of which is the Green Hat which is thinking about thinking and control of the thinking process.
(number of words excluding title: 644 )
References
Kramarski, B., Mevarech, Z. R., & Arami, M. (2002). The Effects of Metacognitive Instruction on Solving Mathematical Authentic Tasks. Educational Studies in Mathematics, 49(2), 225-250.
de Bono, E. (1993). Teach your child how to think. London: Penguin.
^ IMPROVE is the acronym consisting of the following teaching steps: Introducing new concepts, Metacognitive questioning, Practising, Reviewing, Obtaining Mastery, Verification, and Enrichment.
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