When peering deeply into the issues surrounding mathematics education, it is important to remember that the nature of research is without endgame. Every question answered uncovers several more that need asking. Each controversy has two or more schools of thought all with their own merit. The dynamic essence of teaching and learning does not allow for certainties and absolute truths. The search is for balance.
Anderson (1996) critiques the four claims of situated learning, which are:
1. Action is grounded in the concrete situation in which it occurs
2. Knowledge does not transfer between tasks
3. Training by abstraction is of little use, and
4. Instruction needs to be done in complex, social environments.
Anderson analyzes each claim individually, in each case finding evidence to both support and reject the theory. He cites cases both where the claims are upheld and where they are challenged. This type of struggle is common in the research in mathematics education that I have encountered.
Boaler's (2002) study of the Amber Hill and Phoenix Park schools also contains findings that both reinforce and refute the claims of situated learning theory. Receiving a traditional form of procedural and abstract instruction, the Amber Hill students in general performed poorly on the conceptual questions on their GCSE examinations, but did well on the procedural questions. These findings support the third claim of situated learning, that training by abstraction is of little use. In turn it also supports the second claim, that knowledge does not transfer between tasks.
Phoenix Park students were taught mathematics in an open-ended, project-based approach until the final few months leading up to the examination, when they switched to an approach comparable to that of Amber Hill to make sure all examination content was covered for all students. As a result, these students did significantly better than Amber Hill students on conceptual examination questions, and their performance on procedural questions was comparable. The knowledge they had acquired during their project explorations was transferred to the situations they encountered on their examination, thus challenging the second claim and supporting the fourth claim of situated learning theory.
It is easy to get caught up in theories of practice, to uncover something that sticks with you and jump on the bandwagon. Situated learning theory is an acute example of this ever-complicating search for the be all end all of teaching and learning that will bring profound achievement to each and every student. However we are all aware that such an ideal cannot exist, and that theories are meant to be changed and altered and built upon over time, never to be quite finished. After reading Chapter 6 in Boaler, I was close to fall swoop to the apparent power of project-based instruction. After all, the Phoenix Park students developed a more adaptable and therefore useful knowledge of mathematics than those of Amber Hill. Yet I thankfully realized that it would be foolish of me to choose one type of instruction over another, accepting one and rejecting the other. With every individual student possessing his or her very own cryptic learning style, it makes no sense to teach in a single particular manner.
Right now I feel that in our province, the scales of instructional methods are tipped unevenly, due in part to a mathematics curriculum that is too rich in content and lacking in opportunities to make meaningful connections. If the only way to transmit the curriculum content in the time allotted is to stand at the front of the room and introduce objective after objective in an abstract, disconnected manner, it may be time to take a look at the situation.
The search is for balance.
Anderson (1996) critiques the four claims of situated learning, which are:
1. Action is grounded in the concrete situation in which it occurs
2. Knowledge does not transfer between tasks
3. Training by abstraction is of little use, and
4. Instruction needs to be done in complex, social environments.
Anderson analyzes each claim individually, in each case finding evidence to both support and reject the theory. He cites cases both where the claims are upheld and where they are challenged. This type of struggle is common in the research in mathematics education that I have encountered.
Boaler's (2002) study of the Amber Hill and Phoenix Park schools also contains findings that both reinforce and refute the claims of situated learning theory. Receiving a traditional form of procedural and abstract instruction, the Amber Hill students in general performed poorly on the conceptual questions on their GCSE examinations, but did well on the procedural questions. These findings support the third claim of situated learning, that training by abstraction is of little use. In turn it also supports the second claim, that knowledge does not transfer between tasks.
Phoenix Park students were taught mathematics in an open-ended, project-based approach until the final few months leading up to the examination, when they switched to an approach comparable to that of Amber Hill to make sure all examination content was covered for all students. As a result, these students did significantly better than Amber Hill students on conceptual examination questions, and their performance on procedural questions was comparable. The knowledge they had acquired during their project explorations was transferred to the situations they encountered on their examination, thus challenging the second claim and supporting the fourth claim of situated learning theory.
It is easy to get caught up in theories of practice, to uncover something that sticks with you and jump on the bandwagon. Situated learning theory is an acute example of this ever-complicating search for the be all end all of teaching and learning that will bring profound achievement to each and every student. However we are all aware that such an ideal cannot exist, and that theories are meant to be changed and altered and built upon over time, never to be quite finished. After reading Chapter 6 in Boaler, I was close to fall swoop to the apparent power of project-based instruction. After all, the Phoenix Park students developed a more adaptable and therefore useful knowledge of mathematics than those of Amber Hill. Yet I thankfully realized that it would be foolish of me to choose one type of instruction over another, accepting one and rejecting the other. With every individual student possessing his or her very own cryptic learning style, it makes no sense to teach in a single particular manner.
Right now I feel that in our province, the scales of instructional methods are tipped unevenly, due in part to a mathematics curriculum that is too rich in content and lacking in opportunities to make meaningful connections. If the only way to transmit the curriculum content in the time allotted is to stand at the front of the room and introduce objective after objective in an abstract, disconnected manner, it may be time to take a look at the situation.
The search is for balance.
Anderson, J. R., & And, O. (1996). Situated Learning and Education. Educational Researcher, 25(4), 5-11.
Boaler, J. (2002). Experiencing school mathematics: traditional and reform approaches to teaching and their impact on student learning. Malwah (NJ): L. Erlbaum.
No comments:
Post a Comment