It is very interesting to observe how the professor brought them through the problem solving process. After asking the students to discover the pattern, the professor made them explain the reason behind the pattern.
Towards the last part of the video, the professor asks the students “why is it that even though there are a variety of 2 digit numbers, the solution is always a multiple of 9?” He questions why the numbers ranging from 80 to 89 always gives 72 as a solution. Using a student’s explanation, he went further to link what the student explained to mathematical expressions using algebra (refer to picture on the right). This shows how he has designed his instructions in such a way to move from concrete examples to an abstract form.
This shows evidence of transfer of learning. Hence, in teaching through problem solving, he leads the students to learning new concepts/skills. He is also able to show through this problem solving exercise the importance of using algebra.
According to teaching model (Ashlock, Johnson, Wilson & Jones, 1983), as shown on the right, there are three phrases in the teaching process namely, Understanding, Consolidating and Transferring.
The first phrase teaches students to understand a concept or skill. The second phase teaches them to consolidate concepts and skills learnt. The third phrase provides opportunities to transfer their understanding to new situations/scenarios. Problem solving requires students to transfer their knowledge of skills and concepts to familiar situations. Cormier (1987) describes transfer of learning as the application of skills and knowledge learned in one context being applied in another context. For more information on learning theories on transfer of learning, one can visit the website http://otec.uoregon.edu/learning_theory.htm
There are three kinds of transfer of learning. They are transfers from prior knowledge to learning, from learning to new learning and from learning to application Transfer of learning helps to make learning more meaningful for students. It builds bridges across different concepts and skills taught and learnt. It also helps the students in making sense of what they are learning. There are evidences to show that less able problem solvers view problems as being related in a non-structural way (Wickelgren, 1974). Hence, in order to develop good problem solvers, it is important for teachers to use transfer of learning in their teaching.
Rather than classifying one problem as a simple and another as complex, Wickelgren (1974) classifies the relationship between problems as
- Unrelated (when problem a and b have no common elements)
- Equivalent (when problem and b have same problem elements)
- Similar (when problem a and b have some common element)
- Special Case (when a is a special case of b, where problem a is included in b)
- Generalisation (when a is a generalization of problem b, where problem b is included in a)
Research Proposal
I would like to research on the effectiveness of the use of transfer of learning through mathematical problem solving. I would carry out a study on an experimental and a control group. In the experimental classroom setting the students will learn a new skill/ concept through the different types of transfer of learning. On the other hand, the control group will learn the same skill/concept through direct teaching. Later, the students in both groups will be assessed on their understanding, meta-cognitive skills and also their affective traits. The assessment will be in the form of paper and pen test, oral interviews and classroom observations.
The finding from this research will generate useful information for teachers. It will convince teachers on using problem solving as a means to carry out meaning learning experiences for the students. Furthermore, it will also highlight the effects of the different types of transfer of learning (equivalent, similar, special case or generalization) on students’ understanding. It will also surface some important teaching strategies to be carried out in order to maximize the benefits of transfer of learning.
Use of Blogs
The use of blogs in teaching and learning is supported by Vygotsky’s theory (Ferdig, 2004). It provides a social platform for rich communication to take place in a collaborative learning environment. It gives people of common interest to the opportunity to interact, surface new ideas and comment/ critic each others’ views. It further enhances one’s learning and helps to scaffolds one’s construction of knowledge.
Hence the blog on MPS can be a one-stop centre for educators to exchange ideas on problem solving. Teachers can comment on what is their view on problem solving and how they teach problem solving in class. Hence this blog can be used to do the research on transfer of learning. Teachers can post examples of their experiences in using transfer of learning in class and how it has helped the students in their learning.
References
Berinderjeet Kaur & Yeap Ban Har. Mathematical Problem Solving in the Secondary Classroom. National Institute of Education. Singapore.
Gerald Kulm. Information Transfer in Solving Problems. Journal for Research in Mathematics Education. Purdue University.
Yuh Huann Tan, John Ow Eu Gene & Ho Pau Yuen Jeanne Marie. (2005). Weblogs in Education. Educational Technology Division, Ministry of Education.
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