"....think about the problem, then step back
try a different plan of attack
ask for help...ask around
another solution can be found
change directions, replace
if you get stucked, there are other ways
take your time, it will come to you
most problems have answers if you think them through..."
Hahah... written above is actually part of a song lyric that I found in the you tube. Click on the link below to see the whole video clip. When I heard the song, it reminds me of my school days when I was trying to solve mathematic problems. I often get myself very frustrated if I am not able to solve. This song actually gives you another perspective in solving problems. It can be used as a form of encouragement for your students on solving problems not only in mathematics but their everyday lives. Of course, the important message behind is to have the resilience and attitude to keep on looking for a solution and not to give up easily. Definitely, it was something that I could relate to the students in Prof A Takahashi class, who were very determined to figure out the 'mystery' behind the crystal ball.
(Video Clip): http://www.youtube.com/watch?v=XcedSK0NnmI
Based on Prof A Takahashi Lesson Study
Personal reflections/observations from his video:
I was really heartened to see how the students were very engaged in his lesson. It was a very simple lesson to deliver but yet it was made so captivating to the students by simply posing the problem in a very creative manner. The role of the teacher here was more of a facilitator to guide the students in solving the 'mystery' rather than just presenting the solution, which he could do it if he intends to. Indeed, the 'magic crystal ball' was very effective in arousing their attention and stimulating their interest, making them to think how this 'mystery' works. Towards the end of the lesson, it was also observed how the students were intrigued by the 'power of mathematics' behind the mystery, although they looked pretty much exhausted :)
Well, indeed seeing how the students were so engaged by his delivery of lesson, it kind of leads me to think about my own classroom teaching and practices. How much have I engaged my students this while? How much have they actually learnt from me? How much injustice have I done to my students' learning? What could have been better to make them better thinkers? etc...:(
What I feel is productive to research further further into?
Most teachers out there will agree with me that such lesson is certainly very time-consuming. Hey, my lovely classmates, don't you think you agree with me? We need to see the usefulness of such padegogies before teachers are convince of the benefits in the long run. Teachers' beliefs and atittudes are something that it is difficult to change or shape unless they are able to 'see' the results for themselves. Well, not to blame anyone here but rather this is just human nature.
SInce the emphasis have shifted from teaching problem solving to teaching via problem solving (Lester et.al., 1994), many writers have attempted to clarify what is meant by a problem solving approach to teaching mathematics.
So, I am proposing the following research questions:
(1) How the instructions between teaching problem solving and teaching via problem solving differ from each other?
(2) How does the two method of instructions affect students' performance on higher-order thinking questions?
Outline of my research proposal:
-> To conduct literature reviews on teaching problem solving and teaching via problem solving (PS)
-> Based on the reviews, to come up the research methodolgy. What are the operational definitions of teaching PS and teaching via PS? Basically, to come up with a specific type of mathematic instruction that can be measured as teaching PS and teaching via PS. Also, the assessment on higher-order thinking also needs to be operationally defined.
-> To decide on what are things that need to be controlled in this experiment.
Student variables need to be controlled. I need to ensure that the sample of students are of the same capabilites who do not receive any additional help outside curriculum time. Hence, pupil survey on their background is very important. A post test could be given to determine the pool of students in terms of their capabilites. 2 group of students will be selected to undergo the two types of the mathematics instructions.
->Time of lesson and classroom environment needs to also be factored in as this will affect students attitude towards learning. Both instructions need to be conducted during the same time with same typical classroom environment
-> Duration of how much the students will be exposed to the different instructions also needs to be considered. For my research, I am proposing to assess the students after one month of instruction.
Alternatives to my research proposal:
Although the type of instruction has been defined for each method to be used in this research, having two sets of teachers for each group of students may not be fairly accurate since teacher's disposition in class also affect students' learning. Hence, to select the same teacher for both sets of groups will be more reliable in this experiment.
Conclusion - Future Implications to Classroom Practices
Based on the results, teachers will have the knowledge of how well the students will perform in higher-order thinking, depending on the type of math instruction exposed to them. Hence, from this research, time spent for each method of instruction in class should be better justified now. Teachers will realise the importance of instilling thinking skills to prepare them of becoming a better problem solver. Teachers need to plan lessons accordingly also, bearing in mind of the syllabus that needs to be covered given the time that they have in school. Well, teachers may argue about having no time to finish the syllabus but are your students' engaged in their thinking ultimately? To end thhis, let's all of us ponder over this quote by Albert Einstein:
"Education is what remains after one has forgotten everything he has learned in school".
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