Impact of lesson studies on Problem Solving

My blog entry is based on the secondary 2 problem-solving lesson study.

Overall, I was impressed with how the professor patiently prompts responses to link students’ ideas/observations to mathematical expressions and inspired the students to understand how algebra can be used to communicate clearly and simply. I am interested to know the impact of lesson studies on teacher training and development especially in the area of teaching problem solving to students of all abilities.

In segment one, introducing the puzzle, professor was apt at creating a stimulating environment, encouraging responses. I like the way he arouses curiosity and generates an atmosphere of suspense among the students to work along with him, example, the use of crystal ball and “don’t tell others”. I noted his confident, friendly and patient disposition throughout the lessons. Instructions given were clear and simple. It felt like a privilege to be able to be in the expert teacher classroom. I am curious to know the reflections by the teacher observers, their learning point and how they will teach mathematics problem solving differently after the lesson study. What qualities of teachers are most suited to develop problem solving abilities among the students?

In segment two, exploring the puzzle, professor encourages communications-“talk to your partner”, and giving students ample time to figure out the problem as they explore on the why of the puzzle. At this point, my key concern was how a successful teacher should allocate curriculum time to teach problem solving and complete the mathematics syllabus to accomplish what is set out in the mathematics curriculum? How a teacher can balance the use of curriculum time to helping every student becomes a successful problem solver will be an issue for further research. Professor gives feedback on what the students are currently doing – he tells them that he observes that “some are writing on the note, some are looking very hard”. I noticed that the students were “cautious” and whispering ideas to each other – quite not typical in a boys’ class. Could the crowds of teacher observers affect the learning of some students?

In segment 3 – Exploring giving hints, how likely is it for all students to sit through and persist in the task? What could the teacher do for students who already gave up or were frustrated after a while? In pairing the students, were there special consideration to ensure that the strong is paired with a weaker partner? In lesson studies, are the teacher observers assigned to specific groups of students to observe? It looked to me that the teacher observers were observing professor most of the time. Finally, I was again amazed at how professor walked around and looked for and point out students’ ideas on how they solve the puzzle, without expressing any hint of disappointment/displeasure at their “immature” solution paths. Instead, he saw many interesting ideas and the students needed more time. You didn’t feel like you need to rush through the lessons.

Segment 4, 5, 6 – Professor sharing students’ work and eventually linking the observed patterns by students to mathematical ideas– it strikes me here – mutual respect and helping students to find out why. Professor asked for permission to use students’ ideas and respected the student’s decision that he will not present his solution himself. He patiently led students to see and communicate their solution that truly explains why. That ability to help students draw the link (their solutions to mathematical expression) was so powerful that all students were engaged. How will students’ attitudes and beliefs towards mathematics change by the use of the above teaching approach?

The e-learning has generated a few research questions that have direct implications on how we can train mathematics teachers so that the math curriculum outcomes can be achieved. A possible way to carry out the research: interview expert/master mathematics teachers; observe their lessons in the form of lesson studies, do a protocol analysis, interview students’ to find out about how their beliefs and attitudes have changed. It will shed light and offer possible solutions on the many difficulties faced by classroom teachers to carry out problem solving lessons successfully in the classroom.

Post E-learning Reflection
It’s a good idea and a powerful way to learn. For myself, it was time consuming finding a way to load the video as my laptop admin does not support the downloads of some video configurations. Also, when I finally used another computer to play the video, the video was often disrupted with the need to reload again. The screen view was not clear too. Despite the hiccups, learning was enriching. The blog entries also allow one to view the diversity of other peers views and beliefs and pave way for deeper research work and self improvement.

Reference
Masmi, Max, Yutaka, Takeshi (2007). Japanese Lesson Study in Mathematics. Its Impact, Diversity and Potential for Educational Improvement. World Scientific