Presentations at USA in April

I gave quite a few lectures in Boston and San Diego. The slides are available at www.mathz4kidz.com

On Lesson Study

I am a teacher in a primary school in Singapore, currently carrying out Lesson Study in our school. I would like to seek your advice on Research Themes.

I gather that to come up with the Research Theme, the team needs to look at the Ideal Profile of Students and the Actual Situation of Students. This, with the School's and Department's Vision and Mision, the team will construct the Research Theme or Research Focus. My question is once this is firmed up, it will form the basis of all future Research Lessons for Lesson Studies, is that right?

Do we need to come up with a different Research Theme for each cycle of Lesson Study or will the Research Theme be the one that all Lesson Studies be based on. For example, my team has discussed and came up with a Research Theme for Mathematics. Will another Research Theme need to be constructed for a different cycle for Mathematics or can we use this Research Theme we have decided on for all Research Lessons for Mathematics.

Ban Har writes: Based on the school's vision, focus of the curriculum and your students' profile, the research theme is constructed. You are on the right track. You will stick with the same reasearch theme for a while until your team feel that there are new areas that need attention.

Teaching Perpendicular Lines

Question: Should I get students to use set square to draw perpendicular lines in the first lesson or should I give them non-standard tools such as a right-angled triangle?

Hazel, a pre-service teacher in Singapore

This chapter comes after the chapter on angles where students have learnt about right angles. I think before students are taught how to draw perpendicular lines, they need to know what are perpendicular lines so that they are able to check if two lines are perpendicular. I am like to have given them two intersecting lines as well as lines joint at a point and ask them to measure the angles between the lines and to say that those that meet / intersect at right angles are called perpendicular lines. In my opinion, the chapter in the textbook starts too abruptly to get students to draw perpendicular lines without actually being taught what perpendicular lines are.

I like Hazel's idea of introducing other non-standard tools that can be used to draw perpendicular lines. I think a good lesson could involve the students being given some common objects such as ruler, protractor, set squares, triangle tangram set, an index card, ice-cream sticks and asked which of these they can use to draw lines that are perpendicular to each other.

The lesson can conclude with the whole class checking responses that they have generated using the criteria they have learnt.