Reflection on Session 3

In today's session, we had Ms Peggy as our guest lecturer.  The class learned about Lesson Study as a professional development tool, and we examined 2 case studies of centres using Lesson Study. After watching the videos, we came up with 9 areas that can help to make up good teaching:

- sitting position

- level of engagement/involvement 

- use of materials/manipulatives

- flow/sequence of lesson

- classroom management

- communication (teacher-pupil, pupil-pupil)

- questioning techniques (number of questions, types of questions)

- attitudes/disposition of teacher

- differentiation

From the 2 case studies, I see that mathematical investigation is beneficial.  With planned activities that are divergent in nature, students have opportunities to use efficient materials or manipulatives to explore and experiment mathematical ideas and situations in many ways.  While clear instruction, demonstrations, and effective questioning are important, teachers should also observe and offer differentiated tasks to challenge higher ability students, and scaffold to help the weaker ones. Some examples of differentiated tasks are, to let students describe their strategy and do justification, and even let them document the steps they have taken to arrive at their solutions.

  

Tonight, I also learned a fun and engaging way of teaching children number conservation: constructing different structures with 5 unifix cubes each.   When children take part in this acivity, they will be able to see that even though the structures could be different, the number of cubes remained unchanged.  As I involved in the constructions, I thought of and tried out as many designs as I could, making sure that the designs would not repeat themselves.  What I did was visualization - thinking about the shape of the structure mentally and represent it with the materials on hand.  As Van De Walle, Karp & Willams(2010) describe, visualization "involves being able to create mental images of shapes and then turn them around mentally, thinking about how they look from different perspectives - predicting the results of various transformation" (p.429). For a child of a higher ability, a challenging task will be to draw perspective view of the block structures.

  

7-piece square

Another good activity for visualization is forming shapes with tangram (set of puzzle shapes in 7).  It helps us to develop our ability to think and reason in geometric contexts.  As the number of required pieces of tangram increased, the formation of square and triangle became more difficult.  It was challenging, but fun.  I am sure children will also enjoy this activity as they learn.

7-piece triangle

Reference: Van De Walle, J., Karp, K. & Bay-Williams, J. (2010).  Elementary & middle school mathematics.  Teaching developmentally (7th ed.).  Boston, MA: Allyn and Bacon