This is a professional learning week. Together with four other teachers, I attended the Mathematics Teachers Conference 2011 at NIE, entitled “Communication, Reasoning and Connections”. This theme is found in our Singapore mathematical intended curriculum framework under processes. I am most glad to see that the conference had selected such a theme as I too believed that our school curriculum likewise should have elements which focused on these processes. These processes are important to our students and are worth the time and attention of teachers. Below are some of my reflections on the theme.
Reasoning
Reasoning offers powerful ways of developing and expressing insights about a range of events. Students who reason and think analytically tend to note pattern structures, regularities and symbolic objects.
As a mathematics teacher, I strongly believe that reasoning is essential to better understand mathematics. By developing ideas, exploring of phenomena and justifying solutions instead of just solving the content, students could then recognize and expect that mathematics make sense. Hence, such skills can be introduced to all mathematics content areas and across levels. Moreover, all students already bring to school a certain level of reasoning and we should build on these considerable reasoning skills and help students learn what mathematical reasoning entails. In our Primary schools, the students are exposed and used the different heuristic skills.
Connections
In the workshops I attended, both speakers mentioned that students too often perceived mathematics as isolated facts and procedures. They highlighted that this issue was likely brought about through the school implemented curriculum. I agree but I also believed that the textbooks also played a part. They also asserted that students should recognize and use connections among mathematical ideas. But do teachers themselves able to make such connections such as between numbers, algebra and geometry as they are not of everyday experiences. As a classroom teacher, I think that the connections should be instead made so as to build mathematical conceptual understanding. Concept mapping is an example of enabling connections. With conceptual understanding, students will then be able to recognize and apply mathematics in connection to what is known to the unknown world.
Communication
Communicating mathematical thinking and reasoning is important for developing understanding. It is a way of sharing and clarifying ideas. There is a need to emphasis the importance of communication is due to the fact that students do not speak of mathematics other than in the mathematics class. How often I get upset when students are unable to articulate mathematical terms properly, often using word like “this”, “that thing”. Moreover, I think that it is through the communication process that makes the students think and not just “adsorb” what the teacher says. As students are challenged to think and reason about mathematics and communicate their thinking, they will then learn to be clear in both verbal and in written form.
This is an important develment in the teaching and learning of Mathematics: processes or skills. We often overlook these skills in thinking, communication and connections. We often focus on the procedures and tackling the questions. The challenge now is to get all our Maths teachers to adopt these skills as the enduring understanding for Mathematics. With these skills, learning Maths may become more effective, more meaningful and more fun.
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