Math Talk and Conceptual Understanding

I believe that when we make pupils’ understanding the focus of our Math Talk, we are extending the trajectory of mathematical understanding from procedural to conceptual understanding. I found some comments of mathematical understanding at blog http://mathedresearch.blogspot.com/2008/11/creating-optimal-mathematics-learning.html by Associate Professor Reidar Mosvold from University of Stavanger, Norway. He believes that research has suggested that mathematical success can be achieved by focusing on both the individual and social aspects of learning. The development of metacognitive skills and incorporation of discourse in instruction helps pupils to engage in deeper conceptual understandings. However, he feels that studies focus more on the above two practices separately and he proposes a need to do research that focuses on both. This influences my thought about my own research on Math Talk and Mathematical Understanding.

As I interrogate my epistemic thoughts of my research, I am frequently caught in a dilemma. I think it is described by Guba & Lincoln (1994) as the etic/emic dilemma. It was explained as a distinction of grand theories with local contexts. I am constantly confronted by this gap I see in my daily practice and the theories of the teaching of Mathematics. I am in the midst of crafting a research plan that will study in-depth and uncover this distinction. I am faced with this argument from practitioners who feel very strongly that the procedural methods have helped to get fast results in terms of Mathematics achievement. Moreover, our country maintains a sustained sterling achievement in TIMSS results. That leads us to the question of “Where is the need for conceptual-oriented methods?” I think I am coming closer to the discovery of the knowledge in response to that question. An analysis of pupils’ performance in procedural-oriented questions and conceptual-oriented questions has shown that pupils, including those pupils who have achieved high performance in Mathematics, have scored poorly in conceptual-oriented questions.

Thus, eventhough they are getting distinctions in Mathematics examination, they are not scoring well for conceptual-oriented questions. I also realize that our TIMSS items for Grade Four found in the website: http://timss.bc.edu/TIMSS2007/encyclopedia.html are procedural-oriented questions. Indeed, our current practice that focuses on procedural-oriented methods have helped our pupils to achieve good TIMSS score as the teaching method is aligned with the assessment items. Toh and Pereira-Mendoza (2002) stated that , “For Singapore students many of the so-called problem-solving items would be better labeled as routine exercises”.

Finally, the reading of the above sites has led me to the following question: How and why would Math Talk focus on conceptual understanding?