Monday, October 19, 2009
Blog 5
I believe that Math talk is related to mathematical understanding. My thesis explicates a shift in pedagogical concern to an epistemological concern. Pedagogical concern centres on issues pertaining to the content and the way it is taught. Pupils are concerned with the learning of Mathematics and how to perform well in academic scores. Epistemological concern centres on issues pertaining to learn to be like a mathematician. That means while solving mathematics sums, the learner is not only focused on doing the mathematics right (getting correct answers) but also the process of getting the answers. That is to learn to behave like a mathematician who is guessing, proving wrong, generating or creating other possible solutions. An epistemological concern will motivate a researcher or learner to focus more on the process of learning mathematics than the product of learning mathematics.
“What the 2009 NAEP Math Scores Tell Us?”
Lisa Guernsey wrote an article on “What the 2009 NAEP Math Scores Tell Us?” posted on 14 October 2009 at http://www.newamerica.net/blog/early-ed-watch/2009/what-2009-naep-math-scores-tell-us-15346#comment-4156.
Her opening phrase “No progress on the math front” is a reaction to the 4th-graders’ scores. She highlighted that there is room for improvement for Mathematics education and concluded that if we want to improve students’ Math proficiency, we have to improve teachers’ proficiency too.
I personally view the teacher's ability in the effective delivery of lessons that help pupils to learn, in two knowledge domains. The first one is the teacher's content knowledge. That is the teacher's proficiency in the subject. There is another domain which is the teacher's pedagogical content knowledge. This is the ability to make the content easily accessible and thus understood by the pupils. Both domains continually strengthen each other and contribute to the success in the teaching and learning of mathematics. Instead of isolating development on one domain at a time, both domains should not be separated but be developed concurrently. Thus, if we want to improve the students’ Math proficiency, we need to improve not only the teachers’ proficiency (content knowledge) as mentioned by the author, but also their pedagogical knowledge.
Besides testing teacher's proficiency, an effective professional development through Lesson Study, used very effectively in Japan to improve pupils' standard in mathematics, may be considered to improve the two domains mentioned above.
Her opening phrase “No progress on the math front” is a reaction to the 4th-graders’ scores. She highlighted that there is room for improvement for Mathematics education and concluded that if we want to improve students’ Math proficiency, we have to improve teachers’ proficiency too.
I personally view the teacher's ability in the effective delivery of lessons that help pupils to learn, in two knowledge domains. The first one is the teacher's content knowledge. That is the teacher's proficiency in the subject. There is another domain which is the teacher's pedagogical content knowledge. This is the ability to make the content easily accessible and thus understood by the pupils. Both domains continually strengthen each other and contribute to the success in the teaching and learning of mathematics. Instead of isolating development on one domain at a time, both domains should not be separated but be developed concurrently. Thus, if we want to improve the students’ Math proficiency, we need to improve not only the teachers’ proficiency (content knowledge) as mentioned by the author, but also their pedagogical knowledge.
Besides testing teacher's proficiency, an effective professional development through Lesson Study, used very effectively in Japan to improve pupils' standard in mathematics, may be considered to improve the two domains mentioned above.
Saturday, October 10, 2009
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?
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?
Tuesday, October 6, 2009
Symbolic Interactionisn
I like Erna Yackel's article on “Explanation, Justification and Argumentation in Mathematics classrooms”. He talked about how he used the symbolic interactionist perspective in his attempt to investigate explanation, justification and argumentation in mathematics classrooms. This approach interests me a lot as it is compatible with psychological constructivism that focuses on individual learning and is useful when studying students’ inquiry in mathematics as it emphasizes on both individual and group sense-making processes. However, i need to gather your views on how this theoretical framework can help me craft out my research proposal on how and why Math Talk can help in the learning of Mathematics. Anyone has done something like that? I would love to hear your comments.
Saturday, October 3, 2009
Commognitive
Anna Sfard ( 2007) explained the Commognitive as an interpretive framework used to study learning in 2 case studies. There are two assumptions in this framework. Firstly, mathematical thinking can be communicated and secondly, learning of mathematics takes place when there is modification made to the existing individual’s discourse. I share similar notions in my research interest as I am interested to understand how and why Math Talk, that is a form of communication, is related to mathematical thinking and learning in my research. Most research on discourse is used as a means for learning but in this framework, it is used as the object of learning. It provides another epistemological perspective on research on discourse that is used as an object of learning. Personally, I feel that discourse can be both a means for learning and object of learning. I see it as a means for learning when the interactions between the teacher and students provide opportunities for individual and group construction of learning to occur in a classroom. It is an object of learning because when the teacher often uses the pupils’ discourse to identify misconceptions or confirmation of learning. In this way, the teacher can alter her instruction accordingly. What are your views?
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