Response to "Psychology and Mathematics Education" - Efraim Fischbein

This article primarily talks about cognitive psychology (the study of mental processes such as "attention, language use, memory, perception, problem solving, creativity, and thinking") and psychology of mathematics education. In the article, the author states two reasons for the inability of Piaget's ideas to provide a platform to link cognitive psychology and mathematics education. The reasons were that Piaget was not interested in the effects of teaching on children's learning and that Piaget believed that intellectual development was due to logical thinking, which implied that mathematical learning cannot occur from a local context to a global context. The author goes on to argue that employing scientific research strategies may have "played an important role in blocking the advancement of mathematics education." Thus, the author recommends that researchers in mathematics education identify new concepts and terms that are absent in psychology for describing interactions between psychology and mathematics education.

It is interesting to note that research findings based on psychological (scientific) approach to mathematics education may not be generalizable. There could be a connection to Kilpatrick's scepticisms about research findings in mathematics education. That is, Kilpatrick seems to suggest that it is not surprising why the research outcomes are ineffective.

Response to "Muddying the Clear Waters" - Herbel-Eisenmann

The  first stop occurred when researchers and teacher-researchers in the article seem to suggest that revoicing as "something that all teachers should do when they teach." Isn't this one of the things that we, as teachers, do with or without knowing much about research findings on revoicing?  Isn't this what we do on a daily basis when we interact with one another? The renewed research interests in "the idea of revoicing as a potentially powerful discourse" appears to be led by university researchers. In this case, teachers were involved as participants in the research and so, approaching from Kilpatrick's point of view, findings from this research may positively influence school practice.

"Context" seems to be in the way of many research findings. May be this the beauty of qualitative research when studying the lived-experiences of the participants in their day-to-day lives. That is, any interpretation of a study's outcome "depends" on so many factors.

Response to Kilpatrick's

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The Reasonable Ineffectiveness of Research in Mathematics Education
Author(s): Jeremy Kilpatrick
Source: For the Learning of Mathematics, Vol. 2, No. 2 (Nov., 1981), pp. 22-29
Published by: FLM Publishing Association
Stable URL: http://www.jstor.org/stable/40247734
Accessed: 07/01/2015 04:14

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By glancing over the title and the first paragraph of the article, I think that the author would be discussing about the existing state of research in mathematics education. In addition, the author will be using two assumptions, a) ineffectiveness of research in mathematics education is well understood and real and b) the understanding of the ineffectiveness is real, to justify why research in mathematics education is ineffective. My expectation is that the author would provide reasonable insights, which may be of interest when conducting research in mathematics education.

The article begins by questioning whether research in education is effective or has any value. The author uses Suppes' cautious optimism and Scriven's rigorous analysis to question the effectiveness or pay-off of research in education on classroom practice through Suppe's book, Impact of research on education: some case studies. The author extends this "crisis of faith" to probe whether researchers in mathematics education are trying to address questions such as:

1. Have we been doing the wrong things?
2. Have we failed to make contact with school practices?
3. Who, if anyone, is listening to what we have to say?

In trying to address these questions, there appears to be confusion between the impacts of pure (basic) and applied research. Basic research was assumed to be "up in the clouds" seeking generalization theories and seen to be higher in status, whereas applied research was thought to lack "specificity." The author goes on to suggest another model of research where "one cannot label a piece of research as either basic or applied." This is the lens model, in which the reader decides whether the purpose or usefulness of the research is basic or applied.

It was surprising for me to learn that the majority of dissertations in mathematics education do not come from the department of mathematics education or under the supervision of researchers in mathematics education. Even if this unsubstantiated claim is valid, the author seems to suggest that it is not surprising why the research outcomes are ineffective. Should research in mathematics education always come from the community of researchers in mathematics education for the research to have any value? I am suspicious of this line of thought, because Piaget was not a researcher in mathematics education. However, many researchers in mathematics education and mathematics teachers subscribe to Piaget's concepts of accommodation and assimilation, which ties to the Mathematics-Psychology-Philosophy (MAP) vertex on the MAPS perspectives of mathematical education.

Finally, it is startling to note that the author suggests that "lack of attention to theory" as a reason for the ineffectiveness of research in mathematics education. This suggestion implies that researchers in mathematics education hold knowledge-as-elements perspective. According to Ozdemir, novices hold this perspective of knowledge, whereas experts hold knowledge-as-theory perspective. I wonder if the author is vaguely suggesting that the majority of the research articles and dissertations in mathematics education are for or by novices. From the author's point of view, this may imply that the research findings may collectively "not add up to very much."

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An Overview of Conceptual Change Theories

Gökhan Özdemir

Niğde Üniversitesi, Niğde, TURKEY

Douglas B. Clark

Arizona State University, AZ, USA

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Family Math and Science Day at UBC

I had an awesome time at the Family Math and Science Day at UBC on Nov.1, 2014. Tons of pictures can be found here.