This week’s reading response is difficult, as we
must predict what the article is about when we read the first three sentences. The
first three sentences of William Higginson’s “On the Foundations of Mathematics
Education” are the following:
“In the fall of 1726 a book was published in London
with the title ‘Travels into Several Remote Nations of the World’. The author,
described as, “first a Surgeon, and then a Captain of several Ships”, was
reputed to be one Lemuel Gulliver. Behind Lemuel and his fictitious journeys
there was, of course, the brilliant mind and savage wit of Jonathan Swift.”
OK, I totally could not understand what this article
is about. Apparently Lemuel Gulliver is a person in Jonathan Swift’s classic
1725 tale. Well, I confess that I could
not understand the two names until I searched on Google. However, how does
Gulliver’s journey reveal some foundations of math education?
Higginson constructed a MAPS model (M-mathematics,
A-philosophy, P-psychology, S-sociology) that explains the four dimensions of
our math education. If delivering knowledge to students is similar to telling a
new story to audience, a teacher needs to explain “what, when, who, where, why”,
and “how” to students, with “what” in mathematical dimension, “why” the
philosophy, “who and where” the sociology, and “when and how” the psychology. If
students find it hard to understand the math, is it possible that we focus
tooooooooo much on “what”, and perhaps “how”, while somehow ignoring the rest,
so that our students cannot understand the whole story? I personally believe
that it is necessary for us to define explicitly what are “what, where, when,
who, why, and how” under the MAPS setting before we go any deeper.
"The aim of a mathematics educator is to optimize, from both intellectual and emotional viewpoints, the mathematics learning experience of the student." I wonder how the above quote is interpreted today. Is Hardy implying mathematics = truth, allowing for subjectivity? This appears to be similar to the lens model in Kilpartrick's.
回复删除I think that Higginson seems to identify that "there is no one ideal mathematical education for all places or for all individuals in one place." This observation is interesting, because aren't we, as researchers in mathematics education, still searching for appropriate methodologies to address this issue that was identified several decades ago?
I agree that the MAPS model is somewhat confusing. Higginson's model seems to be related to the perspective of Nesher in one of other articles on acquisition of math through interdisciplinary consideration because both see the nature of math education from multi-dimensional viewpoints. Higginson states that the tetrahedron can be broken down into different combinations, such as MA, MP, MAS, MPS and so on, in which each structure has its usefulness to the foundations of math education. I am wondering if he originally developed this model based on the math topic, Combinatorics. This is evidenced by his statement, "In particular, one can approach the model systematically from a logical, combinatorial point of view (p5)."
回复删除I do see that the social-cultural dimensions have a strong influence on math research related to optimality of students' math understandings. I believe that students of different ethnic backgrounds solve math problems in ways that are unique to their own cultures. This calls for a need in research to examine the social-cultural aspects of math education in order to differentiate instruction for multi-cultural groups.
From having explored my colleagues' writings regarding the three viewpoints in these articles, it seems as though there is a great hesitation to approach research without "due" scientific process; were the same hurdles existent during the beginnings of psychology? Would there be the same backlash if there were sufficient interest in beginning a psychology education field? It is bewildering that mathematics education would be simplified to aspects of mathematics in philosophy, psychology, and sociology, because the history of schooling has introduced, if I may, many confounding variables that affect student learning. Which of the four categories would be used to investigate a new student teacher of White, middle-class background in an urban inner-city school? What will occur if a researcher feels compelled to use all of MAPS as a basis for study? Will an MA be considered more important research than MPS? Although Higginson writes that the model is meant to be a “simplification” of a complex structure, perhaps it has been simplified too far into a mathematical model that can be “rigorously” used.
回复删除One astounding omission from the MAPS model is that “place” and “space” are not mentioned anywhere in the authors’ writing. The context of the location in which MAPS would be applied may result in various different results that may not be entirely representative of a given topic. For instance, would the understanding of ratio be better understood in regions where trade was a large part of the economy better than in remote fishing villages? How would MAPS address each of these? What of study with Aboriginal peoples? The desperation to cling to mathematical education as a scientific field yields little room for dynamic policy change and shifts in sociocultural understanding of learners.
Good point about the situated nature of learning, Alex (as opposed to the supposedly universal knowledge of Science)! This began to enter math education just a few years later with work on ethnomathematics...
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