Victory Over Maths????????

Dick Tahta in his Victoire sur les Maths (victory over maths) demonstrates me several examples of children with limited ability in performing math problems because of their psychological issues.

Most of the examples are about Lusiane Weyl-Kailey, a therapist worked in a Paris clinic. All the children mentioned in the article have some kinds of family issues that psychologically prevent them from understanding mathematical concepts.

OK, up to this point I was totally curious about Dick’s idea: how can family issues influence children’s understanding of mathematics?

Well, family issue does, more or less, influence children’s learning abilities. Dick believes if the family issue is somehow relevant to some mathematical concepts, and because a child always tries to AVOID unhappy events in his/her youth, s/he may PRETEND/ALTER the math concepts as a way of changing the reality s/he is facing. (In this article all the children are male.)  

There are things I need to mention here:

      1) Most treatment mentioned in the article took a year. Children are normally put away from math works, and are treated patiently by the therapist.  

    2) Despite the exact treatment plans are not mentioned in the article, I feel that the treatments improved the children’s math work gradually. Meanwhile, the treatments also changed the children’s feelings toward their family members.

     3) It is in Paris, and it takes a year, so the treatment must be expensive. 

     4) Math concepts were relevant to family issues. This implies that math is taught from unconsciousness, especially in early year math education.

Sorry guys for the late post. 

Summary and Thoughts about the article

The author’s demonstration starts with the language used in a US mathematics textbook.

Voice:

operationalize the notion of voice by focusing on the construction of relationships and roles for the author and reader (teacher and students) by examining particular linguistic features of the textbook.

Language choices can construct the reader as a thinker and in other cases as a scribbler.

Interpersonal function (the speaker’s meaning potential as an intruder into the context of the situation) is central as it focuses on personal relationships established in a text, and focuses attention on power and authority.

Inclusive imperative (“consider”, “define”, “prove”) demands that the speaker and hearer institute and inhabit a common world or that they share some specific argued conviction about an item in such a world, and so they construct the reader as a thinker.

Exclusive imperatives (“build”, “bring”, “create”) requires a reader to carry out a specific activity, which construct the reader as a scribbler who performs actions.

In order to do mathematics, people need to both scribble and think.

Ideational function includes (a) who is involved in doing what kinds of processes; and (b) the depiction or suppression of agency.

Textual function can be examined through investigating the ways in which the text maintains consistency.

The material researched here is a 64-page student edition of Thinking with Mathematical Models (TMM, not CMP). It is the only one that both the teacher and the student read (implying students do not read textbooks?).

Findings:

            Sometimes when the authors said they were going to ask questions, they actually used imperatives, i.e., “These questions will help you …”, and more than half the reflections were actually imperatives, which were instructions to direct actions. This confusing of imperative sentences with questions is a common feature of all mathematics textbooks.

Within the imperatives, more than 2/3 are exclusives, emphasizing the reader’s role as a scribbler. In turn, these exclusive imperatives highlight the authors’ authoritative voice as they were in a position of telling the students what to do and how to do.

Meanwhile, first-person pronouns were entirely absent from the student edition, which obscure the presence of human beings in the text and affects “not only the picture of the nature of mathematical activity but also distances the author from the reader, setting up a formal relationship between them”. On the contrary, “you” was widely used in the textbook. Statistics show that the “You + verb” form is the most common form (165 times our of 263 times) in the textbook, normally appears when the authors defined what they thought the reader was doing. Also, the authors used “you may find …” to control the sense that a reader made of something and were defining what s/he should have taken away from an activity. This means that the authors were attempting to define and control the common knowledge in the classroom.

It is true that math textbook in this style keeps students away. I do not want to read a book like this until I really realize that I need to read it. This may explain why students refuse to read textbooks, lol. But what should we do? 

W1 reading response

    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. 

Test blog