7

First, a direct answer: Yes, there is work in mathematics education connected to Gadamer. One soure for such studies is articles by Brent Davis; more generally, google scholar yields such connections readily. Here are some examples of BA Davis' work in which Gadamer is cited: Davis, B. (1997). Listening for Differences: An Evolving Conception of ...


7

From John Stembridge's web site at http://www.math.lsa.umich.edu/~jrs/plans.html : "Are we going to have to think today, or is it going to be all math?" --a student in Phil Hanlon's Math 115 class


6

I like the idea here, but I agree that it misleads students, and might have the opposite of intended effect. Why not hand out a paragraph to the students, and ask them to critique it. Say that the paragraph is a fake student response to an exam question. One sentence in the paragraph could be something like ``Since $A \cap B$, there must be an $x$ so that $...


5

Perhaps (depending on background) give them one of the books by William Dunham, like "Journey through Genius" (Dover, 1990), "The Mathematical Universe" (Wiley, 1997), there are others. He won several awards for expository writing on mathematics, Aigner et al's "Proofs from THE BOOK" (Springer, 2003) is more demanding, but a lot of fun.


3

The notation used on the board in math lectures should be the same as that found in any other mathematical writing. That is: Get a good book, read it very carefully, and follow that same notation precisely. This strengthens connections and prepares the student to read outside texts and articles on their own (which should be one of the principal goals of ...


3

As you realize, this In my brief experience, I’m finding that my written diagrams or notations are not ideal. Admittedly, I will draw operators, numerals, and arrows on-the-fly, and they don’t always clearly communicate the process, especially when looking at them a few days later. is part of your problem. I suspect you may have difficulty ...


3

"Mathematics, a Human Endeavor: A Textbook for Those Who Think They Don't Like the Subject" is a great book. Lots of fun/interesting problems that are accessible to a wide range of math levels. The description says it's targeted at liberal arts math classes that focus on problem-solving: "For instructors of liberal arts mathematics classes who focus on ...


3

I'm afraid that this might not be of use to you, because it's in Hebrew, but this question reminded me of the really nice Beauty of Mathematics course that Gil Kalai organized at the Hebrew University in Jerusalem for non-science undergraduates. The slides from the course (in Hebrew) are available on his blog and they include various subjects such as: ...


3

I once had a colleague when I was teaching in Asia who was new to teaching high school, but was a very accomplished Mathematician. In one of his first lessons he was teaching simultaneous equations, and said that he would teach them two methods to do this. He thought that offering an option would endear him to the students. A student then put his hand up, ...


2

From a student learning real analysis: The sequence diverges because the Cauchy criterion is dissatisfied.


2

This leads me to wonder if it is possible to consider a terrible heresy: Is it possible to imagine mathematics without problems?... What if "conversation" replaced "problem" in the mathematics classroom? I'm going to focus on this other question asked here. Personally, in the math courses that I teach (community college remedial algebra, college ...


2

$A\cap B$ is not true or false; but it is true that the intersection of two disjoint sets is the empty set, that is, that $A\cap B = \varnothing$ is true. This comes down to a question about whether A\cap B is a boolean statement (a proposition): that which can be answered with "true or false". Asking if $A\cap B$ is true or false is no different than ...


2

Most elementary school teachers in the USA get their teaching certification by majoring in "elementary education" as an undergraduate. Curriculum for such programs typically includes a sequence of courses that focus on both the content of mathematics taught in elementary school and how to guide children in their learning. I think this guidance is what you ...


2

Another example of this sort of issue: I have often seen students write things like $\frac84$ when they mean $4\mid 8$ (i.e., $4$ divides $8$.) It takes a while (for some) to see that the former has a numerical value, and the latter has a truth value.


1

I'll go with the common " '$=$' is a key on the calculator" misconception. Many students don't see a problem with and write down things like $$3 \cdot 4 = 12 - 5 = 7$$ when asked to calculate $3\cdot 4 - 5$. This error is caused (or at least reinforced) by the fact that "$=$" can in almost all cases be read as "calculate the left hand side and write the ...


1

People are often keen to develop their knowledge of their current interests so, if you can find out what interests your student (sport, cars, travel, cookery, whatever), you can hang some elegant mathematics on that.


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