For my textual analysis, I thought that an interesting first step might be to do a super quick skim through the journal. I essentially scrolled through as quickly as possible to get a visual sense of the journal. My first impression was that there were a significant number of figures and pictures throughout the issue. When I moved on to look at the table of contents to consider the titles of the articles within the issue, my observation of the large number of pictures within the article made sense! Three out of the nine articles were focused on geometry. The images in these articles varied significantly from the figures in the other articles though, which focused on students' mathematical learning processes. One common feature amongst these figures though was that many of them seemed to be flow charts of sorts. I suppose the idea of using a flow chart is an interesting model when trying to "map out" a child's thinking. What did surprise me though, was the total number of these flow charts. Was such modeling popular in the late 70's and early 80's when this issue was published?
I then went to consider the references in each of the articles. What I found a bit strange was that the articles either had a pretty large number of references or none at all. Something that I have noticed in FLM compared to other journals, is the number of expository articles by particular authors. Expository in the sense of the author reflecting on their own life experiences in the hopes that the reader might be able to relate. I personally think that this is a very nice touch to the journal. Sometimes it can be a bit overwhelming to read so many technical and/or theoretical articles, that having a narrative article of sorts can be very enjoyable, and sometimes feel a bit more applicable for someone working in a classroom. Of course, the expository articles in the issue are the ones with few or zero references. On the other hand, "Student Errors in the Mathematical Learning Process: A Survey" had over a page of references in the two column format! All of the articles seemed to be appropriate for all grade levels; even the article on memorizing or mastering multiplication tables is relevant for older students, even more so in this day and age when calculators are taking over the classroom earlier in students' academic careers. The last article, a narrative by a professor teaching a differential calculus class, was specifically targeted at university mathematics, but as it was a narrative, I think it was appropriate for anyone reading the journal.
What I found most intriguing though, was the cover picture of this article. Upon considering the number of geometry articles and "flow charts" in the article, the uniform tessellation of the plane seemed oddly appropriate.
I found your analysis of the visuals that have accompanied the articles in your journal very interesting. As you stated it seems a likely fit to provide visuals with geometry focused articles. I do find that often visuals accompany FLM articles in order to provide a concrete example of what is being described. I believe this goes along with my feeling that the journal is trying to make the articles accessible to various individuals. I also connect the accessibility factor to the point that you make saying that all articles in the journal can be appropriate for educators involved with all grade levels. This really encourages the reader to read all the articles in each journal rather than just reading one or two. I really feel the journal makes it's readers feel a part of a greater community, engaging in all the articles and reflecting together on things written.
ReplyDeleteInteresting comments. I wonder, do the geometry articles you mention fall into the category of what you describe as "mathematics education research from a mathematics perspective"? If you're interested in this perspective, I think that article on PCK (pedagogical content knowledge) would probably be in line with your interests. For example, an article discussing how to introduce the concept of the limit, or how to best present the introduction of matrix equations in linear algebra. Both of these topics were in the FLM issue I was looking at (they were the first two articles).
ReplyDeleteYour comments on the types of articles in this issue of FLM are consistent with my emerging impression of mathematics education research (MER). There seem to be some recurring themes: PCK, "narratives", theoretical models of mathematical thinking and development.
What is lacking is a consistent effort to look for some novel teaching methods. There are exceptions however. For example, for my term paper I chose the topic of "problem posing" which I believe is still essentially uncharted territory. In fact pretty anything in math education that involves significant creativity and ownership of learning is still essentially uncharted territory. Looking at the BC curriculum, I feel ownership and creativity in learning are both lacking.
The other trend which I see after looking at journals in MER is that: 1) There is no consistent standard for what counts as good research methodology. 2) Many articles are not really research, they are "narratives". As Susan has pointed out, research is about generating new knowledge. Recounting anecdotes doesn't count as generating new knowledge. Otherwise every one of our life stories would be scientifically publishable data. 3) There seems to be a dearth of student perspectives in most research articles.
I'm not opposed to qualitative research, but I like it when it's from the student's perspective. I also like it when the authors at least cite some experimental data or a previously established theoretical framework.