Response to "Integrating history of mathematics in the classroom: An analytic survey"

In Tzanakis and Arcavi’s chapter titled “Integrating History of Mathematics in the Classroom: An Analytic Survey” an argument is given as to why history of mathematics should be integrated in mathematics education.  They do this by listing objections to this integration and then counter these objections by exploring ways in which this integration is beneficial.  They then give an explanation for how this integration can actually happen, and give many applicable examples from a variety of resources to close the chapter.

It is only fair for me to disclose that I am a huge advocate of incorporating history of mathematics into mathematics education.  I do not believe that history should be the main focus, but I think there is great value in using history as an engagement tool.  That being said, I have taken two history of mathematics classes (one in my undergrad degree at the University of Georgia and one at UBC in my masters program), and there have been people in both of those classes who do not agree with using history of mathematics in their classrooms.  Two of the main concerns they mention are that there are no resources for teachers to use and there is already such a time constraint to teach the prescribed material, so how could they possibly incorporate outside material.  I think that these concerns are primarily due to lack of expertise in the area of history of mathematics.  This reading mentioned how one of the objections against history of mathematics was just that – teachers lack expertise in the history of mathematics, and that this stems from the lack of appropriate teacher education programs.  What might help this issue is making a history of mathematics course a requirement.

Another thing that is mentioned several times in this reading is the nature of mathematics.  The authors say that by incorporating history of mathematics into the classroom, student can see that real humans discovered and struggled with the same concepts many years ago.  This is an interesting topic for me because we have talked a lot about the nature of mathematics in our Monday night class.

Lastly, I would like to share a link to a youtube video.  https://www.youtube.com/watch?v=mZHYE8lOIe4 This was for a project I did in the history of math class I took in my undergrad.  Just thought I should share! :)

Response to “How Multimodality Works in Mathematical Activity”

The main goal of Ferrara’s article titled “How Multimodality Works in Mathematical Activity” is to “further elaborate on the ways multimodal aspects are exploited by learners thinking about mathematics by considering as relevant, not the fact that multimodality manifests itself, but how it happens”.  She tries to do this by looking at how one child learns to graph motion through his perceptual, bodily and imaginary experiences.  The setting of the study was at a primary school in the northwest part of Italy.  The study worked with the same students from grade 2 to grade 5 by having them interact with two different tools to interpret graphs related to given movements and to check movements associated to given graphs.

The way in which one student, Benny, described a graph was a main focus of this study.  He was asked to walk out a certain path using a specific graphing tool, which then created a graph of his movements in a position-time graph.  He had a recollection of moments of his own motions, then imagination of qualities of motion in relation to qualities on the graph, and then he could interpret its shape.  This shows how he was able to enter into a temporary possible world so that he could pretend something was happening in order to explain and understand something else.  Also, at a different point in the study, he was able to communicate this process to the teacher and his peers, which is in the social context of knowledge construction. 

When I was first reading this article, I really struggled with the meaning of multimodality.  I understood after reading the example about Benny that it means using imagination and physical action to conceptualize mathematical concepts.  I think teachers try to create this environment for students by primarily using manipulatives.  In this article, the manipulative was the graphing tool.  By experiencing the movements physically and seeing how the movements created the graph, Benny was able to understand position-time graphs.

I like how this article used graphing technology for younger students because I would have thought to use such a technology more in the high school years.  This has made me reconsider how valuable a technology or manipulative is for any age.  Also, in the article they used a lot of story telling to describe scenarios.  For example, they used Mister x and Mister z who were two secret agents who worked in Movilandia, but were invisible there.  However, Mister x and Mister z could communicate with the students through Cartesiolandia, which is a special language that describes the movements performed.  I love how Cartesiolandia sounds like the “Cartesian” for Cartesian plane where we use coordinate points to describe positions on the graph.  Here the teachers are basically doing the same thing, but are making it more accessible and fun for the students to engage with.  I had a precalculus teacher who did a similar thing to describe concepts in trigonometry.  Even though I don’t remember the specific stories today, I remember loving math because my teacher made is accessible for me to engage with by making it fun.

Comments of FLM 1-1 (the first issue of the journal)

Table of Contents:

The first article in the table of contents is titled “About Geometry” and the second article is titled “The Foundations of Geometry”.  While the rest of the articles appear to be about different topics in mathematics education, I have to wonder if all of them are viewed through a geometrical lens.  What I mean by this is that I wonder if all of the articles are framed around the subject of teaching geometry.   For example, one of the other articles is titled “The Stereotyped Nature of School Word Problems”, and I wonder if this article discusses geometrical word problems or just something about geometry in general.

The only article that gives me any insight about a particular age group is the one titled “The Multiplication Table:  To Be Memorized or Mastered?”  Since multiplication is taught at the elementary level, this title leads me to believe that this article will discuss younger children.  All of the other articles do not give any insight about age groups though.

The Articles:

Most of the articles have some sort of illustration, chart, or graph, and most of them range in length from four pages to nine pages (including references).  It is hard to say a general statement about if there are a lot of references cited about the journal as a whole because some articles have at least a whole column of references and others have no references.  All of the articles are in English. 

The article I find most interesting is titled “Two Cubes”.  I find it interesting because it is only one page long with most of the page being filled by an image of two cubes overlapping.  There is a short paragraph and a caption for the image, but no other writing.  It is strange to me that this can even be considered an article.

There are three articles out of nine total that have subheadings.  One of them has the typical subheadings I would think of where all of the information is chunked into about seven different sections, which seem to be in sequential order of explaining a thought/concept.  The other two articles have very few subheadings in them, which makes me wonder why subheadings were even used at all for these particular articles.  For example, one of these articles only has the subheading of “Postscript” and nothing else.  It seems strange to me to only have one subheading.


The Issue as a Whole:
The front cover has an image of a tessellation, and there is an explanation about this particular image on the table of contents page.  Maybe they used an image of a tessellation since the issue might be framed about geometry?  The back cover has a space where annotations can be made about the information in the articles.

The material on the inside of the front cover summarizes the purpose of the journal.  It also gives information about when the journal is published and how to get a subscription.  On the inside of the back cover there is suggestions to writers who might submit an article for publishing.

There is no material between the articles, which I find interesting because I am use to reading journals where each article takes up an exact amount of pages.  This journal is not like that.  An article might take up four and a half pages, and another one might start where that one finishes.  Maybe they are interested in conserving paper or only want the journal to be a certain length each time?

I am not sure what “author identifications” means.  I do not see a particular spot in the journal where the authors are identified in any other way other than listing their names.  By looking at their names, they all seem to be from North America.