A categorization of the “whys” and “hows” of using history in mathematics education

This week I read Uffe Thomas Jankvist’s A categorization of the “whys” and “hows” of using history in mathematics education.  In this article, Jankvist takes a theoretical approach to the discussion of why and how to use the history of mathematics.  He subdivides the whys into two mindsets:  history as a tool for learning mathematics, and history as a goal of mathematics.  History as a tool is the argument that students should learn the history of mathematics and use this knowledge to help them approach and tackle current issues.  Jankvist cites that history can be a “motivating factor for students in the learning and study” (p. 237). The history as a goal mindset refers to how learning about the history of mathematics can help round out a student’s understanding of what mathematics is, where it came from, and how it developed.   He also divides the hows into three categories based on illumination, the modules, and a history-based approach.  The illumination approach uses history as a “spice added to the mathematics education casserole” (p. 246), splashing tidbits and snippets of history into a student’s learning. The modules approach is a method that teaches history as an entire module, or chapter in math education.  Lastly, the history-based approach is more to do with a pedagogical method, teaching topics in a historically relevant way, such as the way that a concept was discovered, and used.

Jankvist goes into a lot of depth with each of these topics, providing compelling arguments for the inclusion of each.  His section detailing the barriers to integration of history is also well thought out, leaving the reader a good understanding of the issues at stake.

When I reflect back on my own teaching, I certainly fall into a distinct pair of categories.  I teach the history of mathematics to my students as a goal, as a way to fill out their understanding of the topic at hand, and to help give them some historical context as to the importance of our discussion.  I also discuss these historical concepts in ways that Jankvist would call illumination approaches, using them as a way to flavor a topic and bring more depth to it.  Teacher education, of course, is a primary antagonist to the inclusion of history of mathematics in the classroom, but this is true on several levels.  Teachers need to be educated on why its inclusion is beneficial, how it might be included, and finally, the contents of its inclusion.  I would certainly teach more history in my classroom if I knew more history, but I don’t.  What do you think: should teachers spend time researching, and learning about the history of mathematics so they too can include it in their lessons?

Learning Angles through Movement: Critical Actions for Developing Understanding in an Embodied Activity

This week I read Learning Angles through Movement: Critical Actions for Developing Understanding in an Embodied Activity by Smith, King, and Hoyte (2014).  In it, they discuss a fascinating study they undertook with a class of third and fourth grade students and a motion tracking device called Kinect.   They developed a motion-controlled angle task for their students to undertake where they would move their arms to form angles that would then be displayed on a screen.  They concluded that the task was able to help the students develop understanding between the abstract, visual representation of angles, and the physically embodied representation of angles.  Previously, the authors noted that “body-based dynamic angles representations [were] difficult [due to a lack of] visual support” (p. 106).  I think that motion-tracking technology like Kinect has such potential to provide support for learning through embodied moving.  I can imagine students learning about linear equations where they are provided a Cartesian plane, but then must move their arms to create the right slope and intercept. 

This study reminds me of an activity I did with a grade 11 class over the Summer.  We were learning about the hard-to-grasp ambiguous case of the sine law, a topic that students almost always struggle with.  But this year I brought some woodworking tools to school and had students build physical triangles as per a set of instructions.    They noticed that in certain cases their group built a different triangle than other groups.  Our last activity had us constructing a triangle with one swinging arm to represent the ambiguity.  The physicality of the activity, being able to tangibly swing the arm of the ambiguous triangle helped the students connect with this otherwise abstract concept.  

The 50th Issue of For the Learning of Mathematics

This week I am reviewing the 50th edition of the math education journal For the Learning of Mathematics.  The grey cover of the journal has the simple titling of the journal all in lower case, with a large 50 taking the majority of attention on the page.  The table of contents immediately tells the reader that the journal touches on a broad number of topics.  The 11 articles focus on topics from ethnomathematics, word problems (from our own Susan Gerofsky), international viewpoints, what appears to be, at first glance, a creative writing piece (Under the Banyan Tree by Tahta) and more.  There are even two articles that take a more meta-level approach, discussing the journal itself (Reflections on FLM by Higginson, and The "Spirit" of FLM by Lee).

The journal itself is formatted with two columns of text and paragraphs barely being indented.  This gives the familiar 'wall of text' feel that so many academic journals take.  Furthermore, in the 47 pages of the journal there are only two pictures (both in the ethnomathematics article), one photocopy of a page of a book, and two mathematical doodles at the ends of articles that don't quite fill up a page. The articles do not have abstracts, which might lend one to more informally read through the journal, rifling through it more casually instead of simply head-hunting particular research interests.

One of the last pages in the articles is a page-long 'Suggestions to Writers' which is very telling of the journal's stylings.  It details that math education should be "interpreted to mean the whole field of human ideas and activities that affect or could affect the learning of mathematics."  This tells the reader that FML has a very broad range of publications which can take many forms, but which all focus on the learning of mathematics.  "It is a place where ideas may be tried out and presented for discussion" tells the reader that FLM is on the forefront of mathematics education, welcoming change and fresh ideas.  It is this last line that, to me, really sells the journal.  I want to read a journal full of articles that hope to shed light on new, and maybe controversial areas within math education.  I want to read articles from a variety of sources and FLM even supports "informal research, especially from the classroom."