A Categorization of the "Whys" & "Hows" of Using History of Mathematics Education

In this week’s reading, Uffe Jankvist looks into the purposes of teaching mathematics through its history, and how it should be done.  Is the purpose to learn about the history of mathematics or is the purpose to use history to supplement and further enrich the curriculum within lessons?

Those who argued for using history as a tool, rather than a goal, put forth that history engages students and gives math “a more human face.” (p.237)  Students can see that the problems that they are dealing with in mathematics, are the very same problems that mathematical geniuses spent much of their lives tackling.  I have noticed that whenever a subject is seen through the lens of history, my students have become more engaged.  I have found that almost every student enjoys a story, and being read to.  If a teacher can incorporate a story into a lesson, that takes the audience through a series of events that culminate in a problem being solved, or even not solved, I believe that there is a good chance that the students will be more interested in the subject matter. 

When using history as a goal, the author was clear that it was not to simply learn the history of mathematics, but rather understand how mathematics has evolved and developed over time.  I personally prefer using it as a tool, because I would find it very difficult to include it in my curriculum.  Then again, maybe there is a way to expose students to the history and by doing so teach a prescribed learning outcome (PLO) at the same time.

Jankvist discusses three different ways of teaching history of mathematics:

1)   The illumination approach – the teaching is supplemented by historical texts

2)   The module approach – historical units are established (separate from the standard units)

3)   History-based approach – the history is not directly taught, however it influences the possible order in which mathematical units are introduced

Any one of these three approaches may be applied to either teaching history as a tool or as a goal.  I find myself leaning more towards the first approach.  I would like to believe that our curriculum is already taking into account the third approach, however I have noticed that some textbooks would have me believe otherwise.  I find that the second approach separates the history from the math too much.

Using history to teach mathematics is definitely not for everyone.  It may confuse the students more than it will benefit them.  Not all teachers are comfortable or knowledgeable in regards to the history.  It is my belief that it should be a decision made by the individual teacher, and not included in the curriculum necessarily. 

How Multimodality Works In Mathematics Activity

In the article, “How Multimodality Works In Mathematical Activity: Young Children Graphing Motion” written by Francesca Ferrara, different experiences are observed and analyzed to see how they affect mathematical learning.  Specifically, Ferrara looks at perceptual, sensory, and motor experiences.  She noticed that there is often a very concrete connection between the perceptual/sensory neurons and their associated motor neurons so that when you think of solving a problem, you are using the same neurons as when you actually solve it.

To work with these established neural connections, Ferrara created a study where she analyzed how primary students used digital technology (graphing calculators & computer software).  By using the technological tools, the students were stimulating their perceptual/sensory neurons as well as their motor neurons.  The students would capture movement and data would instantaneously be displayed on the calculator or computer.

The benefit of these activities was that the children could view the position-time graph being created as their peer moved in front of the motion-capture device.  Often we are given a graph to analyze, but have not actually witnessed how it was created.  I can definitely see how the students can benefit from experiencing the sensory stimuli and creating a direct association with the graph itself.  It should also be noted that these students started to participate in this study when they were in grade 2.  Position-time graphs are not usually seen in mathematical lessons until later.  After seeing the graph create itself while someone walked past the motion sensor, the students were able to not only make sense of what the graph represented, but they could also in a sense re-create how it was made.

There was a second experiment that also involved the students making an association between the movement of an object and the creation of a graph on a piece of technology.

When the students were asked to explain the graphs, they often used physical movements (recreate the action), and their imagination (“pretend that. . .”).  Due to the numerous ways that the students were able to describe the graph, it was deemed to be multimodal.  I think that this style of learning is an excellent one.  By tapping into the motor as well as the sensory aspects of learning, I believe that there is a greater chance that the student will be able to recall what was learned.   Sometimes, basic physical movements can help students retain knowledge such as basic facts.  For example, one could create specific body movements when reciting their 4 times tables.  This style of learning may not always be possible in a classroom setting, but it should definitely be encouraged.