Monday, September 19, 2011

Mathematical engagement - images to delight, ignite and excite

Let’s be honest about this - in some classrooms the teaching of mathematics is as dry the Sahara Desert - and perceived to be as endless by many students. As a result engagement is lower than we would like. This is significant since student engagement is correlated to student success.

Whilst this statement is almost self evident we should be wary of accepting such comments unreservedly - evidence based practice requires that we support our beliefs.  Fortunately this is easy to do.  Any number of studies have endorsed this notion that engagement enhances achievement.   

With this strongly established the next issue is how to generate engagement? Jill Fielding-Wells and Kellie Makar of the University of Queensland found that “Research indicates  that student motivation and engagement are increased if instruction is authentic and relevant...”  Authentic here was defined as that which was cognitively challenging and connected to the world beyond the classroom.  The study found that student engagement could be improved by up to 22% by shifting to inquiry based problem solving as the method of instruction.

For those comfortable with a less  academic but equally authentic anecdotal style there is this piece showing how a high school in the USA significantly improved results in mathematics by introducing a curriculum based around problem solving with an emphasis on generating student engagement - the percentage of students “passing” mathematics skyrocketed from an admittedly low 20% to 60%.   There is thus both academic and “real world” evidence  that engagement is linked to achievement and that engagement can be increased by including certain features into  learning experiences.     In terms of student engagement generally,  it has been found that student engagement is enhanced when students are interested, challenged and feel that the work / task is important.

Several educational reformers,   such as the teams at the Apple Classroom of Tomorrow Today and the Partnership for 21st Century Skills, also advocate the increased and improved use of technology and multimedia in our classrooms to enhance both engagement and learning.

Fortunately the Internet is a rich source of motivational material.  Presenting clips such as the following could be one way of increasing interest and engagement in mathematics lessons.

The following are samples of video that could both ignite interest and engagement.

Ma and Pa Kettle Math.

While it is not the intent of this post to provide lesson plans I would suggest that this video cries out for “unpacking”.  Why do the flawed approaches used here produce the correct answer? Does this approach always “work? Are there other numbers that could be substituted for the numbers in the clip? How might Ma and Pa Kettle be convinced that their techniques are, in fact, wrong?

Pattern blocks

Even very young children could benefit from video enhanced lessons. After watching this clip an obvious question might be “Who would like to create their own version of this?”  Given that this is created via the  “stop motion” technique a simple digital camera and one of the many free video creation programs is all that would be created to really involve the students.  


As well as being fascinating viewing this clip dealing with leaf tessellation lends itself to further investigation of the topic. ( Instructions for making non-regular tessellating shapes abound on the Internet - here’s one - and every free drawing package on the Internet or buried within operating systems has the capability of creating them.)

Older students could unpack just some of the elements of this wonderful video.  I’d suggest that if students were able to identify and explain all the concepts embedded in this engrossing video then their mathematical knowledge would be well beyond the norm - and the beauty of it is, in order to do so, some reasonably advanced teaching and learning would be required.  

The Internet is a rich source of such videos.  There is clearly scope for including web based video into our mathematics classrooms - especially as motivators at the early stage of projects. The use of such images is one way that we can delight,  ignite and excite our students - or at least increase engagement.

Those who found these videos interesting and can see a place for them in their practice might also enjoy an earlier post with a similar collection of clips here.

Those who are interested in using such images but would like some guidance on how they might be included meaningfully into a classroom project might find this post on Project Based Learning useful.

All links go to original sources of documents.

Tesselating shapes PPt;