Storytime, ladies and gents.
Does anyone else ever have those moments in the middle of the night where the brain is just whirring, the dark seems a little too bright, and your eyelids are glued open. Well, it had been a while but a few nights ago I had that sort of night. It was 3 a.m. and I found myself wandering the house trying to find something to get me to drift off. Long story short, I ended up in a bean bag checking out some school work I’d found in the cupboard from high school. One piece in particular, a maths assignment, gave me reason to pause, and reflect on the significance of such a mundane experience. Bear with me.
School. Tenth Grade. Maths.
I had a teacher who was extremely passionate about his maths (he always had bedhead and a ruffled shirt, so it led to him being called a bit mental) in the tenth grade. His lessons were always entertaining but one stood out as an ideal example of teaching theory in a proactive and personal manner.
During maths, he introduced the class to a new project that we would undertake in small groups. His guidance was limited. Very limited. All he told us was that we had to go search high and low in the school for a particular mathematical equation that we would like to prove, disprove, or investigate further.
Roaming around school that day, visualising maths in mundane, everyday activities was fascinating and completely altered my paradigm about how maths was visible in almost everything I looked at! It always seemed to have a practical use. As a tennis player, I persuaded my group to investigate the path of a tennis ball during play, in relation to the equations behind Hawkeye (a replay tool used in sports).
I came away from the assignment absolutely stoked! I had a verve for maths that I had never had before. I could feel my brain buzzing with anticipation for each lesson after that, yearning for the opportunity to once again investigate the close ties that maths has with our daily lives.
The exercise was what Joan Wink (2010) would have called the Transformative Learning part of her three models of pedagogy. This is where the teacher becomes a partner to the student in learning by allowing students to communicate and use problem-solving for themselves to inquire and question how to bring concepts from the classroom into reality, the outside world. The mere act of bringing a content-heavy subject like maths into an authentic learning environment benefits the student in a way that cannot be taught within a classroom environment, incorporating visual, auditory, and kinesthetic (the three learning styles) into one simple assignment.
Furthermore, the emphasis on cooperative learning highlighted Slavin’s (1995) study findings that “Interaction among students promotes achievement of learning goals”. The social aspect of the assignment allowed us to work off each other, and combine our knowledge, challenging each other instead of struggling to complete a task that would be relatively difficult to explore by ourselves. It also actually made me want to do the assignment since I was with mates and obviously at that age the whole world revolved around my friends.
Upon reflection, the major theory behind this teaching method was probably Vygotsky’s Social Learning Theory (1978). By allowing us to work in small groups, my teacher promoted communication between peers which developed into intellectual discussions, further challenging me and helping me to work at a higher level. With the help of my peer, who in this case was my More Knowledgeable Other, I was able to perform better than I would have been able to individually. This was my Zone of Proximal Development (ZPD).
For those of us not altogether familiar with the ZPD, it is this little zone that contains skills and abilities that we are unable to perform or complete on our own, but we are if we receive assistance from someone who is able to perform these skills and abilities. It’s what you cannot do individually but can do with help.
If we became a bit frustrated by the complexity of the assignment, our teacher would provide the scaffolding needed for both of us to reach a higher ZPD and achieve the required goal. Therefore, through this Transformative and cooperative learning style of pedagogy, combined with the principles of Vygotsky’s Social Learning Theory, I was better able to develop my mental cognition and achieve the specified learning objectives.
What does that mean now?
As I sat there - early hours of the morning, in a bean bag chair - I contemplated how that experience had led me to be where I am today. I teach my kids based on a strong belief in personalised, student-centric learning. I teach small group classes in which they complete projects in teams. I enjoy teaching small groups in which chatter is a necessity. I believe in a student’s ability to work things out on their own, only offering help when I can see they are struggling.
That one experience helped shape the educator that I am today, and I couldn’t be more thankful to my “mental” maths teachers for inspiring me without even knowing it.
Slavin, R. E. (1995). Cooperative learning: Theory, research, and practice (2nd ed.). Boston: Allyn & Bacon.
Vygotsky, L. (1978). Interaction between learning and development. In M. Gauvain & M. Cole (Eds.). Mind and Society. (pp. 79-91). Cambridge, MA: Havard University Press.
Wink, J. (2010). Critical Pedagogy, Notes from the Real World. (4th ed.). Pearson.