There is a theory (or idea) in Sports that questions whether or not great athletes – or superstars – can become successful coaches after their playing days are over. The theory acknowledges that superstar athletes don’t understand what it’s like to fail, or what it’s like to need to learn the intricacies of the skills and strategies required for success in their trade. The assumption being that in each of these superstars there is an inherent understanding of the game – and that a superstar’s athleticism allows them to do things that others cannot. In effect, their ability to teach the finer details of a game, or help struggling athletes to fix the errors in their game, is unlikely because the superstar hasn’t experienced conflict of the same nature. Furthermore, their ability to teach is compromised because they likely skipped steps in the processes of skill development because they were picked up naturally. Perhaps the theory is outrageous and simply an observation built upon limited data. But there are enough examples of superstars being failures and role players being incredibly successful as coaches for me to have bought into the theory and consequently spent a paragraph discussing its merits. So how does this relate to my reflections on teaching mathematics? Trust me, I am not that arrogant! However I was always very good at math. I was able to pick up math strategies very early and seemingly very easy. I realize that everyone has their strengths, but I am concerned that teaching math may not be one of mine. I do not have the experience to answer this question yet, but I wonder what will happen when I have given my lesson, allowed students to work in groups, handle implements, and exhausted every one of my teaching strategies...and found that some students still “don’t get it”? This is where the lifelong learning that we have discussed previously comes into play. But this time the onus isn’t on creating a thirst in students to obtain as much knowledge as possible, the onus is on me to continue to better myself as a teacher and gather as much education as I can for my students. This is the reason why I am taking this course, and this is the reason I found great value in the videos required for module nine.
I viewed a number of videos for module 9.1; one depicted an instructor exposing pre-service students to mathematics teaching strategies, while the others were based on practice at the junior level in the Toronto District School Board. While the videos showed instruction to different audiences (not to mention much improved editing capabilities in the latter video), the material supported one another quite effectively. After acknowledging my fears about my capabilities of teaching math at the junior level, I think it is important to look at some of the strategies identified in the videos and reflect on their effectiveness.
· Side note: I will likely bounce back and forth between videos – so I apologize if this results in any confusion; I will try and be as clear and concise as possible.
There needs to be a balance between direct and indirect instruction when teaching mathematics: and neither have to be boring. I found that while the instructor was teaching to the pre-service students (using the overheads), he was animated, passionate, and humorous. I am concerned though that this necessary teaching strategy will be received negatively by students. As a student I remember these types of lessons being my least favourite. How do I combat this (universal) reality? In my opinion direct teaching needs to be attacked using ferocious enthusiasm (ferocious could potentially be a bit of an exaggeration), especially in mathematics. In addition, the content needs to have some real world application in order for students to find merit and authenticity in it (e.g. the oranges from the video). The instructor expects teachers to engage students in helping the math program. He encourages teachers to encourage students to acquire ownership of their learning. He provided a number of oranges to the pre-service students and asked them to (in words junior students would use) investigate what areas of mathematics are viable to them (the students would think about buoyancy, measurements, fractions, etc. Too often it seems that mathematics is presented to students without their ability to examine its use on their own. And too often problems that nobody cares about are given, rather than students discovering their own questions concerning how a specific area of math might be useful.
In order for students to gain ownership of their learning, the instructors use grouping as a primary learning strategy. Grouping in mathematics (similar to language) can be a difficult process. What if I have a weak student coasting along in a group with two or three strong ones? How do I keep groups working at similar paces (and do I even want that to happen)? What are groups doing when I am providing feedback to others? What is the perfect group size? The teacher in the TDSB mentioned that each group should have a pre-determined leader, and that this is a prestigious position to hold. I understand the value of having a “leader”, but one potential drawback is for the low students that may never be given a chance to hold this honour. Personally, I probably wouldn’t make this leadership position so explicit. Despite the questions and potential hiccups, the benefits of grouping are valuable. In order for teachers to put themselves in advantageous positions though, they must develop learning centres with appropriate resources, and a detailed set of carefully designed instructions (keeping in mind that we want students to hold ownership of their learning). In this way the teacher can back off and allow students to engage in self-directed learning. An extension of this strategy is breaking down larger groups into pairs. One strategy used by the teacher in the TDSB, was Think/Pair/Share. Students are given some instruction, and are asked to think about strategies needed to solve the problem or attack the task. In either case teachers can move from group to group providing immediate feedback pertinent to the needs of that specific group. Consequently teachers can use this information to revise their future lesson plans. Once again I need to think about strategies that ensure students remain on task while I am with other groups. Obviously this should be addressed and modeled from the beginning of the year, with students contributing to a set of class “expectations of group work behaviour”, but I suspect some “foul play” is inevitable.
I mentioned resources in the previous paragraph. I think that people (not just students or teachers) forget that math is a language that needs to be felt, held on to, and experienced. Math needs to be felt physically just as much as it needs to be seen visually (sorry if that doesn’t make sense). Providing students with an array of implements (shapes, counting blocks, string, etc.) that can be manipulated is imperative. In most classrooms (especially ones where math is taught) there should be a designated area that contains these manipulatives. This should be an area that is inviting and that students feel confident exploring. However, I have worked with students that only “work” with what is given to them. In other words, if you don’t put what they need in front of them, they are unlikely to respond, or seek out what they need to be successful. In these cases, what makes the most sense? Should I give the students what I think they need, let them fail, or have their parents come up with the answer with them? I suspect finding the strategy that works best for each specific case is the “right” answer (did I mention frustration in my first paragraph?).
Demonstrations used to extend learning were another strategy depicted in the videos. Demonstrations are something that can easily show authentic applications in the sciences or the arts, but at first glance these might be harder to develop for math (or at least more difficult to come up with). However the merits of this (coupled with the enthusiasm we talked about earlier) are profound. The only thing that I would be concerned with is trying to find applications (through demonstration) that are relevant to all students (whether there are 20 or 40 kids in your class). And that is why I was impressed with the instructor’s demonstration about the buoyancy of oranges. Everyone ‘gets’ oranges, yet it seems so simple. So my next logical thought is...am I over thinking this strategy? Another benefit of introducing students’ interests into teaching is the possibility to further reach students through interdisciplinary approaches. The instructor was able to discuss oranges – at first in a math context – then in a geography context. Obviously this is an incredibly condensed simplified example – but it seems so simple. I think sometimes teachers are focused on reaching the expectations of a certain subject that obvious “tangents” (i.e. connections) pertaining to other subjects are either ignored or forgotten. As a teacher I am eager to encourage discussions that veer off into other subject areas (whether it’s intentional or unintentional).
In the interest of not losing my audience, I am going to add a final paragraph to add a few things that intrigued me in videos. The instructor mentioned that sometimes teachers need to say “never mind curriculum pressures – I have to construct learning”. Obviously this isn’t the education tagline, but learning occurs in many ways and I think most educators realize the importance of facilitating learning whenever possible. Another strategy I found effective (although a bit condescending to pre-service students) was the instructor saying “starts with an R, ends with an O” (ratio). This is a useful strategy when trying to elicit learning prior to knowledge. Finally, checking frequently (through a variety of means) for understanding, and including peer evaluations in the assessment process are two strategies that work well in math and other subjects.
Thank you.
