Pedagogy


 * Pedagogy**


 * * documenting teaching strategies/activities that could be used to teach the OSSMC
 * providing sample lesson plans that demonstrate used of a variety of pedagogical strategies for teaching the OSSMC
 * creating a 1-2 teaching philosophy based on sound learning theory (providing concrete examples that demonstrate your approach to teaching) ||

I definitely want to add some stuff regarding intrinsic vs extrinsic motivation here.

I also want to comment on how I think a Tribes environment would have affected my own early education - I have some strong thoughts on this, particularly regarding the possibility of "dumbing-down" the stronger students.


 * Learning Styles**

When I first heard about learning styles over 20 years ago in psych-101, I really didn't "get-it". When I heard about it again in Tribes training, I still didn't "get-it". I am greatly indebted to Julian for bringing my attention to this video, which finally helped me "get-it": [] Ironically, now that I get it, the video actually refutes the common belief that adjusting a lesson to each individual's learning style is good teaching. Rather, the author presents that your learning style relates to your strength in thinking or recalling //qualitative// (as opposed to //meaning-based//) information. Everyone possesses the same collection of different types of memory, as evidenced by these sort of examples: But, note that this visual/aural/kinesthetic information is //qualitative//. The author argues, on the other hand, that most of the information that we want our students to learn is //meaning-based// (eg arithmetic), and hence the individual's learning strength is not particularly relevant. And similarly, where qualitative information is being taught (eg the landmass shape of Canada), then everyone needs to learn this by the most appropriate memory (in this case, visual), not by their strength (eg it would be hopeless to try to learn the shape of Canada by listening to a description of it - even for the most aurally inclined).
 * We think of the shape of a German Sheppard's ears by a visual memory
 * We recognize someone's voice by an aural memory
 * We know how to tie a shoe by a kinesthetic memory

One example that I can think of where the memory/thinking strengths may actually assist one in learning would be for literature. A visual "learner" may appreciate a novel more by seeing it acted out, whereas an aural "learner" may benefit as much from just hearing a novel being read. The problem is, of course, that most of the time, we need to be able to read the printed word ourselves (again a meaning-based skill).

As an interesting sidebar, the government has a website that assesses learning styles: [] When I take the test, I am branded with a broad range of styles - the top three being "Intrapersonal", "Logical/Mathematical" and "Visual/Spatial", and a top 6 all within 10% of each other. I guess that this sums up my personality fairly well: "A loner with an unusual blend on academic achievement and hands-on ability". Maybe it also explains my former difficulty in understanding what a "learning style" was: I myself don't have a narrowly defined style. Regardless, I think that there are far too few questions, and too many ambiguous questions for this test to be particularly reliable.


 * Group Work**

I have had some bad experiences with group work in my academic career. These bad experiences tend to centre around one of two scenarios: Both of these points give me great concern regarding the contemporary "push" for collaborative work. And this concern is most great for me when I contemplate using group work as a teaching strategy for Math. I have a notion that math concepts must be tackled individually. There is some benefit to one student assisting another - maybe moreso for the "giving" student, but ultimately each is on one's own. Except for the instances where one student helps another "get-it", I have yet to see a useful real-life execution of group work for Math. I'll keep my mind open, but I challenge anyone to show me a Math group work exercise that actually benefits all more than individual work would have. For example, no-one is going to benefit more (if at all) from doing long-division practice as part of a group.
 * I did most of the work because I couldn't stand to be a part of a poor quality project
 * The work was shared reasonably equally except by one passenger (usually a jackass to boot!)

I can imagine that group work might be effective if the members of the group are equally matched, in terms of ability, motivation and personality - a difficult, if not impossible logistical arrangement. However I am vehemently opposed to the idea of forming a group that includes one strong member and one weak member - this is almost guaranteed to result in one of the scenarios noted above. I am also especially concerned that this push for collaboration is going to adversely affect a generation of students with high potential as they become frustrated with feeling like they are being taken advantage of, and eventually as they become complacent: "It doesn't matter what kind of work quality I do, we're all going to get the same mark anyway."


 * Motivation**

So it's easy to agree that intrinsic motivation provides a much more effective learning environment than does extrinsic motivation. What I want to assert is that it is generally impossible to foster intrinsic motivation amongst an entire class all the time. And because of this futility, it would be counterproductive to attempt such a feat.

Let me give an analogy that I think helps with understanding. I am a hockey fan. I used to have difficulty understanding how anyone can see a hockey game and not instantly recognize that it's the best sport ever. Then I had an epiphany when watching a basketball game. I now realize how others might feel about hockey. You see, there is nothing that can make be interested in basketball: not a glowing ball, not teams in non-traditional markets, not a superstar on the hometown team. If I can feel this way about basketball, then I have to accept that others can feel the same about hockey.

So back to intrinsic motivation: No matter how profound, clear, engaging, enlightening and exciting you try to make a math lesson, there will ALWAYS be some students who won't care at all! And I am very deliberately stating this as an absolute, because I really believe that it is. It would be an exercise in futility to try to cater to everyone's personal intrinsic motivations. As a result, I think that we need to temper our expectations of ourselves and of our pedagogies. We try to be engaging, we try to avoid materialistic motivations, but more than anything else, we make sure that we deliver the curriculum so that every child has had the opportunity to benefit - whether or not they do. Along the same lines, we need not try to be superhuman in our efforts to address each and every student's roller-coaster of interest and motivation.


 * Why do we Need This (Math)?**

Thanks to Jesse for this insight:

Sometimes when we are asked the "Why do we need this?" question, we might be tempted to respond: "Because you need this foundation on the off-hand chance you pursue a technical education like Math, Physics or Engineering." However, there is another good, and more general reason: "You may not need any given specific topic in later life, but at the very least, you are still learning logical deduction skills that are generally useful in life, whatever your vocation."


 * Homework**

Some camps argue that homework has no effectiveness. It is further argued that those students who "get it" won't benefit from "doing it over and over", while those who "don't get it" won't benefit from practising doing it wrong. There is some merit to both facets, however I feel that there are plenty of cases where the real intent of homework is to provide practice - and this is especially true in math. Here are some simple examples starting from the earliest stages to the latest:


 * Multiplication tables - there's nothing much here to "get". Those that don't learn continue to struggle with math and life. Practice at home is one of the best opportunities to master these.


 * Multiplication and Long Division. Again, everyone can benefit from practice. I'll agree that dozens of problems aren't necessary. I'll also agree that the student who doesn't "get it" won't be able to do it. However, no-one is really going to "get it" by doing one or two problems in class. We all need some practice. And those who don't "get it" - well they probably didn't learn their multiplication tables - yes, now they need a lot more help! But let's not pretend that the average student isn't going to benefit from some practice.


 * Function Integration. Again just practice, even at the senior level. The test is going to have some of these problems, and you won't have much success if you haven't practiced. There is no point in saying "I won't have this kind of test", because I can assure you that these problems will be on your 1st year calculus exam!


 * Application Problems. Even into my 4th year of undergrad, all (successful) students took the initiative to practice solving (unassigned) textbook problems. Practice may not make perfect, but it certainly breeds familiarity and confidence.

Athletes, such as hockey players, practice routine drills over and over. It is the same for mental routines as it is for physical ones - there is a need to practice.


 * Presenting Math Problems**

This video is worth watching whenever you need inspiration on how the presentation of math curriculum might be improved: []