The previous two tutorials on arithmetic have been pretty mind boggling for me. In order to infuse meaning into our lessons, we are supposed to explore the possibilities of using real world contexts to teach mathematical concepts and try to make sense of these concepts to our students. As a student-teacher, I firmly believe that this shift in pedagogy is good for our students as we need to move pass traditional rote learning through memorization and repetition.
However, there are several difficulties and limitations to achieving this especially in a realistic classroom setting with syllabus to complete within tight schedule and preparation for exams on the students’ part as well as disruptions from difficult students. We have already experienced the potential disruption to the pace of teaching something fundamental yet abstract (multiplication of 2 minuses make a plus) in an attempt to make sense of it during tutorial. I have yet to find a satisfactory meaning to that concept personally but there are several logical explanations and examples available to help teach this concept (http://www.mathsisfun.com/multiplying-negatives.html). Furthermore, there are also concepts such as higher calculus (differentiation of tan x) which can be hard to infuse meaning when teaching. (We can try to facilitate learning by showing the derivative of tan x is sec^2 x with graphical method to trace the gradient => back to concrete-pictorial-abstract pedagogy instead of pure memorization of the derivatives). We also cannot neglect the value of rote learning altogether as I feel that practicing the processes involved in problem solving can build up familiarity and confidence in addition to skills.
In conclusion, the onus is really on us to decide for ourselves the delicate balance of what to meaningfully teach our kids and what to drill them on.
I totally agree with your thoughts. With the class dynamics and the tight schedule of finishing the syllabus, introducing some of these mathematical concepts to students to meet objectives would be far more difficult to achieve. We also need to understand that individual students in the class have variation in their learning abilities.
ReplyDeleteThe website you recommend is a good way of introducing the concept of different operations of integers. I recall that I also introduced this concept using the number line and most of the students find it comfortable to follow and comprehend during my 1-year contract teaching.
As for the Algedisk activity, we can implement in the class for extension of their knowledge in later stage provided we have the time availability.