Chapter 2

I appreciate the sections on 'Implications for Teaching Mathematics' and 'Relational Understanding', leading to 'Mathematics Proficiency' and 'Benefits of Developing Mathematics Proficiency' in Chapter Two of the textbook. I feel that I was unfortunate to have functioned largely on instrumental understanding while doing Math throughout my years of schooling, and I am very interested to learn how to teach preschoolers- to set the foundation right early in their lives- to achieve relational understanding in the subject, and toward attaining mathematics proficiency. 


I was fortunate to have a great Math teacher in my final year in Secondary school as I was preparing for the GCE 'O' Levels. Mr Lee Han Seng was a serious, stern, no-nonsense kind of man, but he had a gift for dissecting complicated Math concepts into digestible portions and presenting them very simply and explaining them very systematically, logically and comprehensibly. He developed in me a liking for the subject and he made me see that I had an aptitude for it if only I would change my attitude toward it and be willing to give my all to understand and to practice consistently. Looking back, I was sure Mr Lee did his own 'homework' before stepping into class everyday. I am very sure he thought hard about what was the best way to present the math concept for the day; how to explain it and build up our understanding step by step, to the point where we could comprehend what the math problem exacted of us. 

My Math tutors in the past have all at some point, asked me this same question while I was tackling a problem sum: "Can you tell me why you have to divide/multiply/add/subtract this by this? Do you know why you have to do it or are you just guessing?"" Truth be told, it was purely a guessing exercise for me 70% of the time. Looking back, I feel that it is indeed crucial to understand Math! It is not a rote memorization-then-regurgitation exercise. Math has meaning. A teacher can tell whether a child has gained proficiency in a Math exercise by requiring that and listening to the child to explain the steps/workings he does to solve the problem. To be able to teach Math such that my students will be able to acquire such understanding and proficiency is really my biggest goal for this module, because really, to understand math is the only way to attaining math proficiency. 

The text talked about engaging students in a productive struggle- giving them time to struggle through the mathematical concepts they are exploring. I feel that such a 'struggle' can only be productive if the student has his/her foundational concepts in Math already set in place; only then can new knowledge be built upon prior knowledge. Otherwise, most times, students are just staring blankly at a question, too afraid to make a wrong move, and too afraid to admit that he/she does not know how to attempt the question, and thus, are just sitting there, wasting time. New content has to be scaffolded for less competent math learners. 


At this point I wish I had preserved some of the worksheets or past exam papers containing math problems I had attempted carelessly or thoughtlessly and show how I was made to do corrections, but not with understanding either, to be examined and to re-attempt understanding and doing them now! Unfortunately I had already discarded the lot of them upon graduation from secondary school. I am not a competent Math student, but I am very interested in finding out how this module can transform me into a competent Math teacher!