DEC Scan Journal : May 2013
Volume 32, May 2013 28 Contents Editorial Currents Teaching & learning Research Curriculum support Share this Resource reviews This will certainly convince your friend. But then the teacher moves the cross created from the yellow and red strips so that it is centred at a different spot on the calendar, and asks the questions again. Do you expect the new question to have the same answer as to which group of three numbers has the larger total? As we seek to explain our answer to the general problem, we are engaged in using algebraic reasoning. We return to the class the next day to find that instead of the calendar, the focus of the lesson is a 100-chart with a square marked on it in red (Figure 3). Figure 3 Find the sum of the numbers in the red square The teacher asks, What is the sum of the numbers in the square? Your first impulse is to reach for a calculator but the teacher is not encouraging the use of calculators. These numbers are of greater magnitude than the ones on the calendar but they also suggest a number of patterns. You break up the numbers and jot down your thinking (Figure 4). Can you convince yourself that it will always work? Can you convince a friend? Could you convince someone who did not want to believe it? This is Figure 4 Looking for patterns in numbers That’sjust3lotsof4+5+6and3 lotsof60+70+80. Now, thinking about the idea of balancingquantities,4+5+6is3x5 and60+70+80is3x70. Sotheanswermustbe9x5plus9x 70, or simply 9 x 75. The sum of the numbers is 9 times the middle number. the essence of mathematical reasoning, or more specifically, algebraic reasoning. The new Mathematics syllabus provides many opportunities to develop students’ deductive reasoning more deeply. The challenge remains to make use of those opportunities. Setting goals Enabling all students to benefit from learning to access to the power of mathematical reasoning relies on more than teaching additional content. Developing mathematical habits of mind takes time and skilful curriculum planning. The implementation of the Australian Curriculum: Mathematics through the new Mathematics K–10 syllabus provides an opportunity to focus on valuing mathematical reasoning. It will not be a simple task and, no doubt, many will proffer the belief that mathematics is only about obtaining the right answer, quickly. Those who expound this belief may sadly have been denied the opportunity to access the power of mathematical reasoning. Will setting the goal of being a top five country in PISA help us become a clever country? As a country we should have high expectations for our future. As a sport loving country, perhaps we could learn from athletes when it comes to setting goals. Emil Zatopek, who pioneered the interval training method, was perhaps the greatest distance runner in Olympic history. When it came to setting goals, Emil Zatopek’s advice was simple. You can’t climb up to the second floor without a ladder. When you set your aim too high and don’t fulfil it, then your enthusiasm turns to bitterness. Try for a goal that’s reasonable, and then gradually raise it. In seeking to reach higher educational goals, investigating the role of language, culture and symbolic processes provides fertile ground to start to realise the objectives of Australia in the Asian Century. The new Mathematics syllabus provides many opportunities to develop students’ deductive reasoning more deeply. The challenge remains to make use of those opportunities.