I have been prompted to write this article in response to what seems to be a pervading view among students and parents. That is, that the students are doing badly in mathematics if they only achieve a C standard in their tests. Of course, for some students who are not devoting enough time to their studies, this may be the case, however, for others this benchmark shows that they have reached a satisfactory level. It means that they have a reasonable working knowledge of the skills and procedures taught in class, but may not yet have developed a depth of conceptual understanding which would enable them to apply that knowledge to non-routine problems.
An essential part of the NSW and Australian Mathematics syllabus is “Working Mathematically”. The objective of this is that “students develop understanding and fluency in mathematics through inquiry, exploring and connecting mathematical concepts, choosing and applying problem-solving skills and mathematical techniques, communicating and reasoning” (Mathematics K-10 Syllabus Volume 2, p. 35)
In the International Baccalaureate Diploma guide for Mathematics it says: “lessons that use an inquiry-based approach, starting with practical investigations ….followed by analysis of results…..are often most successful in engaging the interest of students……….and are likely to assist the students …..by providing meaningful context .” (Mathematical Studies SL guide, International Baccalaureate)
In working towards this goal, we aim to give all students the opportunity to engage in genuine mathematical activity that will enable them to become flexible, creative and hopefully, innovative users of mathematics. We want our students to also recognise the connections between other mathematical topics and how mathematics is applied in other disciplines. This is essential in today’s modern world, particularly, with such an emphasis on technology.
In Mathematics in Years 7-10, tests are graded in difficulty, so that only the students who have developed many of these skills will be able to gain an A. As well, in Years 9 and 10, the courses are of a different level and so an A in Intermediate Mathematics may be equivalent to a C in Advanced Maths. The issue is that we should not focus on results to the detriment of the students’ learning and enjoyment of the subject.
In an article last week, Matt Larson (President of the National council of Teachers of Mathematics, USA) related how in 1788 in a first major publication of a mathematics textbook, it recommended that teachers were to state a rule, provide an example and then ask students to repeat a series of practice questions very similar to the example given! Does this rote practice sound familiar? This method was destructive in the way it turned many students against mathematics.
We want all our students to realise their mathematical potential, and it is there in them all!
Fortunately, our new textbooks, while providing some practice exercises, also provide many opportunities to engage with all other aspects of learning about mathematics. They are used as a valuable resource, however, many other rich mathematical tasks are also provided in our classrooms. The students are excited as they learn how to individually use the Geometer’s sketchpad (GSP) package on their computers to explore, investigate and make conjectures. They are also able to explore problems which have previously been left until Years 11 and 12, by using Excel spreadsheets. Not all problems have one correct answer, and some are open-ended.
Some form of formative assessment usually follows after any computer activity, to ensure that the students have truly engaged and learnt from the experience. This may take the form of a reflection sheet, or students may be asked to explain verbally what they have learnt. In Years 7 and 8, there are also some summative assessment tests (two per semester) on the use of both GSP and Excel as valuable tools in their mathematics. These are examples of “assessment for learning” and “assessment of learning” which were mentioned by Chris McCorkell in his article last week.
In the Mathematics Faculty we also stress the importance of students recognising mathematics in the world around them. Examples abound in Hong Kong, but it is interesting to note that students often find it hard to give examples!
Each chapter in the Year 8 textbook begins with a paragraph which gives examples of the use of the particular topic in the real world. For example, Algebraic rules to manipulate avatars in computer games; ratios in gears on bicycles; equations for protecting sea turtles; Measurement and Pythagoras in construction and mobility, in the form of circular wheels; historical aspects relating to architecture, sculptures and art; Percentages in finance, taxes, loans; Geometry in nature; efficient construction used by bees in optimising the use of space to store honey; Linear Relationships and optimal programming in industry; Symmetry, congruence and transformations in both historic and modern architecture, art, physics and optics; Statistics in internet Search engines to analyse search results in valuable ways;
Please ask your children to explain what they are doing in their maths classes to you every now again, and try to discuss any maths you see in the world around you, both in Hong Kong and in your travels. Most importantly, realise that only a small proportion of students in each class are likely to be gaining an A in tests. This does not mean that those who do not are failing. It means that they need to persevere and practise as much as they can, but also think carefully about what they are doing and try to verbally explain it to someone else. A positive mindset towards their maths often works wonders.
We encourage students to come to Mathematics in Room 616 on Tuesdays and Thursdays after school. There they can practise and also seek help if it is required. Most importantly, they need to have some fun whilst engaging in Mathematics!
Robyn Gregory | Head of Mathematics