Providing opportunities for Cross-Topical Application in Maths (Synergy or Level 9 Kung Fu Maths) -


Now, some readers might be thinking, and rightfully so, that synergy is an overused, or even misused, word. Hence, it is prudent to look up its meaning before discussion begins in this section.

The Oxford English Dictionary (OED) defines synergy as “The interaction or cooperation of two or more organizations, substances, or other agents to produce a combined effect greater than the sum of their separate effects”.

The “agents” in this article refer to the different branches or topics in Maths (e.g., Numbers, Algebra, Geometry). Historically, these different branches of Maths sometimes developed independently of each other in time and space. Nonetheless, many of these actually coincided in the things that earlier mathematicians were trying to understand. Today, we have an array of mathematical instruments at our disposal. Using each of them in isolation repeatedly is what many are used to: doing sums after sums, assessment books after assessment books, mock exam papers after mock exam papers… (Okay, you get the idea). This is not to say that practice does not have its place in students’ learning. However, beyond a certain level of mastery, more practice of the same thing over again would yield little further utility.

This is where Cross-Topical activities or problem sums come in. In the following example, we show you how they increase exponentially the potential of what students could learn. Consider Extract G (part 3) from a Primary 6 Joyous Learning worksheet.

Extract G (part 3)

Based on what you have learnt from last week’s heuristics lesson, could you come up with an algebraic expression to represent this pattern? Fill in the table below and use it to guide you in forming the algebraic expression.

Algebraic expression for the sum of interior angles of a polygon

= (n - 2) x 180°

For the Geometry part of this activity, students have already accounted for the sum of interior angles of a polygon through both inductive and deductive reasoning, as shown in Extracts G (part 1) and (part 2). Similarly, for the Algebra part of this activity, the use of an algebraic expression to represent patterns has been imparted to students in an earlier lesson. Cross-topical activities like this call on students to examine their prior knowledge through different lenses. This process synthesizes connections between previously disparate units of knowledge. On a more ambitious note, this could even inculcate the habit of taking a cross-disciplinary approach to solving problems in their lives and, in future, work.

To conclude this section, did you notice that Extracts G (part 1), (part 2) and (part 3) all dealt with the same thing: the sum of interior angles in polygons? They are actually three parts of a same activity in the Joyous Learning Primary 6 worksheet on Geometry. While all three parts invite students to study the same subject, this is not the same as drilling. Each part affords students a different learning experience: inductive reasoning, deductive reasoning and cross-topical application.

Joyous Maths in a nutshell

This article maps out the key components in maths curriculum design: engaging trigger activities, authentic and meaningful contexts, opportunities to discover Maths (inductive reasoning), opportunities to apply Maths (deductive reasoning), and opportunities for cross-topical application (synergy). Authentic (can’t resist the pun!) extracts from our worksheets are provided for the reader to appreciate the thinking and effort that go into materialising these key components. It is the belief of Team Joyous that designing maths curriculum our way, the harder, more time-consuming and brain-sapping way, will pay off. As you can see, curriculum design is a serious science at Joyous Learning.

This article started off with a little chat about the movie Arrival. It is perhaps apt to conclude it by noting the following. In the movie, the two experts tasked with establishing communication with the extra-terrestrial beings are a physicist and a linguist. It is the physicist who discovers the encrypted recurring decimals in the extra-terrestrials' written language. With this discovery, the linguist was able to make a breakthrough in their mammoth task. Talk about cross-disciplinary cooperation!

Read part 1

Read part 2

Read part 3

Read part 4

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