Authentic contexts are contexts taken from real life. Maths problems situated in authentic contexts help students relate better to what they are learning. Besides this, doing Maths in authentic contexts trains students to continue using their mathematical skills in everyday situations, beyond exams. Compare Extracts C and D, from a Joyous Learning Primary 5 topic Numbers to 10 million.
In 2015, Mr Chan’s company earned $2,732,000 in January, $2,106,000 in February, $1,171,000 in March, $1,044,000 in April and $1,014,000 in May. What is the average monthly earnings of Mr Chan’s company in these five months?
In 2015, the top five countries that contributed to Singapore’s International Visitor Arrivals were Indonesia (2 732 000), China (2 106 000), Malaysia (1 171 000), Australia (1 044 000) and India (1 014 000). What is the average International Visitor Arrivals from these five countries in 2015?
Source: Singapore Tourism Board
It is clear that Extract D is a better word problem than Extract C. But why?
The first reason is related to the point of authenticity. Extract D, taken from our Primary 5 maths worksheets, is based on current affairs: statistics on Singapore tourism. Singapore tourism, as a key economic sector of this island, is something students should be exposed to, even if they were totally unfamiliar with it (but this is unlikely for Singaporean students). Conversely, even if Extract C had been based on real-life information, students would not have related to revenue of a company easily.
Hence, authenticity does not automatically equate to meaningfulness; this is not merely a semantic issue. Creating authentic context for maths problems must not be mistaken as random picking of figures and information, which brings us to the second reason.
The meaningfulness of the context must be considered. The key feature of 'Numbers to 10 million' is raising the ceiling of numbers that students have to deal with. The mathematical operations (addition, subtraction, multiplication and division) are not new to them. Hence, one of the objectives, if not the main objective, in teaching this topic must be to nurture students’ confidence in handling numbers to ten million, not just in exams but also in their lives. Such confidence is not likely to come about when students handle the numbers in artificial contexts.
The next extract (Extract E) is based on population figures of Singapore. If we want our students to discuss and write about wider social issues, beyond the trivial happenings, we have to equip them with the fundamentals. This is not to say that students are expected to memorise the population figures; no, it is to help them feel comfortable in using phrases like “a total population of five million” and “a resident population of nearly four million” in discussions, whether it is with their foreign friends or in their school essays.
As of the end of June 2016, the total population of Singapore was 5 610 000 and the resident population was 3 930 000. Total population comprises both residents and non-residents of Singapore while resident population comprises Singapore citizens and permanent residents.
What was the population of non-residents in Singapore at the end of June 2016?
Round your answer in (a) and the total population of Singapore at the end of June 2016 to the nearest million. Then, express the population of non-residents in Singapore as a fraction of the total population in Singapore.
We sometimes lament our students’ lack of concern about issues of their community and environment. However, social issues are dynamic and bear historical context, so it is daunting for young people to “dive” into them. Even adults experience “cold starts” when reading about unfamiliar issues. Yet, we need not despair. Knowing facts like names of residential towns, their relative resident population (see Extract F) and location is a useful starting point to gently ease students into investigating more complex issues. After all, we certainly want such discussions to be empirically grounded!
Below is a breakdown by town of the estimated resident population living in HDB flats in Singapore (as on 31st March 2015 as reported by HDB). Study the data and answer the questions that follow:
Circle the names of the three towns with the greatest resident population (living in HDB flats).
Underline the names of the three towns with the least resident population (living in HDB flats).
How many towns have resident population (living in HDB flats)
(i) below 100 000? (ii) between 100 000 and 200 000? (iii) above 200 000?
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