Since the curriculum was first published in 2010, Australia has performed poorly on international tests in mathematics. This revision provides a rare opportunity to get Australia back on par with our economic peers around the world. Unfortunately, it has fallen short in some key areas.

First and foremost, this revision does not reflect an increased focus on fractions. The current and proposed curriculum seriously lags in the development of this important idea. For example, compared to other countries it greatly delays the teaching of the four basic operations involving fractions. All other countries, who are usually compared to Australian education, are at least two years ahead on teaching operations of fractions. Addition and subtraction of fractions is expected by the end of Year 5 in all Asian, European and North American countries. In Australia, work with addition and subtraction is not completed until Year 7. The development of multiplication and division of fractions is similarly delayed in Australia.

A second but perhaps more important issue with teaching fractions in the Australian curriculum is the lack of time spent on finding equivalent fractions – the necessary prerequisite to work with the four operations. In particular, there is a total absence of two crucial skills involving work with equivalent fractions. These skills include specific work with:

a. finding common denominators. (This is the same as finding the lowest common multiple of two given numbers.)

b. simplifying a fraction or reducing it to lowest terms. (This is the same as finding the greatest common divisor of two numbers – the numerator and the denominator.)

Additionally, when teaching fractions, there is an overemphasis on ‘whole-to-part’ thinking. That is, the idea of taking a whole, breaking it into equal parts and naming each part. Young students also need ‘part-to-whole thinking’. For example:

In this interpretation, the numerator is seen as the count of equal-sized parts and the denominator tells how many equal-sized parts are needed to make a whole. Similarly, they need to see fractions as division. Three pizzas shared among 4 people is 3 ÷ 4 = ¾, so they each receive ¾ of pizza. Other countries explicitly include these interpretations in their curriculum documents. They also include specific strategies for comparing fractions. Most readers would probably make a common denominator to compare 3/7 and 5/8. But a student could be encouraged to reason that 3/7 is a little less than ½ and 5/8 is a little greater one than one half – so why use a common denominator?

The proposed revision does not include alternative comparison strategies (for which there are many) or other interpretations of fractions such as ‘part-to-whole’ thinking or viewing fractions as division. The proposed mathematics curriculum would be stronger if it included explicit descriptions of these vital concepts and skills.

Several minor tweaks have been made to other F-6 content that we can support and manage. But there is one other ‘elephant in the room’ that really needs to be raised.

ACARA’s model for showing the relationship between the six strands and three core concept organisers does little to help the reader understand how everything is connected.

[Source: P.6. Australian Curriculum: Mathematics – All elements F–6]

Mathematics is a clear-cut subject and this model and the descriptions that accompany it only serve to make mathematics cloudy. For example, here is their description of ** mathematising** – a new word, introduced by a highly-paid American consultant.

**“Mathematising – **the process of seeing the world using mathematics by recognising, interpreting and representing situations mathematically. Core concepts important to mathematising draw on the concepts related to mathematical structures and approaches and are …..”

[Source: P.7. Australian Curriculum: Mathematics – All elements F–6]

While we are not against the introduction of new words, the reader needs to be wiser and better for using them. Why do we need a new word to replace those that we know and have used for decades? It makes us wonder if we will be *sciencising* sometime soon!

Furthermore, it is bewildering that a USA consultant was used when the US falls well behind Australia on international tests. We should be talking to our counterparts in Singapore who consistently rank 1 or 2 on these same tests.

We encourage ACARA to review their proposed content descriptions considering what other key countries now do in the teaching of fractions. Unless significant professional learning is provided to teachers during their working week, we also suggest that they develop a better model and simplify its terminology.

Educators interested in learning how to interpret and implement the Australian mathematics curriculum can join our webinar series commencing 10 August 2021.

**James Burnett and Dr Calvin Irons co-founded ORIGO Education in 1995. **