In companion with our post on ACARA’s senior curriculum review, this post is for people to comment on Essential Mathematics. The curriculum can be viewed here and downloaded here.

## UPDATE (02/04/24): GENERAL COMMENTS

Having now read the current Essential Mathematics curriculum with a little (but not a lot of) care, I thought to add a few comments. Here, I’ll make some general comments about the curriculum, and then in a later update I’ll list particular content items that seemed weird or annoying. Note that these comments relate to the curriculum document as a functioning (or not) document, and only tangentially to the curriculum content. It is not clear that there is any current purpose in critiquing the underlying curriculum. In any case, since I have little sense of the meaning or purpose, if any, of Essential Mathematics, I’m not the person to do so.

To begin, when printed the curriculum document is about 40 pages long, of which about 15 pages is devoted to the actual curriculum content, the rest being a very strange not-this-glossary glossary and, mostly, ACARA’s standard blather. The blather is mostly ignorable, and ignored, but one element must be highlighted (p 13):

**Intercultural understanding in Mathematics**

Students understand Mathematics as a socially constructed body of knowledge that uses universal symbols but has its origin in many cultures. Students understand that some languages make it easier to acquire mathematical knowledge than others. Students also understand that there are many culturally diverse forms of mathematical knowledge, including diverse relationships to number and that diverse cultural spatial abilities and understandings are shaped by a person’s environment and language.

This social construction garbage appears to play no active role in the senior mathematics curriculum, but it is garbage and it should be called out for the garbage it is.

Generally, the Essential Mathematics curriculum document is tedious and repetitive, annoying in the entirely predictable ACARA manner. Consider, for example, the advice on the use of illustrative context examples in the four units:

However, these contexts may not be relevant for all students, and teachers are encouraged to find a suitable context that will make the mathematical topics of this unit relevant for their particular student cohort.

Does this advice really need to be repeated four times, in the space of half a page? Similarly, there is advice on the use of technology:

It is assumed that an extensive range of technological applications and techniques will be used in teaching this unit. The ability to choose when and when not to use some form of technology, and the ability to work flexibly with technology, are important skills.

This advice also appears four times, and then a fifth time with slightly different wording.

It is the same throughout. The clear priority in writing the document was to make sure all bases were always covered: the many “priorities”; the various “dimensions”; all the purportedly meaningfulling twaddle that makes the Australian curriculum so meaningless, and here makes the document a bloated, unreadable, and unread, mess. To be clear, the Essential Mathematic curriculum document is not distinctly worse than the usual; it is pretty much the usual. Which is bad.

There is one final aspect of the curriculum worth noting. The document begins with an overview of the senior Australian curriculum generally, including a discussion of the role of a national curriculum within the Federal system (p 4):

State and territory curriculum, assessment and certification authorities are responsible for the structure and organisation of their senior secondary courses and will determine how they will integrate the Australian Curriculum content and achievement standards into their courses. They will continue to be responsible for implementation of the senior secondary curriculum, including assessment, certification and the attendant quality assurance mechanisms. Each of these authorities acts in accordance with its respective legislation and the policy framework of its state government and Board. They will determine the assessment and certification specifications for their local courses that integrate the Australian Curriculum content and achievement standards and any additional information, guidelines and rules to satisfy local requirements including advice on entry and exit points and credit for completed study.

The senior secondary Australian Curriculum for each subject should not, therefore, be read as a course of study. Rather, it is presented as content and achievement standards for integration into state and territory courses.

The point seems to be for ACARA to give itself the license to present an It’s The Vibe curriculum, a license which it duly takes. The Essential Mathematics curriculum is vague even by the vague standards of the F-10 curriculum.

I’m not really sure I understand any of this, the real purpose of such a “national” “curriculum”, and I’m not sure why the F-10 curriculum and the senior curriculum should be different in this respect. You either present a curriculum or you do not, and it is either adopted or it is not. None of this appears to me to have much purpose other than to maintain ACARA’s busy-ness and (self) importance.

## UPDATE (03/04/24): CONTENT ITEMS

The following are Essential Mathematics content items that, at least on the quick reading I gave it all, particularly annoyed me. (There were other contents, as well as annoying aspects of the curriculum that cannot be properly highlighted in this manner.) These are items that seemed poorly worded or vague to the point of meaninglessness, or similar. Perhaps some of these items are fine with a more careful reading or in context. (On the flip side, for some of the items the context is helpful to understand why they are arguably not fine.) In any case, the items annoyed me. If anyone wishes to argue their merits, they are of course welcome to take it up in the comments.

These items are in order, by unit and topic. I will, however, begin with my favourite line, an “examples in context” from Topic 1 of Unit 4:

using data to calculate the relative frequencies of the amounts of household expenditure is this sentence incomplete?

This over-complete sentence appears to have been part of the curriculum for at least six years. Here, now, are the rest.

expressing ingredients of packaged food as percentages of the total quantity, or per serving size, or per 100 grams

comparing the quantities, both numerically and in percentage terms, of additives within a product or between similar products, such as flavours

use leading digit approximation to obtain estimates of calculations (ACMEM004)

apply approximation strategies for calculations. (ACMEM010)

determine one amount expressed as a percentage of another (ACMEM012)

convert units of rates occurring in practical situations to solve problems (ACMEM015)

comparing and discussing the components of different food types for the components of packaged food expressed as grams.

use metric units of length, their abbreviations, conversions between them, and appropriate levels of accuracy and choice of units (ACMEM017)

understand the relationship between volume and capacity (ACMEM028)

estimate volume and capacity of various objects (ACMEM029)

draw a line graph to represent any data that demonstrate a continuous change, such as hourly temperature. (ACMEM042)

investigate real-world examples from the media illustrating inappropriate uses, or misuses, of measures of central tendency and spread. (ACMEM056)

use ratio to describe simple scales. (ACMEM070)

find the surface area of pyramids, such as rectangular- and triangular-based pyramids (ACMEM096)

recognise the need for milligrams (ACMEM099)

recognise relations between volume and capacity, recognising that 1cm^{3} = 1L and 1m^{3} = 1kL (ACMEM102)

use formulas to find the volume and capacity of regular objects such as cubes, rectangular and triangular prisms and cylinders (ACMEM103)

recognise the properties of common two-dimensional geometric shapes and three-dimensional solids (ACMEM105)

use symbols and conventions for the representation of geometric information; for example, point, line, ray, angle, diagonal, edge, curve, face and vertex. (ACMEM107)

apply the tangent ratio to find unknown angles and sides in right-angled triangles (ACMEM117)

apply the cosine and sine ratios to find unknown angles and sides in right-angled triangles (ACMEM119)

describe the faults in the collection of data process (ACMEM134)

find the line of best fit by eye (ACMEM141)

interpret relationships in terms of the variables (ACMEM143)

interpret commonly used probability statements, including ‘possible’, ‘probable’, ‘likely’, ‘certain’ (ACMEM148)

describe ways of expressing probabilities formally using fractions, decimals, ratios, and percentages. (ACMEM149)

identify relative frequency as probability (ACMEM152)

locate positions on Earth’s surface given latitude and longitude using GPS, a globe, an atlas, and digital technologies (ACMEM159)

understand the link between longitude and time (ACMEM162)

solve problems associated with time zones; for example, internet and phone usage (ACMEM166)

review the principles of simple interest (ACMEM168)

understand the concept of compound interest as a recurrence relation (ACMEM169)

It sound like their goal is to make the document so bland and full of meaningless blather that no one will want to read it

My intuition says its because they can then cloak their intentions because everyone is to bored to notice what they are actually doing. That’s why I am happy there are people like yourself who do read through it with a fine tooth comb in order to expose the garbage.

No that’s too conspiratorial. It’s incompetence, not malevolence.

Incompetence definitely plays a significant role I agree. I do apologize, I’ll refrain from attributing intentions I have no way of knowing.

Perhaps I find it difficult to believe the inclusion of social constructivism in a Mathematics Curriculum could be attributed solely to incompetence.