Some titles write themselves.
It’s been a while, but we haven’t forgotten about ACARA and their appalling curriculum. We’ve whacked the curriculum plenty, but there are still a few whacks left on our to-do list.
One of the revolting aspects of modern maths education (and all modern education) is the invasion of “technology”, the idiotic idea that a computer or a TV or a calculator is invariably going to make things more meaningful or fun or 21st century, or something. Perhaps there are instances where this true, although we’re yet to be convinced. Even if true, however, in most scenarios the introduction of such technology is simply destructive, nothing but a distraction from the proper business of teaching. ACARA’s idiotic curriculum is, of course, no different and worse.
The Australian mathematics curriculum is strangled by ACARA’s technology fetishism. The term “digital tools”, for example, appears 123 times, and of course there are many occurrences of the companion words, “virtual” and “software” and so forth. We cannot possibly even list all such usages, let alone critique them. But we do what we can.
Below are the fifty-two curriculum content descriptors that refer to the use of electronic technology in some explicit manner. A reminder, the content is considered to be the, um, content: the mandated material to be taught. This is to be contrasted with the elaborations, which are optional, simply suggestions on how to teach the content. So, what follows are fifty-two instances of ostensibly mandated uses of electronic technology; by contrast, telling students about lowest common multiples or greatest common divisors, for instance, have the status of suggestions.
And one other reminder: ACARA promises that they are not telling teachers how to teach.
FOUNDATION
name, represent and order numbers including zero to at least 20, using physical and virtual materials and numerals (AC9MFN01)
represent practical situations involving addition, subtraction and quantification with physical and virtual materials and use counting or subitising strategies (AC9MFN05)
represent practical situations involving equal sharing and grouping with physical and virtual materials and use counting or subitising strategies (AC9MFN06)
YEAR 1
recognise, represent and order numbers to at least 120 using physical and virtual materials, numerals, number lines and charts (AC9M1N01)
partition one- and two-digit numbers in different ways using physical and virtual materials, including partitioning two-digit numbers into tens and ones (AC9M1N02)
add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies (AC9M1N04)
use mathematical modelling to solve practical problems involving additive situations, including simple money transactions; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem (AC9M1N05)
use mathematical modelling to solve practical problems involving equal sharing and grouping; represent the situations with diagrams, physical and virtual materials, and use calculation strategies to solve the problem (AC9M1N06)
acquire and record data for categorical variables in various ways including using digital tools, objects, images, drawings, lists, tally marks and symbols (AC9M1ST01)
represent collected data for a categorical variable using one-to-one displays and digital tools where appropriate; compare the data using frequencies and discuss the findings (AC9M1ST02)
YEAR 2
recognise, represent and order numbers to at least 1000 using physical and virtual materials, numerals and number lines (AC9M2N01)
acquire data for categorical variables through surveys, observation, experiment and using digital tools; sort data into relevant categories and display data using lists and tables (AC9M2ST01)
YEAR 3
use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation (AC9M3N06)
describe the relationship between the hours and minutes on analog and digital clocks, and read the time to the nearest minute (AC9M3M04)
acquire data for categorical and discrete numerical variables to address a question of interest or purpose by observing, collecting and accessing data sets; record the data using appropriate methods including frequency tables and spreadsheets (AC9M3ST01)
create and compare different graphical representations of data sets including using software where appropriate; interpret the data in terms of the context (AC9M3ST02)
YEAR 4
develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder (AC9M4N06)
use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation (AC9M4N08)
recognise line and rotational symmetry of shapes and create symmetrical patterns and pictures, using dynamic geometric software where appropriate (AC9M4SP03)
acquire data for categorical and discrete numerical variables to address a question of interest or purpose using digital tools; represent data using many-to-one pictographs, column graphs and other displays or visualisations; interpret and discuss the information that has been created (AC9M4ST01)
conduct statistical investigations, collecting data through survey responses and other methods; record and display data using digital tools; interpret the data and communicate the results (AC9M4ST03)
YEAR 5
solve problems involving multiplication of larger numbers by one- or two-digit numbers, choosing efficient calculation strategies and using digital tools where appropriate; check the reasonableness of answers (AC9M5N06)
solve problems involving division, choosing efficient strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction (AC9M5N07)
use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems, choosing operations and efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation (AC9M5N09)
create and use algorithms involving a sequence of steps and decisions and digital tools to experiment with factors, multiples and divisibility; identify, interpret and describe emerging patterns (AC9M5N10)
describe and perform translations, reflections and rotations of shapes, using dynamic geometric software where appropriate; recognise what changes and what remains the same, and identify any symmetries (AC9M5SP03)
acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data (AC9M5ST01)
YEAR 6
apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers (AC9M6N04)
solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies and using digital tools where appropriate (AC9M6N07)
use mathematical modelling to solve practical problems, involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made (AC9M6N09)
recognise and use combinations of transformations to create tessellations and other geometric patterns, using dynamic geometric software where appropriate (AC9M6SP03)
YEAR 7
use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation (AC9M7N09)
manipulate formulas involving several variables using digital tools, and describe the effect of systematic variation in the values of the variables (AC9M7A06)
create different types of numerical data displays including stem-and-leaf plots using software where appropriate; describe and compare the distribution of data, commenting on the shape, centre and spread including outliers and determining the range, median, mean and mode (AC9M7ST02)
conduct repeated chance experiments and run simulations with a large number of trials using digital tools; compare predictions about outcomes with observed results, explaining the differences (AC9M7P02)
YEAR 8
recognise terminating and recurring decimals, using digital tools as appropriate (AC9M8N03)
use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate (AC9M8N04)
use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model (AC9M8N05)
graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution (AC9M8A02)
experiment with linear functions and relations using digital tools, making and testing conjectures and generalising emerging patterns (AC9M8A04)
describe the position and location of objects in 3 dimensions in different ways, including using a three-dimensional coordinate system with the use of dynamic geometric software and other digital tools (AC9M8SP03)
conduct repeated chance experiments and simulations, using digital tools to determine probabilities for compound events, and describe results (AC9M8P03)
YEAR 9
recognise that the real number system includes the rational numbers and the irrational numbers, and solve problems involving real numbers using digital tools (AC9M9N01)
identify and graph quadratic functions, solve quadratic equations graphically and numerically, and solve monic quadratic equations with integer roots algebraically, using graphing software and digital tools as appropriate (AC9M9A04)
experiment with the effects of the variation of parameters on graphs of related functions, using digital tools, making connections between graphical and algebraic representations, and generalising emerging patterns (AC9M9A06)
apply the enlargement transformation to shapes and objects using dynamic geometry software as appropriate; identify and explain aspects that remain the same and those that change (AC9M9SP02)
analyse reports of surveys in digital media and elsewhere for information on how data was obtained to estimate population means and medians (AC9M9ST01)
design and conduct repeated chance experiments and simulations, using digital tools to compare probabilities of simple events to related compound events, and describe results (AC9M9P03)
YEAR 10
recognise the connection between algebraic and graphical representations of exponential relations and solve related exponential equations, using digital tools where appropriate (AC9M10A03)
experiment with functions and relations using digital tools, making and testing conjectures and generalising emerging patterns (AC9M10A05)
design, test and refine solutions to spatial problems using algorithms and digital tools; communicate and justify solutions (AC9M10SP03)
design and conduct repeated chance experiments and simulations using digital tools to model conditional probability and interpret results (AC9M10P02)
From the point of view of using technology (electronic or not) to help learn a mathematical idea, the most important lesson I have learned is:
if a learner needs technology, they need it until they don’t, and after that it should put away.
The putting away bit is not well practiced. As such, the technology goes from learning support to primary way of doing. Moving on can thus be hard.
By placing all this tech in the content, rather than the elaboration, ACARA is not even granting the teacher the choice.
Nor providing the advice/wisdom to …
Well, to be fair, I think ACARA’s stock of wisdom is a little low.
At least they put in the caveat “where appropriate” in some of them, mostly beyond grade 3 after most of the damage is done.
Yeah, sure. As if ACARA considers that a teacher is permitted to interpret “where appropriate” as “never”.
I returned to teaching after 30 years thinking that computers would make teaching much easier. Now I’ve realised they are a great negative in so many ways with few benefits. (And that’s not even touching on the role of CAS calculators).
If you want proof that even on ACARA’s own terms, technology doesn’t work, all you have to do is to try and navigate the Australian Curriculum – it is virtually unintelligible (as distinct from the much simpler Singapore).
Try and understand this! Grade 4 maths https://v9.australiancurriculum.edu.au/f-10-curriculum/learning-areas/mathematics/year-4?view=quick&detailed-content-descriptions=0&hide-ccp=0&hide-gc=0&side-by-side=1&strands-start-index=0&subjects-start-index=0
Thanks, JJ. I assume you mean the curriculum is unnavigable, rather than unintelligible, but it is both.
Maybe this is splitting hairs, but I could navigate to the right page but then I couldn’t make any sense of that page.
If we can’t understand something easily, it may be because of the presentation or it may be because it’s unintelligible.
I am guessing that there are some niche applications that require hyperlink format to make sense. I know that a curriculum isn’t one of them (as Singapore has shown).
So then the question is that either ACARA has chosen the wrong technology for its curriculum or its curriculum is so complex and unintelligible that it needs hyperlinks.
Either way, a piece of research would be to survey teachers anonymously to see how much they understand it. And then ask the Minister for Education to have a go.
The challenge to ACARA would simply be to present the curriculum in a format that is intelligible to teachers (and parents) and the Minister.
Thanks, JJ. Definitely not splitting hairs. I just wasn’t sure, of the many valid complaints, which one you were making.
In terms of the website, yes, it takes effort to design something that dysfunctional. I think *part* if it is due to the “multidimensional” twaddle that ACARA claims as the framework for the curriculum: that means directions are going every which way, all for no purpose. But it’s not just that. The website is clearly designed with the purpose of being Impressive rather than functional.
In terms of the writing, yes, it is appalling. It is still on my to-do list to specifically hammer this, although there’s already been plenty of drive-by hammering on other posts.
That JJ finds the ACARA page (once found) “unintelligible” suggests that s/he comes to it with a prior mental framework that is mathematically and educationally relatively rich.
By contrast, think of the *young* new teacher, who may not have had a privileged education, and for whom what s/he finds is seen as “authoritative” – and is all they have to work with. They must somehow *make* it all intelligible (presumably by accepting the implicit/explicit axioms as being “required”, and then trying to implement an approximation). Unless you/we are missing something, they will work at this for a few years (as everyone has to in those early years), and will then have to make sense of the observed outcomes (namely, that something isn’t delivering). Some may give up in despair. Some will hang on in there, trying to rationalise their everyday (Australian) experience – which may well require them to reset the base line by deciding that some things which used to be routine are in fact “terribly subtle and difficult”.
A very few will look elsewhere and discover that it doesn’t have to be like this.
Keep up the good work!
Thanks, Tony. I honestly have no idea whether teachers (attempt to) read the curriculum, even those teachers that are open to the idea that the curriculum has some merit.
When I taught last year for a term, I cannot remember once the teachers discussing what was to be taught in terms of the (previous) curriculum. In the main, one followed the (appalling) textbook, dressed up with some (appalling) add-on activities. God knows what primary school teachers do, where there is no textbook, good or bad, to guide them.
I consulted the curriculum as I have a Remedial maths class and wanted to know what level of primary maths they were at and what I should aim to cover – needless to say I couldn’t find it. And of course there are no primary textbooks.
Thanks Tony – you’re right, but it’s not only mathematical education (Honours in Pure Maths), it’s probably more life experience – I’m older and spent 25 years in the bureaucracy and no longer even try to believe nonsense when my experienced gut tells me something otherwise (though I’m open to dialogue/critical examination of the research). I know how little we know and that time is the best test of anything and if it’s been done in a certain way for centuries, there’s probably a good reason for it. People like Dylan Wiliam resonate with me when he says that we really don’t know how people learn.
There are now so many shibboleths in education that my gut says need to be questioned [including differentiation when staff-student ratios are the same as 30 years ago, learning intentions/success criteria – when I (let alone students) can barely understand many I see on the web, lack of textbooks in primary – who wants to reinvent the wheel, CAS calculators when even I find them unintuitive, computers in the classroom for students – when I see kids lose so much time Alt-tabbing, teaching without direct instruction – I, like Craig Barton, learned the hard way, use of the term ‘evidence based’, when even ‘evidence informed’ is a stretch, the idea that modern reports are of any use, when I don’t even read my daughter’s etc etc].
As you say, a young person will go with the flow. Not quite sure how you change that more quickly, except a long political battle. And even then, this blog is one of the few ‘safe spaces’ to say such things.
Indeed as you say to Marty – keep up the good work.
Huh. I read it as Tony telling you, and like teachers, to keep up the good work. You’re the guys still trying, against all odds, to teach people.