What makes a great maths curriculum?

Written By Brad Nguyen

Photo by Chris Liverani on Unsplash

Having a clear idea of what a quality maths curriculum entails is an important first step to improving student outcomes.

It’s exciting that increased attention is being given to the quality of maths instruction. The Grattan Institute just published The Maths Guarantee, a report on the state of maths education in Australia and what can be done about it. The Victorian Government is now providing better advice on how to teach maths with the Victorian Teaching and Learning Model 2.0 and its increased focus on explicit teaching. But all this advice can seem like a lot at once for schools looking to improve their practice: Out of all these recommendations, where should we start?

From my experience, ensuring you have a great maths curriculum is a good place to start. A specific and well-sequenced maths curriculum has a great ‘multiplier effect’: it helps teachers plan effectively, it defines the content for explicit teaching and it makes it possible to plan how students will review content, become more fluent and develop mastery.

So what makes a great maths curriculum? I’d argue that a great maths curriculum has 3 components: (1) a plan for acquisition of skills and knowledge; (2) a plan for the review of content to promote long-term retention; and (3) a plan for students to develop fluency in foundational skills. In this blog, I’ll talk about these three components in more detail.

Acquisition

When evaluating a maths curriculum, we want to make sure there is a clear plan for how skills and knowledge are acquired. We want to check for the following:

SPECIFIC - A maths curriculum has to be specific enough to describe in detail what is taught and when. It can’t just be curriculum descriptors copied and pasted from the state curriculum. For example, consider this Vic. Curriculum Level 1 descriptor:

add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies

Sure, this gives us a general direction, but what specific calculation strategies are we talking about? This has to be elaborated in a school’s maths curriculum and the school needs to know when strategies are taught so that review activities can be planned that are aligned with what has been taught. Much better, for example, to specify that in term 1, first graders learn to add within 10, including:

  • Making the parts, then counting all

  • Counting on

  • Doubles

Then in term 2, first graders might progress to adding within 20, including:

  • Making 10

  • Split strategy

  • Doubles

  • Near doubles

CUMULATIVE - A maths curriculum has to build knowledge and skills cumulatively. The progression between lessons and between units should be clear. Here’s an example of progression between lessons, using the topic of subtracting from 3-digit numbers using a standard algorithm:

  • Subtraction with no regrouping

  • Subtraction with regrouping once (regrouping from the tens, or from the hundreds)

  • Subtraction with regrouping twice (first from the tens, then from the hundreds)

  • Subtraction with regrouping from the hundreds (where there is a 0 in the tens place)

An example of progression between units might involve students mastering subtraction from 3-digit numbers and then, in a subsequent unit on length, being asked to apply that skill to solve a problem involving length. In other words, progress in one strand of maths needs to be reflected in the other strands.

COMPREHENSIVE - A maths curriculum has to comprehensively teach the content detailed in the state curriculum. If each descriptor can be linked to some part of the teaching and learning program, that’s a good start but this should be treated with nuance: How much time does each descriptor need? Some, like developing proficiency in addition and subtraction, require a concerted effort over many weeks. Other learning goals, like reading a grid map, don’t require the same amount of time.

COHERENT - A great maths curriculum is coherent across year levels. Lots of the details of maths instruction is a matter of culture: which concrete materials, what language, which mental strategies, what written algorithms. For example, even teaching the standard addition algorithm involves choices: If the ones add to 10 or more, do you write the digit 1 in the tens column at the top or at the bottom? Do you write ‘1’ or ‘+1’? One way is not fundamentally better than the other, but it is better for students if teachers align on these choices rather than go in different directions driven by personal preferences. Aligning on the concrete materials used doesn’t mean ‘We only use MAB’ or ‘We only use place value discs.’ It means there is some logic to how the curriculum progresses from using MAB to using place value discs and if at some point we return to using MAB, it is for good reason. These choices shouldn’t be haphazard.

PROBLEM SOLVING - A great maths curriculum doesn’t just teach students addition, subtraction, multiplication and division. It teaches students to apply those skills to solve problems. This means that opportunities to solve problems are embedded in the curriculum including routine word problems and non-routine problems. This also means explicit teaching of strategies for solving word problems, including bar modelling, identifying problem types (or schemas) and metacognitive supports like attack strategies.

Review

If we really care about students actually retaining what we teach, there needs to be a plan for how content is reviewed so that knowledge is embedded in long-term memory. We want to check for the following:

SPACED - This means having a system for students to engage in retrieval practice days, weeks, months after content is initially taught. People have turned retrieval practice into a complicated science, but any system for spaced retrieval practice is better than none.

RESPONSIVE - I’m of the opinion that the content included in review needs to be responsive. You can’t plan it all at the start of the year and press play. It needs to be planned in response to teachers’ assessment of student needs. This make the review curriculum different from the acquisition curriculum. Perhaps students bomb on a particular assessment item, so the teacher includes similar items in daily review. Perhaps students have trouble with just one specific step of a complex task, so the teacher designs deliberate practice in that sub-skill. Perhaps the teacher notices students are proficient in a strategy but don’t know when to apply it, so they interleave problems so that students have to think carefully about what strategy to use.

Fluency

If students are to progress to more complex problem solving, they need to develop fluency in the sub-skills needed so that working memory is freed up. We want to check for the following:

FOCUSED - Fluency practice needs to be focused on the foundational skills of retrieving basic facts in addition, subtraction, multiplication and division. Other foundational skills involve subitising, counting, written strategies and dealing with fractions. Not everything in maths can be practised to fluency with the same level of intensity, so prioritising is a must.

ROUTINE - Fluency needs to be developed through a familiar format that occurs regularly. It can’t happen once a week. It needs to happen little and often, around 5 minutes a day.

SYSTEMATIC - The content of fluency practice needs to build up systematically in a controlled way. You can’t just ask students to roll 2 dice and multiply the numbers if they have just learned their 2 times tables. You need a system to control the numbers that students are dealing with. This is why printed materials are not a bad thing. Apps that can provide students with a personalised problem set are excellent for this.

Once we have a clear idea of what a great maths curriculum looks like, we are in a better place to know how to improve. We can audit our current practices to see what is missing or what needs improving. We can evaluate curriculum materials to see if or how they might be useful. Improving maths instruction is a complicated matter, but getting curriculum right is a good start.

Brad Nguyen is a primary teacher, learning specialist and consultant.

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Brad Nguyen