What makes a good maths resource?

  • 5 minute read
  • 11 July 2022

As we enter the second half of the year, it’s time for teachers to start thinking about the maths resources they’ll use in 2023. Although once limited to textbooks, teachers today can choose from a whole range of resource options, making the decision more difficult than ever before.

In many ways, when we choose a maths resource we’re choosing the types of learning experiences our students can have. Not only will the resource often outline the content that will be taught and the sequence it will be taught in, it often also suggests how teachers should engage students in these topics. That means teachers need to look for a resource that incorporates evidence-based teaching and learning practices to ensure they’re selecting the most effective option available. 

In this blog, we identify five elements of an effective maths resource to help you as you explore all the options out there for 2023. 

Well scaffolded to develop deep understanding (mastery)

When teaching maths, we want students to develop a deep understanding so they can apply what they’ve learnt and connect this knowledge to new information later down the track.

Yet so many maths resources don’t focus on mastery. Many miss opportunities to truly connect topics and others seem to silo topics completely. Others still focus on gamifying maths, making it fun without the substance. And most are designed to push students through content whether they’re ready or not, leaving room for mistakes and misconceptions that lead to learning gaps. 

Effective resources do things very differently. Firstly, they will understand that maths is learnt on a continuum. Students must learn one concept before they can move on to the next. According to the ‘Matthew effect’ students who miss concepts or skills can find it difficult to master new concepts down the track. Because if they don’t master the foundations, learning new concepts further along can be difficult, or even impossible. Struggling students then become less motivated and problems compound. Resources must therefore scaffold content so students can master concepts along their maths journey. 

A great resource will also take into account the different gaps and competencies each student has so it can deliver each student content within their Zone of Proximal Development. This means students will be challenged enough to remain engaged but have the foundation knowledge to experience success in the content they’re learning. It’s a personalised experience many traditional resources can’t provide, but with research continually supporting the effectiveness of this approach it should be high on the list of things to look for when choosing a maths resource for 2023. 

Questions to ask:

  • How does this resource scaffold content?
  • How does it promote mastery?
  • What does the resource define as mastery and how does it measure it?

Caters to different learning levels 

One major challenge maths resources need to overcome is providing content for students who are at different learning levels. Research shows that students learn best when they’re learning the content that they’re ready for. They often become more engaged, more confident in their mathematical abilities and more interested in the subject when they learn this way.

But many traditional resources struggle to deliver this type of personalised learning. What’s needed is a responsive program that can diagnose student understanding then deliver curriculum-aligned content that takes into account any gaps that may exist. While teachers can deliver diagnostics then select appropriate worksheets for students, this process, particularly when applied to a class of 20+ students, is very time consuming. Not only does it require initial diagnostics or formative assessments, summative assessments should also occur to ensure mastery is achieved and misconceptions are resolved. 

Resources that leverage technology can support teachers through this process by using data from assessments to determine what content students are ready to learn, then delivering that content.

This is one of the reasons that schools across Australia are implementing Maths Pathway — to support teachers to target their teaching using a holistic approach. The model leverages technology to deliver diagnostics and ongoing formative assessments. This provides teachers with live, actionable student data that’s easy to access. It also ensures students get the right content, which consists of carefully scaffolded learning activities that work to build students’ understanding, fluency, problem solving and reasoning skills. Leaving teachers with more time to focus on what matters — teaching their students.

Students using the model master twice as much curriculum in one year as they would in a traditional classroom. Better still, this progress is sustained by students too.

Questions to ask:

  • How does this resource cater to different learning levels?
  • Does it take a streaming approach or a truly personalised learning approach? Read more about streaming vs. personalised learning here.
  • How will it challenge students at the top of the class and support those who are catching up?

Be very critical about the resources you use, and don’t use them just because you have them available to you!
Dr. Catherine Attard

Uses assessment that are proven to work

An effective assessment isn’t just defined by how well aligned it is to the learning objectives it is seeking to measure. For it to be truly effective it needs to provide every student with the opportunity to demonstrate their knowledge, so teachers can identify gaps, plan content and measure progress.

That means when considering resources for assessments we need to think about how they will be perceived by the students undertaking them. Will they understand the question? Will it be too hard or too easy? Will the example make sense to some students and not others? 

While some resources may test their assessments before publishing, others are taking it a step further. Online programs have the benefit of leveraging technology to collect data that can accurately determine how effective an assessment is in real time. Unfortunately, not many resources actually do this. But Maths Pathway captures data from the 80,000 students using our model to continual improve and iterate assessments. If thousands of students are tripping up on the same question, our Learning Team knows about it and they can fix it quickly. Even something simple like a typo can be resolved in minutes. But this continuous improvement isn’t just limited to assessments.

Assessments can also show us when the content we’ve delivered wasn’t well scaffolded or didn’t cut through with students. Again, using data from our students, Maths Pathway can identify trends that allow us to iterate our content to be the best it possibly can.

Questions to ask:

  • What data does this resource have on the effectiveness of its assessments?
  • How static are the assessments? Can they be adapted easily if something isn’t quite right?
  • Do the results of the assessments form a feedback loop with the topic content to ensure it’s as effective as it can be?

Easy to understand

As touched on above, language plays a really important role in the effectiveness of maths content and assessments. Students using maths resources won’t just be at different levels in maths, they’ll also be at different levels in literacy. Students need to apply their literacy skills to comprehend worded mathematical problems before they even apply their maths knowledge to solve it. So if a literacy error occurs, their maths knowledge might not be correctly applied. 

Maths itself also has its own vocabulary that students must become familiar with. According to a study by Di Gisi and Fleming there are three types of vocabulary that students need to be able to solve word problems in maths:

  • Mathematics vocabulary
  • Procedural vocabulary
  • Descriptive vocabulary

 
This means the best resources need to do two things. Firstly they must use clear, concise language so they’re easy for all students to understand. And secondly, they need to support students to develop the three types of maths vocabulary.

Questions to ask:

  • Does this resource use clear, concise language?
  • Does it cover all three types of maths vocabulary?

Promotes a range of learning experiences 

Students learn best in environments that promote a range of different learning experiences. One that incorporates independent, collaborative and whole class learning, alongside practices like rich tasks and maths projects targeted explicit teaching. Individually, these approaches to learning and teaching have benefits ranging from the promotion of critical thinking and active learning to increased confidence and reduced anxiety.

In a classroom that promotes all of these experiences, students are given the opportunity to learn from others, to experience different ways of thinking and to clarify their own thinking.

When evaluating possible maths resources, look at how they structure learning activities. Those that incorporate the above modes will give students more opportunities to experience maths and learn in different ways.

Questions to ask:

  • What types of learning experiences does this resource promote? Will students learn individually, in pairs, groups and as a whole class?
  • Does this resource include rich tasks, robustly assessed projects and targeted explicit teaching?
  • How does this resource promote active learning?
Author: Maths Pathway
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