Explicit Teaching Strategies: Connecting Learning

Explicit teaching is most effective when students can connect new learning to what they already know.

In the NSW Department of Education's explicit teaching strategy resources, connecting learning is identified as a key practice. It involves helping students make links within and across knowledge, skills and understanding, as well as to prior learning experiences (NSW Department of Education, 2026).

In maths, this is especially important. Concepts do not sit in isolation. Fractions connect to decimals, decimals connect to percentages, algebra connects to patterns, and measurement connects to geometry. When students can see how ideas relate to one another, they are more likely to build deeper understanding and apply their learning with confidence.

Connecting learning helps students see maths as a connected body of knowledge, rather than a series of separate topics.

What does connecting learning mean?

Connecting learning means helping students link new information to what they have already learned.

This might involve revisiting prior knowledge, drawing attention to related concepts, comparing strategies or showing how a new skill builds on something students already understand.

The NSW Department of Education explains that teachers support students to make connections within and across learning to develop increasingly complex schemas (NSW Department of Education, 2026). A schema is a connected structure of knowledge in long-term memory. When students build stronger schemas, they can draw on prior learning more easily and use it to understand new ideas.

The Australian Education Research Organisation (AERO) also highlights that learning involves changes to long-term memory, and that explicit instruction supports students by making new information clear and manageable (AERO, 2024).

For example, before teaching students how to compare fractions with unlike denominators, a teacher might revisit:

Students already know how to:

• identify the numerator and denominator
• compare fractions with the same denominator
• find equivalent fractions
• multiply to create common denominators

This gives students a foundation to build on before moving into the new concept.

Why connecting learning matters in maths

Maths is cumulative. New concepts often rely on earlier knowledge, and gaps in understanding can make future learning harder.

A student who does not understand place value may struggle with decimals. A student who has not developed fluency with multiplication may struggle to calculate the area of a rectangle, and without a solid grasp of area, working out the volume of a prism becomes harder still. A student who does not understand inverse operations may struggle when solving equations.

Connecting learning helps students understand how concepts build on each other. It also reduces the chance that students see maths as disconnected procedures to memorise.

Rosenshine's principles of instruction emphasise the importance of reviewing previous learning, as review helps strengthen connections between material students have already learned and supports more fluent recall when they need that knowledge for new learning (Rosenshine, 2012).

The Education Endowment Foundation also highlights the importance of taking account of prior knowledge when planning instruction, as understanding what students already know helps teachers anticipate misconceptions and respond more effectively (Education Endowment Foundation, 2021).

What connecting learning looks like in a maths lesson

Connecting learning can happen through short, intentional moments across a lesson.

For example, in a lesson on solving one-step equations, the teacher might begin by connecting the new learning to students' prior understanding of inverse operations:

"Last lesson, we looked at how addition and subtraction are inverse operations. Today, we are going to use that idea to solve equations."

The teacher can then model a problem such as:

x + 7 = 15

As they solve it, they make the connection explicit:

"To isolate x, I need to undo the +7. Since subtraction is the inverse of addition, I subtract 7 from both sides."

This helps students see the reasoning behind the process, rather than simply following steps.

Connecting learning through gradual release

Connecting learning fits naturally into the I do, we do, you do structure of explicit teaching.

During the I do stage, the teacher models the connection between prior knowledge and the new concept.

During the we do stage, students practise making those connections with guidance. The teacher might ask:

• What have we learned before that can help us here?
• How is this similar to the example we just completed?
• Which strategy could we use, and why?

During the you do stage, students apply the new learning independently while drawing on the connections made explicit earlier in the lesson.

The NSW Department of Education notes that connecting learning is not about asking students to find connections without teacher guidance, or simply referring to a previous activity without explaining how it links to new learning (NSW Department of Education, 2026). The teacher's role is to make the connection clear, purposeful and relevant.

Common challenges when connecting learning

One common challenge is assuming students have retained prior knowledge. A concept may have been taught earlier, but that does not always mean students can recall or apply it when needed.

For example, students may have learned equivalent fractions in a previous unit, but when they begin adding fractions with unlike denominators, they may not immediately see that equivalent fractions are the key connection.

Another challenge is making links too broad or vague. Saying "we have done something like this before" may not be enough. Students need to understand exactly what prior learning is relevant and how it supports the new concept.

Connecting learning is most effective when it is:

Specific: Students know which prior knowledge is being used.

Explicit: The teacher clearly explains the connection.

Purposeful: The connection helps students understand or apply the new learning.

Revisited: Connections are reinforced through review, questioning, modelling and practice.

Mathspace's approach to connected learning and the skills map

At Mathspace, connecting learning isn't just something we ask teachers to do lesson by lesson, it's built into the structure of the platform itself. Underpinning this is Mathspace's skills map: related skills are grouped into a "skills focus," which lays out the sequence in which understanding develops within that skill area across year levels, rather than treating each syllabus year as a separate, self-contained set of content.

Because the skills map spans grade levels, teachers and students can see where a given skill sits in a longer progression, what it builds on, and what it leads to next,  instead of only encountering that skill in isolation within the current year's work. Students can also change their skills focus directly from the skills map, moving to a different point in the progression as their understanding develops.

For more on the thinking behind this, you can explore our webinar on the Victorian Maths Curriculum with Erin Gallagher, Mathspace's Global Head of Education, where she talks through the skills map and how it supports connected learning across year levels.

Supporting connected learning with Mathspace

A lot of connecting learning happens in the moment, in the room. But it starts earlier than that, with teachers knowing, before the lesson even begins, whether their students are ready for what comes next.

Checking readiness before the lesson

In our Years 7–10 resources, every topic comes with a lesson plan that sets out the prior knowledge required, along with a checkpoint teachers can use to confirm students are ready before moving into the new concept.

This is the "making connections explicit" idea in practice. Rather than assuming students remember a prerequisite skill, the connection is named upfront and checked, so teachers can see readiness before the lesson starts rather than discovering a gap partway through it.

The lesson plans also follow the same I do, we do, you do structure, so the gradual release of the connection, from modelling, to guided practice, to independent application, is built into the lesson from the start.

Making connections visible

During explicit instruction, Mathspace's step-by-step solutions can help teachers model how new learning connects to previous concepts.

For example, when solving equations, teachers can show how inverse operations connect to balancing both sides of an equation. When working with percentages, teachers can show how percentages connect to fractions and decimals.

This helps students see the structure behind the method, rather than treating each topic as a separate set of rules.

Highlighting gaps before they become barriers

Behind the scenes, Mathspace's skills maps are built from a knowledge graph that maps how skills relate to one another across the curriculum. This is designed to surface prerequisite gaps ahead of time, so teachers can see where a student may need support before a new topic is introduced, and begin preparing them in advance rather than responding once the gap causes difficulty in class.

As students practise, Mathspace also gives teachers ongoing visibility of where they are succeeding and where they may be struggling. If students are having difficulty with a new topic, the issue may not always be the new concept itself. It may be a gap in prior knowledge, for example, a student struggling with algebraic substitution may actually need support with negative numbers or order of operations.

Together, this gives teachers two points of visibility: gaps flagged ahead of the lesson, and gaps that emerge as students work, so review and differentiation can be targeted rather than guesswork.

Building connections over time

Making a connection once is a start, but it is not the same as it sticking. Our new primary product is being built with spiral review embedded throughout, so that concepts are revisited over time rather than left behind once a topic ends. Repeated, spaced review like this is designed to keep strengthening the connections between concepts the longer students use it, rather than treating each topic as done once it's been taught.

A practical classroom example

Imagine you are teaching students to calculate percentages of quantities.

The learning intention might be:

We are learning to calculate percentages of quantities.

The teacher might begin by connecting the concept to prior learning:

"We already know that 50% means one half, 25% means one quarter, and 10% means one tenth. Today, we are going to use that understanding to calculate percentages of different amounts."

The teacher then models an example:

Find 25% of 80.

Instead of presenting this as a new rule, the teacher connects it back to fractions:

"25% is the same as one quarter, so finding 25% of 80 means finding one quarter of 80."

Students can then work through guided examples before moving into independent practice on Mathspace. As they work, the teacher can monitor whether students are connecting percentages to fractions correctly or whether they need more support with the earlier concept.

Supporting consistent, connected teaching practice

Connecting learning is most effective when it happens consistently, not just in a single stand-out lesson. Mathspace supports this throughout the teaching process, helping teachers:

• Check prior knowledge and readiness before a new topic begins
• Make connections explicit while modelling
• Spot prerequisite gaps ahead of time and as students practise
• Revisit and reinforce concepts over time through spiral review

You can incorporate these into your existing lessons without changing your overall approach. If you'd like to hear more about how the skills map supports this, the webinar mentioned above is a useful place to start.