There is an evidence base that can guide teachers to implement effective mathematics lessons. To begin with, we need to know what to teach and how best to teach it. The *how*part is often the most challenging.

Explicitly teaching maths skills and concepts is an effective approach. But what does explicit teaching mean? When is it used? And what is the best way to incorporate explicit teaching into your maths instruction?

Online modules to support teachers in the explicit teaching of mathematics have been created in partnership with the Australian Association of Mathematics Teachers (AAMT). They are designed for primary school teachers; however, the explicit teaching approach is certainly useful for secondary teachers as well.

The explicit teaching approach incorporates a range of teaching strategies to develop deep mathematical learning and understanding. Explicit teaching can be incorporated into many aspects of your teaching. For example, setting goals and explaining how students will know if they have succeeded is explicit teaching. Directly explaining, demonstrating or modelling maths concepts and skills is explicit teaching. Providing clear and concise feedback is also explicit teaching.

Explicit teaching can be used:

- in any maths lesson
- at various times throughout a lesson
- with the whole group, a small group, or with individual students
- for different purposes such as modelling examples, explaining thinking and demonstrating strategies.

Explicit maths teaching can be broken into seven components. Understanding these seven components allows us to know how to plan and implement maths content using this best-practice approach.

A podcast discussing each of the seven components of explicit teaching is available on the Maths Hub podcast page. These 30-minute podcasts complement the content of the explicit teaching modules.

Let’s unpack the components of explicit teaching further.

**Planning**

Explicit teaching takes careful planning! This planning involves:

- setting goals
- selecting engaging learning tasks
- sequencing learning to build on skills and knowledge
- preparing scaffolds for students, to use as required.

Effective planning also involves knowing the curriculum and knowing your student’s strengths and learning needs.

**Learning needs**

The students in your class have a range of abilities, skills, knowledge and understandings about maths. Tailoring your teaching to these various learning needs requires you to know where your students are at. Assessment is key to this. Find out what your students know about the topic, and then you can plan accordingly.

To meet individual needs, you might consider:

- open-ended tasks
- flexible groupings
- explicit instruction at the point of need.

These strategies allow you to gently ‘push’ each student past their current understandings and skills. The new learning should be challenging for them, without being too difficult.

**Questioning**

There are many purposes for asking questions in the classroom, and using a variety of questions helps support student learning.

- Closed questions – used to gather information about a students’ understanding.
*What is the answer?* - Open-ended questions – used to encourage thinking and provide insight into problem solving and mathematical reasoning.
*What would you do to solve this problem if the height was doubled?* - Reflection questions – used to encourage students to think about their answers and give reasons or explanations for them.
*Are you sure that is the correct answer? How do you know?* - Probing questions – used to extend students’ thinking.
*What other strategy could work here? How else could we find the answer?*

By considering the types and purposes of the questions you ask, you can make your questioning even more effective.

**Dialogue**

Explicitly building a shared mathematical language about the topic being taught has many benefits. It allows students to:

- explain their thinking
- make connections
- ask relevant questions
- share ideas and understandings
- learn from their peers.

Encouraging and facilitating rich classroom discussion supports students to feel a sense of collaboration and helps them to make sense of new concepts and knowledge.

**Modelling**

Modelling mathematical concepts, strategies, skills and understandings is all about showing your students *how*. It involves giving clear, easy to understand explanations, and demonstrating what you would do to solve a problem or complete a task.

The think aloud strategy is key to modelling. As the name indicates it involves explicitly telling your students what you are thinking as you complete a task. This strategy involves using a shared mathematical language as you explain your reasoning – what you did and why.

**Feedback**

Giving explicit feedback is most likely a natural part of your teaching tool kit. It is, however, something that you can refine and continue to improve on.

When providing feedback on a students’ understanding of a new maths concept or development of a skill your feedback should:

- be clear and concise
- explain what the student did well, their strengths and what they understand
- point out and explain any misunderstandings
- suggest ways to improve or move forward.

And don’t forget, there is a whole range of ways that feedback can help both you and your students such as peer feedback, whole-class feedback, one-on-one feedback and teacher-to-teacher feedback.

**Connections**

We know that it is good practice to connect already known knowledge and embedded skills to new learning. Doing this explicitly reinforces these vital connections.

One way to ensure you are building connections is to use the learning intentions and success criteria of the lesson as an anchor. At the beginning of the lesson make these goals clear. During the lesson, circle back to explicitly remind students of the goals they are aiming for. Once the learning goals are met, clearly discuss ways that this new learning can be extended or applied for further practise.

As you can see, explicit teaching can be integrated throughout your mathematics teaching. If this summary has sparked your interest, and you’re keen to find out more, then sign-up to __The Maths in Schools: Explicit Teaching in Maths__ learning modules. This self-paced, professional leaning course offers five modules that are designed around the seven components of explicit teaching.

The modules are aligned to the Australian Institute for Teaching and School Leadership__ __ (AITSL) professional standards, and they include lessons and activities you can use to teach maths concepts from the Australian Curriculum__ __.

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to The Mathematics Hub

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