The internet is overflowing with math teaching tips, tricks, and activities. And most of them work fine when you’re looking for fast lesson ideas.

But as classroom math teachers, we’re still left with one big, glaring question:

What are the best instructional strategies for math *in general*?

Here are 6 pillars of best practice math instruction that make for powerful learning experiences, no matter what curriculum, concept, or grade level you’re teaching.

## Prioritize conceptual understanding

For students to use mathematics flexibly and grapple with complex problems, they need more than memorized facts and procedures.

They need a deep understanding of mathematical *concepts* themselves.

Here’s how you make conceptual understanding a priority in your classroom:

### Use visual strategies

Making a concept visual allows students to see how an abstract concept translates to a physical scenario. Use illustrated problems or hands-on activities, and encourage students to use visual methods of their own (e.g. drawing) when solving problems.

### Use the schema approach

The schema is the underlying pattern behind a mathematical concept. All subtraction problems, for example, revolve around a certain amount of something being taken away from an original amount. Once students grasp the schema, they’ll be able to notice it in a diverse array of different problems.

To do this, put similar word problems (e.g. addition ones) side by side and help students discover what they have in common. See if they can express this in words that might apply to other problems of the same type.

### Explicitly teach the math vocabulary of a concept

Show the different ways a concept might be expressed in words. Addition, for example, might be expressed as two quantities “together” or a “combined amount”. Once they broaden their math vocabulary, they’ll be able to use concepts much more flexibly

## Use cooperative learning strategies

Cooperative learning has three major benefits in math:

- It encourages students to verbalize their mathematical thinking, which in turn gives them greater clarity of thought and self-awareness of their own problem-solving strategies.
- Communicating with others exposes students to different mathematical approaches, which they can use to think more flexibly.
- It mirrors the way math is done outside the classroom, where people with different strengths work together to solve challenging real-world problems.

Here’s how you can use cooperative learning strategies effectively in your math classroom:

### The “puzzle pieces” approach to group work

Use the “puzzle pieces” approach, where each learner is given a unique piece of information to share with the rest of the group to solve a problem. That way every student has to get involved, and everyone has something to contribute regardless of ability level. (Tip: find some examples of puzzle piece activities in our article on enrichment.)

### Take time to reflect

Build in reflection time after a collaborative activity for students to reflect on what worked, which strategies they found helpful, and how being exposed to other ways of reasoning has made them think differently.

### Be strategic when allocating groups

A mix of ability levels will mean top-level students can consolidate their understanding by guiding the activity, while others can learn from more experienced peers.

## Ask meaningful open-ended questions

The best mathematical questions push students into territory where there is no clear-cut “right or wrong”. This is where reflective, creative mathematical thinking starts to happen.

Here are three questions you can use to transform a routine class discussion into one that makes students think, “I’ve never thought of it like that before…”

### “Tell me how you solved that”

Instead of congratulating a student when they get an answer correct and moving on, ask them to talk you (and the rest of the class) through their approach. This achieves two things:

- The student is encouraged to reflect on their own thought process in detail. Instead of just “doing the math” automatically, they’ll understand exactly the steps they took – and begin to see how these might be adapted to future, more challenging problems.
- Other students get the opportunity to see how they could have solved the problem, even if they struggled to do so originally.

### “Did anyone approach this problem differently?”

Asking students to elaborate on different approaches to the same question highlights that there is no single, correct way of doing the math. Moreover, students might discover some new mental math tips or strategies from their peers that they can use in future activities.

### “Does this problem remind you of anything else we’ve done before?”

Before students start shrugging their shoulders in response to an unfamiliar problem, ask them if it reminds them of anything they’ve done before.

They’ll start to recognize previously encountered concepts underneath the surface. This habit of checking for familiarity is what produces flexible and agile mathematical thinkers.

## Focus on problem-solving and reasoning

In the world beyond the classroom, mathematics takes the form of complex problems as opposed to questions. For this reason, the most effective instruction equips students with the problem-solving and reasoning skills they’ll need for real life.

### Teacher tips

Use these guidelines to set rich and challenging problems:

- Make problems open-ended. Instead of funneling students to a particular solution, keep it open to different approaches.
- Set problems that approximate relevant real-world scenarios.
- Set problems that encourage students to collaborate.
- Don’t spell out exactly what students need to do. Let them trial different procedures until they settle on a strategy that works instead.

Find three examples of great problem-solving tasks __here__.

## Start with direct instruction

Direct instruction (also known as “explicit teaching”) provides students with a systematic breakdown of a mathematical concept, before giving them an opportunity for guided practice. In most classrooms it looks something like this:

- The teacher introduces a mathematical concept, connecting it with concepts students understand already.
- The teacher models the math skill to be learned, breaking it down step by step – usually with visual aids.
- Students follow precise instructions to use the skill themselves in a scaffolded, step-by-step way.
- The teacher checks for understanding at each step and provides feedback.

Direct instruction is particularly effective in math because it breaks down complex operations into small, achievable steps. That way, students don’t get lost – and you can pinpoint the precise stages at which students need extra help.

### Teacher tip

When modeling a skill or procedure to students, talk through all your thinking steps – even when you’re not writing. You’ll be surprised by how many “mental moves” you go through to solve even a simple problem, so take it slow and support your explanations with visual aids where possible.

## More instructional strategies for math

### Math activities

STEM activities for elementary students

### Concept-specific instructional strategies

How to teach subtraction with regrouping

How to teach addition with regrouping

### Other instructional strategies for math

Strategies to support struggling math students