Key takeaways
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Using a variety of math instructional strategies across the week keeps students engaged and helps identify gaps in understanding
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Strategies like number talks, math journaling, graphic organizers, and cooperative learning develop reasoning skills alongside math fluency
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Cultivating a growth mindset is the most important of all instructional strategies for math—it builds the confidence students need to persist through challenges
Teaching math is challenging, and many students have an aversion to math. That’s why it’s important to make learning math a positive experience for them. You have the power to change their mindset toward math. They may not always come away loving math, but at the very minimum, they can make peace with it!
As math educators, how can we do this? It’s all about engagement. And how do we create that engagement? We do this by using a variety of math instructional strategies over a week’s worth of lessons.
This article provides a springboard for several ideas to enliven your math lessons. You’ll come away with:
- 8 math instructional strategies that can be used across elementary grade levels
- A thorough explanation and examples for these strategies
- A clearer picture of why instructional strategies for math are important in assessing student understanding
1. “Common Sense” Number Talks
Offer students a problem and give them three different possible answers. Ask them to look at the problem without solving it and determine which answer seems most reasonable.
For example, Anita sees a price tag on a dress. The original cost of the dress was $85.95, but the sign says that there’s a sale—30% off the price tag. Here are three possible prices: $69.00, $53.95, $26.75. Which price would be the most reasonable estimate and why? Then, let students calculate the answer and compare it to their best guess. Which of the original possible prices was the closest? Did they guess it correctly? Have them explain their reasoning. Encourage them to look at the problem in different ways. What operations are they using mentally? Is there any answer they could cross out right away? What rounding and estimating techniques did they use before they actually solved the problem?
2. Math Journaling
Journaling is an effective tool in language arts and can also be a useful strategy in math class. Math journals, whether on paper or digital, provide students with a way to document their answers to open-ended problems. They can include diagrams and illustrations that display the process they used to solve a particular problem. In addition to these “show your steps” notes, journals can be used for student reflection. As their teacher, you can provide appropriate prompts, such as “What did you think was the most difficult part of this problem? Why did you use this particular pathway to solve the problem? Now that you’ve solved it, can you think of an easier route to get the answer?”
One of the key benefits of journaling is “metacognition,” which simply means it gives students an opportunity to analyze their own thinking. Their journal notes will not be shared in class, just with you, their teacher. Even though journal notes are not a formal assessment, the students’ reflections and displayed work will help you to determine areas where understanding can be improved.
3. Graphic Organizers
For students, one of the most difficult challenges is breaking down problems into manageable steps. Graphic organizers can be a huge help in this regard because they provide students with a visual process of categorizing aspects of problems. Before using a new graphic organizer in the classroom, show the students how it’s separated and how color-coding might be used where appropriate.
It’s a good idea to walk through a sample problem so they can get a feel for how the organizer can help them tackle the problem step by step. For a new topic, you can provide partially filled-in organizers to scaffold their fledgling reasoning.
For example, most students have some anxiety related to solving word problems. A graphic organizer mat specifically designed for word problems might be separated into five pieces. In the first box, students explain what they need to solve. In the second, they can list one or more strategies they might use to work toward a solution. In the third, they can explain their step-by-step process. In the fourth, they can provide their answer and their reasoning. Finally, in the last box, they can show how they checked their answer. Word problems are less threatening when they are broken apart in this way.
Another very useful graphic organizer is called the Frayer model. It’s perfect for building math vocabulary and understanding definitions. This organizer is divided into four areas, with the word you are working with in the center.
For example, suppose you’re introducing different types of polygons. The top left-hand box in the Frayer template can provide a definition. Then, students can fill out the top-right-hand box with some properties of that particular polygon. The bottom left box can show some matching examples of that polygon, and the bottom right can show some polygons that don’t match the definition, in other words, the nonexamples.
4. Cooperative Learning
Teaching in small groups has long been part of the instructional toolkit for math. Some teachers are reluctant to use this strategy for fear that the strongest students will dominate the other students in the group, and the others won’t do their part. The truth is that once students enter the world of work, much of their problem-solving will involve working in teams. Cooperative learning provides an opportunity for them to learn new math concepts in a collaborative environment, one that has the potential to increase both their math and social confidence.
It’s a good idea to set up some ground rules before using cooperative learning to work on new math skills. Encourage students to improve their active listening and communication skills. Ask them how they will handle conflicts if not everyone in the group agrees on how to resolve them. Inquire about how they will provide constructive feedback when it’s clear that some students are weaker than others in particular skills.
5. Math Games
Do you remember the game of hangman? You can use it to teach math vocabulary in a classroom setting. Divide the class into groups, then have each group take a turn to guess a letter. Will the class guess the math vocabulary word before the stick figure is drawn? Choose a long word with not too many repeated letters to make the game more challenging than usual. A dodecagon or an equiangular are some examples. After the word is guessed, you might segue to a Frayer model sheet to discuss definitions as well as examples/nonexamples.
Another fun game that gets kids moving and thinking is a place value competition. Give each student a card with a number. The challenge is to have them line up to form the largest possible number. Another variation of this game is to use decimals such as 0.14, 0.05, 0.006, 0.0007, and have the students arrange themselves in a line based on which value is the largest or smallest.
Beyond physical activities, many classrooms also find success by incorporating digital tools into their weekly rotations. By using a math program such as DreamBox Math, you can offer students a gamified environment to practice skills at their own pace on their own devices.
6. Differentiated Instruction
It’s no surprise that the students in your classroom learn best in different ways. Differentiated instruction strategies for math address diverse learning styles, skill sets, and environments. Some students might learn visually, some might learn best by listening, and some might learn best by working with manipulatives. In addition to offering students different ways to learn, another differentiated instruction strategy is to adapt your lesson plans to the range of each student’s skills.
The environment is also a factor. Some students learn best by reading a lesson aloud or watching you work through examples on the board or overhead. Others work best in small groups where they can learn from other students as well. Make the effort to carve out one-on-one time with each student at least once a week to hone in on weak skills. Varying your presentation several times a week ensures that you’re giving all the students in your class the best learning opportunities.
Another engagement strategy is to find out your students’ interests. Do some students love art? Are some excited by music or sports? Word problems in particular can be made more engaging by building them around students’ common interests.
7. Explicit Teacher Modeling
When introducing a new concept, you can model it for students step by step. “First, I’m going to show you how I would do this problem and the thinking I go through. Then, we’re going to do it together in class. Then you’re going to try solving the problem on your own.” A step-by-step walkthrough using manipulatives or drawings while you talk slowly through the process will help students understand that you still have to “think through” different ways to tackle a problem. Teachers don’t automatically know the answer! They have to use number sense and math reasoning, too.
8. Growth Mindset
Probably the most important of all math instructional strategies is to display a growth mindset in the classroom. Some historical examples might be useful here. Even geniuses like Albert Einstein complained about their mathematical challenges. If a student says, “I’m not good at math,” you might share that you weren’t automatically good at math either. Practice and an embrace of challenges with excitement are solid virtues for the mathematics student to cultivate. Encouraging these traits will help them both in math and in life. At the start, emphasize developing a deep understanding of math and a trial-and-error mindset. Timed practice and tests can come later once students have developed the confidence to move quickly.
Using different math instructional strategies in your classroom will help you identify where students are catching on and where their understanding is slow or incomplete. Although this type of observation provides qualitative, not quantitative data, it’s still incredibly valuable information you can use to adapt and enrich your future lessons.
