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Engagement is essential to excellent math instruction, but can be elusive. In this article, we will share six simple ways to make your math class more engaging for students. Plus, download an *Interest Inventory* to share with students to support your engagement efforts.

*Engaging* is a word we hear often in education but rarely define. Webster’s dictionary defines engaging as “tending to draw favorable attention or interest, appealing, captivating, entrancing.” But how does one make mathematics entrancing?

The National Council of Teachers of Mathematics (NCTM) offers some guidance in *Principles to Action,* NCTM’s landmark publication which shares a vision for the future of mathematics education. This resource paints a picture of what engaging teaching should be: “An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically” (NCTM, 2000).

This means that during engaging lessons, students should be working together on challenging multi-faceted problems. These collaborative problem-solving scenarios will help them discover new aspects of the field of mathematics and connect math to the world around them. As students participate in these activities, they must make sense of the ideas presented and be able to explain why they work.

“An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically”

The research that guided NCTM to publish *Principles to Action* illuminated 6 guiding principles for effective teaching of mathematics, two of which are learning and teaching.

“Students must learn mathematics with understanding, actively building new knowledge from experience and previous knowledge” (NCTM, 2000). This type of learning is achieved through developing conceptual understanding. Students must be exposed to tasks that grow their knowledge and improve their procedural proficiency within contexts that are transferable to the real world.

In partnership with learning is a description of teaching: “an understanding of what students know and need to learn and then challenging and supporting them to learn it well.” Teaching cannot happen without learning and vice versa. Teachers must provide stimulating tasks based on their knowledge of the content and the math so that students want to be engaged.

The 8 Standards of Mathematical Practice further illustrate the necessity of students becoming fully immersed in mathematics as a process. The first standard states that students must be able to make sense of problems, be confident in their ability to solve them, and be willing to persevere in solving them (NCTM, 1991). In order for students to do so, teachers must offer engaging tasks that provoke students' curiosity and interest.

In partnership with learning is a description of teaching: “an understanding of what students know and need to learn and then challenging and supporting them to learn it well.” Teaching cannot happen without learning and vice versa. Teachers must provide stimulating tasks based on their knowledge of the content and the math so that students want to be engaged.

Creating math lessons that meet these high standards is no small feat, but it’s easy to get started in making lessons engaging.

Before you begin implementing any of the suggestions in this article, try to learn more about students’ interests by utilizing an *Interest Inventory*. This inventory will help teachers understand their students as individuals, thereby allowing them to design lessons that will be engaging for their students. Teachers or parents can support younger students in completing the inventory!

Completed inventories will be a helpful reference as you experiment with the six simple engagement-boosting ideas listed below; the ideas are listed by the amount of preparation they require.

**Idea #1 - Use a New Tool**

Try utilizing a new tool (like whiteboards, poster paper, sharpies, etc.). It is amazing the enthusiasm that is immediately sparked in students when a new tool is introduced. Suddenly the student who will never write a word with a pencil on paper shows their work for every problem using a marker and whiteboard. The introduction of new tools keeps students interested in learning and expressing their thoughts about how to solve problems using tools beyond paper and pencil. By using tools, students develop skills described in the 5th Standard of Mathematical Practice—knowing when and which tools are useful when faced with a problem.

**Idea #2 - Try Tech**

Kids simply want to use technology: computers, calculators, smart boards, virtual manipulatives, shared whiteboards . . . anything that involves a power button. The challenging aspect of integrating technology for teachers is utilizing it in a purposeful and engaging way; just because an assignment is moved online does not mean that it will spark the interest of students.

Design opportunities for students to see and test what is not possible without the technology. Use observations from these explorations as evidence for deductive reasoning to discover a theorem or fact.

For example, in the grade 6 classroom, supplement geometry instruction with an exploration of GeoGebra, which can be used to create triangles with different side lengths and quickly so students can test many different combinations. The class might record what side length combinations make a triangle and which do not and then look for patterns to determine when a triangle can be made. Students should be able to deduce that the third side length must be between the sum and difference of the other two sides.

**Idea #3 - Think Universally**

Universal Design for Learning (UDL) encourages multiple ways of engagement, expression, and representation. The goal of the Universal Design for Learning guidelines is to create a framework to support teachers in designing learning experiences for all students. Each student is unique in the experiences they have had, the knowledge they hold, and the ways that they can learn best. Constantly challenge yourself to appeal to all types of learners. Deliver messages verbally, visually and orally. Implement activities that involve movement, art, and writing. Allow students choices of how they will represent their knowledge to you and watch their engagement grow.

**Idea #4 - Connect Across Disciplines**

Students are constantly asking why they are learning what they are learning. They are innately curious and want to understand how their understanding of math will help them exist in and make sense of the world around them. Using tasks that connect math to another discipline provides a reason for learning math. Math can be connected to science through experiments and data analysis. Math can be connected to social studies through figures and numbers of historical events. Math can be connected to reading through stories, like folktales, that bring content to life in a new way.

Using tasks that connect math to another discipline provides a reason for learning math.

**Idea #5: Explore Through a Problem**

Multiple Standards for Mathematical Practice call on teachers to provide real-world problems for students to solve. Try a problem-centered approach, by carefully selecting an authentic and deep problem which has multiple pathways for solving. As students begin to explore and make sense of the problem, they will eventually reach a point where they do not yet have the knowledge to move forward. This is when you teach the new concept. The most important part of learning through problem solving is the sharing and debriefing of students' work. During this time is when a teacher can clarify big ideas, emphasize vocabulary, and deepen and connect students' understandings (Trafton & Midgett, 2001).

**Idea #6: Utilize Metacognition**

Last but not least, challenge students to think about their own thinking. Requiring students to focus on multiple layers of thinking during a task will increase their engagement and dedication to the task. This is also how students will begin to understand who they are as a learner and what works best for them.

One common example is the Know, Wonder, Learn (KWL) approach. Students should use a 3 column graphic organizer to record what they already **know**, what they want to learn (**wonder**), and then later, what they have **learned** from the lesson. Doing such requires them to think about the way their brain is processing information while exploring any other content related topic (Little, 2009).

**In Summary**

Teaching for engagement requires creativity, flexibility, and a willingness to try new things. It’s essential and achievable for every classroom. Take the time to dedicate your efforts to one or a few of the engagement-boosting ideas in this article. Doing so will help you create more engaging lessons and offer new perspectives of the beauty of mathematical problems as you explore them more deeply with your students.

Resources

Little, M.E. (2009). Teaching Mathematics: Issues and Solutions *TEACHING Exceptional Chil- dren Plus, *6(1) Article 1. Retrieved [date] from http://scholarship.bc.edu/education/tecplus/vol6/iss1/art1

Furner JM, Yahya N, Duffy ML. Teach Mathematics: Strategies to Reach All Students. Intervention in School and Clinic. 2005;41(1):16-23. doi:10.1177/10534512050410010501

National Council of Teachers of Mathematics (NCTM). *Professional Standards for Teaching Mathematics*. Reston, Va.: NCTM, 1991.

National Council of Teachers of Mathematics (NCTM). *Principles and Standards for School Mathematics*. Reston, Va.: NCTM, 2000.

Pound, L., & Lee, T. (2010). *Teaching mathematics creatively*. Routledge.

Trafton, P. R., & Midgett, C. (2001). Principles and Standards: Learning through Problems: A Powerful Approach to Teaching Mathematics. *Teaching Children Mathematics*, *7*(9), 532-536.