5 Proven High-Impact Teaching Strategies in Mathematics

Decades of research have shown that students learn mathematics more effectively and retain their learning when they have opportunity to explore conceptually, reason, make connections, and think deeply about concepts.² The research also shows that all students are capable of learning and growing their mathematical capacity.³ But if you gather a collection of students in a classroom and set them to work on their own with high-quality instructional materials, will their activities naturally ignite into deep mathematical learning? Not likely, without a strong educator to steer their thinking. There is an “inextricable connection between teaching and learning”⁴ of mathematics because the learning of mathematics is a deep, complex, active process. No matter the setting, grade level, culture, or environment, one thing remains true: Teachers are essential!  

In recent years, Professor John Hattie’s research on visible learning has emerged from a synthesis of thousands of studies that measured the effect size of interventions on student learning.⁵ The research focuses on many factors that impact student learning, including factors related to home, students, teachers, classrooms, schools, and curriculum. Using effect size as a measure of impact, Hattie’s work highlights those factors that have greater than average effect size, yielding more than one year of growth for a year of input. When we narrow the list to factors that are within a teacher’s control, several strategies rise to the top.  

Big Ideas Learning empowers teachers by purposefully integrating five of the teaching strategies proven from Hattie’s most recent meta-analysis⁶ to have some of the greatest impact on student achievement: Teacher Clarity, Feedback, Classroom Discussion, Spaced Practice, and Direct Instruction. Armed with these high-impact strategies, teachers have the power to accelerate learning for ALL students. 

1. TEACHER CLARITY  
Teacher clarity begins with a teacher’s organization, delivery, and communication of learning goals as well as clearly delineated success criteria so students can measure where they are in their learning. But it doesn’t stop there. Teachers who use this high-impact strategy allow the learning goals to shape their instruction, developing an intentional learning pathway with frequent feedback relative to the learning outcomes. Regardless of the learning activities, teachers communicate through mathematically focused probing questions, checking in frequently to connect students’ experiences back to the learning goals, monitoring learning, and adjusting as a result.  

National Council of Teachers of Mathematics’ Effective Teaching Practices recommends establishing clear goals for the mathematics that students are learning, situating goals within learning progressions, and using the goals to guide instructional decisions.⁷ When teachers are aware of the big ideas of mathematics and the learning progressions and goals underpinning those big ideas, they are empowered to leverage mathematical activities to drive student understanding toward meaningful learning.

2. FEEDBACK  
This strategy refers to an integral part of teaching with intent, where the underlying goal is reducing the gap between where a student is at any given time and where they are going based on the success criteria.⁵ Feedback is a two-way strategy, where teachers (1) actively listen as they probe for student understanding to drive instructional decisions, and (2) provide feedback using prompts and cues to help students advance toward learning goals. Through feedback, teachers see where students are in their learning and make instructional decisions determining where to go next.

Feedback from a teacher has the power to open student thinking or close it down. Hattie’s research⁵ shows that feedback’s effects can vary significantly and that some key aspects of high-impact feedback include being timely and actionable. This type of timely, actionable feedback is at the core of effective teaching practice Elicit and Use Evidence of Student Thinking,⁷ which emphasizes teachers' listening and assessing role as they monitor student progress toward understanding and adjust instruction to bring students to the next step in their learning. 

3. CLASSROOM DISCUSSION

Classroom discussion describes an open course dialogue that promotes communication of mathematical thinking between students. This dialogue involves active participation from students who share their ideas and strategies and evaluate and ask questions of their peers’ approaches to solving problems.

Although the teacher plays a vital role in facilitating productive classroom discussions, the teacher is not the center of this discussion which focuses on students’ voices. Meaningful mathematical discussion solidifies students' understanding while honing their ability to reason and construct arguments. 

Student discourse becomes even richer when students Use and Connect Mathematical Representations,⁷ communicating their ideas not only verbally but using visual, symbolic, contextual, and physical representations. 

 4. SPACED PRACTICE

When practice is broken up into multiple, shorter sessions over a longer period, it is referred to as spaced practice, and the strategy is proven to accelerate learning. By contrast, mass practice means fewer long-practice sessions. Providing spaced practice, accompanied by feedback and reflection opportunities, helps students to build a solid understanding and make connections between mathematical topics.

In essence, spaced practice enables students to build procedural fluency from conceptual understanding. As practice with a key concept is spaced over time, students can use various methods and gain a repertoire of strategies they can call upon to solve mathematical problems accurately, efficiently, and flexibly.⁹   

5. DIRECT INSTRUCTION
Although direct instruction is sometimes equated with the transmission of knowledge from an active teacher to a passive student, this is not its intended meaning. Direct instruction involves seven steps, including:

1. Teacher defining clear learning intentions, 
2. Teacher identifying success criteria aligned with those intentions, 
3. A hook to build students’ engagement,  
4. A guide for how the lesson will be presented with key lesson elements,  
5. Guided practice with feedback from the teacher,

6. A closure to help students organize, consolidate, and reinforce their learning, and  
7. Independent practice so students can gain mastery of the content.⁶

The Common Core State Standards for Mathematics emphasizes mathematical rigor as a balanced approach leading to equal focus on three aspects of learning: Conceptual Understanding, Procedural Fluency, and Application. A balanced approach to instruction that includes both inquiry-based learning and direct instruction enables students to attain a deeper understanding of concepts with discovery and exploration activities, while building procedural skills and applying them in a direct instruction model. 

Purposeful Focus 
As educators, many of the things we do can have a positive effect on student learning, but purposefully focusing on teaching strategies in mathematics has been proven to have the highest impact on student achievement. It 43rexddnot only accelerates learning, but molds students in the process, making them independent mathematical thinkers capable of interacting with their world. 

About the Author

Amy SanFrotello is a seasoned product leader with over three decades of experience contributing to K-12 mathematics programs at Big Ideas Learning and Larson Texts. For ten years, she has had the privilege of leading product vision and is passionate about bringing meaningful product to the classroom for deep student learning. In her present role as Director of Product Research Application, she brings visibility to how product features exemplify and are grounded in educational research and best practices. Amy holds a B.S. in Applied Mathematics from Penn State Erie.

About California Math & YOU 

California Math & YOU is a comprehensive, pedagogically rich K-12 mathematics program that builds a strong conceptual foundation for students through an immersive digital experience. Written by renowned author, Ron Larson, and his expert authorship team, California Math & YOU features engaging and relevant material that sparks students' curiosity and learning, while empowering teachers to successfully meet the needs of all learners. California Math & YOU is built on the California Mathematics Framework and is completely aligned to the California Common Core Standards (CA CCSS).

Learn More

References