Pictured above: Students from partner school Lakewood Elementary actively engage in exploring different ways to solve math problems and share their thinking.
By: Meg Bowen
The Paradox: Why Does Low Math Achievement Persist Despite Higher Quality Instructional Materials?
Selecting high-quality instructional materials (HQIM) for math has become much easier now that objective third-party curriculum resource reviews such as EdReports are readily available. Most math textbook publishers now use the same criteria and high standards established by EdReports to guide the development of curriculum resources, resulting in better alignment to standards, improved focus on the major work of each grade level, and integration of mathematical practices throughout lessons.
So why do so many math classrooms today look virtually the same as math classrooms twenty years ago? Why hasn’t student math achievement skyrocketed as a result of improved curriculum resources? These questions have confounded districts across the country after investing so much in high-quality instructional materials for math.
The Classroom Experience
Imagine walking into a math classroom and hearing a steady hum of student discourse as students explain their thinking and challenge teammates to explore different ways to solve problems. Contrast that with a classroom where students are silently solving problems individually and then passively watching as the teacher demonstrates how to solve those same problems. Which classroom experience do you think better supports student engagement and ultimately improves math achievement? The difference isn’t the curriculum. The difference is the model of instruction.
The Missing Ingredient
What’s missing from improved curriculum resources? A model of instruction that:
- Transforms the teacher’s role from directly instructing students on how to solve problems to facilitating and coaching.
- Enables students to build their own understanding by working on rigorous tasks collaboratively in interdependent teams.
Some teacher guides in curriculum resources encourage teachers to give students time to grapple with problems, but none provide the structures and tools required to successfully launch student-led team learning. Those teacher guides don’t explain how to ensure students are engaging in productive struggle and reaching that sweet spot where deeper learning happens.
“I was so used to rescuing students before; sometimes I’d have 12 kids calling my name. It was overwhelming. Once students started working in teams, I realized that the more I take myself out of it, the more the kids become engaged and self-reliant through productive struggle. Students are checking each other’s thinking, debating, finding consensus, and having aha! moments in their teams. I remember one time I asked them, ‘Look, do you guys want me to just tell you how to find the answer?’ And they said, ‘No! No, we will figure this out.’ That had never happened before in my eight years of teaching at the time. It was amazing.”
Samantha Topps-Brown
Mathematics Teacher at North High School, Des Moines Public Schools (quoted in The Power of Student Teams, p. 94-95).
An Instructional Model That Complements Any Curriculum
Instructional Empowerment’s Model of Instruction for Deeper Learning TM bridges the gap between HQIM and pedagogy, providing teachers and leaders with the structures and tools needed to move quickly from teacher-led classrooms to student-led team learning where student agency, engagement, and achievement soar. Deeper learning of the curriculum occurs as students collaborate in teams with rich discourse on rigorous tasks that prepare them for academic and real-world success. Implementation progressions outline the intended outcomes for each step of the journey, with toolkit components crafted to support both students and teachers along the way.
Example: Math Task in Teacher-Directed vs. Student-Led Team Learning
The same lesson from the same curriculum can result in a totally different student learning experience, depending on which model of instruction you implement.
8th Grade Math Standard: 8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
Traditional Teacher-Directed Instruction task:
(1) The teacher delivers a detailed lecture explaining the angle sum property of triangles and the exterior angle theorem, using diagrams on the board or slides.
(2) Students copy notes and watch as the teacher demonstrates how to solve related problems.
(3) Students work independently on a worksheet, solving problems such as:
-
- Calculate the measure of an exterior angle given two interior angles.
- Identify missing angles in a triangle based on provided values.
(4) The teacher circulates to answer questions. Students primarily work alone, with little peer interaction or opportunity to explore their reasoning.
Student-Led Team Learning task:
(1) Through an abbreviated mini lesson, the teacher provides just enough foundational information to set students up to engage in productive struggle.
(2) As a team, students read the task directions, look at the examples, and talk about how to use the team mat.
(3) Individually, students use the examples to do an exploration and write an informal argument about the measure of an exterior angle of a triangle.
(4) Teams engage in peer discourse and come to team consensus. They write the team’s informal argument in the middle of the mat.
(5) Individually, students create an example to test the team’s informal argument.
(6) As a team, students share and compare examples and determine if the team’s informal argument held true for all examples.
Key Benefits of the Model of Instruction for Deeper Learning
Opening Access to a Rigorous Math Curriculum for All Students
As noted in the recent article published by The 74, “Why Teachers Don’t Use the High-Quality Instructional Materials They’re Given,” many educators feel their students cannot handle the rigor of HQIM and therefore look elsewhere for lesson material (Steiner, 2024).
The power of student-led teams lies in their ability to leverage and build on each other’s strengths, achieving more together than they ever could individually. One of the most common reactions teachers have after they begin implementing the Model of Instruction for Deeper Learning is, “I had no idea my students could do that!”
Improved Teacher Capacity and Professional Satisfaction
Teachers no longer need to turn to social media for learning activities because the Model of Instruction for Deeper Learning teaches educators how to transform adopted math curriculum problems into highly engaging rigorous tasks worthy of interdependent teams. With no script to follow, teachers rediscover the joy of teaching as they coach student teams to utilize their student resources and find viable solutions rather than ask the teacher.
Increased Math Achievement and Student Engagement
Students look forward to engaging with their team as their sense of self-efficacy dramatically increases. Math class becomes a dynamic environment where students think like mathematicians and connect their learning to real-world applications. And those disappointing math scores on state assessments? Those become a distant memory just like the math class of twenty years ago.
About the Author
Meg Bowen, M. Ed., has spent more than thirty years in the field of education serving students, teachers, and administrators in North Carolina, Virginia, Maryland, and Florida. A graduate of the University of North Carolina Charlotte and James Madison University, Ms. Bowen completed doctoral coursework in curriculum at the University of Maryland.
Ms. Bowen has developed curriculum and supported its implementation in both elementary and secondary settings. After serving for several years as Assistant Principal and Principal, she became the Director of Elementary Curriculum for one of the nation’s largest school districts. Ms. Bowen now serves as the Executive Director of Customer Experience and Growth at Instructional Empowerment (IE), where she works diligently to ensure districts value partnering with IE so much that they continue to collaborate with us even after they achieve their initial goals. She encourages partner schools to reach and achieve model school status, where all students are engaged in rigorous learning activities and achieve their full potential.
References
Steiner, D. (2024). Why teachers don’t use the high-quality instructional materials they’re given. The 74. https://www.the74million.org/article/why-teachers-dont-use-the-high-quality-instructional-materials-theyre-given/
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