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Promoting More Effective Mathematics Instruction

Guiding and supporting teachers to ensure deeper learning

Built on proven best practices, and based on decades of firsthand instructional experience, the Dixon Nolan Adams Mathematics resources from Solution Tree focus on taking approaches to professional development that can enhance the knowledge, skills and effectiveness of mathematics teachers, promoting deeper student understanding and improving student achievement.

This web seminar featured the renowned mathematics education experts and professional development authors Juli Dixon, Edward C. Nolan and Thomasenia Lott Adams, who discussed ways to promote more focused mathematics instruction, how to provide effective teacher support, and how to help guide teachers to implement more rigorous mathematics standards in a way that will ensure deeper student learning and higher levels of mathematics achievement.

Professor, Mathematics Education
University of Central Florida

We have three goals with our resources. These goals are designed to support you as administrators and instructional leaders.

  1. Promote focused mathematics instruction in your school or district.
  2. Provide effective teacher support.
  3. Guide implementation of rigorous standards, regardless of the standards that you’re using in your state and district.

Our first goal of promoting focused mathematics instruction begins with the idea of an creating an effective mathematics lesson.

Dixon Nolan Adams Mathematics supports students doing the sensemaking as a key in looking at effective mathematics instruction. The TQE process—tasks, questions and evidence—is very helpful for ensuring that students are doing the sensemaking. The TQE process means that we have tasks that support students to connect with the learning goal, we use productive questioning to help students engage in mathematical practices, and we collect and use student evidence within the formative assessment process.

The following mathematics problem serves as an example: Students are asked to determine how they would package 4 5/6 pizzas into serving-size bags with 2/3 of a pizza in each bag. They need to figure out how many servings they’ll have if they use up all the pizza.

The learning goal for this exercise is for students to be able to make sense of the remainder of a fraction division problem. They need to make sense of what’s left over. We can make seven servings, but then there’s this 1/6 of a pizza left over. In a test of two student groups, one said 7 1/6 servings, and the second answered 7 1/4 servings.

As you watch the sample classroom video, you might have expected me to correct the students at the point of error. However, I withhold that correction. I withhold the specific and immediate feedback so that students can continue to do the sensemaking. When we have focused mathematics instruction around rigorous standards, we give students time to think. We withhold the answer until we have a discussion, and then we resolve the conflict. We have cognitive dissonance, and then recreate equilibrium, and learning takes place.

Master Teacher, UTeach Program
Towson University

There are five instructional shifts that schools and districts have begun to use across North America.

The first shift is that students provide strategies rather than learning them from the teacher. It’s not the teacher initiating the strategy and then supporting the students using the strategy—it’s the students doing the thinking first.

What happens when the students don’t come up with the strategy that the teacher has planned for and knows is needed to help support the students in achieving their learning goal? This is where we bring up the second shift, what we call the “as-if strategy,” where the teacher says, “I heard a student say…” In that case, the students connect to the presented strategy even though it’s not a student doing the presenting. The idea is discussed as one that comes from the students.

The third shift that we look for when we observe classroom instruction is for students to create the context. Imagine providing an expression or equation and asking students to create a context that aligns to that numeric or algebraic representation. That can be a struggle for some students, and this is where the TQE process is critical for teachers to have planned out what questions they’re going to ask, and to anticipate what evidence they are going to collect and how they’re going to use that evidence in order to make sense of student learning.

The fourth instructional shift is for students to do the sensemaking. A critical element in all of our work is when the students understand the learning goal and teachers support them in getting there. Sometimes that can be teacher support because the student is struggling; sometimes it can be the teacher extending the learning because the student shows early understanding and the teacher can enrich and deepen the learning experience. The key is that all students are included in this sensemaking piece.

Our fifth instructional shift is to create learning environments where students are talking to students—setting up the classroom where the teacher is not needed as the conductor of the questioning, but rather where the talking is naturally occurring between students. This happens wonderfully in small-group instruction where students can talk to one another and make sense of the learning tasks. Students share strategies and learn mathematics, which is enhanced by a focus on the mathematical practices.

Professor of
Mathematics Education
Associate Dean for Research and Faculty Development
University of Florida

How do we help you guide your teachers to effectively implement more rigorous mathematics standards? How do you support schools and teachers to use the five shifts? How do you support teachers to apply the TQE process? How do we make sure that we are providing opportunities for teachers to develop mathematics instruction where students are doing the sensemaking? These are all vital questions.

From our perspective, it is important that teachers have the content knowledge for teaching mathematics. That is critical to the work that we do.

First, when there’s an emphasis on gradual release, it can hinder a student’s flexibility in thinking and it can hinder a teacher’s flexibility to make sure that they are using best practices in the mathematics classroom. In many instances, it produces cognitive dissonance when students don’t have the opportunity to think freely because they may be bound by the teacher presenting the strategy first in the gradual release process.

Second, when we post objectives and essential questions, there are many times when we may be taking away the “aha moment” for students. When this happens, students don’t have the opportunity to engage authentically in mathematical experiences because they’ve already been told what they can expect to learn. There isn’t any room for students to think deeply on their own or to engage in cognitive dissonance that will help them face misunderstandings about the content.

Third, when we provide immediate feedback that quickly tells a student what a teacher thinks about a response, we often rob students of the opportunity to think more deeply and to consider their own misunderstandings. These are all points that we want you to keep in mind in thinking about the necessary elements of an effective mathematics program.

Juli, Ed and I can visit with schools or entire school districts to engage in these conversations about content-based strategies that also focus on effective instruction. We also offer in-depth content institutes designed to build teacher’s capacities, to dive deeply into important mathematical concepts and to address learning progressions.

To watch this web seminar in its entirety, please visit: