In this time of state testing, many educators are focusing on how to improve their math scores…and rightly so. Rather than focusing on improving scores, let’s focus on improving mathematics instruction. The scores will take care of themselves.

So…how do we improve math instruction?

In this blog, I’ll share the six steps for improving math instruction in your school district or at your school site.

1. High expectations
2. Ambitious mathematics instruction
3. Sustained and on-going mathematics professional learning for teachers and administrators
4. Common assessments at the chapter level
5. Strategic intervention system
6. Establishing an accountability plan

High expectations

When teachers hold high expectations for their students, it significantly enhances student achievement and engagement. The Opportunity Myth (TNTP, 2018) highlights that many students are not given access to grade-level content, despite meeting classroom expectations, which limits their potential. When educators challenge students with rigorous material and believe in their ability to succeed, students demonstrate greater academic growth. Similarly, John Hattie’s meta-analyses (2009) show that teacher expectations have an effect size of 0.43, indicating a substantial impact on student learning. High expectations foster a culture of perseverance, self-efficacy, and deeper learning, ultimately preparing students for long-term success. When teachers’ high expectations for their students is paired with the teacher’s own sense of self efficacy, the effect size jumps to an astounding 1.57!

Also in The Opportunity Myth, teachers with high expectations of their students are more likely to provide for their students access to grade-appropriate assignments, strong instruction, deep engagement, and high expectations. As a result, these students made significant academic gains, with those starting behind catching up at over five times the rate of their peers who did not receive such opportunities.

High expectations matter.

Ambitious instruction

Defining what ambitious math instruction looks like in the classroom is essential to ensuring that all students engage in meaningful, rigorous mathematical learning. Cobb and Jackson (2011) emphasize that ambitious mathematics instruction goes beyond procedural fluency, focusing on deep conceptual understanding, reasoning, and problem-solving through student discourse and exploration.

The MCOE Math Team defines ambitious instruction through our Math Hierarchy of Needs framework.

In the same way that Maslow’s Hierarchy of Needs is a roadmap for how a person might experience the joy of experiencing self-actualization, with needs lower down in the hierarchy being satisfied before individuals can attend to needs higher up, the Math Hierarchy of Needs is a roadmap for how teachers and leaders might guide students towards becoming mathematically literate humans.

Ambitious math instruction requires satisfying students’ needs at each and every level. It is the role and responsibility of school districts to ensure that all five levels occur in each and every classroom.

1. Material Needs: Teachers with math knowledge for teaching, essential standards, curriculum, math tools

• • Every student has a teacher with appropriate mathematics content knowledge and the pedagogical knowledge for teaching mathematics.  Math lessons are rooted in a solid understanding of the standards through rigorous, high-quality instructional materials employing mathematical tools that enhance student learning.

2. Mindset & Culture: All students can learn, mistakes are normalized

• • Every student is immersed in a mindset and culture that intentionally communicates all students can learn math at high levels in an environment that considers each and every student’s unique background, experiences, cultural perspectives, traditions, and knowledge.  Mistakes in mathematics are normalized. Students regularly experience high-quality, grade-appropriate lessons and assignments.

3. Student-centered Instruction: Meaningful discourse to promote conceptual understanding, procedural fluency, problem-solving, and application

• • Every student regularly experiences instruction that is student-centered and is designed to maximize students’ use of language. Lessons create space for students to participate in discourse to promote conceptual understanding, which then leads to procedural fluency, problem-solving, and application.

4. Equitable Assessment: Feedback and intervention to achieve at grade level

• • Every student is regularly and humanely assessed in order to have understanding of their own growth and to receive productive feedback for next steps in learning.  Students use the feedback to know where they are in their learning, assess any misconceptions that need to be addressed, and then use the results to drive the next level of learning.

5. Math Literacy: Confident problem-posers and problem-solvers

• • Every student has the opportunity to analyze, reason, and communicate ideas effectively as they pose, formulate, solve, and interpret mathematical problems.

While the math hierarchy might describe WHAT ambitious math instruction is, Deborah Loewenberg Ball and her colleagues (2008) highlight the importance of a specific teacher skill called mathematical knowledge for teaching (MKT). She notes that effective math instruction only occurs when teachers skillfully facilitate discussions, pose high-quality questions, and respond to students’ mathematical thinking in ways that advance understanding. Without a clear definition of ambitious instruction, classroom practices can vary widely, often reinforcing inequitable learning experiences. Establishing a shared vision ensures that teachers implement strategies that promote deep mathematical understanding and empower all students as capable problem-solvers.

Sustained and Ongoing  PD and coaching

It has long been recognized that mathematics-specific instructional coaching leads directly to improved math instruction in the classroom and to increased student achievement. It is critical for teachers (in all stages of their career) to engage in curriculum-based professional learning in which they co-participate in teaching practices with instructional coaches through  the coaching cycle: lesson planning, observing instruction, debriefing the lesson.

The professional development teachers receive should be short –no more than three hours– and should focus on using the adopted curriculum teachers already have. Teachers learn how to effectively implement the curriculum in alignment with the recommendations of the California Mathematics Framework. The math coach leads the teachers through designing a lesson plan and then the team of teachers co-teach the lesson, which is then followed by a debrief session. Teachers reflect on the lesson and discuss changes they would want to make the next time they teach this lesson.

The professional learning is then followed by in-class coaching to individual teachers. This provides teachers with the opportunity to implement the new teaching strategies with the math coach in the room to provide additional support as needed.

Chapter-by-chapter common assessments

Get rid of iReady. Get rid of NWEA.

There…I said it.

Both of these products are seductive latchkey products that students can be plugged into and adaptively spit out some scores for each student. Ostensibly, these scores drive further instruction or intervention.

The problem, however, these scores are meaningless for a variety of reasons.

First, since the tests are adaptive, students are subjected to math content that is NOT grade-level appropriate. Both assessments treat math concepts as a sequence of stepping stones; each stone acting as a gateway before accessing the next stepping stone. The truth, however, is that mathematical concepts are more like an interconnected concept web providing a near infinite number of pathways from point A to point Z. For example, a latchkey testing product may prevent a 5th grade student from showing the grade-level content he has mastered simply because he does not know skills from previous grades such as how to read an analog clock or measure lengths with a ruler.

The adaptive nature of both products also mean some students are exposed to problems from higher grade levels. Teachers then feel compelled to divert precious teaching time to content from other grade levels so that the data will show growth in the next testing cycle.

A second issue with these products is they are comprehensive assessments that cover content that has not yet been taught. Students are frustrated by math concepts they have not yet been taught which could lead to math anxiety. Teachers are frustrated because they now have to scamble prior to each testing cycle to cram math content before the test that ordinarily would be taught later in the year. This wrecks havoc on the pacing and sequencing calendar teachers created during the summer.

I could go on, but I’ll share just one last issue: The tests do not measure what, how, or whether the students are learning RIGHT NOW. If a teacher just taught fractions, the test should be on fractions. (Sure maybe some review questions thrown in.) The data of a fractions test immediately after teaching the fractions unit is useful for teachers and meaningful for students.

In California we have a FREE assessment system that ALL teachers can use instead of iReady and NWEA. The CAASPP assessment system provides a number of Interim Assessment Blocks (IABs) and Focused Interim Assessment Blocks (FIABs) that are grade-level appropriate and each covers a targeted math concept. The resulting data is useful because it is directly related to the content students just learned which allows the teacher to immediately plan meaningful intervention either embedded within future lessons or in a small-group setting.

Not in California? Or you teach a grade not tested by CAASPP? Then create grade-level common assessments that all teachers give. Get together to analyze the data to identify instructional strategies that work better than others. Use the data as the basis for teachers to form a learning community that encourages and engenders professional growth.

Strategic Intervention system

The data through the common assessments mentioned prior will undoubtedly identify students who need more support than can be embedded within future lessons. Students will need access to an effective strategic intervention system that aligns, supports, and integrates with the primary math instruction. Intervention should emphasize six recommendations:

1. Recommendation 1: Systematic Instruction

• • Provide systematic instruction during intervention to develop student understanding of mathematical ideas.

2. Recommendation 2: Mathematical Language

• • Teach clear and concise mathematical language and support students’ use of the language to help students effectively communicate their understanding of mathematical concepts.

3. Recommendation 3: Representations

• • Use a well-chosen set of concrete and semi-concrete representations to support students’ learning of mathematical concepts and procedures.

4. Recommendation 4: Number Lines

• • Use the number line to facilitate the learning of mathematical concepts and procedures, build understanding of grade-level material, and prepare students for advanced mathematics

5. Recommendation 5: Word Problems

• • Provide deliberate instruction on word problems to deepen students’ mathematical understanding and support their capacity to apply mathematical ideas.

6. Recommendation 6: Timed Activities

• • Regularly include timed activities as one way to build students’ fluency in mathematics.

Accountability

All partners need to perform their roles and responsibilities if we want to improve student mathematical achievement. District and site administrators who attend the math PD and demonstrations become equipped to support teachers through observing instruction in the classroom and identifying barriers to implementation of the targeted math initiative. Also, teachers would greatly benefit from a system of peer observations to learn from one another.

Creating a strategy roadmap that clearly identifies the actions and goals of all the partners involved. Collecting data on the actions being implemented will enable barriers to be recognized and fixed as soon as possible.

In Conclusion

The recipe for improving math instruction is not complicated. It is just six easy-to-understand things: high expectations, ambitious instruction, sustained support for teachers, frequent common assessments, strategic intervention system, and accountability.

SIMPLE does not mean EASY, however. While the plan may be simple, carrying it out requires all partners to be patient, curious to learn new ways of teaching, and willing to navigate the uncertain and unfamiliar. For the sake of our students, let’s get to work.

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