Mathematics Classroom:

**Key Success Indicators**

In their book, *Building Teachers’ Capacity for Success: A Collaborative Approach for Coaches and School Leaders, *Peter Hall and Alisa Simeral help coaches and teachers effectively target areas of growth with their Continuum of Self-Reflection model. In addition to a teacher’s reflective tendency, each stage of self-reflection (unaware, conscious, action and refinement) corresponds to a set of classroom characteristics as outlined below. This model is helpful for both teachers and school leaders as it provides insight into what to expect in classrooms overall as teachers become more effective.

Classroom Characteristics:

The* Continuum of Self Reflection: Coach’s Model (Hall & Simeral, Figure 4.2)*

These characteristics parallel what one would expect to find in a mathematics classroom at each stage of self-reflection. However, it may be helpful for benchmarking purposes to further refine these characteristics and add a few additional “key success indicators” that we would expect to see at the refinement stage relative to each of the following categories:

**Learning Environment**

As noted by Cathy Seeley in her book *Faster Isn’t Smarter,* the importance of the learning environment cannot be overstated:

From the arrangement of furniture that facilitates discussion, thoughts and exploration to the feeling students experience when they walk into the classroom, the teacher establishes an atmosphere where mathematics and learning are important. Most of all, the teacher creates a place where the students feel safe to take risks and are willing to share ideas while learning to value the opinions of others.

In a 2003 study published in the *Journal for Research in Mathematics Education*, researchers found that when coupled with a like-minded pedagogical curriculum, a standards-based learning environment—defined as an environment in which students make conjectures about mathematical ideas and explain their responses or strategies—has a positive impact on student achievement. They found that this achievement was particularly strong on performance assessments measuring mathematical reasoning, problem solving and communication skills—performance assessments not unlike those expected from PARCC & Smarter Balance.

**Reasoning & Sense-Making**

The Common Core Standards requires a balanced approach between procedural skill and fluency and conceptual understanding. Students are expected not only to have knowledge of procedures—when and how to perform them (doing so flexibly, accurately and efficiently)—but they should also understand the underlying concepts. They should be able speculate, reason, defend and debate their thinking and solve problems in more ways than one.

This higher level of cognitive demand requires that teachers understand and provide the conditions necessary for learning—to know what information, such as academic language, they need to provide and what information students need to discover on their own through a process of constructive struggle. When the conditions are right, students will develop the skill, fluency, conceptual understanding and perseverance necessary to make sense of math.

**Focus & Coherence**

According to the designers of the Common Core Mathematical Standards, the purpose of the fundamental principles of focus and coherence is to “fuel greater achievement in a deep and rigorous curriculum, one in which students acquire conceptual understanding, procedural skill and fluency, and the ability to apply mathematics to solve problems.” (K-8 Publishers’ Criteria) Their goal, through a significant narrowing of scope, is to have students deeply understand core content. Closely tied to focus is the idea of coherence—that a clear understanding of core content builds and deepens over time through a “careful, deliberative progressive development of ideas.” (McCallum & Zimba, Mathematic Fluency: A Balanced Approach)

This emphasis on focus and coherence, means that teachers must know the content deeply and flexibly enough to make that content accessible to all students—to understand various reasoning strategies and misconceptions.

**Formative Assessment**

In 2006, the Council of Chief State School Officers’ (CCSSO) Formative Assessment for Students and Teachers (FAST) State Collaborative on Assessment and Student Standards (SCASS) defined formative assessment in the following way:

Formative assessment is a **process** used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students’ achievement of intended instructional outcomes.

The operative word in their definition being “process”—that formative assessment is not simply a pretest of material to be covered but an ongoing activity where a teacher acquires and interprets information gained through listening, observation, examination, and guided questioning to effectively plan and differentiate instruction. Formative assessment is a dynamic process in which effective teachers are able to adjust their teaching in real time.

**Measuring for Success**

By understanding and benchmarking math classrooms relative to key success indicators in the categories of learning environment, reasoning & sense-making, focus & coherence, and formative assessment, educators can better understand and address critical challenges at the classroom, school and district level.

*Sources:*

“Distinguishing Formative Assessment from Other Educational Assessment Labels.”

*The Council of Chief State School Officers*. N.p., 2006. Web. 18 Oct. 2013.

Hall, Peter A., and Alisa Simeral. *Building Teachers’ Capacity for Success:
A Collaborative Approach for Coaches and School Leaders.*

Alexandria, VA: Association for Supervision and Curriculum Development, 2008. Print.

*K-8 Publishers’ Criteria for the Common Core State Standards for Mathematics*.

N.p.: Common Core State Standards Initiative, 2013. Print.

Kilpatrick, Jeremy, Jane Swafford, and Bradford Findell. *Adding It Up: Helping Children Learn Mathematics. *Washington, DC: National Academy, 2001. Print.

*Mathematics Fluency: A Balanced Approach*. Perf. Professor William McCallum and Dr. Jason Zimba. *The Hunt Institute and CCSSO Release Common Core Implementation Video Series*. James B. Hunt, Jr. Institute for Educational Leadership and Policy & Council of Chief State School Officers, 19 Aug. 2011. Web. 18 Oct. 2013.

Reys, R. E., R. Lapan, G. Holiday, and D. G. Wasman. “Assessing the Impact of Standards-Based Middle Grades Mathematics Curriculum Materials on Student Achievement.” *Journal for Research in Mathematics Education* 34.January (2003): 79-95. Print.

Seeley, Cathy L. *Faster Isn’t Smarter: Messages about Math, Teaching, and Learning in the 21st Century : A Resource for Teachers, Leaders, Policy Makers, and Families*. Sausalito, CA: Math Solutions, 2009. Print.