Mathematics Pedagogy: Knowledge, Skills, & Dispositions

Mathematics Pedagogy: Knowledge, Skills, and Dispositions  

Elementary Mathematics Specialists (EMSs) support the classroom and grade-, school-, or district-wide use of ambitious and equitable mathematics instruction. They serve to enhance the planning, teaching, learning, and assessing of mathematics, and provide critical direct and indirect support for improved student mathematical understanding and identity development. In these efforts, EMSs have robust mathematics pedagogical knowledge and practices, with this section describing what EMSs understand and implement with PK-6 students as well as support others (e.g., general education teachers, special education teachers, teacher candidates, paraeducators) in doing so. It is important to note that the standards within the pedagogy domain build upon one another, from knowing students to using that information in support of the planning, implementing, and assessing cycle. Also, while the emphases of the standards—knowing, planning, teaching, and assessing—are presented separately, they are inherently and necessarily interwoven when it comes to the pedagogical knowledge and practices for teaching mathematics. Further, in the varied roles through which EMSs support ambitious and equitable mathematics instruction, they draw heavily upon their mathematical knowledge for teaching, including the knowledge, skills, and dispositions described in the Mathematics Content Standards.   

EMSs’ varying roles in schools and districts, such as generalist or specialist teacher, interventionist, leader, or coach, hold differing responsibilities that may involve work with students, teachers, or a combination of both (59). If working with students, these standards describe the pedagogy-focused knowledge, skills, and dispositions needed to support student learning. If working with teachers, the standards describe the pedagogical understandings, capabilities, and mindsets to support teachers in developing. Outlined in the Mathematics Leadership Standards are some of the specific approaches for supporting collegial learning with particular attention to the unique learning needs of adult learners. 

While this section focuses on pedagogy in support of student learning, much of this pedagogy is also relevant in support of teacher learning. For example, EMSs know and leverage teachers’ diverse backgrounds and mathematical competencies during professional learning. EMSs have asset-based views and focus on mathematical strengths in their work with teachers in order to foster teachers’ confidence in mathematics. EMSs create a community of learners where teachers are encouraged to be curious, take risks, and ask questions, which cultivates teachers' sense of feeling supported and receptiveness. Further, teachers are encouraged to reason and make sense of their mathematical thinking, within a context that affirms and elevates multiple and varied strategies for solving problems. During interactions, EMSs position teachers as holders of expertise and assign competence through naming or publicly drawing attention to teachers’ contributions. Over time, teachers learn to recognize, value, and rely on their own mathematics strengths as well as those of others. These are just a few examples of the pedagogy presented here that is also applicable to teachers as learners.

Standard P.1. Knowing Students to Foster Positive Mathematics Identity

P.1.a. Knowing students’ diversities and strengths to develop positive mathematics identity 

Standard P.2. Planning for Responsive Instruction and Making Curricular Decisions

P.2.a. Planning for instruction based on learners and meaningful content

P.2.b. Understanding and using curriculum effectively

Standard P.3. Implementing Ambitious and Equitable Mathematics Instruction

P.3.a. Fostering a mathematics learning community

P.3.b. Focusing on a deep understanding of mathematics

P.3.c. Leveraging multiple mathematical competencies

P.3.d. Affirming students’ diversities and mathematics identities 

Standard P.4. Assessing Student Understanding and Learning

P.4.a. Engaging in the formative assessment cycle

P.4.b. Using summative assessments formatively