The Mathematical Education of Teachers II (MET II)

Summary

The Mathematical Education of Teachers II (MET II) report focuses on the mathematics education and professional development needs of K-12 mathematics teachers. The writers present the recommendations in MET II as an update to those in the previously published MET I report. The report is intended to be a resource for educators who teach mathematics and statistics to PK-12 mathematics teachers, and for policy makers and education administrators at the school-district, state, national, and institutional levels.  The report describes the traditions of teacher education and mathematics and includes a review of the math knowledge needed for teaching. The report situates the teachers’ pre-service education needs in the context of the Common Core State Standards (CCSM) and other aspects of the current educational landscape.

The first chapter introduces two pillars for PK-12 education: 1) highly-qualified teachers in all classrooms and 2) a rigorous curriculum. The report addresses each pillar by describing mathematics teachers’ preparation and professional development needs to support the first pillar and the mathematics content, from CCSS, to support the second. This chapter serves as the basis for the remainder of the report and includes operational definitions for grade-level groupings of elementary (K-5), middle school (6-8), and high school (9-12). To be effective, teachers need to not only have more than their students’ understanding of the content but also an understanding curricular coherence,   how the math that they teach relates to earlier and later grade content. Teachers need to make sense of definitions, the mathematical consequences of different choices, and mathematical assumptions to effectively create, select, and modify tasks.  The authors recognize that the mathematical knowledge that teachers need at the 3 grade-levels does vary and note that professional development is critical to allow teachers to continue to grow as beginning teachers, those with several years of experience, and those with many years of experience of whose skills can be enhanced.

Chapter two addresses five issues including: 1) the role of mathematicians in teacher education and advocates that they play an even greater part in supporting K-12 mathematics teacher education; 2)  common beliefs about math, practices in teaching math, teacher effectiveness and their influences on learning; 3) practices in teaching mathematics and their influences on learning; 4) teacher effectiveness and mathematical knowledge; and 5) a description of the changes in the context for teacher education and changes since MET I was published in 2001.

Chapter three includes six recommendations in two groups. The first four focus on the mathematics that teachers need to know and the remaining two describe the role of mathematicians in teachers’ math education.

The mathematics for teachers recommendations include:

1. Mathematics courses that develop teachers’ understanding of the mathematics they will teach.
2. Courses that allow time to engage in reasoning, explaining, and sense making of the mathematics that they will teach. Recommended semester-hours for courses include 12 semester-hours on fundamental math for elementary teachers, 24 semester-hours of mathematics for middle school teachers, and the equivalent of an undergraduate mathematics major for high school teachers are explained within chapters four, five, and six.
3. Professional development opportunities to promote continued growth in teachers’ mathematical knowledge. In-service professional growth opportunities should allow teachers to transition from new teacher, mid-career teacher, to master teacher.
4. Formal courses and professional development experiences should develop teachers’ “habits of the mind” leading them to think and problem solve mathematically and include reasoning, explaining, modeling, seeing structure, and generalizing.

The recommendations related to the roles for mathematicians in teacher education include:

1. Recognition of teacher education as part of the mathematics department’s mission and collaboration between mathematics and mathematics education faculty.
2. Recognition of the need to improve mathematics teaching at all levels and inclusion of mathematicians in the mathematics education community. Partnerships should include mathematicians and mathematics faculty in two- and four-year institutions as well as faculty and K-12 mathematics teachers at the state, regional, and local levels.

Chapter four focuses on elementary teachers and begins with the authors asking “What mathematics should future elementary teachers study to prepare for their careers?” and similar questions regarding the coursework, professional development, and support from mathematicians for K-5 mathematics teachers. The chapter uses the CCSS to present a list of essential ideas for K-5 teachers. The topics include: counting and cardinality, operations and algebraic thinking, number and operations in base ten, number and operations – fractions, measurement and data, and geometry.  The chapter concludes with a section on the preparation and professional development of elementary (K-5) teachers and notes that those who teach special populations, e.g. English language learners or students with special needs, should receive the same level of preparation and professional development as is recommended for those with direct responsibility for teaching mathematics.

The fifth chapter focuses on teachers in the middle grades (6-8), and the essential ideas as they relate to the common core state standards (CCSS) including ratio and proportional relationships, the number system, expressions and equations, functions, geometry, and statistics and probability.  The second part of the chapter includes discussion about the preparation and professional development of middle grades teachers. The authors note that to be prepared to teach the intellectually challenging topics in the CCSS teachers will need to be adequately prepared and recommend a minimum of 24 semester-hours, 15 of which should include courses specifically for prosepctive middle grades teachers. The remaining nine hours should consist of courses that deepen the teachers’ mathematical knowledge. This distribution of courses provides middle grades teachers with a balance of what to teach and how to teach.  As mentioned in chapter one, the authors note the need for teachers to connect the content they are teaching with what students have previously learned, in elementary school, and will learn in high school.

Chapter six tackles the topic of high school (grades 9-12) mathematics teachers’ preparation and professional development. The chapter includes two themes: 1) the mathematics topics in courses for prospective teachers and the professional development experiences for practicing teachers and 2) the practice of teaching including an examination of connections between the topics covered in middle grades and that which they will see in college. The inclusion of strands of proficiency: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition, form the basis for the dimensions in which teachers are responsible for deepening their students proficiency.  The authors note that experience with reasoning and proofs and experience with technology are cross-cutting themes that should be integrated across the spectrum of undergraduate mathematics.  

The mathematical preparation of high school teachers should include courses from three categories:

• Those taken by a variety of undergraduate majors including single- and multi- variable calculus, introduction to linear algebra, statistics and probability.
• Those taken by all mathematics majors including introduction to proofs, abstract algebra, modeling, differential equations, group theory, number theory, and the history of math.
• Those created for prospective teachers that include electives that can be modified to meet the needs of prospective teachers. In addition to courses the authors also recommend research experiences for teachers enabling them to develop the expertise to know mathematics as scholars, as educators, and mathematicians, and as teachers.