Standard P.2. Opportunities to Learn Mathematics
An effective mathematics teacher preparation program provides candidates with opportunities to learn mathematics and statistics that are purposefully focused on essential big ideas across content and processes that foster a coherent understanding of mathematics for teaching.
Effective programs include content courses that address these content needs of middle level teachers of mathematics. As described in Part 1 of this chapter, middle level candidates must be prepared to teach a broad range of mathematics topics, understanding the content, progressions, relationships among content, not just at the middle level, but before and after middle level. Further, middle level candidates need to understand historical and cultural aspects of mathematics. Regardless of licensure options (e.g., K–8, 5–8, 6–12, or any other) effective preparation of middle level mathematics teachers includes opportunities to learn deeply the mathematics content that is taught at the middle level as well as mathematics content that comes before and after.
Effective programs for teachers of mathematics at the middle level include content preparation aligned with The Mathematical Education of Teachers II (MET II) (CBMS, 2012) and Statistical Education of Teachers (SET) (Franklin et al., 2015). [Elaboration of P.2.1, P.2.2 and P.2.3]
Consistent with the recommendations of MET II and SET, the following coursework is needed to prepare middle level teachers:
- At least 15 semester hours (or equivalent) of mathematics and statistics courses designed specifically for future middle level teachers, including courses that engage middle level candidates in opportunities to demonstrate the mathematical practices.
- At least 9 semester hours (or equivalent) of mathematics and statistics courses beyond the precalculus level, including at least one statistics course.
The content within these courses must address the content needs of middle level teachers of mathematics. Across the more than 24 hours of coursework, a high-quality middle level mathematics preparation program provides coursework that addresses the following mathematical concepts (content lists and course recommendations are from MET II [CBMS, 2012] and SET [Franklin et al., 2015]):
Number and Operations. Number and operations in base ten, fractions, addition, subtraction, multiplication, and division with whole numbers, decimals, fractions, and negative numbers. Possible additional topics are irrational numbers or arithmetic in bases other than ten. (6 semester-hours recommended)
Geometry and Measurement. Perimeter, area, surface area, volume, and angle; geometric shapes, transformations, dilations, symmetry, congruence, similarity; and the Pythagorean Theorem and its converse. (3 semester hours recommended)
Algebra and Number Theory. Expressions and equations, ratio and proportional relationships (and inversely proportional relationships), arithmetic and geometric sequences, functions (linear, quadratic, and exponential), factors and multiples (including greatest common factor and least common multiple), prime numbers and the Fundamental Theorem of Arithmetic, divisibility tests, rational versus irrational numbers. Additional possible topics for teachers who have already studied the above topics in depth and from a teacher’s perspective are polynomial algebra, the division algorithm and the Euclidean algorithm, and modular arithmetic. (3 semester hours recommended)
Statistics and Probability. Describing and comparing data distributions for both categorical and numerical data, exploring bivariate relationships, exploring elementary probability, and using random sampling as a basis for informal inference. An effective program for middle level teachers requires not only an introductory course to statistics but also a course that includes data collection and analysis. Such an experience emphasizes active learning with appropriate hands-on devices and technology with teachers probing deeply into the topics taught in the middle grades, all built around seeing statistics as a four-step investigative process involving question development, data production, data analysis, and contextual conclusions (ASA/NCTM, 2015; CBMS, 2012; Franklin et al., 2015). (6 semester hours recommended)
Implicit in these lists is the importance of candidates' understanding the mathematical content of elementary as well as high school levels. For example, one of the two course recommendations in the area of number may be a mathematics course for elementary school teachers focused on rational numbers. Additionally, designers of a well-designed middle level mathematics program strategically consider the sequence in which courses occur, including the extent to which courses are taken prior to or concurrently with education courses, mathematics methods courses, and clinical experiences. Although having mathematical knowledge is a prerequisite to teaching mathematics, having mathematics course opportunities later in a program can have more connection to a middle level candidates' classroom teaching. A well-designed program provides at least one content-course experience that is concurrent with a candidate’s clinical experience so that connections can be made between the content being learned and content that is being taught in the clinical setting.