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Robust preparation of future secondary mathematics teachers requires attention to the acquisition of mathematical knowledge for teaching. Many future teachers learn mathematics content primarily through mathematics major courses that are taught by mathematicians who do not specialize in teacher preparation. How can mathematics education researchers assist mathematicians in making explicit connections between the content of undergraduate mathematics courses and the content of secondary mathematics? We present an articulation of five types of connections that can be used in secondary mathematics teacher preparation and give examples of question prompts that mathematicians can use as applications of teaching secondary mathematics in undergraduate mathematics courses.

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This paper introduces lessons designed to incorporate applications to teaching high school mathematics in an undergraduate Discrete Mathematics course. Because many prospective high school teachers do not take courses that are specifically designed for teachers, providing materials aimed at teacher preparation that can be easily integrated into courses that serve a general mathematics major is one strategy for addressing mathematics teacher preparation. We developed lessons using four guiding features: choosing appropriate content; making school mathematics connections; incorporating active learning; and providing robust lesson notes. Our interview-based findings document how the lessons were used by instructors and analyze the mathematical ideas and understandings that arose from the use of the lessons at two different sites.

The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). Accordingly, many high school curricula include a method that uses finite differences between data points to generate polynomial functions. That is, students may examine differences between successive output values (called first differences), successive differences of the first differences (second differences), or successive differences of the (n - 1)th differences (nth-order differences), and rely on the following: