A Study of the Development of the Paradigms in Physics Program

sequence required science courses in order of increasing mathematical sophistication

offer “math bits” to provide just-in-time mathematics instruction for understanding upcoming science content

design “math bits” to help students generalize the mathematics, to see how a technique might apply to another situation or topic in an earlier or upcoming science course

design “math bits” to help students recognize similarities and differences among mathematics language and usage as well as science language and usage for similar topics

include mathematics needed by all majors to succeed in required science courses

encourage students ready for advanced topics, especially those headed for graduate school, to enroll in the graduate level mathematical methods course in the discipline

assign an experienced faculty member who has taught many of the courses and has a detailed grasp of the content and mathematics needed in the upper division curriculum

assign a senior faculty member who has strong collaborative and mentoring skills

assign a senior faculty member who can be flexible but also firm if needed to maintain the time and independence necessary to preserve embedding “math bits” in the courses

assign a faculty member who enjoys mathematics and can communicate ways that learning mathematics while learning science enhances understanding both disciplines.

advocate for just-in-time mathematics instruction rather than using this time for additional science applications or more science content.

explain the importance of students being able to see the math in its general form so they can see where they are using the same math in multiple contexts, sometimes with a variety of notations and different language

make the need evident by engaging students interactively so the primary instructor becomes aware of their struggles and the need to address these difficulties directly

recognize that faculty are used to teaching their own courses in their own ways and may find it difficult to give instructional time to someone to teach mathematics separately

offer in two pieces, one early on and one that comes later with more advanced materials

begin with the science content, even if only for a few instructional hours, to provide context and to help students recognize how the “math bits” they are learning will be useful

perhaps offer as a one week interlude in the middle of a course

well before the course begins, arrange for on-going discussions in which the “math bits” instructor and the primary instructor achieve and articulate a common vision for the course

recognize that these instructors may differ on what constitutes the science, the relevant mathematics, and the importance of introducing students to a generalized form of the mathematics

outline what the science content will be and what the relevant “math bits” might be

group together “math bits” that will take more than a day to teach within at most two sets of math sessions

identify any isolated “math bits” that the primary instructor should teach along with the associated science content

recognize that faculty travel, research priorities, family commitments, and even just comfort with flexibility may affect the primary instructor’s available time and interest in such collaborative planning

discuss the primary instructor’s role during “math bits” sessions: best if primary instructor stays in the classroom and is aware of and can build upon the “math bits” instructor’s approach, language, notation, and content

be both willing to be flexible as well as firm when working with colleagues

expect some negotiations to become complex and try to keep a clear sense of what the most essential aspects are.

agree on regular due dates, shared format, and way of including “math bits” in homework assignments and exams

try to complete the mathematics instruction within the agreed upon time in order not to affect the instructional plans of the primary instructor

welcome ideas for something new but also recognize when last-minute requests are not feasible to meet

deepen your own knowledge by designing ways to embed “math bits” in multiple courses