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Section 4.3 Design and Implement Math Bits

  • Embed mathematics instruction within all of the junior-level paradigms courses

    • 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

  • Distinguish between the mathematics needed to graduate as a science major and that needed for graduate study in the discipline

    • 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 a separate instructor for teaching “math bits” within a science course

    • 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.

  • Maintain a commitment to generalizing the mathematics

    • 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

  • Recognize that “math bits” scheduling needs are different for different courses. For example:

    • 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

  • Plan collaboratively with the primary instructor of the science 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 flexible and firm with colleagues

    • 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.

  • Establish an effective routine for sharing homework assignments.

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

  • Respect time issues

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

  • Listen and respond to the primary instructor's requests when feasible

    • welcome ideas for something new but also recognize when last-minute requests are not feasible to meet
  • Inform faculty about “math bits” plans and engage them in talking substantively about mathematics content during some upper division curriculum meetings

  • Enjoy learning new mathematics yourself

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