Emilie Naccarato presenting, co-author Gulden Karakok


Goal: talk about themes occurring in flipped classrooms in tertiary maths in USA

Flipped class:

  • Some course content on technology accessed outside class
  • More time in class for related, meaningful activities
  • Same contact, face-to-face hours
  • (notice the loose way a flipped class can be arranged – many ways to arrange)

Existing studies

Descriptions of implementation and student perceptions.

Looking at student performance in flipped vs traditional courses. Big differences in studies – no consensus on what works best (but implementations vary a lot).

Need to link expectation and goals of a flipped class to the implementation – can’t simply compare all versions of a flipped class.

How do you assess differences when learning goals and implementations are so different?

You need alignment. Schoenfeld (2000) emphasized “identifying important topics and specifying what it means to have a conceptual understanding of them. With this kind of information … [they] could then decide which aspects of understanding were most important, which they wanted to assess, and how.” (p. 642) in Schoenfeld, A. H. (2000). Purposes and methods of research in mathematics education. Notices of the AMS47(6), 641-649.

This study looked at 19 staff from 14 institutions, mostly in early-university courses.

3 themes

  1. Motivation for implementing flipped classrooms
    1. External – institutional policies.
    2. Intrinsic – recognition that being a mathematician is more than number crunching.
  2. Procedural and conceptual knowledge
    1. Procedural comes before conceptual, so spend class time on conceptual (deeper) knowledge.
    2. Others didn’t separate this way. Tended to focus on higher order thinking, self-regulated learning.
    3. Use videos to prime students to what they’re going to do in class (from prior courses), refresh prerequisites. (They still considered this ‘flipped’ even though the class time was still lecture-heavy.)
  3. Aspects of Implementation
    1. Outside class
      1. Videos
      2. Guiding notes
  • Student questions
  1. Pre-post quizzes/assignments
  1. During face-to-face time
    1. Homework collected / notes checked

Other suggestions for implementation:

Pick a topic (say for 2 weeks) at first, then try a course.

Having 2-3 people to help answer questions in class time.

Little evaluation of ‘spoken objectives’ like increasing confidence in students.

Some questions

  • How does the flipped classroom model affect cognitive, metacognitive and other ‘spoken’ objectives? How can we assess them effectively?
  • Are there certain mathematical concepts or courses that lend themselves better to a flipped classroom environment?
  • What mathematical concepts can be effectively learned in a video or via other technological tools and what kind of in-class activities and assessments should be implemented for these concepts?

Could students be gaining because they are simply spending more time on task? How do you measure improvement? Emilie mentioned a study where the flipped version caused much greater student performance but the goals, activities and assessment were all focussed on procedures rather than concepts. (It’s quite easy to improve procedures with more time on task…)

How clear is this post?