Chris Rasmussen, chris.rasmussen@sdsu.edu, maa.org/cspcc

Presentation at the 11th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (‘Brazil Delta 2017 for short)

There are 4 regular international conferences on undergraduate mathematics:

RUME (USA), DELTA (Southern hemisphere), one in the UK, one in Europe

How do you make sense of Ax = b where x and b are vectors? (Larson & Zandieh, 2013). There are multiple representations:

- Linear combination, vector addition
- System of equations, intersection of 3D lines
- Transformation, one vector mapped to another

Chalk Talk practices include

- Verbalising everything written on the board
- Board choreography
- Using pointing gestures to highlight key issues, and connections
- Using rhetorical questions to signal transitions, reflection or to check for understanding

Students in lecture-oriented classes has 1.5 times the chance of failing compared to inquiry-oriented classes. Inquiry-based learning is especially good for women. *The continued use of traditional lecturing without some form of active learning can be seen as a way to limit the success of many students. *

The graph shows a decrease in the failure rate from 34% to 22% when active learning is included in university lectures. Active learning in this study includes “occasional group problem-solving, worksheets or tutorials completed during class, use of personal response systems with or without peer instruction, and studio or workshop course designs”. Studies in the meta-analysis used active learning for 10-15% of class time (e.g. using clickers) to 100% in lecture-free classes. (Freeman et al, 2014)

Laursen et al 2014 – in inquiry-based courses, women did not achieve lower than men, but they did in traditional courses. The deficit is not in women but in the approach to teaching.

Free pdf: Bressoud, D., V. Mesa, C. Rasmussen. 2015. Insights and Recommendations from the MAA National Study of College Calculus. MAA Press.

**Ambitious Teaching**

- “… characteristics include the use of group projects, the inclusion of unfamiliar problems both in homework and on exams, requirements for students to explain how they arrived at their answers, and a decreased reliance on lecture as the primary mode of instruction. A factor analysis revealed these to be highly correlated and independent of a second group of instructor characteristics that were labeled as Good Teaching (Chapter 7). Note that characteristics included in the ambitious teaching factor are consistent with instruction that is often referred to as active learning or student-centered instruction. “
- “teaching designed to meet the ambitious learning goal of developing conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive dispositions” (Bressoud, Mesa, Rasmussen, 2015 p. 93)

Classes where there is good and ambitious teaching have ‘switching’ (to another non-STEM degree) rate of 7% compares to 16% for classes that have low levels of good and ambitious teaching.

**Switching to ambitious teaching** is influenced by

- the significant effort needed
- sufficient dissatisfaction with the current instructional approach
- a departmental culture of sharing
- teachers’ sense of autonomy
- teachers’ professional development experiences e.g. at mathematics education conferences, workshops

**Sustaining innovations** in instruction requires

- continual adjustments to new conditions
- a solid grasp of reform-related instructional strategies
- social networks characterized by strong ties, in-depth interaction, and high levels of expertise [e.g. Teaching Teas]

Training for graduate students is needed for tutorials to move away from a traditional tutorial where, for example, students ask a question and the tutor shows how to do it, to one where one hour of the 2-hour tutorial is active learning where students work in groups [maybe whiteboard workshops].

44% of USA universities that teach graduate maths say they think active learning is very important but only 17% think they are doing it well.

Some American universities are experimenting with calculus courses that infuse pre-calculus rather than doing a pre-calculus course before the calculus course.

Break down semester courses into term courses so students don’t get left behind after failing the first test. They can use the winter break to catch up the second term course.

Recommended book: The Saber-Tooth Curriculum, a satirical book on education and change first published in 1939 by Harold Benjamin under a pseudonym.

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