MAA MathFest 2019 David Taylor , Roanoke College

1. No Student Is an Island: A Plethora of Pedagogical Practices for Collaborative Mathematics Classrooms MAA MathFest 2019 David Taylor, Roanoke College

2. Background • I have been teaching at Roanoke College for 12 years. • For academic year 2018-2019, I participated, along with 25 colleagues from all disciplines across campus, in an online course offered through the Association of College and University Educators (ACUE). • “Effective Teaching Practices: Career Guidance and Readiness”

3. Today • Focus on four ideas to use in mathematics classes that encourage collaboration or self-reflection and align courses with course objectives: • Peer Review • Student-Created Rubrics • Aligning Assessments • Reflecting on Learning Outcomes

4. Peer Review • Course: Calculus II (MATH 122) • Assessment: Mastery-Based Testing • Method: • Students are given a practice mastery topic to try on their own for five minutes. • In pairs, students review each other’s work, determine whether or not the topic would have been mastered, and discuss what went well and what needed improvement. • As a class, we discuss what they saw and learned, see an instructor solution, and have a discussion about what it truly means to master a topic.

5. Peer Review • Course: Calculus II (MATH 122) • Assessment: Mastery-Based Testing

6. Peer Review • Course: Calculus II (MATH 122) • Assessment: Mastery-Based Testing • Outcome: • Observationally, the rate at which students achieved mastery increased most after the first peer review session, and less so after additional peer review sessions. • Takeaway: • Peer review sessions are helpful for learning content, but even more helpful for promoting discussion about what mastery means.

7. Student-Created Rubrics • Course: Introductory Statistics (INQ 240) • Assessment: Course Project • Method: • After doing one project and receiving feedback, students are tasked to create a rubric for the second (and third) projects. • In groups of two or three, students are asked to reflect on what went well on the first project and what could use improvement. • Then groups are asked to write down two or three categories for the rubric, followed by achievement level descriptions. • As a class we select about five categories for the rubric and refine the achievement level descriptions.

8. Student-Created Rubrics • Course: Introductory Statistics (INQ 240) • Assessment: Course Project

9. Student-Created Rubrics • Course: Introductory Statistics (INQ 240) • Assessment: Course Project • Outcome: • Students appear more invested in the project and show more improvement between projects than in the past. • Takeaways: • A bit of prompting and questioning during the process helps a lot, since students aren’t experts in rubric creation and there are items instructors know need to be included in some way. • Grading felt “better” knowing that the rubric was a collaborative effort.

10. Aligning Assessments • Course: All • Assessment: Choosing Them • Method: • Nilson (2010) extended Bloom’s taxonomy in an effort to help instructors write powerful learning outcomes and determine the cognitive level of those outcomes. • Using those cognitive levels, use best practices to choose assessment techniques that are capable of measuring how well students are meeting the course-level learning outcomes.

11. Aligning Assessments

12. Aligning Assessments

13. Aligning Assessments

14. Aligning Assessments • Course: All • Assessment: Choosing Them • Takeaways: • This doesn’t require a wholesale course change; most of what I was doing already mapped well. • Learning more about mapping assessments to learning outcomes made me rethink and rewrite my learning outcomes. • The learning outcomes are now worth time discussing them on “syllabus day” and throughout the semester, rather than a required item on the syllabus.

15. Reflecting on Learning Outcomes • Course: Real Analysis (MATH 381) • Assessment: Reflection on Learning Outcomes • Method: • Research shows that students appreciate a class more when its learning outcomes and goals can directly relate to future courses or potential careers. • I wanted students in Real Analysis to reflect on the learning outcome “students will be able to demonstrate an understanding of mathematical language and techniques of mathematical proof.” • I gave them a take-home quiz on the second day of class.

16. Reflecting on Learning Outcomes

17. Reflecting on Learning Outcomes • Course: Real Analysis (MATH 381) • Assessment: Reflection on Learning Outcomes • Takeaways: • It was a great assignment to learn more about my students and to get a sense of what they wanted to do after graduating. • Their reflections on the learning outcome and how they would talk to a future employer were amazing, but all over the place as a class. • I will modify this learning outcome in the future by breaking it into two, each that are more specific and following best practices.

18. Final Thoughts • I was the only mathematics professor in our cohort of about 25 faculty taking the ACUE course. • Several “ideas” didn’t seem to map well to mathematics classes at first, but elements of those ideas can map extremely well (for example, peer review). • Paying more attention to the syllabus and learning outcomes throughout the entire semester can really help students appreciate the course itself and see how it maps into a larger program and can help with future careers.

19. Questions? • I’d be happy to answer questions and/or engage in pedagogical discussion! • Contact: taylor@roanoke.edu