Challenges and Opportunities in Teaching First-Year Mathematics

1. Three Countries, Two Continents: Common Challenges and Opportunities in Teaching First-Year Mathematics Dr. VeselinJungić Simon Fraser University

2. SFU Faculty of Science Math Note: 1 AFTE = 30 credit hours

3. SFU Faculty Of Science

4. SFU First-year Math Courses • Foundations of Analytical and Quantitative Reasoning - All • Precalculus - All • Calculus I & II - Sciences & Engineering; Business & Social Sciences; Life Sciences • Geometry for Computer Graphics - Interactive Art • Linear Algebra - Sciences & Engineering • Discrete Mathematics - CS & Math

5. Faculty

6. Challenges For First-year Mathematics Teaching  FYiMaths Project, 2012-2014, Australia

7. Across the Ocean There is plenty of evidence suggesting that university mathematical teaching communities in Australia, Canada, and the United States are facing similar challenges and opportunities.

8. Example Buckmire, Ron. (2019). Education: A Survey of Significant Developments in Undergraduate Mathematics Education Over the Past Decade. Notices of the American Mathematical Society. 66. 1. 10.1090/noti1761.

9. Ron Buckmire “Most significant results, events, or developments in undergraduate mathematics education of the last decade”: • Curricular Pathways • Pedagogical Innovation • Demographic Changes • Expanding Career Options

10. A Trailer • Curricular Pathways: discusses the lack of mathematical knowledge and preparation • Pedagogical Innovation: investigates the obstacles of “traditional mathematics pedagogy and poor student engagement” • Demographic Changes: raises the issue of the diversity of students’ backgrounds • Expanding Career Options: suggeststhat building first-year courses around mathematical modeling could be the way to address the challenge of teaching ‘service’ mathematics courses

11. Australia

12. First Year in Maths - FYiMaths • 2012-2014 • Led by Dr. Deborah King, University of Melbourne • Funded by the Australian government Officer for Learning and Teaching

13. FYiMaths To promote and support strategic change and improvements in first-year learning and teaching in the mathematical sciences throughout the Australian higher-education sector, with significant benefits for the student experience.

14. FYiMaths To develop and enhance deeper understanding and knowledge of learning processes in the mathematical sciences, particularly with regard to transition from [high] school to university, and subsequently from university to the wider professional community.

15. FYiMaths FYiMaths project final report. The establishment of the FYiMaths Network, “a ‘community of practice’ providing an informal and supportive group for academics and educators to access information, exchange ideas, address shared challenges and collaborate on research and policy questions”.

16. USA

17. USA Mathematical Association of America: • Characteristics of Successful Programs in College Calculus (2009) • Progress through Calculus (2015) • Precalculus to Calculus: Insights and Innovations Conference (2016) • Guide to Evidence-Based Instructional Practices in Undergraduate Mathematics (2018)

18. USA AMATYC, AMS, ASA, MAA, and SIAM jointly sponsored “The Common Vision” project with the ultimate goal to “galvanize the mathematical sciences community around a modern vision for undergraduate programs and to spur grassroots efforts within the community as a foundation for addressing the collective challenges we face”.

19. A Common Vision for Undergraduate Mathematical Science Programs in 2025 (Saxe & Braddy, 2016) “We want to re-iterate the fact that all seven curricular guides declared that the status quo is unacceptable. The specific areas that all the guides agreed require significant further action fall into one of four categories: curricula, course structure, workforce preparation, and faculty development. These are, of course, interdependent and do not exist in isolation.”

20. A Common Vision for Undergraduate Mathematical Science Programs in 2025 (Saxe & Braddy, 2016) “(…) Improving teaching and learning requires well-coordinated efforts by multiple stakeholders, including faculty, administrators, employers, professional associations, and funding agencies.”

21. Expanding Career Options In 2012, the President’s Council of Advisors on Science and Technology (PCAST) castigated the mathematics community for instruction that was “dull and unimaginative,” recommending that introductory courses be turned over to “faculty from mathematics-intensive disciplines other than mathematics.” Buckmire, R. (2019). A Survey of Significant Developments in Undergraduate Mathematics Education Over the Past Decade. Notices of the American Mathematical Society, 66 (1), 46-51.

22. Manifesto: A declaration of values For the reference: Abell, M., Braddy, L., Ensley, D., Ludwig, L., & Soto-Johnson, H. (2018). MAA Instructional Practices Guide. Retrieved from Mathematical Association of America: Washington, DC: https://www.dropbox.com/s/42oiptp46i0g2w2/MAA_IP_Guide_V1-2

23. Manifesto: A declaration of values “Mathematics instructors stand at a crossroads. We must gather the courage to take the difficult path of change. We must gather the courage to venture down the path of uncertainty and try new evidence-based strategies that actively engage students in the learning experience. We must gather the courage to advocate beyond our own classroom for student-centered instructional strategies that promote equitable access to mathematics for all students.”

24. Manifesto: A declaration of values “We stand at a crossroads, and we must choose the path of transformation in order to fulfill our professional responsibility to our students. This Instructional Practices Guide can serve as a catalyst for community-wide transformation toward improved learning experiences and equitable access to mathematics for all students. Society deserves nothing less.”

25. Canada

26. Canada “Canada’s university mathematical teaching community is facing a number of significant challenges and opportunities. These range from managing increasingly diverse classes of incoming students, to understanding and addressing the impact of modern technology on teaching and delivering courses, to keeping course content relevant for various academic programs and, most importantly, to effectively supporting students to achieve their personal, academic and career goals.” Jungić, V., & Lovrić, M., (2017). Call for National Dialogue: The Present and Future of Teaching First Year Mathematics at Canadian Universities. Canadian Mathematical Society Notes, 49 (5), 10-12.

27. First-year Mathematics and Statistics Courses Repositoryhttps://firstyearmath.ca/ Shareable dynamic online database contains extensive data collected from mathematics and statistics instructors across the country. Data includes course content, resource and technology used, learning outcomes, modes of delivery, connections with other courses, as well as informal descriptions of various practices in teaching these courses.

28. First-year Mathematics and Statistics Courses Repository 1. Who is the intended audience? Within Canada, university faculty (chairs, associate chairs, deans, professors, lecturers, sessional instructors) in mathematics and statistics departments, college instructors, high school teachers (grade 12 mostly) who are interested in learning about first-year mathematics and statistics, as well as education developers and publishers.

29. First-year Mathematics and Statistics Courses Repository 2. How will this information be shared? The information is shared with approved members of the repository. Those who are interested will fill out a questionnaire. After the questionnaire, the information is verified by the page administrators, and the page administrators determine if the information fits the purpose of the repository, where after access (login and password) will be granted.

30. First-year Mathematics and Statistics Courses Repository 3. How frequently is the data updated? This would depend on the curators at each institution. As the main purpose of the database is to provide a snapshot of teaching first-year mathematics and statistics. It would be ideal if the curators visit their part of the database as often as possible to update the existing data and enter any missing data.

31. First-year Mathematics and Statistics Courses Repository

32. First-year Mathematics and Statistics Courses Repository

33. First-year Mathematics and Statistics Courses Repository

34. What Do We Teach?

35. Canadian National Dialogue The response of the Canadian mathematics teaching community was overwhelming.

36. Meetings 2017 - 2019 • 2017 Canadian Mathematics Education Study Group Meeting in Montreal, Quebec, Working Group “Teaching First Year Mathematics Courses in Transition from Secondary to Tertiary” • 2017 Canadian Mathematics Society Winter Meeting in Waterloo, Ontario, Education session “Rethinking First Year Experience” • 2018 “First Year University Mathematics Across Canada: Facts, Community and Vision” conference. Fields Institute in Toronto, Ontario • 2019 “First Year Mathematics Repository Workshop” in the Banff International Research Station (BIRS) in Banff, Alberta • 2019 “First-Year University Mathematics in Canada: Time to Rethink our Curriculum?” conference. University of Alberta, Edmonton, Alberta

37. Common Observations of Meetings • Talent and innovation • Young people • # of females about the same as # of males • Strong feelings against the commercialization of learning resources • “It felt like a community I have been seeking for a long time.”

38. Personally … … it became apparent that in Canada answers to the set of common challenges in teaching first-year mathematics courses may depend on the size of the university (large vs. small), institution’s mandate (research intense vs. teaching intense), financial model (public vs. private), geographical location (have vs. no-have provinces), and so on.

39. Banff 2019 How do different institutions and different instructors find the balance between introducing a relatively complex math content and meeting the needs of the specific program that the course “services”?

40. Banff 2019: Some Outcomes • Service courses provide unique opportunities to teach mathematics that is interesting, exciting, and stimulating, and that addresses authentic life situations. This is where we are forced to re-think the mathematics content, to benefit not only service courses, but all math courses. • Service courses are mostly taught by younger instructors; often they are on limited-term contracts or hold more permanent, but non-tenure track positions. • A successful design of a service course requires continuous communication with faculty in all departments whose students will be taking the course. • Much-needed innovation in math and stats instruction happens in service courses!

41. Overall Conclusions from Meetings Challenges, problems, objectives and strategies that have been discussed are definitely not new: they have been around for decades As it seems that our previous efforts have not managed to alleviate any of the dominant problems, we have to ask ourselves: should we, post-secondary teaching practitioners and our students, hope that this time it will be successful?

42. Overall Conclusions from Meetings Our answer is “Yes”, and our optimism is based on the fact that there is a widespread consensus that “the status quo is unacceptable”. The recent initiatives indicate that there is growing awareness that we, the global mathematics and statistics teaching community, have to put additional effort into supporting our current and future students to learn mathematics and to achieve their academic goals.

43. Acknowledgment This presentation’s material was created in collaboration with the following colleagues: Dr. Andie Burazin, University of Toronto Mississauga, and Dr. Miroslav Lovrić, McMaster University

44. Thank You! Dr. VeselinJungić Email: vjungic@sfu.ca