**A Volume On Authentic Applications **

#### Link: Authentic Applications

Kseniya Garaschuk (Fraser Valley) and Anton Mosunov (Waterloo)

Mathematics instructors rarely have to be convinced that the subject they teach is important, but getting this point across to students is often a challenging task. In June we organized a session at the CMS Summer Meeting, bringing together first-year mathematics instructors to share authentic applications from their courses to enhance the curriculum in various service courses (life sciences, business, computer science, etc). Instructors who presented at this session, as well as those who responded to the consequent call for contributions, each authored a short article for the volume on *Authentic Applications*. The applications you find in this volume are authentic in the sense that they are based in the “real-world” first, with math derived out of the context, rather than the other way around. Among others, this collection includes articles on modelling the optimal length of pregnancy, using calculus to model UV index, and linear algebra of Google search. Notable exceptions include Section 10 that involves an imaginary but charming application for a math majors course and Section 11 that describes various open education technologies, such as CoCalc and PreTeXt, that can be used to teach applied content to students. We invite you to present these fascinating applications to students in your classes!

**Supplementary Materials for Section 6, Emily Kozlowski, Introductory Statistics Authentic Final Project:**

Final Project R Tutorial [TXT file]

Final Project Template [Word file]

real_estate2 [CSV file]

STAT 231 R Tutorial AS5 [TXT file]

STAT 231 S21 Final Project SOLNs [PDF file]

STAT 231 S21 Final Project [PDF file]

**High School Math Curriculum in Canadian Provinces & Territories**

**Provinces **

**Alberta: **https://www.learnalberta.ca/content/mychildslearning/highschool_math.html

**British Columbia: **https://curriculum.gov.bc.ca/curriculum/mathematics

**Manitoba: **https://www.edu.gov.mb.ca/k12/cur/math/framework_9-12/index.html

**New Brunswick: **https://www2.gnb.ca/content/gnb/en/departments/education/k12/content/anglophone_sector/curriculum_anglophone.html

**Newfoundland & Labrador: **https://www.gov.nl.ca/education/k12/curriculum/guides/mathematics/

**Nova Scotia: **https://curriculum.novascotia.ca/english-programs/mathematics/high-school

**Ontario: **http://www.edu.gov.on.ca/eng/curriculum/secondary/math.html

**Prince Edward Island: **https://www.princeedwardisland.ca/en/information/education-and-lifelong-learning/mathematics-curriculum

**Quebec: **http://www.education.gouv.qc.ca/en/teachers/quebec-education-program/secondary/

**Saskatchewan: **https://www.edonline.sk.ca/webapps/moe-curriculum-BB5f208b6da4613/

**Territories**

**Northwest Territories: **https://www.ece.gov.nt.ca/en/services/jk-12-school-curriculum/mathematics

**Nunavut: **https://www.gov.nu.ca/education/information/curriculum-learning-resources-0

**Yukon: **https://yukon.ca/en/school-curriculum

**CEGEP: ***Collège d’enseignement général et professionnel*

*Collège d’enseignement général et professionnel*

**Les CEGEPs de Quebec: **

https://www.cegepsquebec.ca/en/

**Presenters at our Meet Up:**

Julie Plante (Vanier College): CEGEP Presentation for Math Universities [Presentation Slides]

Jean-Philippe Villeneuve (Cegep de Rimouski): CEGEP – Between High School and University [Presentation Slides]

Andree-Ann Pugin (Cegep de l’Outaouais): Teaching Mathematics in CEGEP [Presentation Slides]

**Teaching & Learning Resources**

**Books**

** Math Proofs:**

- Gila Hanna and Michael de Villiers: Proof and Proving in Mathematics Education: The 19th ICMI Study [Link; Downloadable PDF file available]
- University of Calgary: The Proof Handbook [Website]

**Writing Math:**

- Francis Su: Teach Math like you’d teach writing [https://www.francissu.com/post/teach-math-like-youd-teach-writing]

**Course Resources**

**Activities:**

- Peter Taylor (Queen’s): Collision Model Activity [Presentation Slides]; Collision Model Notes [Slides]
- Ana Duff (Ontario Tech): Modelling CPI Investigation and Sample Student Work [Presentation Slides]; Canadian Mobile Subscriptions Investigation [Presentation Slides]

**Alternative Delivery:**

- Andrea Hyde (College of the Rockies): Teaching Math and Stats in “Alternate Delivery” Format [Presentation Slides]

**Collaborative Learning:**

- Vanessa Radzimski (Fraser Valley): Collaborative Learning Online [Presentation Slides]
- Perusall [Website]
- Hypothesis [Website]
- H5P [Website]; H5P links [Website]

**Course Outline:**

- Sean Fitzpatrick (Lethbridge): Course Outline [Website]

**Course Planning:**

- Mateen Skaikh (Thompson River): Planning Calculus Week-by-Week [Google Doc]

**Icebreakers:**

- Alfonso Garcia-Saz (Toronto): Alfonso’s Ice Breaking Puzzle [Google Doc] (prepared in collaboration with Nicholas Remedios, based on an idea by Chris Tuffley)
- Carmen Bruni (Waterloo): Icebreaker – Important! Only click on one link! No cheating! Earliest Birthday (ignore year!) [Google Doc]; Second Earliest Birthday [Google Doc]; Third Earliest Birthday [Google Doc]; Latest Birthday [Google Doc]
- August 24, 2020, Icebreakers Meet Up … All Icebreakers [Website] by Tyler Holden (UTM)

**Math Proofs:**

- Bran Katz: Proof Validation [Google Doc], also on Youtube

**Teaching & Learning Apps & Websites:**

- Peter Taylor (Queen’s): Rabbitmath
- Jonathan Herman (UTM): MathMatize platform to review linear algebra and pre-calculus
- Perusall
- Hypothesis
- H5P; H5P links
- Bolster [App] https://bolster.academy/demo/ (contact: marc@bolster.academy & edna.james@algomau.ca) Free Demo: https://bolster.academy/pilot/
**Möbius**[PDF]Möbius is the best learning platform for creating and deploying online STEM courses. Providing lessons, assessments and interactive learning activities, it unfolds the potential for the STEM student to acquire knowledge at a guided yet self-defined pace.For all additional information about Möbius, please contact: Milan Milovic (milan.milovic@digitaled.com) or fill this form to book a demo https://digitaled.com/contact/book-a-demo

**Student Engagement:**

- Barb & Brian Forrest (Waterloo): Asynchronous Student Engagement [Presentation Slides]

**First-time Teaching Resources**

**Apps:**

- Bolster [App] https://bolster.academy/demo/ (contact: marc@bolster.academy & edna.james@algomau.ca) Free Demo: https://bolster.academy/pilot/
**Möbius**[PDF]Möbius is the best learning platform for creating and deploying online STEM courses. Providing lessons, assessments and interactive learning activities, it unfolds the potential for the STEM student to acquire knowledge at a guided yet self-defined pace.For all additional information about Möbius, please contact: Milan Milovic (milan.milovic@digitaled.com), or fill this form to book a demo https://digitaled.com/contact/book-a-demo

**Documents:**

- MAA Instructional Practices Guide [PDF]: https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide
- UDL Quick Tips [PDF]: UDL Quick Tips

**Professional Development Programs:**

- NExT [Program]: https://www.maa.org/programs-and-communities/professional-development/project-next
- CoMInDs [Program]: https://www.maa.org/programs-and-communities/professional-development/cominds

**Training:**

- University of Waterloo Instructor Training [PDF]: Instructor-Training_Courses

**Videos:**

- BIRS (Innovations in Instructor Training) [Video]: https://www.birs.ca/events/2019/2-day-workshops/ 19w2231/videos
- Sample Teaching Videos [Video]:

**Handouts**

**Math Proofs:**

- Kitty (Xiaocheng) Yan (SFU): Logic and indirect proof; Logic and proof; Proof validation
- Thi Dinh: Thi Bible

**Teaching Documents:**

- MAA Instructional Practices Guide [PDF]: https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide
- UDL Quick Tips [PDF]: UDL Quick Tips

**Podcasts**

**Math Proofs:**

- Intellectual Mathematics: http://intellectualmathematics.com/opinionated-history-of-mathematics/

#### Professional Development Programs

- NExT [Program]: https://www.maa.org/programs-and-communities/professional-development/project-next
- CoMInDs [Program]: https://www.maa.org/programs-and-communities/professional-development/cominds

**Websites**

**Fun Videos:**

- Timothy Growers (solving math problems in real time), one example: https://www.youtube.com/watch?v=NmEVwJ_lJ1A

**Learning Apps & Websites:**

- Peter Taylor (Queen’s): Rabbitmath
- Jonathan Herman (UTM): MathMatize platform to review linear algebra and pre-calculus
- Bolster [App] https://bolster.academy/demo/ (contact: marc@bolster.academy & edna.james@algomau.ca)
- Perusall
- Hypothesis
- H5P; H5P links

**Math Proofs:**

- Bran Katz: Proof Validation on Youtube
- Liping Ma: https://buildingmathematicians.wordpress.com/tag/liping-ma/
- A Resource Bank for Writing Intensive Mathematics Courses: http://proof.ucalgaryblogs.ca
- Math with Bad Drawings: https://mathwithbaddrawings.com/2021/05/12/against-mathematical-proof/
- Pascal having “Consequences” to introduce induction: https://gallica.bnf.fr/ark:/12148/btv1b86262012.texteImage

**Sample Teaching Videos:**

- BIRS (Innovations in Instructor Training) [Video]: https://www.birs.ca/events/2019/2-day-workshops/ 19w2231/videos
- Sample Teaching Videos [Video]:

**Past Publications**

#### 2024

- Chow, A. N., Morris, K. A., & Rabbah, G. (2023). Hysteresis and Stability,
*SIAM Review*, 65(4). Retrieved from: https://epubs.siam.org/doi/10.1137/21M1420733 - Coles, M., & Piccolo, C. (2023). A term-long course on post-secondary mathematics teaching for graduate students: The start of their teaching journey.
*PRIMUS*, 1–14. Retrieved from: https://doi.org/10.1080/10511970.2023.2235688 - Jungić, V., Menz, P., & Pyke, R. (2024). Differential calculus problems and solutions from fundamentals to nuances,
*World Scientific*. Retrieved from: https://doi.org/10.1142/13324 - Jungić, V. (2024). What my students have taught me about being a teacher,
*Times Higher Education*. Retrieved from: https://www.timeshighereducation.com/campus/what-my-students-have-taught-me-about-being-teacher

#### 2023

- Chow, A. N. (2023). Hysteresis as an Authentic Mathematics Application,
*For the Learning of Mathematics*, 43(1), 36-39. - Burazin, A., DeDieu, L., Jungić, V., & Lovric, M. (2023). Teaching-Stream Faculty in Canada – How are We Doing?,
*Canadian Mathematical Society Notes*, 55(1). Retrieved from:**https://notes.math.ca/en/article/teaching-stream-faculty-in-canada-how-are-we-doing-2/** - Burazin, A., L., Jungić, V., & Lovric, M. (2023). On a Class of Integrals related to Wallis Integrals. arXiv:2305.08966. Retrieved from:
**http://arxiv.org/abs/2305.08966** - Burazin, A., L., Jungić, V., & Lovric, M. (2023). Wallis m-integrals and their properties,
*Scientia, Series A: Mathematical Sciences*, 33, 61-71. - Burazin, A. & Lovric, M. (2023). Which Years are the Unluckiest?,
*Canadian Mathematics Education Study Group Newsletter*, 39(2). Retrieved from:**https://view.genial.ly/646d6bbb52b6be00129eee34** -
Jungić, V. (2023). Basics of Ramsey Theory,
*Routledge*. Retrieved from: https://www.routledge.com/Basics-of-Ramsey-Theory/ Jungic/p/book/9781032260372 - Burazin, A., DeDieu, L., Jungić, V., & Lovric, M. (2022). Make Teaching-stream Count,
*University Affairs*. Retrieved from: https://www.universityaffairs.ca/opinion/in-my-opinion/it-is-time-to-make-teaching-stream-faculty-count/ - Burazin, A., Jungić, V., & Lovric, M. (2022). From the lecture notes of …,
*Canadian Society Notes*, 48(5). Retrieved from: https://cms.math.ca/publications/crux/issue/?volume=48&issue=5 - Maciejewski, W. (2023). The Siren Call of Calculus: A Review of Steven Strogatz’s Infinite Powers: How Calculus Reveals the Secrets of the Universe,
*The Mathematics Enthusiast*, 40(1). Retrieved from: https://scholarworks.umt.edu/cgi/viewcontent.cgi?article=1601&context=tme

#### 2022

- Brinkman, E., Corless, R., & Jungić, V. (2021). The Theodorus Variation, Maple Transactions, 1(2).
- Bruni, C. (2021). A Graduate Student Instructor Training Seminar.
*Canadian Mathematical Society Notes*, 53(6). Retrieved from: https://notes.math.ca/en/article/a-graduate-student-instructor-training-seminar/ - Burazin, A. (2022). Snapshot from a bumpy academic year, through a math professor’s lens, University Affairs. Retrieved from: https://www.universityaffairs.ca/opinion/in-my-opinion/snapshots-from-a-bumpy-academic-year-through-a-math-professors-lens/
- Burazin, A., Jungic, V., & Lovric, M. (2022). From the Lecture Notes of . . .,
*Crux Mathematicorum*, 48(5). Retrieved from: https://cms.math.ca/publications/crux/issue/?volume=48&issue=5 - Burazin, A., Jungic, V., & Lovric, M. (2021). Growing Pains: Becoming a University Student.
*Canadian Mathematical Society Notes*, 53(5). Retrieved from: https://notes.math.ca/en/article/growing-pains-becoming-a-university-students/ - Chen, P., Sibia, N., Zavaleta, A., Liut, M., & Williams, J. (2022). Investigating the Impact of Voice Response Options in Surveys. ACM SIGCSE 2022, 1124.
- Chow, A. (2022). From the Lecture notes of…,
*Crux Mathematicorum*, 48(6). Retrieved from:

https://cms.math.ca/publications/crux/issue/?volume=48&issue=7 - Holden, T., & Burazin, A. (2022). Mandatory Assignments and Learning Achievements in a Mathematics Service Class,
*PRIMUS*. Retrieved from: https://doi.org/10.1080/10511970.2022.2040666 - Jungic, V., & Burazin, A. (2021). On Experimental Mathematics and Mathematics Education,
*American Mathematical Monthly*, 128(9). - Jungić, V. (2022). The Ramsey Theory Podcast: No Strangers At This Party, Spotify.
- Jungić, V. (2002). Two-Eyed Seeing: Mathematics and Indigenous Traditions and Cultures,
*Maple Transactions*2(1), Article 15186. - Jungić, V. (2022). Math Catcher Outreach Program,
*Notices of the American Mathematical Society*, 69(8), 1369-1375. - Jungić, V. (2022). An introduction of van der Waerden’s theorem through examples and exercises, Part I,
*Crux Mathematicorum*, 48(7), pp. 412-420. - Jungić, V. (2022). On density of planar sets avoiding unit distance,
*U(t)-Mathazine*, 7, pp. 2-5. - Lewitzky, R. A. (2022). Facilitating learning in online undergraduate mathematics and statistics courses,
*International Journal of E-Learning*, 21(2), 163-179. Retrieved from: https://www.learntechlib.org/primary/p/218702/ - Lewitzky, R. A. (2022). Creating communities of inquiry in research and scholarship via online videos.
*Scholarly & Research Communication, 13*(2). Retrieved from: https://doi.org/10.22230/src.2022v13n2a425 - Parkinson, J., Bockmon, R., Cutts, Q., Liut M., Petersen, A., & Sorby, S. (2021). Practice Report: Six Studies of Spatial Skills Training in Introductory Computer Science, ACM Inroads, 12(4), pp. 18–29.
- Singh, K., Mei, J.B., & Jungic, V. (2022). Life of a Working Ramsey Theorist: Conversation With Tom C. Brown, Journal of Humanistic Mathematics, 12(1), pp. 399-407.

#### 2021

- Burazin, A., Jungic, V., & Lovric, M. (2021). A Cultural Challenge: Teaching Mathematics to Non-mathematicians.
*Maple Transactions,*1(1). - Burazin, A., Jungic, V., & Lovric, M. (2021). Open letter to my soon-to-be student: Math likely tops the list of things you worry about, but there is good news,
*Academic Matters*. Retrieved from: https://academicmatters.ca/open-letter-to-my-soon-to-be-student-math-likely-tops-the-list-of-things-you-worry-about-but-there-is-good-news/ - Burazin, A. (2021). What teaching issues we need to think about as we transition back to in-person learning.
*University Affairs*. Retrieved from: https://www.universityaffairs.ca/opinion/in-my-opinion/what-teaching-issues-we-need-to-think-about-as-we-transition-back-to-in-person-learning/ - Burazin, A., Jungic, V., & Lovric, M. (2021). Teaching during the pandemic: an open letter to my students,
*University Affairs*. Retrieved from: https://www.universityaffairs.ca/opinion/in-my-opinion/teaching-during-the-pandemic-an-open-letter-to-my-students/ - Glynn-Adey, P., & Li, Z. (2021). In Tetracycles: a SET Deck Magic Trick.
*Math Horizons*, 28(4), 16-18. - Kondratieva, M. (2021) Trusting Your Own Eyes: Visual Constructions, Proofs, and Fallacies in Mathematics. In: Danesi M. (eds) Handbook of Cognitive Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-44982-7_38-1
- Liut, M., & Petersen, A. (2021). Incorporating Resubmission into Skills-based Courses at the University of Waterloo Teaching and Learning Conference (UWTL). YouTube Video.

#### 2020

- Awuah, R., Gallagher, K. M., & Dierker, L. C. (2020). Taking project-based statistics abroad: Learning experiences and outcomes of a project-based statistics course in West Africa.
*Statistics Education Research Journal*, 19(3), 18-31. - Burazin, A., Jungic, V., & Lovric, M. (2020). Math, WiFi and no social life: The harsh realities starting university in a pandemic,
*The Hamilton Spectator*. Retrieved from:https://www.thespec.com/opinion/contributors/2020/08/27/math-wifi-and-no-social-life-the-harsh-realities-of-starting-university-in-a-pandemic.html - Burazin, A., Jungic, V., & Lovric, M. (2020). Let them cheat: Why it’s tempting for college and university instructors to look the other way. CBC News. Retrieved from: https://www.cbc.ca/news/opinion/opinion-academic-cheating-1.5576990.
- Deza, A., Hu, H., Maisuria, V., Liut, M., Petersen, A., & Simion, B. (2020). Using Discussion Board Data to Hire Teaching Assistants. Sixth SPLICE Workshop at L@S 2020.
- Glynn-Adey, P. (2020). Using a wiki to collect student work in Vector Calculus. International Journal of Mathematical Education in Science and Technology.
- Veselin Jungic published his opinion piece “Despite the pandemic, the rules of academic integrity still apply” in University Affairs, 21 April 2020.
- CBC, 23 September 2020: [Andie, Veselin, Miroslav] Let them cheat: Why it’s tempting for college and university instructors to look the other way (over 300 comments!)

#### 2019

- CMS Notes Editor-in-Chief Robert Dawson (St. Mary’s) published a short opinion piece “Why Do We Teach What We Teach?” in the latest issue (51(3), June 2019) of CMS Notes. To access it, visit CMS Digital Archive https://cms.math.ca/notes/
- CMESG Newsletter/Bulletin 35(2) May 2019 (pages 2-5) published the report “First Year Mathematics Repository Workshop BIRS, Banff, AB, February 8-10, 2019” by Andie Burazin, Veselin Jungic and Miroslav Lovric.

#### 2018

- A critique “Rethinking Teaching First-Year Mathematics in University” by Andie Burazin and Miroslav Lovric, appeared in the Proceedings of the 2018 CMESG meeting in Squamish, B.C. (pages 123-130).