1. A Scale-up Class Model for Multivariate Calculus
Gus Greivel & Scott Strong
Department of Applied Mathematics and Statistics
Supported by ONR Grant #N 1

2. The SCALE-UP Model:
Origins in improving undergraduate Physics instruction and learning at North Carolina State University…
Student Centered Active Learning Environment with Upside-down Pedagogies (originally for Undergraduate Physics)
Key Ideas Include:
Provides a learning environment specifically created to facilitate active, collaborative learning.
Students can be given something interesting to investigate.
Instructor and TAs are free to roam around the classroom – asking questions, sending one team to help another, or asking why someone else got a different answer.
Groups are carefully structured and give students many opportunities to interact. 2

3. SCALE-UP – Multivariate Calculus:
While students have been working with 2-D coordinates for the better part of a decade, the initial explorations of the 3rd dimension can be challenging…
Expose students to graphical/visualization tools (Mathematica “Plot” and “Manipulate” commands)
Invite group discussions of the subtleties involved with applying existing knowledge to problems in higher dimensions
Calculus III invites a richer and more realistic set of applications for STEM students…
The Studio environments provides more time and resources for students to “dig in” to larger applications (Students can be given something interesting to investigate).
Instructor and TAs can provide real-time support to better guarantee “success” in the exploration of these richer problems. 3

4. Grant Objectives:
Long history of success with the SCALE-UP model in Physics at Mines… referred to as “Studio Physics”
This grant leveraged that success to fund explorations of extending the model to a larger set of classes at Mines, integrating the model both vertically (upper-division Physics) and horizontally (Mines core courses).
Specific objectives include:
Reinforcing a growth mindset
Developing leadership and teamwork skills within the context of disciplinary coursework
Developing computational and modeling skills within the context of disciplinary coursework
Open-ended problem solving 4

5. Initial Pilot and Subsequent Development:
The grant was awarded in October of We have had five Calculus III Honors Cohorts in the studio environment since the Fall of 2015.
Greivel and Strong have iteratively developed the honors studio environment based on feedback from students and course assessments…
Worksheets and associated Mathematica notebooks
Honors Calculus Project as a component of the course
Frequent surveys of the students to update/modify our studio practices
Groomed a cohort of undergraduate TAs
Experimented with studio submission formatting and grading rubrics (graded with emphasis on reflection and organization, in addition to correctness) 5

6. Examples of Student Work:
As first-year undergraduates, our students have adopted reflective practices (even in rote homework sets)
HW PDF Juliana A., Juliana A., April W.

7. Examples of Student Work:
Our students have explored concepts and tools well beyond the explicit expectations of assignments
HW PDF Juliana A., Juliana A., April W.
Nomin’s Mathematica gif
Cooper’s group’s project report
John Helend’s co-authored term project, Liam’s Mathematica tutorials

8. Examples of Student Work:
Our students have attempted and succeeded on assignments that were well above the level of the course
HW PDF Juliana A., Juliana A., April W.
Nomin’s Mathematica gif
Cooper’s group’s project report
John Helend’s co-authored term project, Liam’s Mathematica tutorials

9. Results:
Extremely high performance with respect to assessments of course learning outcomes and exam performance
But this is not a surprise given the cohort selection
Student feedback: Mixed, but generally positive and, considering the audience of first-year undergraduates, they have…
Adopted reflective practices (even in rote homework sets)
Explored concepts and tools well beyond the explicit expectations of assignments
Attempted and succeeded on assignments that were well above the level of the course
Engaged the subject matter over multiple additional semesters (as TAs)
Developed content for future students that connects course materials to topics they find interesting and relevant. 9

10. Results: A few excerpts from students course evaluations…
“I love how this course is truthfully challenging. I have never been more interested in math [than] I am now. I appreciate the project-based structure.” (Fall 2016)
“I really enjoy the studio portion of this course. I think it is one of the most effective ways to learn the material, and it is fun to do it in a group setting. I also had fun doing the term project and I think it was a really good balance of review, as well as relevant new information that I really enjoyed learning about.” (Spring 2017)
“The additional studio element of this course was very helpful. It provided an environment that helped us visualize the problems and enabled groups to have discussions. The ability to visualize material and discuss your work and answers helped [us learn] the material and increased retention of learned material.” (Fall 2017)
“I love the studio portion of the class, as it gives us more in depth examples to work on and use to understand the material.” (Spring 2018) 10

11. Results:
Some “unexpected” outcomes for the undergraduate TAs in this course…
Undergraduate TAs have multi-semester engagement with the mathematics department, leading to a slight uptick in majors.
Several of our TAs engage the department and the campus more deeply, leading to an increase in undergraduate research, awards and recognitions.
One of our first TAs was in the inaugural class of Knight-Hennessy Scholars at Stanford University, citing this experience as a key component in her interest in pursuing graduate studies. 11

12. Lessons Learned:
Where appropriate*, this instructional model can be leveraged to effectively engage our students with an eye toward…
Enriching disciplinary content (challenge problems, term projects)
Developing a co-created learning environment where the students have greater input into their learning experiences
Encouraging group interactions around disciplinary content
Reinforcing key educational concepts, like growth mindset, within the context of disciplinary coursework (rather than in a college success seminar)
Modeling intellectual struggle, collaboration, etc.
If adopted, this instructional model can (and should) be tuned to the specific environment in which it is being employed…
Iterative development process
Requires appropriate developmental resources (time, space, TA budget, etc.) 12

13. Questions? 13