In accordance with the Royal Military College of Canada (RMC) Institutional Quality Assurance Process (IQAP), this Final Assessment Report (FAR) provides a synthesis of the external evaluation and internal response and assessments of the undergraduate program in Mathematics offered by the Faculty of Science. This report identifies the significant strengths of the program, together with opportunities for improvement and enhancement, and sets out and prioritizes the recommendations that have been selected for implementation.
This report includes an Implementation Plan that identifies who will be responsible for approving the recommendations set out in the Final Assessment Report; who will be responsible for providing any resources entailed by those recommendations; any changes in organization, policy or governance that will be necessary to meet the recommendations and who will be responsible for acting on those recommendations; and timelines for acting on and monitoring the implementation of those recommendations.
Overview of Program Review Process:
The Program Self-Study Reports was completed in August 2019 for the program under review, the BSc in Mathematics. The Self-Study Report contained the Degree level expectations, an analytical assessment, course outlines, program-related data, survey data from the Office of Quality Assurance and appendices with sample examinations and CVs of faculty members of the program. Two arm’s-length external reviewers (Dr. Franco Saliola, Département de mathématiques, UQAM, and Dr. Will Traves, Department of Mathematics, United States Naval Academy) were selected from a list of possible reviewers and approved by the Deans of Science and Graduate Studies. An internal reviewer, Dr. James McKay, Department of Political Science, was also selected to participate on the ERC. They reviewed the self-study documentation and conducted a site visit to RMC on 12 and 13 December 2019. During the site visit, the ERC met with the Vice-Principal, Academic, Dr. Phil Bates, the Associate Vice-Principal, Research, Dr. Mike Hennessy, the Dean of Science, Dr. Gregg Wade, the Department Chair, Maj David Eisenhauer, Mathematics program coordinators: Alain Gosselin and Charles Paquette, the Head Librarian, Ms. Sarah Toomey, as well as several members of department faculty. The ERC also had the opportunity to meet with several students currently enrolled in the programs. The ERC subsequently produced a Report based on the Self-Study and site visit. The report was circulated to department members and discussed at a departmental meeting.
The reviewers submitted their report in March of 2020. In their report, they found that the overall quality of the programmes offered is comparable to programs at other Canadian universities.
Significant Strengths and Areas of Concern of the Program:
The ERC identified a number of strengths of the BSc Mathematics Program:
- Committee members indicated they were extremely impressed by the dedication of all the faculty and staff (including military and civilian) to the unique mission of the RMC;
- They noted the department’s efforts to address the failure rate in the first year Calculus sequence by modifying the curriculum, which impressed the committee; and
- All of the UG students were enthusiastic about their program, courses and professors. They commented that the small class sizes fostered an atmosphere of active learning.
The ERC identified a number of areas of concern for the BSc Mathematics Program, and noted suggestions for program enhancement:
- A number of faculty members expressed concerns about the current level of teaching and service loads relative to the staffing level. They also reported that hiring staff to teach courses was extremely laborious and time-consuming, in part because the process and requirements for hiring are not clear and change frequently;
- Three quarters of the courses taught by the department support the delivery of the Core Curriculum or other degree programmes. This is an unusually high level for departments at the RMC;
- The Mathematics programme is small, but questions from committee members about recruiting of students conveyed the impression that there was no deliberate effort to attract students other than the annual briefings to 1st Year Science students at RMC and CMR-SJ; and
- UG students reported that the department offered too few math courses in their 4th year.
The Program Chair, after consultation with faculty and staff in the program, submitted a response to the Reviewers’ Report in June 2022. The Dean of Science prepared this Final Assessment Report in August, 2022. Specific recommendations are discussed, and follow-up actions and timelines provided.
Summary of the Reviewers’ Recommendations with Dean’s Responses
The ERC identified a number of areas of concern or issues that require attention. These issues are discussed in the order that they appear in the ERC Report:
Recommendation 1
The Department needs to work with senior leadership at the RMC to develop a long-term HR plan to address the department’s anticipated needs and to smooth the hiring process.
Departmental Response:
The need to hire more regular faculty is by far the most pressing problem in the department. Anything that RMC can do to help smooth the hiring process (reducing the amount of paperwork done by the department to better focus on candidates and interviews) is more than welcome.
Dean’s Response: Recent experience suggests that indeterminate hiring of UTs, from the perspective of the Dean’s office (which is intimately involved in all stages of the process), runs relatively smoothly. Permission to replace retiring faculty is provided in a timely fashion, the process for competitive hiring is clear and straightforward, and the development of Letters of Offer following candidate selection is efficient. It is however acknowledged that the staffing process within the Department of National Defence is more onerous than one might find at a civilian university. There is nothing that the institution can do to change the official processes.
On the general subject of workload, RMC is currently supporting a Joint Committee reviewing workload distribution across all Faculties of the College. The findings of the committee should inform and address concerns related to teaching and service loads.
Recommendation 2
The process of engaging sessionals needs to be streamlined in order to reduce the administrative burden on the Department. One way of doing this, as well as addressing the service task burden, would be to hire more terms as opposed to casuals or part-time exclusions.
Departmental Response:
Anything that can be done to reduce the onerous tasks of recruiting, hiring and mentoring of the department’s unusually large number of term professors and sessional instructors is welcome.
Dean’s Response: The Dean agrees that hiring of Term UTs/Sessional instructors can be fraught with frustrations, including very long lead times (incompatible with identification of suitable individuals to fill positions), burdensome paperwork, etc. Recent changes to the responsibilities of the Faculty of Science CR-04 Claim Clerk, adding assistance with departmental staffing administration and an increase in the number of people working in Faculty Services, should help to alleviate these pressures.
Recommendation 3
Sufficient numbers of term or indeterminate professors should be engaged to ensure the delivery of first year courses by more experienced faculty.
Departmental Response:
Fully agreed; see 1.1. In general, we have a significant number of non-permanent faculty (sessionals, terms or military faculty) delivering 1st-year courses. It is very hard to increase the number of experienced faculty delivering first-year courses, given that near half of our courses overall are delivered by non-permanent UTs. As an example, for the 2021-2022 academic year, 7 members of the department were responsible for delivering MAE/F101. Of these, 2 were inexperienced (in that they have been teaching at the College only recently). Also, only 3 were permanent UTs. The department will make every effort to keep the number of experienced faculty delivering first-year courses relatively high, given the available resources.
Dean’s Response: The Dean agrees that experienced indeterminate faculty are required to effectively deliver MAE/F101 and other introductory courses. At minimum, the course coordinator would be such an individual. While it is likely unrealistic that the large service teaching requirements of the department will ever be fully satisfied by indeterminate faculty, identifying means by which to build a cadre of experienced Term UTs would be of great value. This could be accomplished through utilization of longer-term Term UT contracts, guaranteeing that those in a tenuous employment position are engaged over multiple years.
Recommendation 4
The department should develop a deliberate approach to recruiting potential students into the BSc Mathematics program. The Mathematics program should hold a ‘course fair’, where students could come, read course outlines, and talk with professors prior to pre-registration and the discipline selection process.
Departmental Response:
This is a good suggestion, which would however require further time and effort from the faculty. Each year, in January, the Department meets the first-year students in science for program briefings. When in-person briefings are possible, we should encourage science students to come to the department and discuss with the professors (which would be a department tour in other departments, where there are actual things to be shown). Ideally, first-year engineering students should also be part of the science program briefings, but it would require the college approval.
Dean’s Response: The Dean concurs that recruitment of undergraduate and graduate students into both the Mathematics and Computer Science programs should be a high priority. Creative recruitment tactics such as those proposed are certainly encouraged.
Recommendation 5
We encourage the department to implement a similar approach [to the 1st year calculus sequence] to the second year courses as well.
Departmental Response:
This is a good idea, which requires significant additional resources (offering MAx226 in winter as well, and a spring session of MAx227). This alone would justify one more UT in mathematics. We have explored the possibility of expanding the current module system into a two-year program. The department designed such a system that would allow weak engineering students to catch up by the end of second year.
Dean’s Response: As pointed out by the department, an initial exploration of such a strategy indicates that it would have high resource demands, including both teaching and scheduling complexity. The current focus is to achieve the greatest success in first-year mathematics, with consequent benefits in second year thanks to better preparation and deeper understanding of fundamental concepts.
Recommendation 6
The department should consider placing students who do poorly on the placement test into a slower-paced pre-Calculus and Calculus class that extends into the “catch up” time in the summer.
Departmental Response:
A committee has been formed to look at 1st-year calculus to improve success rate. The committee’s report has been presented to and accepted by both Faculty Board and Faculty Council. This option was considered by the committee but deemed unfeasible for many reasons.
Dean’s Response: The report of the Mathematics Review Committee for Science and Engineering explored a large range of options that could potentially improve success in first-year calculus. Adding a pre-calculus class, for some or all of incoming first-year students, was discussed but ultimately abandoned. Instead, the current modular structure was retained, and additional practical work sessions were assigned to the course. The activities of the Math Help Centre were reviewed and strengths and weaknesses were identified. High-school performance thresholds and prerequisites were also discussed.
Recommendation 7
The department might consider expanding its active learning approach to its first year classes, by trading coverage of some lecture material for group work at the blackboards.
Departmental Response:
MCS has implemented this change one year ago with the 1st-year calculus sequence: more tutorial and active learning. This follows from recommendations of the calculus committee. We may not see the real effect of this change given the delivery mode of last year. Moreover, there may be an increase towards the failure rate accounted for the online delivery (and exams) of the last two years. This is supported by a significant increase in the AIV tied to online exams.
Dean’s Response: The Dean enthusiastically supports continued development of novel teaching approaches by faculty in the department. Active teaching and learning training will be provided annually to all faculty beginning in 2022.
Recommendation 8
UG students reported that the department offered too few math courses in their 4th year. This could be addressed by consolidating some 3rd and 4th year math courses.
Departmental Response:
This is a good idea. However, most of our optional courses in mathematics are available to both 3rd and 4th year already (hence already optimized to be available to most students). In the current climate, optional courses with low enrollment are not being given, reducing even more the options. The undergraduate math programme would certainly be significantly improved by the addition of even just 2 new courses.
Dean’s Response: The Dean concurs that low enrolment in the Mathematics undergraduate programs is a significant impediment to the offering of a broad suite of senior courses. Diversity of course offerings could be increased by annual alternation of electives, or by polling program students during the pre-registration period to identify their preferences.
Recommendation 9
The Department should promote the CORS Diploma.
Departmental Response:
The Canadian Operational Research Society (CORS) diploma has proven difficult to implement since many courses of the CORS are electives taken in other departments, it is almost impossible for a student to get this (given restrictions with offerings in other departments and scheduling conflicts). A better solution would be to develop our own program (or stream, or certificate) in operations research or analytics. We have been in contact with ADM (DIA) to see if external funding would be possible, and they have been very supportive so far. There is actually an interest from DND to develop a program in analytics at RMC. Approving a program (or certificate or stream) in analytics would require additional resources and we need the help of RMC administration to make this happen. We have had an unsuccessful attempt at this a few years ago, mainly due to an administrative error out of our control.
Dean’s Response: The Dean supports the development of an Analytics undergraduate stream. Such a venture would likely increase enrolments and would therefore help to address Recommendation 8 as well.
Recommendation 10
The department should increase the number of interesting mathematics courses.
Departmental Response:
We already have several interesting courses available to a wide audience (MAx234, MAx236, MAx384 and MAx386). Also, tied with the suggestion above: if we have a program or stream in analytics, we would need to develop relevant applied courses. One has recently been developed: “Defence Analytics” but without an actual program in analytics and being optional/elective (and RMC to close optional courses with low enrollment), this course has only been offered once and may not be given again.
Dean’s Response: The Dean concurs with the department’s response and also notes that low enrolment in the Mathematics undergraduate program is a significant impediment to the offering of a broad suite of senior courses.
Recommendation 11
The department should organize some "popular math" events at RMC such as professors giving presentations on fun and pertinent topics; inviting speakers from outside RMC to give presentations; developing "mathematics walking tours" of campus; as well as finding other creative ways for first year students to meet and interact with professors in the department.
Departmental Response:
Enrollments in mathematics is low, but comparable to other universities (relative to the size). What makes mathematics programs more popular in other universities (e.g. US Naval Academy) is their unique character. We believe that offering an analytics component, which is in high demand in the CAF, would provide this unique component in our program and increase popularity. The ERC has proposed some options, namely,
- Professors can give presentations on fun and pertinent topics.
- Invite speakers from outside RMC to give presentations.
- Develop "mathematics walking tours" of campus (there are various cities where this has been done, for example Montreal).
- Find other creative ways for first year students to meet and interact with professors in the department. As it stands, a student might take a math course with a sessional and no other mathematics course, consequently not meeting any of the professors in the department.
For comment 4, it is addressed in 1.3 (but tied to available resources in the department). Points 1 and 2 sound like good ideas which could be explored. Point 3. Is also an excellent idea, but is more resource demanding. Again, this desirable goal would be difficult without an increase in the department’s faculty.
Dean’s Response: Without significant enrolment in either the Mathematics undergraduate or graduate programs, an increase in the number of indeterminate Mathematics faculty would be difficult to justify. Hence creative approaches to attracting students (as proposed by the ERC in this Recommendation, as well as by the department in Recommendation 9) are key to these programmes’ future.
Recommendation 12
The department should expand the student assessment that was conducted at the beginning of the academic year to a placement test that determines a student's readiness for the calculus sequence. Introduce some preparatory modules for the students with weak backgrounds. Students can use the summer session to "catch up" if they take a preparatory module.
Departmental Response:
A placement test would provide an additional tool in assessing first year students. However, a previous comparison showed that a calculus capability assessment was giving essentially the same indicator as high school marks towards MAx101 performance. Also, with the current module structure, all students go through a high school review (that is, the Fundamental module) which they must pass. Given this and our limited resources, we see no real advantage in having a placement test. The possibility of running a math Boot Camp during the summer was extensively discussed by the calculus committee but deemed unfeasible.
Dean’s Response: The Dean concurs with the department’s response. The current best feasible model is the existing modular structure with a mandatory review of high-school mathematics (the Fundamentals module). During the course of that module instructors are able to identify students with insufficient preparation and ensure that they attend additional practical work sessions and take advantage of the Math Help Centre.
Recommendation 13
Improve student success in first year by developing a student-tutoring program focused on providing support to first year students. The department should incentivise senior level math students to participate in the program with academic credits or other measures. The program should provide on-site, after hours service to make it as accessible as possible (to complement service limitations of the Math Help Center).
- Provide academic credit or some other incentive for 3rd and 4th year students who mentor the first year students. The USNA has a popular program like this called the Midshipman Group Study Program (MGSP). USNA allows any student that earned an A in a course to apply to mentor students in that class. The MGSP is highly competitive but even the top students need guidance and oversight in order to do a good job mentoring first year students.
- Have these students provide "on-site" math help in the dorms in the evenings or at times when it is hard to staff the Math Help Center.
- An added bonus of a student tutoring program is that the upper-year cadets often talk to first-year cadets about the math major. The upper-year students are some of USNA’s best recruiters.
Departmental Response:
These 3 points are all excellent ideas. There is currently a programme called “AcParents” where a first year is paired with a second year student “Academic Parent” in their field that the first year is to use as a resource. However, we do not know if this program has any oversight, and the academic departments have no input on this as far as we know. Also, the success center advertised peer-tutoring in December 2021, however, MCS has not been contacted for tutoring in mathematics, so we do not seem to have control of this. MCS and the success center should work together so that tutoring is better aligned with our Math Help Center and student needs, which is open to all students registered in a mathematics course at the college. Ideally, tutoring should be rewarded/encouraged in some way (leadership and military values), as supported by the ERC.
Dean’s Response: All instructors understand that the best route to understanding a subject deeply is to teach it. The Dean would support the development of a Faculty-level academic credit for tutoring and mentoring of junior students by their senior peers.
Recommendation 14
Immediate action is necessary to ensure that graduate students have online access to a suitable library facility.
Departmental Response:
The library committee is aware of this. Note that Queen’s library is open to the public (you may need a visitor card). A survey has been sent to MCS in 2020, and it seems that no major journal is missing from the RMC library (or through the EBSCO database), as claimed otherwise in the ERC report.
Dean’s Response: While access to electronic journals through RMC’s library continues to be an issue for some departments, the Department’s response reassures the Dean that access to appropriate electronic journals is not an issue for Mathematics. Clearly, relying on Queen’s University does not represent a viable long-term strategy.
Implementation Plan
| Recommendation | Proposed Follow-up | Responsibility for Leading Follow-up | Timeline for Addressing Recommendation |
|---|---|---|---|
| 1. The department needs to work with senior leadership at the RMC to develop a long-term HR plan to address the department’s anticipated needs and to smooth out the hiring process. | A 5-year Departmental Business Plan is being developed and discussed with leadership. | Dept Head | Dec 2022 |
| 2. The process of engaging sessionals needs to be streamlined in order to reduce the administrative burden on the Department. | Faculty claims clerk will be trained to assist with sessional and TA hiring administration. | Dean of Science | May 2023 |
| 3. Sufficient numbers of term or indeterminate professors should be engaged to ensure the delivery of first year courses by more experienced faculty. | Develop a pool of committed term/sessional instructors. | Dept Head | May 2023 |
| 4. The department should develop a deliberate approach to recruiting potential students into the BSc Mathematics program. | Develop creative strategies to increase enrolment. | Dept Head | May 2023 |
| 5. The department should implement a similar approach [to the 1st year calculus sequence] to the second year courses as well. | As addressed by the Math Review Committee report, the focus of pedagogical development and resources will remain in first-year calculus, with expected benefits to students in second year as a consequence of better preparation and understanding. | N/A | N/A |
| 6. The department should consider placing students who do poorly on the placement test into a slower-paced pre-Calculus and Calculus class. |
As discussed, this option was fully explored by the Math Review Committee and rejected as unfeasible. |
N/A | N/A |
| 7. The department might consider expanding its active learning approach to its first year classes, by trading coverage of some lecture material for group work at the blackboards. | Encourage faculty to adopt novel teaching approaches. Provide active teaching/learning training in partnership with the Teaching and Learning Support Centre. | Dept Head/Dean | Dec 2022 |
| 8. UG students reported that the department offered too few math courses in their 4th year. This could be addressed by consolidating some 3rd and 4th year math courses. | The Department could ensure elective courses alternate annually, and that program students are consulted to determine their elective preferences each year. However, as discussed, low enrolment in Mathematics programs is a barrier to offering a larger number of specialized courses. Action responding to this recommendation relies on actions related to recommendations 4 and 9. | Dept Head | May 2023 |
| 9. The Department should promote the CORS Diploma. | Continue development of an undergraduate Analytics stream. | Dept Head | Dec 2023 |
| 10. The department should increase the number of interesting mathematics courses. | As discussed, low enrolment in Mathematics programs is a barrier to offering additional specialized courses. Action responding to this recommendation relies on actions related to recommendations 4 and 9. | Dept Head | May 2023 |
| 11. The department should organize some "popular math" events at RMC. | Develop creative strategies to increase enrolment. | Dept Head | May 2023 |
| 12. The department should expand the student assessment that conducted at the beginning of the academic year to a placement test that determines a student's readiness for the calculus sequence. | As discussed, the student assessment was abandoned in lieu of high-school grades and observed progress in the Fundamentals module. | N/A | N/A |
| 13. Improve student success in first year by developing a student-tutoring program. | Develop a Faculty-level credit in mentoring/tutoring. | Dean of Science | Dec 2022 |
| 14. Immediate action is necessary to ensure that all students have online access to a suitable library facility. | As discussed, access to all required Mathematics library resources appears to be satisfied. | N/A | N/A |
Conclusion:
The ERC Report provided positive feedback on the outcomes of the undergraduate program in mathematics. It confirmed that the Department of Mathematics is delivering an academically rigorous program to its students and that its standards meet those of similar programs in Ontario. However, the ERC did identify areas that had room for improvement, and RMC is, or has already taken, taking steps to address the issues raised. RMC will continue to work toward more streamlined hiring and improve student success in mathematics.
The Dean of Science, in consultation with the Head of the Department of Mathematics, is responsible for monitoring the Implementation Plan.