### Required Resources and Recommended Technology for College and University Mathematical Sciences Departments

Mathematical sciences departments should prepare students to use mathematics in a modern technological environment. As noted in the 2015 * CUPM Curriculum Guide* [16]:

Employers want graduates to have experience with technology, be it programming or using software applications. Using an appropriate tool to solve a problem is a universally-valued skill. Effective communication of ideas often requires technology for images, data representations, and notation. Most important, for professional and personal needs, students need the ability to learn to use emerging technologies. We therefore have a responsibility to encourage and enable our students to learn technologies alongside their mathematics.

To achieve this objective, faculty, departments, and institutions should collaborate to ensure that essential resources are available for faculty and students. Additionally, faculty and administrators should work together to develop appropriate solutions for their institutions. Many problems can, and will, arise as students, faculty, and departments adapt to the changing roles of technology in research, education, and applications.

Required Resources A) Resources for Faculty B) Resources for Students

Appendix: Recommended Mathematical Computational Tools and Programming Languages

A) All faculty should be provided with the basic resources necessary for them to perform the teaching and the scholarly activities they were hired to do. These include the following:

i) Sufficient office space.

ii) Well-lit classrooms with adequate board space and projection facilities.

iii) Library holdings and subscriptions necessary for the development of teaching and scholarship.

iv) Computing resources necessary for teaching and scholarship. [12]

v) Staff support, including administrative assistance and computing support.

vi) Professional development funds and resources.

New faculty should have access to these resources when they begin work in a faculty position.

B) All students should have access to all the basic resources required for learning the mathematical sciences and preparing for their future careers. These include the following:

i) Computing resources necessary for their work.

ii) Study space, including shared or common space near faculty.

iii) Space for faculty consultation.

iv) Basic academic support outside the classroom.

v) Library resources sufficient to support student learning and provide enrichment materials for undergraduate student support.

In addition, university administrators should ensure that appropriate and legally required accommodations, such as adaptive technology, are made for any faculty, staff, or students with documented disabilities.

Details about the required resources are given below.

i) __Office Space:__ All full-time faculty members should have private offices. Each part-time faculty member should have a desk and office space that allows confidential conferences with students outside the classroom. Where possible, faculty offices should be located near other faculty with common research or teaching interests to facilitate collaboration. [11]

ii) __Classrooms:__ Classrooms should be safe, clean, well lit, and equipped with adequate board space and computer projection equipment and screens. This includes enough whiteboard or chalkboard space to allow instructors to write out all the details of a typical proof or argument without erasing and in a large enough hand that students can read it easily. Many classrooms designed for teaching nonmathematical subjects do not have sufficient board space for mathematical instruction. Where possible, classroom design should emphasize flexibility, with the potential for reconfiguration to adapt to a variety of teaching styles and methods. The SCALE-UP classroom design model from North Carolina State University is a good example: “The class spaces included a laptop computer with access to the Internet, 7-foot-diameter round tables, computer projection screens at opposite ends of the room, and large whiteboards covering the walls.” [15] The Learning Spaces Collaboratory also has advice on classroom design.

iii) __Library:__

a. Library holdings and subscriptions should be sufficient to meet the scholarly needs of the program faculty. They should also provide resources for helping faculty improve their teaching. Departments can review the MAA’s Basic Library List for suggestions. If specific library materials are not available on site, they should be readily available electronically or through a process such as interlibrary loan.

b. Libraries should be staffed, scheduled, and located in such a way that their mathematical sciences holdings are readily available to all faculty members and students.

c. Library holdings and subscriptions should be reviewed regularly by a committee that includes representation from the mathematical sciences.

iv) __Computing:__ Faculty should have access to all the computing resources they need to perform their jobs, including the following:

a. Up-to-date hardware and software.

b. Fast internet access.

c. All necessary data sets, and storage for very large data sets, as needed. This is discussed in a recent report by the National Academies of Sciences, Engineering, and Medicine: “It is precisely in the realm of moving from raw data via analysis to knowledge that the mathematical sciences are essential. Large, complex data sets and data streams play a significant role in stimulating new research applications across the mathematical sciences, and mathematical science advances are necessary to exploit the value in these data.” [13]

d. Training and time to learn to use new tools.

e. Well-trained computing support staff. Computing support staff should be able to maintain the primary mathematical and instructional software packages used by the faculty and students.

These resources can have a profound impact on the teaching and learning of mathematics. As noted in the MAA’s *Instructional Practices Guide*, “In today’s world, technology is ubiquitous and applicable to many aspects of instructional practice. As such, instructors should continually examine how and where technology fits into their work.” [11] Departments should regularly examine their investments in computing resources to ensure that needs are being met.

v) __Staff Support:__ Faculty should have access to basic staff support, including department administrative assistance (secretarial support), computing support, and tutoring center support staff. Faculty should not be used as support staff unless it is a documented expectation of their employment, they are given a corresponding reduction in other duties, and their work on these assignments is recognized for tenure and promotion decisions.

vi) __Professional Development Funds and Resources:__ Professional development is essential to faculty success. All full-time faculty members should have access to the resources necessary to participate in appropriate professional development. As the National Research Council concludes, “The use of learning technology in itself does not improve learning outcomes. Rather, how technology is used matters more.” [13] Without support and training, incorporation of new technology may not actually be beneficial.

a. Faculty should receive funding to attend at least one professional conference each year.

b. Where possible, the institution should pay the membership dues for each full-time faculty member to join at least one of the mathematical sciences professional societies (e.g., MAA, SIAM, AWM, NAM, AMS, ASA, AWC, ACM).

c. Faculty who are expected to do scholarship should be given a sabbatical or research leave at appropriate intervals.

d. Faculty should receive support for course development, incorporating new technology into their courses, and for other major pedagogical changes to their courses. This includes teaching load reductions for significant course development and training for new technology and new pedagogical methods. [5, 7, 9]

i) __Computing:__

a. For courses that use online homework or require use of specialized software, students should have ready access to a computing lab or other resources to allow them to complete their assignments, especially if they do not have their own computer or their own copy of the required software packages.

b. The National Research Council observes that “Computation is central to the future of the mathematical sciences, and to future training in the mathematical sciences . . . [I]t is apparent that an ability to work with data and computers is a common need . . . and indeed students with this training will be much more employable in those areas.” [14] Thus, students should have access to the most important computational tools and methods of the discipline. Students majoring in the mathematical sciences should learn to use the standard software tools and computing languages used in business, industry, and government within their disciplines. This should include at least one general purpose computer programming language and at least one of the industry-standard tools for numerical computing (see the appendix for details). [13, 16, 18] Note: Popular software tools include many that are free or open source; accessing these tools need not represent a significant expense to the school, but it requires the institution to provide computer support staff (see items c and d, below).

c. Faculty who interact with students should know how to use the relevant software and computing languages. [7, 8, 11]

d. Computing support staff should be available to ensure that all the necessary classroom and lab machines are properly configured, and that software is properly installed and maintained. Students should be taught how to access the resources they need, whether the access is local or remote. Particular care should be given for instructions on accessing any remote resources available to students both within labs and for home and personal computers. Access instruction may come from faculty or support staff depending on an institution’s organizational structure.

e. Handheld calculators, including programmable graphing calculators, are not a suitable replacement for modern mathematical and computational tools. Nevertheless, graphing calculators still play a significant role in many secondary school mathematics curricula, so departments should teach prospective secondary school teachers how to use calculators appropriately. [7]

ii) __Study Space:__

a. All students should have quiet space available to study and do homework.

b. Mathematical science majors should have a dedicated common study area where they can collaborate and study together. This area should be located near faculty offices to allow opportunity for frequent contact between students and faculty.

c. When designing new or remodeled space for mathematical sciences departments and students, institutions should consult with both faculty and students about how to best use the space to maximize student learning. [15]

iii) __Faculty Consultation:__ Faculty should have well-publicized, regular, and frequent office hours, and faculty offices should be easily accessible to students, and faculty. [11]

iv) __Tutoring Support:__ Students in lower-division mathematical sciences classes should have access to basic tutoring support outside the classroom, allowing them to get help at times that faculty are not available. This is commonly done in a tutoring center, staffed primarily by graduate students or advanced undergraduate students. Tutors should be familiar with the software and other technology being used in the classes for which they are tutoring.

v) __Library:__ Library holdings should be sufficient to support student learning and provide enrichment materials for student projects.

a. Holdings should include the publications labeled *Essential, Highly Recommended, *or *Recommended*, on the MAA's Basic Library List for undergraduate mathematics.

b. Holdings should include enough advanced materials to support students in mentored research.

c. Libraries should be staffed and scheduled, and have materials located in such a way (locally or electronically) that their mathematical sciences holdings are readily available to the mathematical sciences faculty and their students.

… because computation is often the means by which methods from the mathematical sciences are applied in other disciplines and is also the driver of many new applications of the mathematical sciences, it is important that most mathematical scientists have a basic understanding of scientific computing. [13]

-- the National Academies of Sciences, Engineering, and Medicine

SIAM’s *Math in Industry* resource states, “In this study we also took a closer look at the technical skills that graduates need, which tend to fall into three overlapping domains: mathematics, computation, and specific application domains . . . Computational skills include, at a minimum, experience in programming in one or more languages.” [18] So, it is important for students to learn a general-purpose programing language as well as some standard numerical computing tools. In certain cases, the tools may be part of the general programming language (e.g., *NumPy* and *SciPy* in *Python*), but this is not essential. We recommend that the choice of which tools and languages to teach students be dictated by what is commonly used in industry, business, and government for mathematical computation. [13, 16, 18] At the time of this writing (2018), these include the following:

##### Mathematical Tools

a. For statistics, *R*, *Python*, or *SAS*. (See https://www.r-project.org/ for *R*, and https://www.python.org/ for *Python*.) [2]

b. For mathematics, *Python*, (including *NumPy* and *SciPy*), *MatLab*, or *Octave*.

c. Note that *Maple* and *Mathematica* also have some numerical tools, but are not widely used in industry. Nevertheless, with careful thought and work, those could be used to teach students the necessary numerical computing principles.

d. *Sage/CoCalc* is similar to *Maple* and *Mathematica*, but also allows the use of *Python* and *R* code. (See https://cocalc.com/)

e. *Julia* is not yet in wide use, but it appears to be rising in popularity and is potentially very powerful. (See https://julialang.org/)

f. For data science, either *Python* or *R*, as well as *SQL*. This should also include standard tools and packages for data manipulation, such as *Pandas* or *tidyr*, and standard tools for machine learning, such as *scikit*-learn and *TensorFlow*. [3, 4, 6, 14, 19] “*Python* and *R* are both widely used by data scientists, often in tandem, since they have different strengths and weaknesses.” [12]

##### Programming Languages** **[1]

a. Python.

b. *C *or * C++*.

c. Possibly *Java*. Although *Java* is a very popular language, it does not seem to be used as much as *Python* or *C/C++* in mathematical applications. Also, it appears to be declining in overall popularity, especially in mathematical settings.

Many popular programming languages are in wide use for non-mathematical applications but are not commonly used for mathematical computation. Therefore, these languages should not be the primary language for mathematical sciences students. These include languages such as *Javascript*, *PHP*, *Perl*, and *Ruby*. Also, many popular languages are platform specific, including *C#, Swift, Objective-C*, and *Visual Basic*. Unless it is known in advance that students’ careers will be primarily focused on programing for those platforms, these should not be the primary programming language for mathematical sciences students.

Many of the mathematical tools listed above are powerful tools for their specific application, but are too specialized to be considered general-purpose, full-scale programming languages. These include *R, MatLab, Octave, Maple, SAS*, and *Mathematica*. Typical teaching practice with these languages, such as simple use for plotting or calling pre-built functions, does not include functions, control flow, etc. Therefore, learning these alone will generally not provide sufficient programming skill for typical students. Only if these languages are taught explicitly as a programming language with functions writing, control flow, debugging, commenting, recursion, I/O, data types, exception handling, etc, could they be sufficient. In addition, students should be able to write working programs consisting of more than a hundred lines of code. The following concerning statistics students also applies to mathematics students: “It is no longer adequate training for statistics students to be able to analyze data using graphical user interfaces or to write simple scripts that do not use modular approaches (including writing functions and code using control flow) to process data.” [10]

##### References

[1] ACM Joint Task Force 2013. *Computer science curricula 2013: Curriculum guidelines for undergraduate degree programs in computer science.* Technical report, Association for Computing Machinery (ACM) IEEE Computer Society.

[2] American Statistical Association 2014. Curriculum guidelines for undergraduate programs in statistical science. *Retrieved from* http://www.amstat.org/education/curriculumguidelines.cfm. (2014).

[3] Anderson, P. et al. 2014. An Undergraduate Degree in Data Science: Curriculum and a Decade of Implementation Experience. *Proceedings of the 45th ACM Technical Symposium on Computer Science Education* (New York, NY, USA, 2014), 145–150.

[4] Anderson, P. et al. 2014. Data Science As an Undergraduate Degree. *Proceedings of the 45th ACM Technical Symposium on Computer Science Education *(New York, NY, USA, 2014), 705–706.

[5] Bottino, R.M. and Chiappini, G. 2014. Using Activity Theory to study the relationship between technology and the learning environment in the arithmetic domain. *Handbook of International Research in Mathematics Education.* Routledge.

[6] Cassel, B. and Topi, H. 2015. Strengthening data science education through collaboration. *Workshop on Data Science Education Workshop Report *(2015), 27–2016.

[7] Drijvers, P. 2015. Digital technology in mathematics education: Why it works (or doesn’t). (2015), 135–151.

[8] Drijvers, P. et al. 2010. Integrating Technology into Mathematics Education: Theoretical Perspectives. *Mathematics Education and Technology-Rethinking the Terrain.* C. Hoyles and J.-B. Lagrange, eds. Springer US. 89–132.

[9] English, L. 2009. Setting an agenda for international research in mathematics education. *Handbook of international research in mathematics education*. (2009), 3–19.

[10] Hardin, J. et al. 2015. Data Science in Statistics Curricula: Preparing Students to “Think with Data.”* The American Statistician. *69, 4 (Oct. 2015), 343–353.

[11] Instructional Practices Guide | Mathematical Association of America: https://www.maa.org/programs-and-communities/curriculum%20resources/instructional-practices-guide. Accessed: 2018-03-16.

[12] Jarvis, D.H. et al. 2014. Computer Algebra System (CAS) Usage and Sustainability in University Mathematics Instruction: Findings from an International Study. *Electronic Journal of Mathematics & Technology*. 8, 4 (2014).

[13] National Academies of Sciences, Engineering, and Medicine 2013. *The Mathematical Sciences in 2025. *

[14] National Academies of Sciences, Engineering, and Medicine 2017. *Envisioning the Data Science Discipline: The Undergraduate Perspective: Interim Report.*

[15] Park, E.L. and Choi, B.K. 2014. Transformation of classroom spaces: traditional versus active learning classroom in colleges. *Higher Education.* 68, 5 (Nov. 2014), 749–771. DOI:https://doi.org/10.1007/s10734-014-9742-0.

[16] Schumacher, C., Siegel, M., et al.. 2015. *2015 CUPM curriculum guide to majors in the mathematical sciences*.

[17] Singer, S.R. et al. 2012. *Discipline-based education research: Understanding and improving learning in undergraduate science and engineering*. National Academies Press.

[18] Society for Industrial and Applied Mathematics 2012. Mathematics in Industry. *Retrieved from* https://www.siam.org/Publications/Reports/Detail/Mathematics-in-Industry. (2012).

[19] Veaux, R.D.D. et al. 2017. Curriculum Guidelines for Undergraduate Programs in Data Science. *Annual Review of Statistics and Its Application. *4, 1 (2017), 15–30. DOI: https://doi.org/10.1146/annurev-statistics-060116-053930.

#### Contributers

Edward Aboufadel (CFD chair), Grand Valley State University

Connie Campbell, Gulf Coast State College

Timothy Flowers, Indiana University of Pennsylvania

Debra Lynn Hydorn, University of Mary Washington

Tyler J Jarvis, Brigham Young University

Gavin LaRose, University of Michigan

M. Leigh Lunsford, Longwood University

Audrey Malagon, Virginia Wesleyan University

Benedict K Nmah, Morehouse College

Emily E Puckette, University of the South

Karl Schmitt, Valparaiso University