Authors: Jennifer Palisse; Deborah King; Mark MacLean

Authors: Inae Jeong; Tanya Evans

Authors: Tanya Evans; Euan Lindsay

Lecture capture (LC), the process of recording face-to-face lectures for future viewing, has become a common technology in Western universities in the twenty-first century, yet research on its effectiveness has lagged behind its implementation. In the wake of the Covid-19 pandemic, the urgency of obtaining clear answers about the impact of LC is paramount. The recent worldwide shift to online teaching as an emergency response to the COVID-19 pandemic has resulted in an unprecedented use of LC at scale. In this presentation we report on a systematic review of the current literature that we conducted on the efficacy of LC in tertiary mathematics education. The literature is consistent in the opinion that students and administrators positively view LC for its utility and flexibility despite the moderately strong evidence that most institutions face attendance drops. However, most students do tend to see attending lectures/watching recordings as an “either-or.” The literature predominantly reports a negative association between attainment and the use of LC as a substitute to live lectures. The proportion of students who choose to skip live lectures has steadily increased over the last decade as the student campus culture adjusts to LC. Within this group, LC is used imperfectly, providing false benefits and promoting surface learning strategies. There is evidence that regular use of LC by this large group of students may diminish the quality of their learning. We offer research-informed, evidence-based recommendations to mitigate the unplanned and counterproductive impact of LC implementation.

REFERENCES

Lindsay, E., & Evans, T. (2021). The use of lecture capture in university mathematics education: a systematic review of the research literature. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-021-00369-8

Within mathematics education research, the importance of body movement in students’ thinking is increasingly being recognized. As Yoon et al. suggested, at this conference in 2011, students’ movements during mathematical activity are more than a means of communication, or an adjunct to understanding: movement can provoke new mathematical knowing. As body movement provides a new variable for mathematics education research, a variety of methods for observing and analysing movement have arisen. Movement analysis has a long history across many fields including performing arts, industrial work studies, and computer interface technology. One well-established movement framework, Laban’s movement elements, classifies how the body moves in space. Laban’s elements also recognize, and pay careful attention to, the often omitted, but inherent, dynamic qualities of movement, thus providing a link between affect and cognition, two modes of knowing that are often separated. Privileging a variety of ways of knowing mathematics was proposed by Tang et al., at this conference in 2017, as a way to improve equity and engage a wider variety of students in the mathematics classroom. By employing Laban’s movement elements, this study investigates the movements of a group of bridging education students as they engage with a mathematical task. This study demonstrates how the dynamic qualities of movement contribute to students’ emerging mathematical knowing and suggests students’ movements as an important resource the mathematics classroom.

Authors: Antony Dekkers; Nadine Adams; Roland Dodd; Clinton Hayes

This paper provides a brief overview of the preparatory programs offered at Central Queensland University and a detailed explanation of how the video teleconferencing (Zoom) is currently utilised to enhance the delivery of the suite of mathematics bridging units during Covid 19.

While there is the belief that technology breaks down boundaries and enables us to connect to our students more easily, regardless of all the available technology, mathematics instruction is still best given in a “talk and chalk” format (Adams & Hayes, 2019). Instructional videos that allow the student to watch handwritten instruction are almost part of the standard subject design. They allow students to learn at a convenient time that fits within their lifestyle and commitments but videos lack the interactive component that makes face-to-face teaching preferable. During the COVID 19 pandemic this preferred method of mathematical instruction was unavailable therefore, online lectures conducted using a combination of Zoom, a Tablet PC and PDF Annotator were offered as an alternative. Providing students with a comparable experience much closer to that of face-to-face.

Inquiry-based learning promotes engagement, curiosity, and experimentation. Rather than being 'instructed to,' students are empowered to explore subjects by asking questions and finding or creating solutions. It's more a philosophy and general approach to education than a strict set of rules and guidelines.

Inquiry-based learning works well when you are in small class situations where students can work together on tabletop activities, but how do you adapt this approach when you are forced to teach online? How can you simulate classroom activities designed to explore statistical concepts?

Going online meant I had to change delivery and I have found myself combining the exploration of concepts through inquiry-based activities with more storytelling. Storytelling is not used much in mathematics and statistics and yet can be very beneficial. It can provide the background needed to create context and has learning beyond a topic or technique. I have found that many assessments that I create for students are about telling that story. Beyond the statistical skills and knowledge, I want my students to be able to tell the story for their data and make decisions that are personal or community changing.

I will share my experiences of teaching online using inquiry-based learning and storytelling.

Authors: Terrence Tsui; Nazim Khan

Mathematics is traditionally considered necessary for engineering courses. Over the last three decades the mathematics requirements for entry into engineering programmes has steadily weakened in Australia. Further, the mathematics component of engineering programmes has progressively decreased. This research aims to investigate the following two questions. Firstly, is mathematics a barrier for students to complete an engineering programme? And secondly, is performance in mathematics associated with performance in engineering?

We investigated the significant factors associated with weighted average mark (WAM) and the completion status of engineering studies at both an undergraduate level and a Masters level. Of particular interest was student mathematical background.

Furthermore, a survey of students in enrolled in engineering at the University of Western Australia was conducted to obtain more in depth views of student attitudes and perceptions towards how mathematics and statistics has affected their engineering studies. Binary logistic models were fitttted to the survey data. Additionally, focus group interviews was conducted to gain insight on student perspectives of how effective mathematics is taught in their courses. The results are discussed in relation to the importance of mathematics and statistics for the engineering curriculum.

REFERENCES

A. Finkel, T. Brown, J. Wright, and M. Wienk. Mapping university prerequisites in australia. Technical report, 2020.

R. King Australian Engineering education student, graduate and staff data and performance trends, 2019.

J. Flegg, D. Mallet, and M. Lupton. Students' perceptions of the relevance of mathematics in engineering. International Journal

of Mathematical Education in Science and Technology, 43(6):717{732, 2012.

AMSI. Year 12 participation in intermediate and higher mathematics remains stubbornly low, 2020.

https://amsi.org.au/?publications=year-12-mathematics-participation-in-australia-2008-2019

R. Bolton. Maths enrolments at school still as bad as ever. Financial Review, Nov 9, 2020.

https://www.afr.com/work-and-careers/education/maths-enrolments-at-school-still-as-bad-as-ever-20201103-p56b1e

L. Galligan, D. King and M. Axelsen. Fewer Australians are taking advanced maths in Year 12. We can learn from countries doing it better. The Conversation, Nov 11 2020.

https://theconversation.com/fewer-australians-are-taking-advanced-maths-in-year-12-we-can-learn-from-countries-doing-it-better-149148

Authors: Yik Ching Lee, Jeff Nijsse

With the transition to online learning during the COVID-19 pandemic, online assessments enable various additional possibilities to facilitate the breach of academic integrity. A high percentage of breach of academic integrity was observed after the initial transition online in early 2020. This presentation discusses the strategies and challenges in a Foundation Physics paper of a Certificate of Science and Technology programme to prevent and to discourage students’ unethical behaviour, whilst meeting the university’s Authentic Assessment standards.

In the subsequent semester, a new initiative highlighting academic integrity was introduced and the assessment structure modified. A programme-wide initiative was cross-promoted in different classes by different lecturers to turn students’ attention toward the values of academic integrity. Weekly problem sets aimed to change the purpose of assessment to enhance students’ learning. Only a small percentage of mark was given for each problem set, so the cost and effort to cheat in this form of assessment does not retribute, and students were incentivised to correct wrong answers. Practical experiments were replaced by inquiry-based online simulations and video-based analysis. Different measures were also implemented in the final assessment so that each student gets an equivalent but different version of the assessment to prevent collaborative cheating.

Designing a better assessment system is preventative implies that students will still try to cheat but it may be more difficult. Motivating students to take control of their own learning by removing the incentive to breach academic integrity is an idealistic (and unrealistic) goal but virtuous in its attempt and communicates desire for knowledge and learning.

REFERENCES

Arnold, I. J. (2016). Cheating at online formative tests: Does it pay off? The Internet and Higher Education, 29, 98-106.

Cizek, G. J. (1999). Cheating on tests: How to do it, detect it, and prevent it. Routledge.

Gallant, T. B., & Drinan, P. (2006). Organizational theory and student cheating: Explanation, responses, and strategies. The Journal of Higher Education, 77(5), 839-860.

Rowe, N. C. (2004). Cheating in online student assessment: Beyond plagiarism. Online Journal of Distance Learning Administration, 7(2).

Zain, A. R. (2018). Effectiveness of guided inquiry based on blended learning in physics instruction to improve critical thinking skills of the senior high school student. In Journal of Physics: Conference Series (Vol. 1097, No. 1, p. 012015). IOP Publishing.

Authors: Sergiy Klymchuk, Tanya Evans, Priscilla Murphy, Jason Stephens, Mike Thomas

Authors: Greg Oates; Tanya Evans

Mathematics curriculum reform is a hot topic in many countries. A review of the Australian Curriculum F-10 was announced in June 2020, which while conducted across all eight learning areas, prioritised Mathematics and Technologies. Considerable consultation has been undertaken in 2021, with implementation from the start of 2022. However, it is notable that the higher years have not been included in this review, nor are stakeholders from higher-education levels featured noticeably in the advisory groups, with respect for example to informing horizon knowledge of where students are headed after Year 10 and through Years 11, 12 and onto first-year university (Years 12 and 13 in New Zealand).

In New Zealand, a Royal Society Te Apārangi Expert Advisory Panel on Mathematics and Statistics was convened between January and June 2021, with a brief to provide advice to the Ministry of Education on the English-medium Mathematics and Statistics curriculum in Aotearoa New Zealand. While this review is again focused at the school level, a key focus of this review was to build and strengthen the pathways for students towards studying higher level mathematics. The report is due for publication in mid-to-late 2021, so we anticipate recommendations from this panel will be available for discussion in this presentation.

The presentation will consider and discuss ways in which we might better facilitate mathematical curriculum alignment, and communication and between teachers, in the higher school years and those responsible for first-year courses in the quantitative sciences at tertiary level.

REFERENCES

Australian Curriculum, Assessment and Reporting Authority (ACARA). (2021). Terms Of Reference - Review Of The Australian Curriculum F-10. https://www.acara.edu.au/docs/default-source/curriculum/ac-review_terms-of-reference_website.pdf?sfvrsn=2

Galligan, L., Coupland, M., Dunn, P. K., Martinez, P. H., & Oates, G. (2020). Research into teaching and learning of tertiary mathematics and statistics. In Research in Mathematics Education in Australasia 2016–2019 (pp. 269-292). Springer, Singapore.

Klymchuk, S., Gruenwald, N., & Jovanoski, Z. (2011). University lecturers’ views on the transition from secondary to tertiary education in mathematics: an international survey. Mathematics Teaching-Research Journal Online, 5(1), 101-128.

Oates, G., Reaburn, R., Brideson, M., & Dharmasada, K. (2017). Understanding of limits and differentiation as threshold concepts in a first-year mathematics course. In M. Borba, I. Neide & G. Oates (Eds.), Proceedings of Brazil Delta ʼ17, The Eleventh Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (pp 108-120). Univates, Brazil: Delta.

Royal Society Te Apārangi. (Under Development). Advice on refreshing the Mathematics and Statistics learning area of the New Zealand Curriculum. https://www.royalsociety.org.nz/what-we-do/our-expert-advice/our-expert-advice-under-development/mathematics-education/

Thomas, M. O. J., Klymchuk, S., Hong, Y. Y., Kerr, S., McHardy, J., Murphy, P., Spencer, S., & Watson, P. (2010).The transition from secondary to tertiary mathematics education. Teaching & Learning Research Initiative Nāu i Whatu Te Kākahu, He Tāniko Taku.

Thomas, M. O., de Freitas Druck, I., Huillet, D., Ju, M. K., Nardi, E., Rasmussen, C., & Xie, J. (2015). Key mathematical concepts in the transition from secondary school to university. In The proceedings of the 12th international congress on mathematical education (pp. 265-284). Springer, Cham.

Authors: Katherine Seaton; Melissa Tacy

Authors: Rachel Passmore; Anne Patel

Improving levels of statistical literacy has been a focus for many introductory statistics courses in our data rich world. The Covid-19 pandemic has resulted in an elevation in the mathematical and statistical demands of items appearing in the media. Gal and Geiger’s (2021) research revealed a dearth of information on exactly what is involved in these new demands. Their research analysed statistical and mathematical products (STaMPs) from four different countries and discovered new or enhanced types of knowledge and skill demands. A question that emerges from this research is how students can be supported to develop their ability to critically evaluate media articles that they read, view, or listen to.

A Foundation Statistics course has been offered on the Tertiary Foundation Certificate programme at the University of Auckland for the last 3 years. This programme offers students a second chance at a tertiary qualification and has a diverse student cohort. Successful graduates of the programme go on to a range of undergraduate study options including Science, Social Science, Engineering and Arts. One of the goals of the Statistics course is to improve students’ ability to critically evaluate media articles. Hence, a range of STaMPs were selected, for students to work on throughout the semester, with the support of question prompts and criteria for evaluating statistically based reports.

This presentation will share some examples of STaMPs used in this course, examples of student responses to these at the beginning and end of the course and feedback from the students.

REFERENCES

Gal, I. & Geiger, V. (2021) An Analysis of Media Items about the Coronavirus pandemic: New insights for Statistical Literacy, unpublished.

Authors: Jungeun Park; Douglas Rizzolo

Many statistics educators are making use of readily available technologies to incorporate interactive questioning within more traditional lectures, such as PollEverywhere and Kahoot!. These recent technologies allow efficient participation for large numbers of students in real-time and simultaneously by allowing anonymous or crowd-sourced answers, minimising the embarrassment for asking “stupid” questions or giving “wrong” answers.

Past research has focused on the different modes of questioning (open-ended, multiple choice, continuum, visual and short answer); I propose an alternative classification based on the intended purpose of the question (understanding, discussion, participation, self-evaluation and feedback). Through better understanding of the purpose of a question, it is possible to improve the phrasing to foster more engagement and productive interaction within lecture environments. Increased engagement is supported by tracking student participation data in lectures; this is also supported qualitatively by student responses to surveys conducted both within and outside the lecture context.

This work draws primarily on experience from a second-year introductory statistics course (Analysis of Biological Data) which is taught using a flipped classroom model, with one-hour interactive lectures each week. These question development methods have also been applied successfully in more traditional lecture environments for large (200+) undergraduate and postgraduate statistics classes.

REFERENCES

Abd Rahman, N. & Masuwai, A. (2014). Transforming the Standard Lecture into an Interactive Lecture: The CDEARA Model. International Journal for Innovation Education and Research, Vol.2-10, p 158.

Anderson, L.W., & Krathwohl, D.R. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. New York: Longman.

Borda, E., Schumacher, E., Hanley, D., Geary, E., Warren, S., Ipsen, C. & Stredicke, L. (2020). Initial implementation of active learning strategies in large, lecture STEM courses: lessons learned from a multi-institutional, interdisciplinary STEM faculty development program. IJ STEM Ed 7, 4.

Burke, A.S. & Fedorek, B. (2017). Does “flipping” promote engagement?: A comparison of a traditional, online, and flipped class. Active Learning in Higher Education, 18(1).

Freeman, S., Eddy, S.L., McDonough, M., Smith, M.K., Okoroafor, N., Jordt, H. & Wenderoth, M.P. (2014). Active learning boosts performance in STEM courses. Proceedings of the National Academy of Sciences, Jun 2014, 111 (23) 8410-8415.

Larson, L. R., & Lovelace, M. D. (2013). Evalating the efficacy of questioning strategies in lecture-based classroom environments: Are we asking the right questions? Journal on Excellence in College Teaching, 24(1), 105-122.

Mazur, E. (1997). Peer instruction: A user's manual. Upper Saddle River, N.J: Prentice Hall.

Authors: Sania Mahajan; Paul Hernandez Martinez; Antony Edwards

All students in mathematics should have access to excellent undergraduate education in a supportive environment. Providing students, early in their career, diverse opportunities to study mathematics as practiced by researchers and scientists, is critical. The Summer Undergraduate Research Experience (SURE) program at Kent State University is designed to fund promising undergraduate researchers for eight weeks over the summer to engage in faculty-supervised research. The SURE program supports students with either a $2,800 stipend (40 hours/week) or $1,400 stipend (20 hours/week). In mathematics, statistics, and computer science, selected scholars complete research projects involving Number Theory, Matrix Theory, Probability Theory, Big Data, Artificial Intelligence, Biological Modeling, Graph Theory, and Differential Geometry. During the academic year similar undergraduate research projects continue to be supported through departmental Undergraduate Research Assistant (URA) programs as well as Choose Ohio First (COF) scholar programs. The reimagined approach to virtual undergraduate research is unique and presents many opportunities for SURE, URA, and COF scholars. The presentation will highlight ways to build a successful model for virtual undergraduate research. Women and ethnic minorities are underrepresented in mathematics. We posit that properly developed outreach and enrichment programs such as SURE will result in attracting and retaining students across the totality of the population. The virtual environment provides a platform for building a strong model for research using the right technological tools. In the presentation we will feature methods helpful in creating similar enrichment programs, sample research projects, dissemination of undergraduate research, student and faculty feedback, and implementation of meaningful evaluation metrics.

REFERENCES

Need for Undergraduate Research Experiences

Bransberger, P. and Michelau, D. (2016). Knocking at the College Door: Projections of High School Graduates, 9th Edition. Boulder, CO: Western Interstate Commission for Higher Education.

Grawe, N. (2018). Demographics and the Demand for Higher Education, Baltimore, MD: Johns Hopkins University Press.

Kasturiarachi, A., Bathi. (2004). Counting on Cooperative Learning to Uncover the Richness in Undergraduate Mathematics. PRIMUS, Vol. XIV, No. 1, 55-78.

Kuh, G. D. (2008). High-impact educational practices: What they are, who has access to them, and why they matter. Washington, DC: Association of American Colleges and Universities.

The Mathematical Sciences in 2025. National Research Council, Washington, D.C., 2103.

Treisman, P., Uri. (1992). Studying Students Studying Calculus: A Look at the Lives of Minority Mathematics Students in College. College Mathematics Journal. 23 (5): 362-372.

Zhao, Chun-Mei; Kuh, George D. (2004). Adding Value: Learning Communities and Student Engagement. Research in Higher Education, v.45 n2 p115-138, Mar 2004.

Engagement in Undergraduate Research Experiences

Angelo, T., A., and Cross, K., P. (1993). Classroom Assessment Techniques: A Handbook for College Teachers. Jossey-Bass Publishers, San Francisco.

D’Angelo, John, P., and West, Douglas, B. (2018). Mathematical Thinking: Problem Solving and Proofs (2nd ed). Pearson Inc., New York, NY.

Duckworth, Angela. (2016). Grit: The Power of Passion and Perseverance. Scribner, New York, NY.

Gawende, Atul. (2010). The Checklist Manifesto: How to Get Things Right. Metropolitan Books, New York, NY.

Friedman, Anver, Littman, Walter (1995). Industrial Mathematics: A course in Solving Real-World Problems. SIAM, Philadelphia, PA.

Kasturiarachi, A., Bathi. (1997). Promoting Excellence in Mathematics through Workshops Based on Collaborative Learning. PRIMUS, VII (2), 147-163.

Promoting Undergraduate Research in Mathematics (2007). Proceedings of the American Mathematical Society. Joseph A. Gillian, Editor, AMS, Providence, RI.

Lang, James, M. (2016) Small Teaching: Everyday Lessons from the Science of Learning. Jossey-Bass.

Verschelden, Cia. (2017) Bandwidth Recovery: Helping students Reclaim Cognitive Resources Lost to Poverty, Racism, and Social Marginalization, Stylus, Sterling, VA.

Tertiary mathematics educators have been shifting towards an active learning approach to teaching. Many external factors support or hinder their transition towards evidence-based instructional practices, including, of recent international interest, the physical learning spaces. In this study in the U.S., I observed and interviewed instructors of introductory-level courses who taught in different types of classrooms during the same semester; in this paper, I focus on two of the instructors. A practicality theory lens, paired with qualitative coding methods that highlighted comparisons and tensions, revealed the challenges that instructors faced as they navigated the variability in learning spaces. Through analysis of classroom norms and pedagogical decisions and justifications, I found that particular resources, layouts, and features of classrooms influenced the feasibility of implementing active learning practices and the instructors’ perceptions of an active learning approach in these spaces. This study presents implications for institutions wanting to support instructors as they transition to student-centered teaching approaches, especially instructors who must adapt between different types of learning spaces.

Authors: Yik Ching Lee; Phil Robbins

DOMjudge is an open-source automated grading system widely used to run programming contests. Here, we present the implementation of this tool to facilitate tutorial exercises and practical assessment for our Foundation Programming paper in the Certificate of Science and Technology. The paper provides students with an introduction to coding using C#.

This online automated grading system was successfully employed following the emergency switch to online learning during the COVID-19 lockdown, and it continued to be used post-lockdown as a blended delivery approach. Exercises were developed to guide students through programming concepts such as input, output, decision making and for loops. Clear instructions and expected output were prescribed for each exercise, pre-defined test cases were compared against the output of a submission, and students were given instantaneous feedback on their submission. Although feedback is limited, it gives students an indication if the code is correct or not. The record of submission was used to track progress of students. DOMjudge has also proven to be useful in conducting practical assessment, it showed students the correctness of submission. This allows better assessment of a student’s programming skills including trouble-shooting skills.

Students’ feedback on the use of DOMjudge are positive. They gained greater autonomy without having to wait for tutors feedback. This helps students to build self-efficacy in their learning.

REFERENCES

J. Eldering, T. Kinkhorst, and P. Warken, DOMjudge—programming contest jury system (August 2017), Available online at: http:// www.domjudge.org/

Cheang, B., Kurnia, A., Lim, A., & Oon, W. C. (2003). On automated grading of programming assignments in an academic institution. Computers & Education, 41(2), 121-131.

Authors: Rachel Rupnow; Brooke Randazzo

Isomorphism and homomorphism are topics central to the teaching of abstract algebra (Melhuish, 2015) but research on students’ and, especially, mathematicians’ understandings of these topics remain limited. Weber and Alcock (2004) examined mathematicians’ reasoning around isomorphism while proving theorems and highlighted the use of sameness and relabeling language to describe isomorphism. Hausberger (2017) highlighted the use of structure-preservation language in textbooks to describe homomorphism. More recently, Rupnow (2021) examined two mathematicians’ language for both isomorphism and homomorphism in interview and teaching contexts and observed four clusters of metaphors: sameness, mapping, sameness/mapping, and formal definition. Nevertheless, these studies leave questions about whether other types of reasoning remain undiscovered. To address this, we examine nine mathematicians’ language for isomorphism and homomorphism based on interviews focused on their understandings and ways of teaching isomorphism and homomorphism in abstract algebra. In order to analyze language use, we use a conceptual metaphor lens (e.g., Lakoff & Núñez, 1997), in which the cross-domain transfer of ideas between well-developed source domains and target domains of interest is centered. Here the target domains of isomorphism and homomorphism are informed by source domains such as sameness and relabeling. Building on Rupnow’s (2021) prior work, we use thematic analysis (Braun & Clarke, 2006) and consensus coding to highlight new metaphors within the sameness cluster, including connections to other mathematical branches’ analogues of isomorphism, as well as a fifth metaphor cluster centered around isomorphism and homomorphism as tools for changing perspectives.

REFERENCES

Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101.

Hausberger, T. (2017). The (homo)morphism concept: Didactic transposition, meta-discourse, and thematisation. International Journal of Research in Undergraduate Mathematics Education, 3(3), 417–443. doi: 10.1007/s40753-017-0052-7

Lakoff, G., & Núñez, R. (1997). The metaphorical structure of mathematics: Sketching out cognitive foundations for a mind-based mathematics. In Lyn D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 21–89). Mahwah, NJ: Erlbaum.

Melhuish, K. (2015). Determining What to Assess: A Methodology for Concept Domain Analysis As Applied to Group Theory. In M. Zandieh, T. Fukuwa-Connelly, N. Infante, & K. Keene (Eds.), Proceedings of the 18th Annual Conference on Research in Undergraduate Mathematics Education (pp. 736–744). SIGMAA on RUME.

Rupnow, R. (2021). Conceptual metaphors for isomorphism and homomorphism: Instructors’ descriptions for themselves and when teaching. Journal of Mathematical Behavior, 62(2), 100867. doi: 10.1016/j.jmathb.2021.100867

Weber, K., & Alcock, L. (2004). Semantic and syntactic proof productions. Educational Studies in Mathematics, 56(2-3), 209–234.

Acknowledgements

This research was funded by a Northern Illinois University Research and Artistry Grant to Rachel Rupnow, grant number RA20-130.

Linear algebra is a core topic for mathematics students. Many science and engineering students are required to take a course in linear algebra at university. Research in linear algebra education shows that many undergraduate students find linear algebra difficult and may only gain a shallow understanding of its powerful concepts and often forget them soon after completing the course. In this study, we investigated introducing subspaces to linear algebra students in one single lecture. To examine the nature of students’ thought processes, we employed Tall’s (2008) three worlds of mathematical thinking as a theoretical framework. The main challenge for teaching was engaging students to blend the embodied, symbolic, and formal worlds meaningfully.

REFERENCES

Tall, D. O. (2008). The transition to formal thinking in mathematics. MERJ, 20(2), 5-24

Authors: Hamide Dogan; Edith Shear; Angel Contreras; Lion Hoffman

We investigated understanding of the linear independence concept based on the type and nature of connections displayed in seven non-mathematics majors’ interview responses to a set of open-ended questions. Through a qualitative analysis, we identified six categories of frequently displayed connections. There were also recognizable differences in the way the connections were applied by the participants. Overall, our findings pointed to an understanding in the form of two main clusters of connections. The two clusters were connected only by linear combination ideas. Each cluster, furthermore, was distinguishable via representation types. The first cluster contained arithmetic/algebraic modes and the second cluster included, mostly, geometric ideas. This paper discusses similarities and differences within and between clusters supported by participant responses. In light of the findings, we provide suggestions for the improvement of linear algebra education of non-mathematics student population.

REFERENCES

Altieri M. and Schirmer, E. (2019). Learning the concept of eigenvalues and eigenvectors: A comparative analysis of achieved concept construction in linear algebra using APOS theory among students from different educational backgrounds. Journal of ZDM:Mathematics Education. Springer. 51(7). pp. 1125-1140.

Caglayan, G. (2019). Is it a sh space or not? Making sense of subspaces of vector spaces in a technology-assisted learning environment. Journal of ZDM: Mathematics Education. Springer. 51(7). pp.1215-1238.

Dogan, H. (2019). Some aspects of linear independence schemas. . In S. Stewat, C. Andrews-Larson, and M.Zandieh (Eds.) research on teaching and learning in linear algebra. Springer Journal of ZDM: Mathematics Education, 51(7), 1169-1181.

Dogan, H. (2018a). Mental Schemes of Linear Algebra: Visual Constructs. In Stewart, S., Andrews-Larson, C., Berman, A., Zandieh, M. (Eds.) Challenges and Strategies in Teaching Linear Algebra. ICME-13 Monographs series. Springer. Part III, pp. 219-240.

Dogan, H. (2018 b). Differing instructional modalities and cognitive structures: Linear algebra. Linear Algebra and its Applications. (542) pp. 464-483.

Dogan, H. (2004). Visual instruction of abstract concepts for non-major students, Int. J. Eng. Educ. 2 (2004) 671.

Dogan, H. (2006). Lack of Set Theory-Relevant Prerequisite Knowledge. International Journal of Mathematics Education in Science and Technology. 37, 41-41.

Dogan-Dunlap, H. (2010). Linear Algebra students’ modes of reasoning: Geometric Representations. Linear Algebra and Its Applications. 432, p. 2141-2159.

Dorier, J. and Sierpinska, A. (2001). Research into the Teaching and Learning of Linear Algebra. In Derek Holton (Ed.) The Teaching and Learning of Mathematics of University level. Kluwer Academic Publishers, Dordrecht, 255-273.

Dorier, J., Robert, A., Robinet, J., and Rogalski, M. (2000). The obstacle of formalism in linear algebra. In J.-L. Dorier (Ed.), On the Teaching of Linear Algebra, Mathematics Education Library, vol.23, Kluwer Academic Publishers, pp.85–124.

Glaser, B. (1992). Emergence vs. Forcing: Basics of Grounded Theory Analysis. Sociology Press. Mill Valley, CA. 1992.

Harel, G. (2019). Variations in the use of geometry in the teaching of linear algebra. Journal of ZDM: Mathematics Education. Springer. 51(7). 1031-1042.

Harel, G. (2018). The learning and teaching of linear algebra through the lenses of intellectual need and epistemological justification and their constituents. In Stewart, S., Andrews-Larson, C., Berman, A., Zandieh, M. (Eds.) Challenges and Strategies in Teaching Linear Algebra. ICME-13 Monographs series. Springer. Part I, pp. 3-28.

Harel, G. (2000). Principles of learning and teaching mathematics, with particular reference to the learning and teaching of linear algebra. In: J. Dorier (Ed.), On the Teaching of Linear Algebra, Kluwer, Dordrecht, pp.177–189.

Harel, G. (1997). The linear algebra curriculum study group recommendations: moving beyond concept definition. Resources for Teaching Linear Algebra, MAA Notes, 42, 107–126.

Hillel, J. (2000). Modes of description and the problem of representation in linear algebra. In J.-L. Dorier (Ed.), On the teaching of linear algebra (pp. 191–207). Dordrecht: Kluwer.

Johnson, W. L., Riess, D. R., and Arnold, T. J. (2002). Introduction to Linear Algebra. Pearson Education Inc. 5th edition.

Payton, S., (2019). Fostering mathematical connections in introductory linear algebra through adapted inquiry. Journal of ZDM:Mathematics Education. Springer 51(7). 1239-1252

Oktac, A. (2019). Mental Constructions in linear algebra. Journal of ZDM: Mathematics Education. 51(7). Springer 1043-1054

Selinski, E. N., Rasmussen, C., Wawro, M. and Zandieh, M. (2014). A Method for Using Adjacency Matrices to Analyze the Connections Students Make Within and Between Concepts: The Case of Linear Algebra. Journal for Research in Mathematics Education, Vol. 45, No. 5 (November 2014), pp. 550-583

Sierpinska, A. (2000). On some aspects of students’ thinking in linear algebra, In J.-L. Dorier (Ed.), On the teaching of linear algebra. pp.209–246, Dordrecht, The Netherlands: Kluwer Academic Publishers.

Stewart. S., Troup, J., Plaxco D (2019). Reflection on teaching linear algebra: Examining one instructor’s movements between the three worlds of mathematical thinking. Journal of ZDM: Mathematics Education. Springer. 51(7). pp. 1253-1266.

Trigueros, M. (2018). Learning linear algebra using models and conceptual activities. In Stewart, S., Andrews-Larson, C., Berman, A., Zandieh, M. (Eds.) Challenges and Strategies in Teaching Linear Algebra. ICME-13 Monographs series. Springer. Part I, pp. 29-50.

Turgut (2019). Sense making regarding matrix representation of geometric transformations inR2: A semiotic mediation perspective in a dynamic geometry environment. Journal of ZDM: Mathematics Education. Springer 51(7). 1199-1214

Karakok, G. (2019). Making connections among representations of eigenvector: What sort of a beast is it? Journal of ZDM: Mathematics Education. Springer 51(7). 1141-1152

Kazunga, C. and Bansilal, S. (2018). Misconceptions about determinants. In Stewart, S., Andrews-Larson, C., Berman, A., Zandieh, M. (Eds.) Challenges and Strategies in Teaching Linear Algebra. ICME-13 Monographs series. Springer. Part II, pp. 127-146.

Wawro, M. (2014). Student reasoning about the invertible matrix theorem in linear Algebra. ZDM Mathematics Education (2014) 46:389–406

Zandieh M., Adiredja A., and Knapp, J. (2019). Exploring everyday examples to explain basis:insights into student understanding from students in Germany. Journal of ZDM: Mathematics Education. Springer. 51(7). pp.1153-1168.

Authors: Suzanne Snead; Lyndon Walker; Birgit Loch

Authors: Poh Hillock; Juan Carlos Ponce Campuzano

Authors: Ayse Aysin Bilgin; Judyth Hayne; Huan Lin; Anna Wells

Just as we entered into the last Decade of Action to accelerate progress towards achieving the United Nations Sustainable Development Goals (UN SDGs) in the 2030 Agenda, a global pandemic hit us in early 2020. As the pandemic took hold, it impacted all three dimensions of sustainable development: economic, social and environmental. The pandemic highlighted how interdependent we are reminded us that global solidarity is essential to address what United Nations describes as the “world’s biggest challenges”.

The higher education sector plays an indispensable role in championing the UN SDGs agenda. Business schools are pivotal to influence and educate their students to become responsible and sustainable business practitioners. To this end, it requires business degrees to incorporate the UN SDGs into the curricula design, by creating new learning content and methods to develop students' interdisciplinary and transdisciplinary skills. The importance of statistically literate citizens and business people is more obvious than ever before since data is ubiquitous and can be used for evidenced-based decision making.

In this presentation, we will share our experiences of how we embedded sustainability into a large first-year Business Statistics unit in a metropolitan University in Sydney. By aligning learning design and assessments to the UN SDGs, we hope to influence students to take initiatives supporting the UN SDGs. Ultimately, we expect students to become responsible innovators contributing to create an inclusive and sustainable global economy.

REFERENCES

Principles for Responsible Management Education (n.d). Management education and sustainable development goals: transforming education to act responsibly and find opportunities. Retrieved from https://d1ngk2wj7yt6d4.cloudfront.net/public/uploads/PDFs/SDGBrochurePrint.pdf

United Nations Sustainable Development Goals Retrieved from https://sdgs.un.org/goals

Authors: Amy Renelle; Stephanie Budgett; Rhys Jones

Over the past century, mathematics and programming have become closely interlinked, mathematics informing computational methods, and computers acting as essential tools for mathematical discovery.

Plenty of mathematics departments now have one or two courses which give a taste of programming- often folded in between matrix algebra, and differential equations.

Students coming into coding bring with them various assumptions and mindsets directly from mathematics; many of these are helpful, but some act as stumbling blocks and pitfalls. In this presentation, I look in on a few of the places where underlying assumptions common to mathematical classrooms can actively hinder students when it comes to coding, and a couple ways to construct lessons, tutorials and ciricula in order to avoid potential pitfalls. I’ll be focusing on results from first year mathematics courses where students are introduced to Matlab, but the ideas are applicable in many programming contexts.

Authors: Michael Jennings; Merrilyn Goos; Peter Adams

The transition from secondary to tertiary mathematics has been the subject of increased research in recent years. What is still lacking though is research into the perspectives of university lecturers on this transition.

This talk focuses on two areas of the transition: lecturer perspectives on the reasons students choose or don’t choose higher level mathematics in the last two years of secondary school, and lecturer perspectives on Year 12 students’ calculus skills and understanding. Twenty lecturers from across Queensland completed two online surveys. Fisher’s exact test was used to determine statistical significance.

With regard to subject selection reasons, the results show that lecturers thought friends played an important role in influencing one’s decision to choose or not choose higher level mathematics. Students, however, said otherwise. When investigating students’ calculus skills and understanding, it was apparent that some lecturers not only had little idea of what was taught at school but also how it was taught. Klymchuk (2011) had similar findings. In addition, there were also statistically significant differences between lecturer and teacher perspectives on how difficult the calculus questions would be for students. These results show the clear need for more dialogue between school teachers and lecturers to help improve the transition from secondary to tertiary mathematics.

This talk reports on one part of a two-year longitudinal study into the transition from secondary to tertiary mathematics from the perspectives of students (n=1000), school teachers (n=60), and university lecturers (n=20).

REFERENCES

Klymchuk S., Gruenwald N., Jovanoski Z. (2011). University lecturers’ views on the transition from secondary to tertiary education in mathematics: An international survey. Proceedings of Volcanic Delta 2011, the 8th Southern Hemisphere Conference on Teaching and Learning Undergraduate Mathematics and Statistics (pp. 190-201). Rotorua, New Zealand.

Authors: Ching-ching Yang; Jenn-Tsann Lin

Authors: Jeff Nijsse; Yik Ching Lee

This presentation demonstrates the use of Desmos teacher activities to teach concepts in foundation physics. Activities have been developed1 using the online education platform Desmos (2021) to introduce students to kinematics. Online exercises are more important than ever in the pandemic era of short-notice lockdowns and remote teaching. Having interactivity available in a template that can be demonstrated in lecture, or, if necessary, can be accessed independently by students at home, is a valuable resource.

One-dimensional kinematics exercises were developed using the teacher-Desmos feature to introduce students to the topic. Students are taken through a range of possibilities with the help of an interactive script to provide input, output, and visual feedback. This is accomplished through the computation layer scripting language built into the platform. The subsequent 2-D topic builds on the first instance and enhances student understanding of concepts such as velocity vectors, constant acceleration, and maximum range. Students can type answers into the activity that are stored for feedback or peer viewing.

Showing students a Desmos graphing calculator version with equations exposed created confusion and distracted from engaging with the concepts of kinematics. The teacher activity version puts the code (and equations) in the background leaving students free to discuss concepts at hand. Displaying and annotating the velocity vectors and range made it easy to highlight characteristics of projectile motion. Student engagement was better using an interactive web-based activity than paper-based structured learning or mixed media and student conversation revealed rich discussion.

1. Activity links available at: https://github.com/millecodex/Delta2021

REFERENCES

Desmos. (2021, August 16). Teaching with Desmos. https://teacher.desmos.com/

Students without university entrance are often diverted into a six-to-twelve month bridging or foundation programme. Successful completion usually leads to a degree programme which they would not otherwise have been able to enter (Benseman & Russ, 2003). In the programme each student must pass a mathematics course to satisfy academic numeracy requirements. However, there are a small number of students who struggled with mathematics at school and who once again find themselves in an uncomfortably familiar situation where they had poor learning experiences. These students have known or unknown mathematical learning dis/abilities (MLDs) which often accounts for their continuing frustrations with little progress in mathematics and subsequent anxieties. Little is known about how many of these students are assessed for MLDs, nor how many have missed out for whatever reasons.

In this study, students who repeated bridging mathematics, were invited to share their experiences, in semi-structured interviews. Early findings suggest that these students are all too familiar with repeating mathematics courses, with almost all being held back in their school years. They also shared a dread of having to do more mathematics, particularly workplace numeracy or academic numeracy once they are into their degree studies. Some gave accounts about familial or outside assistance with school mathematics, but most regarded progress from these resources as minimal at best. As well as providing stories about the challenges they met with mathematics particularly at school, the participants also offered some ideas about what a useful learning environment for adult learners (with LDs) might look like.

REFERENCES

Benseman, J., & Russ, L. (2003) Mapping the territory: A survey of bridging education in New Zealand. New Zealand Journal of Adult Learning, 31(1),43-62.

Authors: Julia Collins; Steven Richardson; Justin Brown; Eben Afrifa-Yamoah; Rowena Harper

Face-to-face examinations have long been a cornerstone of university mathematics assessment (Iannone & Simpson, 2011; Thoma & Nardi, 2016), but with the advent of Covid-19 universities are increasingly opting for online assessments. The difficulty in monitoring students taking large-scale mathematics assessments in an online setting creates a significant challenge in maintaining assessment integrity. Students have the potential to seek assistance from friends, family, tutors, online ‘tutoring’ sites such as Chegg, and online calculators such as Wolfram Alpha that not only present the solution to a problem, but the working as well. While a huge amount of literature exists about academic misconduct more broadly, research specific to mathematics/calculation-based assessments has been lacking to date (Seaton, 2019).

Our research project seeks to investigate student and academic staff perceptions in relation to behaviours that exist in a 'grey area' separating clear misconduct from appropriate/reasonable use of available resources and technology. In a recent survey of Australian university staff and students, we asked participants to rate various academic misconduct scenarios on a scale of “No misconduct” to “Clear misconduct”. These scenarios range from more traditional sources of help, such as friends and tutors, to newer forms of help such as online calculators and online forums.

This talk will discuss the methodology of the survey instrument and present preliminary findings from the survey data, seeking to explore the consistency with which students categorise specific scenarios as clear misconduct, and the differences between staff and student attitudes towards academic misconduct.

REFERENCES

Iannone, P., & Simpson, A. (2011). The summative assessment diet: how we assess in mathematics degrees. Teaching Mathematics and Its Applications, 30, 186-196. http://doi:10.1093/teamat/hrr017

Seaton, K. A. (2019). Laying groundwork for an understanding of academic integrity in mathematics tasks. International Journal of Mathematical Education in Science and Technology, 50(7), 1063-1072. https://doi.org/10.1080/0020739X.2019.1640399

Thoma, A., & Nardi, E. (2016). A commognitive analysis of closed-book examination tasks and lecturers’ perspectives. In E. Nardi, C. Winslow, & T. Hausberger (Eds.), Proceedings of INDRUM 2016: First conference of the international network for didactic research in university mathematics (pp. 411-420). University of Montpellier and INDRUM.

One of the many challenges posed by the COVID-19 pandemic has been the need to alter assessments to run in an online environment. In this talk, I focus on the course for which I found this process most challenging – a general mathematics course taught to a large audience of students from a number of different degree programs.

In the past, most test and exam questions in the course were computation-based, and the teaching materials are designed with this in mind. However, in an online open book examination, students can access computer algebra systems capable of carrying out most computations, and assessment design must take this into account. An additional constraint is that our test and exam must consist of multiple choice problems. This means we are vulnerable to students sharing solutions, and must also defend against misconduct of that kind. This talk will discuss how we worked within these constraints to design fair tests and exams.

Authors: Don Shearman; Leanne Rylands

The COVID-19 pandemic has provided an imperative for change in the way we teach and support mathematics. The Mathematics Education Support Hub, Western Sydney University, offers a diverse array of support workshops for students. All workshops were delivered face to face before March 2020, and then moved to online delivery, with most remaining online to now (September 2021).

In the context of a series of nursing numeracy workshops and a series of refresher workshops for incoming undergraduates, we will discuss some metrics which have been used in an attempt to measure the effects of this change of delivery mode in terms of effectiveness and reach. These include results of pre- and post-tests used in both modes of delivery, face-to-face attendance, time spent in Zoom sessions, and the plethora of data provided by the learning management system. We will also discuss dimensions of the change from face-to-face to online delivery that are not measured by these metrics, and how the metrics might inform future development of the workshops.

Effects of spaced, repeated retrieval practice and test-potentiated learning on mathematical knowledge and reasoning in an authentic educational setting are investigated in the study. Research participants were a cohort of second-year pre-service mathematics teachers. A revised taxonomy table was utilized to measure the knowledge and reasoning proficiency of participants. Findings indicate that the intervention was effective in enhancing categories, where familiar algorithmic reasoning and procedural knowledge were required. It was less effective with categories requiring flexible and creative use of conceptual and procedural knowledge. Theories of storage and retrieval strength and conceptual knowledge are used to explain the findings.

Authors: Anita Campbell; Mashudu Mokhithi; Jonathan P Shock

Growth mindset (Dweck, 2006) is the belief that our intelligence is not set at a predetermined maximum level. A person on the fixed mindset end of the mindset scale believes that most students who are accepted to study university mathematics have a high set level, and that those who have to work hard to do what others may find easy have a low set level. Growth mindset is important for motivating students to seek challenges, try alternative approaches, and use feedback to improve. Boaler (2015) describes six principles for designing learning tasks that should promote growth mindset in mathematics classrooms. We call these principles Boaler’s taxonomy. While Boaler’s work has predominantly been applied in school mathematics contexts, we have established that these principles can be applied to university mathematics assessment tasks (Campbell et al., in press). We consider Boaler’s taxonomy in relation to Bloom’s taxonomy as a guide for developing mathematics assessment tasks for first-year mathematics courses.

REFERENCES

Boaler, J. (2015). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching. San Francisco: Jossey-Bass.

Campbell, A. L., Mokhithi, M., & Shock, J. P. (in press). Exploring mathematical mindset in question design: Boaler's taxonomy applied to university mathematics. In Research in Engineering Education Symposium and Australasian Association for Engineering Education Annual Conference (REES AAEE 2021), 5-8 December 2021, Perth and online.

Dweck, C.S. (2006). Mindset: The new psychology of success. How we can learn to fulfill our potential. New York: Ballantine Books.

Authors: Will Tidwell; Cynthia Anhalt; Brynja Kohler

Authors: Thabiso Khemane; Pragashni Padayachee; Corrinne Shaw

Misconceptions and a poor understanding of the concept of the double integral lead to difficulties in learning Vector Calculus. The main objective of this research is to investigate undergraduate engineering students’ misconceptions when learning double integrals at a South African university. To frame this research and which forms the focus this presentation, systematic literature review was carried out using Scopus, Science Direct, EBSCOhost and Engineering village databases. The search was restricted to published English language articles relating to misconceptions in double integrals and functions of two variables in the timeframe 1 January 2010 to 31 December 2020. The search yielded a total of 53 publications.

From these studies, the findings reveal that students struggle with concepts that are generally considered to be evident during teaching. We also noted that misconceptions in double integrals were related to students’ lack of understanding of prerequisite concepts and advanced mathematical thinking because of the hierarchical nature of mathematics and the independence of mathematics concepts. These prerequisite concepts include trigonometric substitution and algebra. It was also discovered that the frequent misconceptions are generated by errors that are indicative of a misunderstanding or misinterpretation of a double integral question. The findings of this review will inform researchers, teachers and other decision makers on student’s understanding of double integrals and may contribute to the development of proactive plans to support teaching and learning of undergraduate mathematics. The findings could also be drawn on when planning curriculum and continued professional development activities for mathematics educators, lecturers, and students.

Authors: Yannis Liakos; Saba Gerami; Vilma Mesa; Thomas Judson; Yue Ma

Authors: Victor Martinez-Luaces; Jose Antonio Fernández-Plaza; Luis Rico

Inverse problems have traditionally been forgotten, despite their essential role in different disciplines (Bunge, 2006). Unfortunately, Mathematics Education is not the exception to this rule as it was observed by different authors (Groestch, 1999, 2001; Martinez-Luaces, 2011).

This situation implies, among other things, the absence of an elaborated theoretical framework. For this purpose, Groestch (1999, 2001) adapted the well-known IPO-model commonly used in Computer Science and other disciplines (see, for example, Martinez-Luaces, Fernandez-Plaza, Rico & Ruiz-Hidalgo, 2021). This first attempt could be a good starting point if only the cultural/conceptual dimension of Didactic Analysis is considered (Rico & Ruiz-Hidalgo, 2018). Nevertheless, it does not take into account the other three dimensions (cognitive, ethical/formative and social), which deserve to be considered.

This work reflects on some examples previously described (Martinez-Luaces, Rico, Ruiz-Hidalgo & Fernandez-Plaza, 2018; Martinez-Luaces, Fernandez-Plaza & Rico, 2020; Martinez-Luaces, Fernandez-Plaza, Rico & Ruiz-Hidalgo, 2021) and also analyzes data obtained in a doctoral thesis fieldwork (Martinez-Luaces, 2021), which concern other dimensions of the Didactic Analysis.

The final purpose of this reflection and analysis is the construction of an appropriate theoretical framework for inverse problems in Mathematics Education and in order to achieve this goal, this communication aims to be a starting point for deeper development in future works.

References

Bunge, M. (2006). Filosofía y Ciencia. Problemas directos e inversos. Retrieved on May of 2021 from: http://grupobunge.wordpress.com/2006/07/20/119

Groestch, C. W. (1999). Inverse problems: activities for undergraduates. Washington D.C.: Mathematical Association of America.

Groetsch, C. W. (2001). Teaching-Inverse problems: The other two-thirds of the story. Quaestiones Mathematicae, 24 (1), Supplement, 89-94.

Martinez-Luaces, V. (2011). Problemas inversos: los casi olvidados de la Matemática Educativa. Acta Latinoamericana de Matemática Educativa, 24, 439-447.

Martinez-Luaces, V., (2021).Posing inverse modeling problems for task enrichment in a secondary mathematics teachers training program. Doctoral Thesis presented at University of Granada, Spain. Retrieved on May of 2021 from: https://digibug.ugr.es/handle/10481/68580

Martinez-Luaces, V., Fernández-Plaza, J. A., & Rico, L. (2020). Inverse modeling problems in task enrichment for STEM courses. In K. G. Fomunyam (Ed.), Theorizing STEM Education in the 21st Century. London: IntechOpen.

Martinez-Luaces, V., Fernández-Plaza, J. A., Rico, L., & Ruiz-Hidalgo, J. F. (2021). Inverse reformulations of a modelling problem proposed by prospective teachers in Spain. International Journal of Mathematical Education in Science and Technology. 52(4), 491-505.

Martinez-Luaces, V., Rico, L., Ruiz-Hidalgo, J. F & Fernández-Plaza, J. A. (2018). Inverse Modeling Problems and Task Enrichment in Teacher Training Courses. In R. V. Nata (Ed.) Progress in Education (pp. 185-214) New York: Nova Science Publishers.

Rico, L. & Ruiz-Hidalgo, J. F. (2018). Ideas to work for the curriculum change in school mathematics. In Y. Shimizu & R. Vithal (Eds.), ICMI Study 24, pp. 301-308.

Authors: Jungeun Park; Douglas Rizzolo

Approaches to online education have evolved much within the past two decades with increasing research exploring the incorporation of active learning techniques (Irani & Denaro, 2020) and contemporary pedagogical methods (LeSage et al., 2021). With the increasing integration of online delivery methods, the discussion arises of how effective these delivery methods are. Online mathematics education has cultivated itself as an essential element of many higher institutions, often being met with criticism regarding student satisfaction and varying completion rates. Common barriers to online learning involve a lack of access to technology or the internet, low interaction, and a lack of motivation and support (Muilenburg & Berge, 2005). While the uptake of online learning can be attributed to new innovations such as the inception of MOOCs, the COVID-19 pandemic has helped to usher rapid transitions to deliver courses remotely.

With the emergence of a substantial number of case studies of undergraduate mathematics courses delivered during the COVID-19 pandemic, a scoping review was conducted. In this presentation I will report on a preliminary qualitative analysis on common themes and illuminate potential limitations of online delivery, where efforts can be delegated for future research. The case studies used in this scoping review were sourced from Scopus, ProQuest, and Google Scholar databases. The findings revealed the importance of preparation of such delivery methods and informs how this pandemic is an opportunity to reshape our approach to effective transitions to online learning.

REFERENCES

Irani, S., & Denaro, K. (2020). Incorporating Active Learning Strategies and Instructor Presence into an Online Discrete Mathematics Class. Proceedings of the 51st ACM Technical Symposium on Computer Science Education, 1186–1192. https://doi.org/10.1145/3328778.3366904

LeSage, A., Friedlan, J., Tepylo, D., & Kay, R. (2021). Supporting at-Risk University Business Mathematics Students: Shifting the Focus to Pedagogy. International Electronic Journal of Mathematics Education, 16(2), em0635. https://doi.org/10.29333/iejme/10893

Muilenburg, L. Y., & Berge, Z. L. (2005). Student barriers to online learning: A factor analytic study. Distance Education, 26(1), 29–48. https://doi.org/10.1080/01587910500081269

Authors: George Kinnear; Anna Wood; Richard Gratwick

Authors: John Banks; Paul Fijn; Robert Maillardet; Anthony Morphett; Rosie Pingitore; Alba Santin Garcia; Trithang Tran

Authors: Adam Bartonicek; Stephanie Budgett; Claudia Rivera-Rodriguez

Authors: Kim Locke; Igor Kontorovich; Lisa Darragh

The challenges of transitioning from secondary school to university mathematics are widely recognised. For international students studying in a host country where language, culture and educational systems may differ substantially from home, these challenges may be experienced in unique ways. This study forms part of a wider exploration to understand international student experiences during the mathematical transition from school to university.

Detailed accounts of the first-year experiences of two international students were gathered in semi-structured interviews. The students, from Malaysia and Sri Lanka respectively, had schooled largely in other countries before completing their first university mathematics course in New Zealand. Using identity as a lens for interpretation, an analysis of their accounts highlighted the importance of collaborative strategies as they sought to make sense of new mathematical content. Preliminary findings revealed differences in how collaborative groups were formed and in the types of interaction within these groups.

The preliminary findings promote understanding of how international students might engage with others as they grapple with first-year mathematics. This knowledge will be relevant to all who teach undergraduate mathematics to a culturally diverse student body.

Authors: Igor' Kontorovich; Sina Greenwood

In the mathematics community, proving a theorem is a collective endeavor that has a role in generating mathematical knowledge and understanding (e.g., Rav, 1999). This role is often actualized through social interactions that unfold in research collaborations, seminars, paper peer-reviews, and other structured situations where a proof undergoes a series of transforms. This approach to proofs is very different from typical university classrooms, where a proof quickly reaches the point of endorsement by the classroom community.

We report on an ongoing project in a cross-level topology classroom, where students have been provided with opportunities to construct proofs in pairs, share them with the whole class at the board, and receive feedback from their peers and the course teacher. The overarching aim of the project is to explore opportunities for generating mathematical knowledge and understanding that emerge on individual and classroom levels through progressive transformations of a proof. In this presentation, we mobilize the commognitive framework (Sfard, 2008) to explore students’ learning in this process. Specifically, we analyze an interaction between two students as they collaboratively constructed a proof, and the subsequent public re-proving of the same statement by one of them at the classroom board.

REFERENCES

Rav, Y. (1999). Why do we prove theorems? Philosophia Mathematica, 3(7), 5–41.

Sfard, A. (2008). Thinking as communicating: human development, the growth of discourses, and mathematizing. Cambridge University Press.

Complex functions are essential mathematical objects not only in complex analysis but also in algebra, differential geometry and in many other areas such as numerical mathematics and physics. Visualising complex functions is a non-trivial task since they will produce a graph existing in a four-dimensional space. In this presentation, I provide an overview of the method known as domain colouring to visualise and explore complex functions. I also present a set of open-source online tools which main goal is to help students, and anybody interested in this topic, to create significant connections between visual representations, algebraic calculations and abstract mathematical concepts about complex functions.

REFERENCES

Ponce Campuzano, JC. (2018). Domain coloring. https://jcponce.github.io/domain-coloring/

In May of 2020 Christoper Sangwin and George Kinnear published a paper called: Coherently Organised Digital Exercises and Expositions (CODEX). In this talk I will outline what that paper is about and show you the resources that we in the Department of Mathematics and Statistics at the University of Canterbury were inspired to build after reading the paper. I will present the work of many people across our department to show you the tools we used and the modules we have built.

REFERENCES

Sangwin,C & Kinnear, G. (2020, May 29). Coherently Organised Digital Exercises and Expositions. https://doi.org/10.31219/osf.io/jhngw

Authors: Anupam Makhija; Meena Jha; Deborah Richards; Ayse Bilgin

The statistics presented in news such as unemployment rate, climate change, interest rates, and recently COVID-19 infection, or vaccination rates are of interest to most people. Logically, we expect more students wanting to study statistics but unfortunately, many students find statistics “boring” or irrelevant to their lives and studies.

Enhancing curiosity through relevance and meaningful feedback (Wang, 2019) can address the issues related to Statistics education. A game designed to educate students in Statistics education based on United Nations Sustainable Development Goals (UNSDG) (Sustainable Development Goals, 2021) could be a solution to examine the effect of feedback, and relevance on enhancing curiosity from a psychological perspective.

The Statistical game in this context consists of four levels including questions developed using Bloom’s taxonomy. The game outlines a story around UNSDG datasets related to poverty, education, and health, where feedback is supplied to learners via various characters. This presentation will report on the design of the game and the feedback strategies to enhance learners’ curiosity. Participants’ data will be collected through system interaction, and self-reporting using validated instruments. This study presents a promising approach for educators in refocusing their efforts to improve Statistics education by fostering a level of curiosity through relevance and meaningful feedback on a digital platform.

REFERENCES

Sustainable Development Goals | United Nations Development Programme. Undp.org. (2021). Retrieved 24 September 2021, from https://www.undp.org/sustainable-development-goals.

Wang, Z., Gong, S. Y., Xu, S., & Hu, X. E. (2019). Elaborated feedback and learning: Examining cognitive and motivational influences. Computers & Education, 136, 130-140.

Compulsory capstone courses for all undergraduate pathways in the Faculty of Science at the University of Auckland were introduced in 2019. One of the main goals of the Science capstone courses was to provide a vehicle for students to demonstrate the attributes of the B.Sc graduate profile.

In semester one, 2021, the first iteration of the statistics capstone course was offered, and the second iteration was completed in semester 2. Details about the structure of the course will be shared as will student feedback from the first cohort who completed pre- and post-course surveys.

One research question was to establish whether graduate profile attributes could be demonstrated in a statistics capstone course. To do this each assessment task in the course was classified by graduate profile attribute and level of importance. Student marks for each assessment enabled the production of a ‘grade’ by attribute and an overall graduate profile ‘grade’ for each student. To test the validity of this automated method, student work was qualitatively coded and then scored using a framework synthesised from the American Statistical Association (2014) guidelines for statistics graduates, the VALUES rubrics (AACU, n.d.) and the University of Auckland graduate profile. Work to compare the two classification methods is on-going but some preliminary results will be shared.

The statistics capstone course is still a work in progress, with new challenges in the second iteration because of larger numbers of students, overseas online students, and changing from an in-person to an online working environment due to Covid lockdowns.

REFERENCES

American Statistical Association. (2014). Curriculum Guidelines for Undergraduate Programs in Statistical Science. Retrieved March 22, 2020, from American Statistical Association: https://www.amstat.org/asa/education/Curriculum-Guidelines-for-Undergraduate-Programs-in-Statistical-Science.aspx

Association of American Colleges and Universities. (n.d.). VALUE Rubrics. Retrieved March 14, 2020, from Association of American Colleges and Universities: https://www.aacu.org/value-rubrics

Authors: Ayse Aysin Bilgin; Frank Valckenborgh

In a third-year capstone unit for science students, the curriculum is designed around the UN Sustainable Development Goals (UN SDGs). The assessments are structured such that the main assessment is a group based-project proposal that addresses one or more of the UN SDGs with a final written report and corresponding video pitch/presentation.

The majority of these students are enrolled in majors in which they may have completed a first-year mathematics and/or statistics unit, but no further studies in mathematics and/or statistics. The authors have used this opportunity to develop some student-centred activities that specifically address the mathematical and statistical critical thinking skills of these students before they graduate, and at the same time provide additional perspective on the importance of quantitative thinking in issues of sustainability.

The mathematical thinking component is based on Al Bartlett’s celebrated lecture Arithmetic, Population, and Energy (Bartlett, 1978), and evolves around several simple in-class activities that relate to linear and exponential growth, embedded into a minimum of theory to provide the conceptual framework. The statistical thinking is based on Wild and Pfannkuch (1999) and uses additional examples to emphasise how statistics should be reported.

In this presentation, we will provide more detail about these activities which might be adopted/adapted by others for their classes.

REFERENCES

Bartlett, A. (1978). Forgotten fundamentals of the energy crisis. American Journal of Physics, 46, 876–888.

Wild C.J. and Pfannkuch M. (1999). Statistical Thinking in Empirical Enquiry. International Statistical Review. 67(3):223-265.

Foundation mathematics courses play a key role in today’s tertiary education system, allowing mathematically underprepared students to engage with their chosen STEM degrees. In this talk I reflect on the process of reimagining a foundations of mathematics course that has no pre-requisite but adequately prepares students for further calculus courses.

There are several key issues that needed to be addressed in the course design. For example, there is strong evidence in the literature to suggest that self-efficacy has an impact on student motivation, persistence, and chance of success. Another target issue is to provide students with opportunity to learn and revise core numeracy concepts such as a symbolic understanding of the equals sign, and fraction arithmetic.

I will give an overview and motivation for the redesigned course structure, and outline the main elements of the course. These include a co-requisite structure to cover core numeracy skills; weekly homework delivered online to allow for instant feedback and interleaving; collaborative problem solving workshops; and an option to take the course at a slower pace. I will also reflect on lessons learned throughout the first implementation of this course and some promising initial outcomes.

REFERENCES

Barton, C. (2018). How I Wish I’d Taught Maths: Lessons Learned from Research, Conversations with Experts, and 12 Years of Mistakes. John Catt Educational Limited.

Bengmark, S., Thunberg, H., & Winberg, T. M. (2017). Success-factors in transition to university mathematics. International Journal of Mathematical Education in Science and Technology, 48(7), 988–1001.

Bettinger, E. P., & Long, B. T. (2009). Addressing the needs of underprepared students in higher education does college remediation work? Journal of Human Resources, 44(3), 736–771.

Goodyear, P. (2015). Teaching as design. Herdsa Review of Higher Education, 2(2), 27–50.

Hokanson, B., & Miller, C. (2009). Role-based design: A contemporary framework for innovation and creativity in instructional design. Educational Technology, 21–28.

Ian Jones & Dave Pratt. (2012). A Substituting Meaning for the Equals Sign in Arithmetic Notating Tasks. Journal for Research in Mathematics Education, 43(1), 2–33.

Skaalvik, E. M., Federici, R. A., & Klassen, R. M. (2015). Mathematics achievement and self-efficacy: Relations with motivation for mathematics. International Journal of Educational Research, 72, 129–136.

Sofroniou, A., & Poutos, K. (2016). Investigating the effectiveness of group work in mathematics. Education Sciences, 6(3), 30.

Williams, T., & Williams, K. (2010). Self-efficacy and performance in mathematics: Reciprocal determinism in 33 nations. Journal of Educational Psychology, 102(2), 453–466.

At the Swan Delta Conference in 2019, I spoke on the value of teaching mathematics and coding to foundation art and design students, based on my experience over two semesters. Today I will discuss interventions aimed at improving motivation and engagement.

My goal is to motivate foundation art and design students to enjoy creating mathematical art. Mathematics is beautiful. I want my students to agree with me and to eagerly anticipate creating their own mathematical art. How do I achieve this? My students arrive with weak backgrounds in mathematics, wondering why they are studying it. Based on my experience, motivating mathematics students to explore mathematical art and coding is relatively easy compared to motivating art and design students to explore mathematics and coding. So how do we go uphill?

I have experimented with two investigation assignments, handed out in the first class. The first task is to research and report on the life and work of a mathematical artist, contemporary or from the past. The second task is to research and report on repeating patterns from the student’s own culture. In the first two offerings of this course, the research on a mathematical artist was done towards the end of the teaching programme. Moving it to the beginning has provided definite benefits with respect to engagement and motivation. The two assignments are complementary and work well when done together. Introducing Islamic geometric design based on arcs early has also caught interest. Insights based on questionnaire responses and observations are shared.

When marking test papers as a mathematics educator, what to do when confronted with blank spaces where the answers should have been written. Are all blank spaces worthy of the same mark?

Did students have no knowledge of what the topic; or did students just not understand the question but

has knowledge; or anxiety issues taking place or did students just have the ‘Blank Moment’? These situations would all be awarded the same mark but the reasons for the blanks are not equal.

Recently, to combat this problem, a system of exchange of marks for clues on starting or proceeding further in a question has been introduced. The benefits are two-fold as the students are provided instant feedback when in the ‘thought-zone’ of the question and the educators may use these questions as a guide to improving ‘learning moments’ in class. The use of SOLO taxonomy will give both. educator and student, a guide to where their learning lies and where it can improve.

This presentation will describe how the current system is being applied for online tests throughout the recent trimesters. It will be an interactive session to show how the ‘clue-giving’ will arouse the little grey cells as Hercule Poirot often said when solving a mystery.

REFERENCES

Biggs, J., & Collis, K. (1982). Evaluating the quality of learning: the SOLO taxonomy, New York: Academic Press.

For the past 10 years, I have taught academic writing to students, many of whom identify more as mathematicians than as writers. Over this time, I have developed mathematics-based metaphors to teach productive writing behaviours, such as Writing-as-Modelling, Writing-as-Problem Solving, and Writing-as-Proving (Yoon, 2019). In this presentation, I share practical workshop-style writing activities that draw on similarities between writing and mathematics. These include: structuring an argument; writing as a social activity; using other peoples’ texts in writing. I show how these activities can help mathematics students develop some of the behavioural, artisanal, social and emotional features of productive academic writing (Sword, 2018).

REFERENCES

Sword, H. (2018). Air & Light & Time & Space: How Successful Academic Write. Harvard University Press.

Yoon, C. S. (2019). The Writing Mathematician. In M. Pitici (Ed.) Best writing on mathematics 2018 (pp. 205-216). Princeton, NJ: Princeton University Press.

Authors: Kaitlin Riegel; Tanya Evans; Jason Stephens

The construct of self-efficacy, developed by Bandura (1977; 1997) as part of his social cognitive theory, is a central construct in mathematics education and known as one of the best predictors of mathematical performance (Siegel et al., 1985). Self-efficacy refers to learners’ expectations and beliefs about their ability to learn new material, develop new skills, and master tasks. As self-efficacy is interwoven with cognition and achievement (Usher & Pajares, 2009), it is vital to understand how it develops and changes. The dominant instructional design theories recognise the importance of self-efficacy and posit that enhancing self-efficacy leads to improved achievement.

For tertiary educators, it is of particular concern to promote, and not hinder, the development of student self-efficacy within the time constraints of a single semester. We conducted a quasi-experimental, repeated measures study in a second-year university service mathematics course to test the effects of frequent online quizzes (Evans et al., 2021; Riegel & Evans, 2021) on assessment-related self-efficacy in students (N = 277). Modelling demonstrated that self-efficacy around one form of assessment influences self-efficacy in another form of assessment and performance on one form of assessment indirectly influences self-efficacy in another. The results suggest that repeated experiences on low-risk summative assessment can influence the efficacy of students going into an exam. However, high-weight, exam-like assessments during the semester can overwhelm these effects. The findings are discussed together with implications that educators should plan courses so that assessments are designed to support the development of student assessment self-efficacy.

REFERENCES

Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191–215. https://doi.org/10.1037/0033-295X.84.2.191

Bandura, A. (1997). Self-efficacy: The exercise of control. W H Freeman/Times Books/ Henry Holt & Co.

Evans, T., Kensington-Miller, B., & Novak, J. (2021). Effectiveness, efficiency, engagement: Mapping the impact of pre-lecture quizzes on educational exchange. Australasian Journal of Educational Technology, 163-177. https://doi.org/10.14742/ajet.6258

Riegel, K. & Evans, T. (2021). Student achievement emotions: Examining the role of frequent online assessment. Australasian Journal of Educational Technology, 75-87. https://doi.org/10.14742/ajet.6516

Siegel, R. G., Galassi, J. P., & Ware, W. B. (1985). A comparison of two models for predicting mathematics performance: Social learning versus math aptitude–anxiety. Journal of Counseling Psychology, 32(4), 531–538. https://doi.org/10.1037/0022-0167.32.4.531

Usher, E. L., & Pajares, F. (2009). Sources of self-efficacy in mathematics: A validation study. Contemporary Educational Psychology, 34, 89-101. https://doi.org/10.1016/j.cedpsych.2008.09.002

Authors: Gizem Intepe; Jim Pettigrew et al

Authors: Anita Campbell; Pragashni Padayachee

Resources for the teaching and learning of mathematics include those provided or recommended by the teacher supplemented by others available elsewhere, such as knowledgeable friends and family, the library and effectively limitless online resources. Many online resources available as supplemental material can be helpful for learning yet teacher curation takes a great deal of time and risks missing important student perspectives. Student curation would be preferable to teacher curation as choice would reflect students' perception of their learning needs rather than possibly far-removed teacher perception, yet a traditional course provides no means for students to share information about these opportunities with one another. In two Calculus courses a “knowledge network” initiative was launched to provide a platform for students to share supplemental materials with one another. Image hotspots located on a course concept network offered embedded links to student-selected videos, tools and websites. Other than a check for relevance and accuracy by a teacher the initiative was student-driven; students voluntarily selected the resources, shared them within their learning community and reported benefit within the calculus courses and beyond.

Authors: Anita Campbell; Tracy S. Craig; Batseba L. Mofolo-Mbokane; Pragashni Padayachee

With a cumulative experience of 100 years of teaching higher education mathematics students, we are four academics at three different higher education institutions over two continents. Our common history is that we were all members of the 2015 Elephant Delta organising committee. From February 2021 we held fortnightly Zoom meetings to share ideas, discuss challenges and explore the potential for collaborating on research.

We place high importance on our teaching and the learning of our students. Forming an online community of practice (CoP) forged by our experiences and thoughts on assessment during the pandemic led us to identify five propositions to guide our university mathematics teaching: (1) Open book assessment has value; (2) Verbalising helps learning; (3) Assessment can promote self-directed learning; (4) Assessment can develop higher order thinking skills (HOTS); and (5) Assessment as learning and for mastery learning benefits students. Our meetings and homework pushed us to think about why we teach what we teach, assess how we assess, and how we can make both more relevant to a changing world. We learnt more deeply about assessment by interrogating each other’s work, observing and identifying misconceptions or errors (made by ourselves and others), and learning different ways of solving problems through discussion. We noted that sustaining the CoP required comfort in being confronted and criticized. The next aim of our CoP is to research moving away from written feedback on assessment in favour of voice or video comments.

The value of mathematics as a service subject for BCom students might be underestimated, despite the fact that the skills these students need to work with mathematical concepts in a financial context are becoming increasingly important. The aim of the investigation unpacked in this paper was to expand our insight into students’ acquisition of these important skills by exploring what value an additional measuring tool based on the Rasch measurement model can add to students’ raw scores in an online multiple-choice test. The first focus was to explore new ways to identify the difficulties distance learning students’ have with the content of the module by shedding more light on the possible knowledge patterns of struggling students. The second focus was to gain more insight into the difficulty levels of our first attempt at multiple-choice online assessment for this group of students. The Rasch measurement model has been designed to construct a variable measured in units called logits that places student ability and question difficulty on the same continuum or linear scale. A Rasch analysis was done using Winsteps 4.8.0.0 software. With the Rasch measurement tools, such as summary measure for person (student) and item (question), a Wright map, item measures for fit statistics and an identification of students’ unexpected answers to questions, we could quickly gain more insight into students’ ability and into question difficulty. These measurements prove that a Rasch analysis offers a window into the mathematical skills of these participating students. This is helpful for identifying at-risk students and aids test development.

Authors: Claire Mullen; Jim Pettigrew; Anthony Cronin; Leanne Rylands; Don Shearman

Authors: Visala Satyam; Milos Savic; Emily Cilli-Turner; Houssein El Turkey; Gulden Karakok

Authors: Lais Fernanda Smakovicz; Elisa Henning

This work presents a teaching sequence to teach Correlation in undergraduate Basic Statistics courses, which aims to identify a relationship between the bicycle infrastructure quality in the city of Joinville, measured through the BEQI score, and demographic and socio-economic factors. The use of bicycles as a means of transportation is a regular practice in many cities such as Joinville, Southern Brazil, nationally known as “the City of Bicycles”. An appropriate infrastructure, however, is fundamental to promote the use of bicycles. In Joinville, the quality of bicyclable streets was evaluated through the Bicycle Environmental Quality Index (BEQI) (Henning et al., 2019). The guiding question for the proposal is: Is there a relationship between streets with better bicycle infrastructure and factors such as income, number of inhabitants and number of commercial activities? Starting from the problem design, the proposed sequence addresses data collection, scatter plot construction, coefficient correlation calculation and the subsequent results discussion. The BEQI scores are presented using spreadsheets and viewed on city maps. The remaining data are extracted from official municipal documentation. To complement the activities, an R (R CORE TEAM, 2021) tutorial, with the RStudio interface, shows the basic R functions for scatter plots and for correlation coefficient calculation, along with specific packages for that purpose.

REFERENCES

Henning, E., Baldo, F., Hackenberg, A. M., Karnopp, T. F., Longen, A. F., & Utiama, G. M. (2019). Programa De Extensão Nemobis. Anais 37º SEURS, Florianópolis, Brasil.

R Core Team (2021). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.

Authors: Leonardo Andre Broering; Elisa Henning

This work presents a teaching sequence to teach hypothesis testing to compare two groups. The idea is based on the COVID-19 pandemics and the locally-applied restrictive measures in the city of Joinville. The proposal seeks, using Student’s t-test, to identify any differences between the average active COVID-19 cases before and after certain restrictive measures. Three specific periods were analyzed regarding public transportation restrictions and a curfew. All the data are available in Joinville’s City Hall’s website. The proposal addresses data preparation and a tutorial on comparative boxplots and Student’s t-test with an Excel spreadsheet. The results showed significant differences between the average of active cases before and after the selected events, evidencing the reduction in the number of cases after restrictive measures were applied. The proposal can be extended for other places and the results allow for extensive discussion, both in the context of the problem or the limitations of the performed statistical analysis.

Keywords: Restrictive measures. COVID-19. Student t-test.

REFERENCES

PMJ - Prefeitura Municipal de Joinville. Dados Casos Coronavírus Município de Joinville. URL: < https://www.joinville.sc.gov.br/publicacoes/dados-casos-coronavirus-municipio- de-joinville/>. Acessed in: 20/05/2021.

Authors: José Guadalupe Rivera Pérez; Ana Luisa Gómez Blancarte

The American Statistical Association recommends the use of real data with context and purpose for teaching statistics. The context of the data has an important role in understanding how and why the data were generated or collected, and to give meaning to the statistical results in solving real problems. Based on this recommendation, the goal of this study is to explore, among other topics, how Mexican undergraduate teachers use real data in their course of statistics. The study involved 750 teachers who solved an online questionnaire with Likert scale items. Teachers’ answers were organized into items that allowed us to know: 1) if the teacher uses real data in his or her statistics classes, and 2) how they seem to use these data. In the first case, it was found that 88.2% of the teachers use real data in their classes; furthermore, 94.5% of the teachers consider that the data are related to the profession of their students. In the second case, 97.1% of the teachers propose activities for students to apply statistical methods that allow them to find patterns, relationships, trends, or characteristics of interest in the data. Results also showed that disciplinary areas with the lowest use of real data were mathematics, technology, and engineering. These results offer us a snapshot of the status of undergraduate statistics education in Mexico and provide us with reference points around which to conduct future research to deepen our understanding of teachers' use of data in their classrooms.

REFERENCES

ASA. (2016). Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report 2016. American Statistical Association. Retrieved from http://www.amstat.org/education/gaise.