Facilitating Friendship: The Future of Mathematics Education?

By Alicia Anderson

My relationship with maths class over the years has been sinusoidal, to say the least. I really took to the patterns and logic of mathematics as a kid. I loved measuring my classmates’ arm-spans and heights to use as coordinates on a line graph to show a linear trendline. Then, somewhere in the silence of paper pages and the scribble of pens, my spark went out. Equations that used to glitter, faded into a dull, anxious greyscale. While some subtopics were fun, I mostly slogged through NCEA and university maths in a disengaged haze only because it was a requirement for my new love — physics.

My mathematics journey — one in which I grit my teeth for the sake of another pursuit — is not unique. Maths has a notorious reputation for “gatekeeping” career opportunities — being necessary for finance, construction, and technology to name a few examples — which makes its pervasiveness of low achievement and low engagement all the more troubling.

In the 2019 Trends in International Mathematics and Science Study (TIMSS), the scores of New Zealand year nine students had the most significant drop since the study began in 1994 [1]. And while the 2020 NCEA Annual Report shows improvement in NCEA Level 1 literacy attainment over the last ten years, very little has changed with regard to gaining NCEA Level 1 numeracy. Figure 1 shows a steadily increasing trendline from 79.3% to 85.1% of year eleven students attaining Level 1 literacy from 2011 to 2020, respectively, with a range of 7.8% across the data set. For level 1 numeracy, however, the range is only 5.1% over the last ten years, with 82.4% of year eleven students in 2011 passing numeracy requirements and 83.6% passing in 2020 [2]. Many students, both in New Zealand and overseas, stop learning mathematics altogether as soon as it’s no longer compulsory [3]. For many schools in New Zealand, this is after NCEA Level 1. Most students are 16 years old by this time as well and therefore are no longer required by law to attend school. Numeracy attainment data at NCEA levels 2 and 3 is skewed to be in the 90% [2]. A likely reason for this is that those who failed the compulsory NCEA Level 1 have either dropped maths, or dropped school entirely. These achievement statistics don’t speak for those who stay in maths solely for a particular career path where maths is still necessary, but learning those skills feels more like removing wisdom teeth.

Literacy and Numeracy for NCEA Level 1

Table I shows the percentage of Year 11 students attaining NCEA Level 1 Literacy and Numeracy by the end of each year

Year	Literacy	Numeracy
2011	79.3%	82.4%
2012	82.4%	80.4%
2013	83.9%	81.1%
2014	85.3%	82.9%
2015	86.4%	84.6%
2016	86.5%	85.1%
2017	87.1%	85.5%
2018	86.2%	84.4%
2019	85.5%	83.4%
2020	85.1%	83.6%

* This figure has been adapted from the NZQA 2020 annual report [2]

So although I had the persistence to continue until I was back on the positive gradient, what I couldn’t understand for the longest time was how I could love physics as much as I hated maths. If maths is so essential to physics, then what happened for a paradox like this to occur?

Despite ongoing research and pleas from mathematics education academics to make significant changes in teaching practice, maths is still being taught in classrooms in a very outdated, solitary manner that is no longer seen in the rest of the sciences or the humanities. The International Academy of Education has recommended collaboration through small-group learning as an effective teaching tool since at least as early as 2000 [4]. However, classrooms across schooling levels still operate under solitary textbook exercises and worksheets from even as early as year three [5].

For me as a struggling student, this made the absence of noise the most memorable aspect of my first university mathematics tutorial. We were permitted to raise a hand for assistance, but that semester I was the only student to ever do so. The silence offered no anonymity, so, with no friends to lean on, each request for help required fresh courage. Every time the tutor taught a question to me, I felt the entire class learn how stupid I was. It reinforced my internal rhetoric that I was the dumbest student in the room; no one else needed help because they must be getting all the answers right. When I spent more tutorial time crying in the bathroom stall than getting help from the tutor, I stopped attending tutorials. I failed that paper.

More research has been done in investigating students who attend education but under-achieve. One journal summarised their findings under the acronym T.I.R.E.D for Tedium, Isolation, Rote-learning, Elitism, and Depersonalisation [6]. Varying combinations of these reasons result in the limiting belief that the only people who succeed in mathematics are those who are exceptionally talented. I believe solutions targeted towards addressing isolation would have knock-on effects that would mitigate the remaining four issues listed.

When I had a polar opposite experience to that first tutorial in a later semester, my performance and engagement skyrocketed. In the first session, the tutor asked who liked group work, in which there were a fair few of us who answered that we did. Having a tutor who promoted collaboration gave me a study group I could sit in lectures with, which led to a more efficient understanding of the content due to how much less stressful it was receiving explanations from my classmates, who were now becoming my friends [6]. My newfound sense of belonging in maths resulted in grades of As and Bs. From these new friendships, I felt a new identity as a learner of mathematics develop within myself.

This belonging continued into the following semesters where I was now confident enough to ask questions during the lectures, which often had around 40 students in attendance. With the additional hurdle of classmates spectating, dynamic participation in higher-level maths requires confidence that isn’t just overcoming shyness but being either certain of contributing intelligent answers and questions or being unafraid of the contrary. Overcoming such feelings is not an instantaneous process, but class friendships appear important in mitigating them [3], [4], [6]. The 2019 TIMSS results were also better for students who felt a belonging in the classroom [1]. Feeling a sense of belonging through friendship with peers fosters increased participation in front of the whole class. This leads on to both greater engagement with the class material and high test performance, which is why it would benefit educators to prioritise facilitating such connection in their classes.

Of all the schooling subjects, mathematics class evokes the most emotive response from the general population. Such strong opinions on maths are created informally through social experiences and social interactions. Schools and universities by nature are socialising hubs, implying a need for teachers to set up a classroom culture, so students become familiar with each other quickly [3]. Games, when selected carefully, can also help reinforce learning outcomes and team-building [7]. The games which are most successful at building classroom belonging are ones that encourage teamwork and creative problem solving, rather than rote-memorisation and speed [8]. Opportunities to collaborate on problems in groups of about four or five, then presenting worked solutions as a group are also needed [3], as is class material which acknowledges the cultural identities in the classroom [9].

The art of learning has always been a social affair: from learning to walk, to being taught your first curse words, much to the distaste of caregivers. It turns out I didn’t magically start hating maths, then re-enjoying it just as mythically. As much as I liked applying maths skills to the physics experiments we were writing reports on, my true joy stemmed from tackling challenges together with my classmates as a community of learners. Put simply, physics just allowed me to do maths with some friends.

References

[1] RNZ, “NZ students record worst results in maths and science,” Dec. 09, 2020. https://www.rnz.co.nz/news/national/432451/nz-students-record-worst-results-in-maths-and-science.

[2] A. Gray and D. G. Klinkum, “Annual Report NCEA, University Entrance and NZ Scholarship Data and Statistics 2020,” NZQA, 2021. [Online]. Available: https://www.nzqa.govt.nz/assets/About-us/Publications/stats-reports/NCEA-Annual-Report-2020.pdf?fbclid=IwAR16EDWZzYMnYDB96-6Pu-2a_oJg7hkHl5mJK1z9geW196kPNfWqdA-dNB8.

[3] L. Darragh, “Constructing confidence and identities of belonging in mathematics at the transition to secondary school,” vol. 15, no. 3, pp. 215–229, Jul. 2013.

[4] D. A. Grouws and K. J. Cebulla, “Improving student achievement in mathematics,” no. 4, 2000, [Online]. Available: https://www.iaoed.org/downloads/prac04e.pdf.

[5] F. Walls, “‘Doing Maths;’ Children Talk About Their Classroom Experiences,” vol. 2, pp. 755–764, 2007, [Online]. Available: https://content.talisaspire.com/auckland/bundles/60dccdd21b02c94e56609a94.

[6] E. Nardi and S. Steward, “Is Mathematics T.I.R.E.D? A Profile of Quiet Disaffection in the Secondary Mathematics Classroom,” vol. 29, no. 3, pp. 345–367, 2021, [Online]. Available: http://www.jstor.org.ezproxy.auckland.ac.nz/stable/1502257.

[7] G. Anthony and M. Walshaw, “Effective pedagogy in mathematics,” no. 19, Aug. 2009.

[8] L. Darragh, “Playing maths games for positive learner identities,” no. 1, pp. 36–42, 2021, [Online]. Available: https://doi-org.ezproxy.auckland.ac.nz/10.18296/set.0166.

[9] Hunter, J., Miller, J. Using a Culturally Responsive Approach to Develop Early Algebraic Reasoning with Young Diverse Learners. Int J of Sci and Math Educ 20, 111–131, 2022, [Online]. Available: https://doi-org.ezproxy.auckland.ac.nz/10.1007/s10763-020-10135-0.