January 27, 2017

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FR The Fields MathEd Forum hosted by the Fields Institute’s Centre for Research in Mathematical Sciences is dedicated to presenting the latest research and best practises from researchers and educators at all levels of mathematics education. At the January forum, I had the opportunity to listen to researchers share their current research projects in mathematics education. Here are a few of the highlights from the forum.

**Students’ and teachers’ mental solving of algebraic equations: from differences to challenges**

Jérôme Proulx, Professor at the University of Quebec in Montreal, shared the study that he conducted on the differences between student and teacher mental strategies for solving algebraic equations. The main goal of the study was to compare teacher and student strategies when solving the exact same algebraic equations. Through mental calculation sessions in which both students and teachers had only 15 seconds to solve the same equation, the researchers were able to gather notes and videos about the problem-solving strategies that each group used. The students and teachers were invited to share their strategies with those in the room. Proulx found that, once the ball got rolling, students were able to identify their strategies, even if they solved it without really thinking about what strategy they should use. This was particularly true because of the differences between their strategy and those strategies used by their classmates. This study showed that teachers and students often did not use the same mental techniques. This would certainly create disconnects between teachers and students. The question is: should we work to get rid of this diversity, or on the contrary, embrace it? Related to this question is the topic of automaticity, which was raised during the discussion period. At higher levels, educators prefer that their students use generalized strategies that they can use to solve any equation, rather than strategies that are perhaps more efficient but only effective for simpler equations. Proulx responded that, because the students in his study were quite early in their studies of algebra, the need for automaticity was not yet necessary. In higher levels, it is useful because they use the process of solving equations as a stepping stone to something else. At the introductory level, the diversity of strategies can be used to expose different aspects of student understanding.

**ICT use to improve the self-regulation skills of students taking a college foundational mathematics course**

Carol Carruthers from Seneca College conducted a study to identify “how the affordances provided by digital writing tablets (a learning intervention that is perceived to support metacognition) enhance self-regulation of students in a foundational mathematics college course”. The study, which was conducted with both females and males of 25 years of age or younger, shows that the type of information and communication technology used appeared to be related to the development of self-regulation abilities, such as time management and study practises. The affordances of a learning intervention allow students to improve their self-regulation skills and recognize self-regulation as a beneficial skill. The impact of information and communication technologies can be used to teach students how to regulate their learning. Carol said that further studies on this topic would be very beneficial to improve the understanding of how ICT can be used to develop student’s self-regulation skills.

**Implementing interactive texts in undergraduate mathematic **Margo Kondratieva, from Memorial University, explained how using interactive texts in mathematics can allow students to interpret mathematical definitions and theorems, observe invariants through dynamic interactions, find patterns and produce their own conjectures. While the formal approach to proofs in mathematics learning is necessary, it sometimes turns out to be a little too heavy for students. This is especially true at the beginning of their undergraduate studies. Margo also pointed out that learners who are exposed to formal approaches in learning mathematics are more likely to develop anxiety towards it, due to the difficulty in making sense of what they are taught. Even if watching a lecturer is still the most common experience for a student, it can lead to the student trying to imitate without really understanding what they are doing. When the students themselves were surveyed on their thoughts on the interactive text developed for their course, they found the text to be very well-organized and interesting, but not necessarily helpful to their studies. They said that alternative approaches like videos may be more helpful for them. During a discussion I had at the forum, a fellow educator pointed out that this may be a function of the level of student. At the undergraduate level, students may be so unfamiliar with an exploratory approach to understanding mathematics that they do not see its value. They would prefer a video to ‘just show them what to do’ more directly. This is not to say that this style of video would be more or less effective to students, but if the students have become used to a certain style of math instruction, a different style may be discarded simply because it is not what the students are used to. Margo is looking at ways of improving the text to enhance student engagement in her math classes.

Attempting to improve health numeracy through an online instrument

Taras Gula from George Brown College and Miroslav Lovric from McMaster University discussed their project to develop an online learning tool that will help health sciences students and professionals strengthen their health numeracy. Although numeracy is related to mathematics, it is not exactly the same thing; numeracy is much more concrete. It involves using mathematical skills in practical and real-world problems. A few striking examples of why health numeracy is vital in the healthcare field were discussed. This included the recent story of two students who were rushed to the hospital after being given 30g of caffeine, instead of 0.3g as part of a scientific study at Northumbria University.

Climate change in mathematics classrooms icme Yasmine Abtahi from the University of Quebec in Montreal and Richard Barwell from Ottawa University sought to better understand the contribution of mathematics education to climate change awareness. They surveyed teachers in Ontario and Norway to determine if and how teachers are handling this topic and how students can be educated about this issue. Climate change studies and reports contain many mathematical concepts (graphics, statistics, probabilities, etc.), making these studies relevant in mathematics classrooms. In Norway, teachers devote more time to instruction surrounding climate change than in Ontario, mostly in classes involving natural sciences. In Ontario, this topic is more commonly addressed in the mathematics classrooms. According to the survey, both countries have students dealing with charts, graphs, and data. In both Norway and Ontario, the main reason that teachers cited for teaching climate change effects is to educate students about climate change itself. The study shows that even if teachers do teach climate change as a theme in the mathematics classroom, most of them also include it in other subjects.

The forum was, as usual, very interesting and highlighted the different aspects of digital math pedagogies which improve student outcomes. From the use of ICT and digital texts in college and universities, to online tools to increase health numeracy and the use of the extensive access to data provided by the internet, these talks largely centered on use of technology in the mathematics classroom. This is despite the topic of the Forum this month being current research in mathematics education in general. I suspect that this may be a statement on the landscape of mathematics research. Many educators and researchers are clearly looking at how we can most effectively harness the power of technology to better improve student learning and engagement in our mathematics classrooms. I look forward to hearing much more from the research community on this topic!

*Angelica Mendaglio*

Click here to find and watch videos of all of the talks Click here to view the forum agenda