Dept of Mathematics Education seminar: 16 November 2022

40 mins Presentation + 20 mins Q&A: Lucy Rycroft-Smith

Summarising mathematics education research for teachers: art or science?

(University of Cambridge) [lr444@cam.ac.uk]

Abstract

Knowledge brokering is not currently well defined, either outside of or within educational contexts, but is often suggested to be as a type of mediation and/or boundary spanning (e.g.. Malin & Brown, 2020) which supports knowledge flow between research, practice, and policy in a variety of ways.  The idea of transforming research knowledge in education comes from theoretical work looking at knowledge brokering across disciplines by Meyer (2010, p. 118), who suggested “knowledge brokers do not only move knowledge, but also produce a new kind of knowledge: brokered knowledge.”  Research knowledge can be transformed into brokered knowledge in several ways:

• it can be made accessible by changing the language it is encoded in
• it can be made into a different format, medium or modality
• it can be rescaled: distilled, synthesised, or summarised
  • implications for practice can be inferred or induced

Whether this knowledge transformation is good (in the sense of either ethical or effective) is both important and underresearched. In a comparative judgement study, we asked a group of 28 mathematics teachers and a group of 19 mathematics education researchers to rank twenty research summaries, from different sources, in terms of their success at communicating the research to teachers, and explain which features contributed to this ranking. Overall the findings suggest moderate consensus both within and between the two groups, and some important areas of difference. Both groups agreed that graphic design was the most important element of a research summary; that being summarised, having implications for practice and being easy to read or accessible and well-structured were key features of a research summary; and that the length of the research summary or the time it might take to read were also important. I will briefly present and discuss the findings and implications for knowledge brokering in education.

This study, and a wider examination of the ideas around knowledge brokering in education, suggest key tensions around ‘dumbing down’ (ie elimination of nuance and meta-information) and reduction of teacher agency, either because evidence makes its way to teachers only through top-down policy change (reducing agency), or because the nature of evidence is disingenuously presented to teachers as simplistic ‘recipes for success’ (Farley-Riipple & Grajeda, 2020, p. 4). Similarly, there is a real danger that a bias is created towards straightforward, implementable, generalisable research findings being generated and synthesised, as opposed to examining the contested nature and paradoxes of a wide range of research knowledges (e.g. Aldridge et al., 2018; Stylianides & Stylianides, 2020). This relates to a ‘scientific’ models of  knowledge and learning, and whether one subscribes to or resists “the banking system of education” (hooks, 2014, p. 4).  I explore also my current study, which is art-based research, exploring the boundaries of knowledge brokering in the context of mathematics education. Art-based research can “provoke, challenge and illuminate as it expands perceptions and imagines new innovations that are capable of transforming knowledge” (Moon, 2013, p. 35), which makes it a particularly good fit for exploring a new field that such as educational knowledge brokering. Further, arts-based research can be used at any point in research processes – whether generating, interpreting and/or communicating knowledge - to offer exciting insights, do boundary-crossing work, promote dialogue, challenge assumptions, examine perspectives, and provoke paradigm shifts (Parsons & Boydell, 2012).

40 mins Presentation + 20 mins Q&A: Dr Venera Gashaj

An embodied cognition approach to the development of mathematical cognition

Loughborough University [venera.gashaj@gmail.com]

Abstract

The idea that seemingly abstract cognitive processes, such as mathematical thinking, may be related to bodily movements and spatial awareness is in line with theories of embodied cognition (Piaget, 1952; Vygotsky, 1997; Abrahamson & Trninic, 2015). My ongoing research program concerns a holistic view of mathematics cognition, development, and learning. It aims to incorporate the body, brain, environment, emotions, and attitudes to form a more robust, empirically grounded view of the processes of learning and development.

The body. In a two-year longitudinal study, we assessed the relations between motor skills, executive functions, basic numerical skills (symbolic and non-symbolic), and mathematical achievement. Symbolic skills were related to executive function, whereas non-symbolic skills were related to fine and gross motor skills (Gashaj Oberer, Mast, & Roebers, 2019a, 2019b; Oberer, Gashaj, & Roebers, 2017, 2018). Altogether, these findings strongly support the conjectures regarding the importance of motor skills for developing numeracy and mathematical reasoning. Furthermore, we are investigating how the relationship between mathematical and motor skills changes over time—becomes weaker with age as overt actions become increasingly internalized (Gashaj & Trninić, under review).

The brain. Another project investigates the changes in whole-brain dynamics related to the development of mathematical cognition. We investigate in a longitudinal study how the spontaneous activation of the whole brain (resting state) changes when children engage in a mathematical task (Gashaj, Escrichs, & Deco, under review). Thus, we focus on the whole brain and its communication—not only on areas that are functionally involved in the task. This approach shows that domain-specific skills or brain areas are involved in mathematical processing and change during the acquisition of mathematics. However, domain-general skills and brain areas communicate and support the already well-known activated regions.

The Environment. Our environment shapes our cognition by giving us opportunities for exploration. Thus, a stream of my research focuses on the home learning environment, including playful (Gashaj, Dapp, Trninić, & Roebers, 2021) and overtly physical (Dapp, Gashaj, & Roebers, 2021) home activities. Translating these findings into practice, we also develop playful learning designs in which students can grasp mathematics in a virtual reality environment while learning about derivatives (Chatain et al., 2022).

Emotions and Attitudes. Students’ affective disposition can be a more critical predictor of entry into STEM subjects than enrollment and grades (Maltese & Tai, 2011). Therefore, I am interested in how feelings such as math anxiety are felt and overcome in elite STEM students (Gashaj et al., in preparation a) as well as primary school children (Gashaj, Thaqi, Mast, Roebers, submitted). In a more practical sense, I am interested in learning designs that lead to confusion and how those designs impact students with math anxiety (Gashaj, Trninić, & Formaz, 2022), and how anxiety disorders such as post-traumatic stress disorder might affect numerical cognition (Gashaj, Zeffiro, & Müller-Pfeiffer, under review).

References

Abrahamson, D., & Trninic, D. (2015). Bringing forth mathematical concepts: Signifying sensorimotor enactment in fields of promoted action. ZDM, 47(2), 295-306. doi 10.1007/s11858-014-0620-0.

Chatain, J., Ramp, V., Gashaj, V., Fayolle, V., Kapur, M., Sumner, R. W., & Magnenat, S. (2022, June). Grasping Derivatives: Teaching Mathematics through Embodied Interactions using Tablets and Virtual Reality. In Interaction Design and Children (pp. 98-108).

Dapp, L. C., Gashaj, V., & Roebers, C. M. (2021). Physical Activity and Motor Skills in Children: A Differentiated Approach. Psychology of Sport and Exercise, 54, 101916.

Gashaj, V., & Trninic, D. (2022, under review). Adding up fine motor skills: developmental relations between manual dexterity and numerical abilities. PsyArXiv. doi:10.31234/osf.io/x8njq.

Gashaj, V., Baumgartner, V., Rossi, S., von Bergen, A., Connolly, H., Kapur, M., & Cipora, K. (in preparation a). Are mathematics anxiety and being positive about mathematics mutually exclusive? An exploratory study in elite STEM students. (https://osf.io/3vhsf/)

Gashaj, V., Escrichs, A., Deco, G. (under review). Whole Brain Differences in the development of mathematical cognition: Evidence from a longitudinal study in Children. Developmental Cognitive Neuroscience.

Gashaj, V., Oberer, N., Mast, F. W., & Roebers, C. M. (2019 a). Individual differences in basic numerical skills: The role of executive functions and motor skills. Journal of experimental child psychology, 182, 187-195. doi: 10.1016/j.jecp.2019.01.021.

Gashaj, V., Oberer, N., Mast, F. W., & Roebers, C. M. (2019 b). The relation between executive functions, fine motor skills, and basic numerical skills and their relevance for later mathematics achievement. Early education and development, 30(7), 913-926. doi.org/10.1080/10409289.2018.1539556.

Gashaj, V., Thaqi, Q., Mast, F. W., & Roebers, C. M. (submitted). Numerical Skills, Home Numeracy, and Math Anxiety predict Mathematics Achievement in Second Grade.

Gashaj, V., Trninić, D., Formaz, C. (2022). When failing generates Math Anxiety instead of productivity. In Chinn, C., Tan, E., Chan, C., & Kali, Y. (Eds.). Proceedings of the 16th International Conference of the Learning Sciences - ICLS 2022, (pp. 1465-1468). Hiroshima, Japan: International Society of the Learning Sciences.

Gashaj, V., Zeffiro, T., & Müller-Pfeiffer, C. (under review). Numerical Processing in Posttraumatic Stress Disorder (PTSD). Neuroimage.

Oberer, N., Gashaj, V., & Roebers, C. M. (2018). Executive Functions, visual-motor coordination, physical fitness and academic achievement: Longitudinal relations in typically developing children. Human Movement Science, 58, 69-79.

Oberer, N., Gashaj, V., & Roebers, C. M. (2017). Motor skills in kindergarten: internal structure, cognitive correlates and relationships to background variables. Human Movement Science, 52, 170-180.

Piaget, J. (1952). The child’s conception of number. New York: Norton.

Vygotsky, L. S. (1926/1997). Educational psychology (R. H. Silverman, Translator). Boca Raton, FL: CRC Press LLC. doi: 10.4324/9780429273070