Nonviolent communication, compassion and mathematical resilience

We consider mathematics anxiety to be a result of cultural violence. We explore the possibilities offered by Marshall Rosenberg’s nonviolent (compassionate) communication (NVC), developed as a means of addressing conflict, to contribute to the existing work on mathematical resilience (MR), which seeks to address mathematics anxiety and avoidance. Nonviolent communication assumes that compassion is innate, that human behaviour comes from needs, which are indicated by feelings, and stresses the importance of empathy. This resonates with MR, and in particular validates the Growth Zone Model, an important and successful MR strategy involving the non-judgmental awareness and articulation of feelings and needs and the link between these

How can we address mathematics anxiety more effectively as a community?

Mathematics anxiety has been discussed for over 60 years. The majority of those suffering belong to an identifiable subgroup, often identified as ‘female’, or learners with a ‘feeling’ rather than a ‘thinking’ preference, or empathisers. These learners prefer to understand the value, meaning, purpose and narrative of the mathematical tools they are required to learn. Ten years ago, we planted a seed for a change in practices that engender anxiety to those that build a positive stance. This seed has grown into a group of teacher and research practitioners working to overcome mathematics anxiety and build mathematical resilience. The paper discusses what is known, by these researchers and teachers, and how to develop innovative communication in order to work internationally toward elimination of the acquired, disabling condition of mathematics anxiety

The mathematics resilience approach to mathematics anxiety : is this supported by self-determination theory?

One approach to the problem of mathematics anxiety, that of developing mathematical resilience (Lee & Johnston-Wilder, 2017) focuses on enabling learners to remain in the growth zone, where learners experience challenge and manage any threat. This approach, involving the use of three tools (the growth zone model, hand model of the brain and the relaxation response) has been successful in small-scale studies. We show here how the theory and practice of MR can be grounded in self-determination theory (SDT) (Deci & Ryan, 2000), with connections to SDT concepts of: autonomous motivation; the basic psychological needs of autonomy, competence and relatedness; and emotion regulation. Extensive research evidence has indicated that the satisfaction of basic psychological needs leads to well-being and that frustration of these needs leads to ill-being, indicating the potential of SDT to support research and practice in the specific area of ill-being known as mathematics anxiety

A survey of mathematics anxiety and mathematical resilience among existing apprentices

This research develops knowledge of the extent to which apprentices in the UK are affected by mathematics anxiety, including issues related to prior mathematics achievement, gender, and choice of apprenticeship, as well as outlining significant implications for both the supply and progression of STEM Apprentices. To what degree is mathematics anxiety an issue for Apprentices? • Mathematics anxiety has a noticeable impact on about 30% of the respondents. Another 19% have a tendency to be anxious but may not show such clear signs. • The degree of mathematics anxiety in apprentices is roughly equal to that in the rest of the population. Here it is known to both negatively impact on daily life (e.g., calculating a tip at a restaurant) and on formal education, “ultimately resulting in lower exposure to math, reduced practice using mathematics principles, and reduced workforce math competence”. (Brunye, 2013) • The high prevalence of mathematics anxiety in the overall apprentice population has a confounding influence on some statistically significant differences in mathematical anxiety associated with three key characteristics: prior mathematics achievement; gender; and STEM and nonSTEM apprenticeship study. In respect of these key characteristics our findings highlight that: o Mathematics anxiety is more prevalent among apprentices who have not yet gained Grade 2 mathematics. o Mathematics anxiety is more prevalent among female apprentices than male apprentices. o Females are more likely to be found on non-STEM apprenticeships than on STEM apprenticeships. o Mathematics anxiety is more prevalent among non-STEM apprentices than STEM apprentices. o One sixth of STEM apprentices experience their mind going blank when faced with mathematics. In this report, we argue that mathematics anxiety is affecting both recruitment and progress of STEM apprentices. What are the implications for the supply of STEM Apprentices? • Addressing mathematics anxiety in the pre- or early- apprentice population may be significant in increasing the pool of potential STEM apprentices in two ways: o Making progression possible: Increasing the number of pupils reaching higher levels of mathematics attainment, so increasing their potential for apprenticeship study, (particularly STEM apprenticeships) requiring higher levels of mathematics skill. o Making progression more probable: Increasing the number of pupils for whom mathematics anxiety is not a barrier when considering STEM apprenticeships as their next step. What are the implications for the success of STEM Apprentices? • For some apprentices, mathematics within this framework is significantly different from school mathematics. Mathematics anxiety is a significant problem on apprenticeships, STEM or nonSTEM, with harder mathematics than expected. • Previous research establishes that mathematics anxiety is highly likely to be hindering well-being and progress (for example, Brunye 2013). It is also established that purpose and utility makes mathematics more accessible to people who have previously been excluded from mathematics, and more so for females. • For many people, the problem “is only in maths”. We suggest that addressing mathematics anxiety could be significant to overall apprenticeship success and well-being and have positive impacts on both recruitment and progress for many apprentices

Using ICT and dialogic teaching : impact on mathematical resilience and attainment in algebra of a Kenyan school year group

This paper is set in the context of a whole year group learning early secondary algebra using ICT in Kenya. It argues that studies about impact of ICT would benefit from paying explicit attention to the support offered by collaborative interaction of elements (pupils, teachers, language and computers) in lessons, that is, the affective dimension of pupils' mathematical learning. In this paper, we explore the changes in learning mathematics experienced by students given an extended course using Grid Algebra [1]. Following Luckin et al [2], we explore the use of ICT combined with a fundamental shift in pedagogy, a shift that transforms teaching and learning by focusing on the learning experience. We examine the effect of introducing a technological tool combined with dialogic teaching upon a year group: on pupils’ interest in algebra, their involvement and engagement in mathematical learning, their conceptual understanding and their attainment. The study employs a mixed-method strategy, and data include: written work, observations, interviews and pupil questionnaires. We examine the impact on a year group, showing ways in which understanding was improved and the experience was positive for the learners. We use the construct of ‘mathematical resilience’ [3], a description of what is required to promote effective learning of mathematics, to analyse why this example of ICT use was so effective. The paper concludes that appropriate use of computer software can have a significant impact on effort and attainment. Additionally, emphasising affective aspects which reinforce ICT use in mathematics instruction can create an enabling environment for active pupil learning

Mathématiques : Un lieu d’amour bienveillant et de renforcement de la capacité de résilience

Places of mathematical learning are not always places of loving kindness. Instead, they are sometimes loci of undetected cultural violence (Galtung, 1969) and associated harm. We explore how Cousin’s (2015) interpretation of love in the context of early years relates to building mathematical resilience across the lifespan. Our interpretation of loving kindness in the context of older learners includes unconditional positive regard (Rogers, 1961) and the explicit building of this into the classroom milieu. Education is understood in this work in a broad sense, not only as a means of acquiring knowledge and skills, but also an arena for making connections and gaining a shared understanding about what it is to be human (Tagore, 1933). One of the tools found helpful in the practice of loving kindness, especially where learners have experienced significant prior harm, is the growth zone model (Lugalia, Johnston-Wilder, & Goodall, 2013), informed by the hand model of the brain (Siegel, 2010) and the relaxation response (Benson, 2000). With unconditional positive regard, and with such tools, learners may be empowered to become less avoidant and more engaged with mathematics. They may also acquire resilience, including coping skills, to on greater challenges, once perceived as dangerous. Loving kindness in mathematics is enabling.Les lieux d'apprentissage de mathématiques ne sont pas toujours des lieux d'amour bienveillant. Au contraire, ce sont des fois des centres de violences culturelles non-détectées (Galtung, 1969) et, en relation, du mal. Nous explorons la relation entre l'interprétation d'amour en contexte des jeunes années proposé par Cousin (2015) et le développement d'une capacité de résilience en mathématiques tout au long de la vie. Notre interprétation de l'amour bienveillant en contexte des étudiants plus âgés, inclut un regard positif inconditionnel (Rogers, 1961) et sa mise en oeuvre expresse dans le milieu scolaire. L'éducation, compris au sens large du terme, n'est pas seulement un moyen d'accumuler des connaissances et des compétences, c'est une scène pourétablir des liens et acquérir une compréhension commune de ce que signifie être humain (Tagore, 1933). Un des outils jugés nécessaire dans la pratique de l’amour bienveillant, particulièrement là où les apprenants ont une expérience significative des méfaits antérieurs, est le modèle de zone de croissance (Lugalia, Johnston-Wilder, & Goodall, 2013), enrichi du modèle du cerveau dans la main (Siegel, 2010) et de celui de la réponse de relaxation (Benson, 2000). Avec un regard positif inconditionnel et de tels outils, c’est fort possible que les apprenants soient capables de devenir moins évitants et à s’investir dans les mathématiques. Ils pourraient également acquérir une capacité de résilience, y compris des stratégies d'adaptation, afin d'assumer des défis plus difficiles, une fois considérée dangereux. L'amour bienveillant en mathématiques est habilitant

Measuring mathematical resilience : an application of the construct of resilience to the study of mathematics

To meet the challenge of accelerating demands for quantitative literacy in the work force, improvements are needed in mathematics education. Student skill must be increased at all ability levels while also reducing the achievement gap across gender, racial and ethnic groups to increase their participation in advanced mathematics coursework and representation in mathematics related careers (National Mathematics Advisory Panel, 2008). Research has shown that affective traits such as motivation and attitude are linked to increased likelihood of taking advanced mathematics courses (Ma, 2006) and are significant predictors of improved cognitive activity and achievement (Buff, Reusser, Rakoczy,& Pauli, 2011; Ethington & Wolfe, 1986). In addition, males generally score more favorably than females on affective variables related to mathematics achievement and persistence (McGraw, Lubienski, & Strutchens, 2006; Sherman & Fennema, 1977; Wilkins and Ma, 2003). Although psychological resilience has been researched extensively (Luthar, Cicchetti, & Becker, 2000; Luthar, 2007) the study of mathematical resilience, defined as a positive adaptive stance to mathematics which allows students to continue learning despite adversity, represents a new approach (Johnston-Wilder & Lee, 2010; Rivera & Waxman, 2011). Math anxiety looks at maladaptive response to learning mathematics and is well-studied (Hembree, 1990; Richardson & Suinn, 1977; Tobias, 1978). In contrast, resilience incorporates factors associated with optimal functioning. Although mathematical resilience has been identified as important for success (Johnston-Wilder & Lee, 2010; Rivera & Waxman, 2011), little consensus exists around its definition and no measures of resilience have been rigorously developed and/or validated. Rivera & Waxman (2011) identified the use of teacher nomination of resilient students as a limitation of their study, further motivating development of an instrument. This presentation will report on efforts to develop and validate an instrument measuring mathematical resilience. Ultimately, the measure will aid in developing and testing models that gauge the role of mathematical resilience in student achievement and persistence in advanced coursework. These models can be used to develop interventions to improve mathematical resilience, achievement, and quantitative literacy (Johnston-Wilder & Lee, 2010)

Mathematics : a place of loving kindness and resilience-building

Places of mathematical learning are not always places of loving kindness. Instead, they are sometimes loci of undetected cultural violence (Galtung, 1969) and associated harm. We explore how Cousin’s (2015) interpretation of love in the context of early years relates to building mathematical resilience across the lifespan. Our interpretation of loving kindness in the context of older learners includes unconditional positive regard (Rogers, 1961) and the explicit building of this into the classroom milieu. Education is understood in this work in a broad sense, not only as a means of acquiring knowledge and skills, but also an arena for making connections and gaining a shared understanding about what it is to be human (Tagore, 1933). One of the tools found helpful in the practice of loving kindness, especially where learners have experienced significant prior harm, is the growth zone model (Lugalia, Johnston-Wilder, & Goodall, 2013), informed by the hand model of the brain (Siegel, 2010) and the relaxation response (Benson, 2000). With unconditional positive regard, and with such tools, learners may be empowered to become less avoidant and more engaged with mathematics. They may also acquire resilience, including coping skills, to on greater challenges, once perceived as dangerous. Loving kindness in mathematics is enabling