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

Developing peer coaching for mathematical resilience in post- 16 students who are encountering mathematics in other subjects

A significant number of students are known to have mathematics anxiety (Johnston-Wilder et al 2014). When such students begin to specialise, they may deliberately choose courses to keep mathematical content to a minimum or seek to avoid it altogether. Nevertheless, many courses employ more mathematics than expected, requiring students to apply mathematical thinking or mathematical ideas in their work, and this can often result in significant distress. Typically students feel alone in facing such issues as mathematics anxiety. In previous work, we used the term ‘mathematical resilience’ to describe the positive stance towards mathematics that enables learners to overcome barriers and set-backs that can be part of learning mathematics. In this paper, we present and discuss the outcomes of a course in ‘peer coaching for mathematical resilience’ for students who have chosen not to take courses with explicit mathematics, but who continue to encounter mathematics within other subjects. Mathematical resilience can be engineered by a strategic and explicit focus on the culture of learning mathematics within both formal and informal learning environments. Such a culture can be engineered by using coaches specifically trained to support emergent resilience. We aimed to develop a group of peer coaches in school, who support each other and their peers to develop mathematical resilience. Coaches for mathematical resilience develop a culture of ‘can do’ mathematics which works to counter the prevalent culture of mathematics helplessness and mathematics anxiety in the general population. The coaches are not required to know the answer but rather to know ways that might yield an understanding of the mathematical ideas involved which thus leads to an answer. A previous paper described the development, pilot and outcomes of the level 1 Coaching for Mathematical Resilience course, in which participants were adult trainers, mostly maths-anxious, working in an apprenticeship context. This paper discusses the outcomes of the same course for a group of 5 school students (Sept to Nov 2014), who volunteered to become ‘peer coaches for mathematical resilience’ in school. The course provided a safe and collaborative working environment in which the school students learned to manage their own reactions to mathematical ideas, to explore choices and to reflect on how to support someone else to find the resources to overcome their own barriers to learning mathematics. The data confirm that once a school student has begun to develop their own personal mathematical resilience, they can successfully coach themselves and others to manage their anxiety and develop as resilient learners and users of mathematics. Learner outcomes improved noticeably as a result

Developing mathematical resilience in school-students who have experienced repeated failure

Mathematics qualifications in the UK and many other countries represent valued cultural capital. In the UK, the typical qualification sought for employment in teaching, nursing, policing and many other professions is a GCSE award (minimum grade C) in mathematics. Although GCSE is typically taken at age 16, there is no logical or statutory reason why the award cannot be gained earlier or later. The UK government has recently determined that any student aged 16 to 19 who has not achieved at least grade C in GCSE mathematics should be enrolled on an approved mathematics course as part of their programme. Many students repeatedly fail to pass the examination; often such students re-sit the examination several times. We hypothesised that students, faced with a re-sit in mathematics, who complete a course to develop their mathematical resilience at the beginning, would be more likely to achieve the desired result. The construct ‘mathematical resilience’ has been developed by Johnston-Wilder and Lee [1] to describe a positive stance towards learning mathematics. Mathematical resilience can be engineered within both formal and informal learning environments by a strategic and explicit focus on the culture of learning mathematics. Previous papers (for example, [2]) have described engineering the growth of mathematical resilience through training adult coaches for mathematical resilience to work alongside learners outside the school environment. This paper discusses a course in mathematical resilience; the course was versioned for school students in year 12, students who had repeatedly failed to achieve the required grade in GCSE mathematics, and who were now preparing to retake the examination yet again. This short course, which ran from September to November 2014, was focused on helping students to overcome affective barriers and develop more resilient strategies for working with mathematical ideas, rather than on memorising mathematics content. The 17 students had been given very strong direction by the school to attend this course; they were told that if they attended and subsequently failed GCSE mathematics again, they would have shown they were making the effort and future opportunities would be approved for them to re-sit, however if they did not attend and failed again, they would be asked to leave the school. The course aimed to develop students’ mathematical resilience, so that they could more effectively support one another when facing difficulties in mathematics. This work developed a culture of ‘can do’ mathematics to counter the prevalent culture of mathematics helplessness, failure and mathematics anxiety. Participants learned to consider and manage their own reactions to mathematical ideas, to explore choices and to reflect on how to support themselves and each other to overcome their barriers to learning mathematics. The data confirm that, once an individual has begun to develop their own mathematical resilience and has worked through their own anxieties and negative stance towards mathematics in a safe and collaborative environment, they can then successfully coach themselves and others to develop mathematical resilience. Outcomes for these learners will be discussed

Developing coaches for mathematical resilience

The construct ‘Mathematical Resilience’ [1] has been developed to describe a positive stance towards mathematics that enables learners to develop approaches to mathematical learning which enable them to overcome the barriers and setbacks that can be part of learning mathematics for many people. A resilient stance towards mathematics can be engineered by a strategic and explicit focus on the culture of learning mathematics within both formal and informal learning environments. As part of that cultural engineering, we have developed the notion of coaches specifically to support emergent resilience. The work described here is focused on developing coaches who can work beside learners, helping them to think about and use resilient learning ideas when facing difficulties in mathematics. Coaches develop a culture of ‘can do’ mathematics which works to counter the prevalent culture of mathematics helplessness and mathematics anxiety in the general population when faced with mathematical ideas. The coaches are not required to know the answer but rather to know ways that might yield an understanding of the mathematical ideas involved and thus lead to an answer. This paper discusses the outcomes of a pilot course (April to June 2013) designed to develop ‘coaches for mathematical resilience’. The course recruited 11 participants who regularly work with apprentices, both young and more mature, in a work-based environment and who are required to learn and use mathematics as part of their on-going training. They became part of the course due to recognition of their own lack of knowledge about how to overcome deep seated antipathy to mathematics in themselves and in those with whom they work. The data confirms that in order to become an effective coach, an individual first needs to develop their own personal mathematical resilience, work through their own anxieties and negative stance towards mathematics in a safe and collaborative environment, before they can coach a learner to develop as a resilient learner of mathematics. An environment that enables an individual to learn to be a mathematics resilience coach will need to expose the learners to mathematical ideas in order to enable participants to consider and manage their own reactions to mathematical ideas and reflect on how to help someone else find the resources to overcome their own barriers to learning mathematics

Developing coaches for mathematical resilience : level 2

The construct ‘Mathematical Resilience’ [1] has been developed to describe a positive stance towards mathematics that enables learners to develop approaches to mathematical learning which allow them to overcome the barriers and setbacks that are frequently part of learning mathematics for many people. A resilient stance towards mathematics can be engineered by a strategic and explicit focus on the culture of learning mathematics within both formal and informal learning environments. As part of that cultural engineering, we have developed the notion of coaches specifically to support emergent resilience. The work described here is focused on developing coaches who can work beside learners, helping them to conjecture and use resilient learning ideas when facing difficulties in mathematics. Coaches develop a culture of ‘can do’ mathematics which works to counter the prevalent culture of mathematics helplessness and mathematics anxiety in the general population when faced with mathematical ideas. The coaches are not required to know the answer but rather to know ways that might yield an understanding of the mathematical ideas involved and thus lead to an answer. Our previous paper described the outcomes of the level 1 course, in which participants became skilled at peer-coaching. This paper discusses the outcomes of a second pilot course (Sept to Nov 2013) designed to develop ‘coaches for mathematical resilience’ at level 2, equipped to work with learners under the direction of a mathematics tutor outside the course. The 10 participants at Level 2, who regularly work with apprentices, both young and more mature, in a work-based environment continued with part 2 of the programme because of the positive outcomes from level 1. In the Level 1 course, they had worked to develop their knowledge of how to overcome deep seated antipathy to mathematics in themselves and in those with whom they work. The data confirms that once an individual has begun to develop their own personal mathematical resilience, worked through their own anxieties and negative stance towards mathematics in a safe and collaborative environment, they can then successfully coach learners to develop as resilient learners of mathematics. They become able to help those learners to find or develop the resources and skills to overcome their own barriers to learning mathematics and to manage any anxiety that may be engendered. Importantly, when the coach learns not to take any responsibility for the mathematics, but rather to focus on the learning skills and well-being of the learner, t learner outcomes are improved

Stories of mathematical resilience : how some adult learners overcame affective barriers

Some non-traditional adult learners in higher education lack mathematics qualifications, have had negative experiences of mathematics in the past, feel anxious about mathematics, lack confidence, or protect themselves by avoiding the subject. As part of a widening participation initiative, a lifelong learning centre at a large university in England developed a programme of free mathematics lessons for these learners. This paper discusses the findings from a small-scale narrative study which analysed the mathematical stories of four of these learners. The research found that, although previous feelings about mathematics lingered, participants overcame their emotional barriers to learning mathematics with sensitive support from others, specific teaching and learning strategies, and by increasing their mathematical resilience. They were able to move away from feeling frightened of mathematics, to persevere and feel more comfortable with it. The notion of perezhivanie (Vygotsky, 1994) was used to conceptualise the barriers created by past, strong emotional experiences and developing ability to manage the associated feelings