Optimistic problem-solving activity: enacting confidence, persistence, and perseverance

Williams, Gaye

doi:10.1007/s11858-014-0586-y

Cited by 30 publications

(17 citation statements)

References 17 publications

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“…Even where such conditions are not met, the student enthusiasm for STEM tasks, including mathematics tasks, reported by some teachers and students, provides a justification for inclusion of inter-disciplinary STEM activities within the mathematics curriculum. The development of positive dispositions in relation to mathematics, particularly mathematical problem solving (see for example Williams, 2014), is increasingly recognized to be an important curriculum purpose. Further, the argument that these inter-disciplinary activities promote critical and creative thinking beyond what is allowed in traditional approaches, is exemplified to varying extents in these case studies, through the innovative applications of mathematical ideas to situations such as creating strip maps for a race course, investigating the mathematics behind safety ratings, linking billy-cart motion to design features, and developing mathematics to design ramps.…”

Section: Resultsmentioning

confidence: 99%

“…This case study shows that the structure of the 'think big' aspect of the responses to each project gives opportunities to select and explore new mathematical ideas and the nature of the task is critical to the degree to which this is possible (Kieran et al, 2008;Williams, 2002). Students require opportunities to explore unfamiliar mathematical ideas by recognizing the relevance of known mathematics, building-with it in unfamiliar sequences and combinations, and synthesising these (constructing) to realise something mathematically profound (Dreyfus, Hershkowitz, & Schwarz, 2001;Williams, 2007Williams, , 2014. Key to achieving this is teacher awareness of the mathematics embedded within a STEM activity.…”

Section: Case 1: Stem Ed-a Collaborative Cross-subject Programmentioning

confidence: 99%

See 1 more Smart Citation

Interdisciplinary Mathematics Education

Doig¹,

Williams²,

Swanson³

et al. 2019

ICME-13 Monographs

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Section: Resultsmentioning

confidence: 99%

Section: Case 1: Stem Ed-a Collaborative Cross-subject Programmentioning

confidence: 99%

Interdisciplinary Mathematics Education

Doig¹,

Williams²,

Swanson³

et al. 2019

ICME-13 Monographs

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“…Thus maths anxiety is acquired, and disabling; it is also treatable. Using the growth zone model (figure 1), learners can begin to distinguish between the feelings that occur when faced with a challenge that requires persistence and perseverance [13] with initially uncertain results (growth zone), and those that arise when a threat to well-being is perceived (anxiety zone) when the anxiety interferes with thought and needs addressing before trying to do any more maths. The problem is that teachers with maths anxiety are being asked to teach students who also have maths anxiety, without the skills and training to support their students or themselves.…”

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confidence: 99%

“…Mathematical resilience has been developed to describe a positive stance towards mathematics whereby learners develop approaches to mathematical learning which help them to overcome the affective barriers and setbacks that can be part of learning mathematics for many people [1], and develop confidence, persistence and perseverance [13]. 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 [1].…”

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confidence: 99%

Developing Teaching for Mathematical Resilience in Further Education

Johnston-Wilder¹,

Pardoe²,

Almehrz³

et al. 2016

ICERI2016 Proceedings

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The construct 'Mathematical Resilience' [1] has been developed to describe a positive stance towards mathematics whereby learners develop approaches to mathematical learning which help them to overcome the affective 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 engineering, we have developed the notion of 'Teaching for Mathematical Resilience'. The work described here is focused on developing teachers who know how explicitly to develop resilient learners of mathematics. This paper discusses the development and evaluation of a 4-day course developed and delivered by a team of mathematics educators and professional coaches (referred to as the PD leads); the paper is a sequel to a previous paper in which we concluded that many teachers would benefit from more than a 1 day introduction due to high levels of personal mathematics anxiety and increased expectations on teachers of mathematics in Further Education in England.The course was developed in 2015; first presentations ran between January 2016 and March 2016 and recruited participants who work as teachers of numeracy or mathematics in the Further Education (FE) sector in the Midlands of the UK. Many of these teachers were being required to teach beyond their own level of mathematical confidence.Although there are always aspects of a course than can be improved by reflective practitioners, the overall impact of the project as expressed by the participant teachers who received it was very positive. Teachers' awareness was increased of negative past experiences as a possible cause of difficulty with mathematics; teachers became aware of how patterns of behaviour such as avoidance and disruption may have developed as safe-guarding habits and how mathematics anxiety can be transmitted from teacher to student in a vicious cycle.Teachers were supported to work through personal anxieties towards mathematics in a safe and collaborative environment, which included a professional coach, and to develop elements of personal mathematical resilience and awareness of the affective domain. Teachers developed an extensive range of tools, strategies and approaches to 'take off the emotional handbrake' of learners, to recognize and address anxiety, re-engage learners and build resilience. The tools included tasks designated ALIVE (Accessible, Linked, Inclusive, Valued and Engaging). The strategies included coaching skills.A common theme was just how much such a course was needed and appreciated by participants. The work is being further extended and developed through local mathematics teacher networks (MathsHubs).Keywords: Mathematical resilience, growth zone model, mathematics anxiety, ALIVE tasks, coaching THE CONTEXTA significant proportion of the population in UK suffers from maths anxiety and maths exclusion, including many teachers of ma...

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“…Johnson-Wilders & Lee (2010:2) defined mathematical resilience as "positive adaptation that allows learners overcome barriers that are frequently present when learning the subject or that quality by which some learners approach mathematics with confidence, persistence and wiliness to discuss, reflect and research". Simply put, mathematical resilience is development of confidence and willingness to learn mathematics amidst difficulties, and the courage to bounce back after failures (Williams, 2014). Kooken, Welsh, Mccoach, Johnston-Wilder, & Lee (2012) sees resilience in mathematics as positive response to challenges in studying mathematics characterized by persistence, good attitude, value and belief leading to better performance and success in the subject.…”

Section: Review Of Related Literaturementioning

confidence: 99%

Achievement Motivation And Emotional Intelligence As Predictors Of Mathematical Resilience Among Secondary School Students

Joy¹

2019

ASSRJ

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This study investigated achievement motivation and emotional intelligence as predictors of Mathematical resilience among senior secondary school students in Rivers Nigeria. Two research questions were answered and two hypotheses were tested at 0.05 alpha level. The population of the study comprised all 24,727 senior secondary school (SS2) students in the 247 public secondary schools in Rivers State. Sample size of 1690 was obtained using 20% of the population in simple random sampling technique. Three self-designed non-cognitive instruments titled Achievement Motivation Scale" (AMS), "Emotional Intelligence Scale" (EIS) and "Mathematical Resilience Scale" (MRS) were used for data collection. The AMS contained 14 items; EIS contained 17 items while MRS contained 20 items respectively. Face and content validities were carried out by the researchers along with three other experts in test, measurement and evaluation. The Cronbach reliability coefficient of 0.75, 0.72 and 0.77 were obtained for AMS, EIS and MRS respectively. Linear and multiple regressions were used to answer the research questions while t-test and ANOVA associated with linear and multiple regressions were used to test the null hypotheses. It was found among others that achievement motivation significantly predicted mathematical resilience. Emotional intelligence and achievement motivation jointly and significantly predicted mathematical resilience. It was recommended among others that guidance counselors should help students to reshape their minds from fixed to growth mindsets in order to become mathematical compliant as opposed to mathematical anxious.

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Optimistic problem-solving activity: enacting confidence, persistence, and perseverance

Cited by 30 publications

References 17 publications

Interdisciplinary Mathematics Education

Interdisciplinary Mathematics Education

Developing Teaching for Mathematical Resilience in Further Education

Achievement Motivation And Emotional Intelligence As Predictors Of Mathematical Resilience Among Secondary School Students

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