Pressure, Threat, and Fear in the Classroom: Pupils' and Teachers' Perceptions of Soft Failure in an 11+ Context

This thesis concerns both pupils’ and teachers’ perceptions and reactions to soft failure. Whilst there is widespread agreement that errors and impasses in the classroom can be pedagogically useful, pupils do not always respond positively to soft failure, potentially limiting their learning. Teachers, whilst keen to support pupils experiencing temporary academic setbacks, can unintentionally cement perceptions that errors should be avoided, leading to a co-construction between teacher and pupil of a classroom climate that is unfriendly to error making. In taking a bio ecological and interdisciplinary approach, this thesis addresses a gap in error climate studies through examining the intersection of sociocultural and psychological factors that impact perceptions of, and reactions to, soft failure. This thesis argues that pupils’ reactions to soft failure are imprinted, not only with immediate classroom proximal processes, but also from processes within the home, wider values, and ideologies. Drawing upon the case study genre and bound by the entry and exit points of a selective education system, findings from observations and interviews with Y7 and Y5 pupils suggest the facilitation of classroom peer ecologies orientated towards performance and demonstrating success. Through conceptualising gender as heteroglossic, Y7 grammar school girls were seen to enact masculine, highly competitive performances which reinforced a pressured climate where negative evaluation and soft failure was feared. However, these findings are complicated by pupils’ divergent and fluctuating responses and reactions to soft failure, situated and contextualised by teachers’ error handling, classroom organisation and school processes. Therefore, to establish when soft failure matters for pupils, this thesis explores the interplay of competing values, goals, and interactions. In doing so, the antecedents of soft failure adaptivity are identified, with the perceived threat to pupils’ dignity – which I reason must be understood in an adolescent context — argued as the fulcrum on which soft failure appraisals are made

An Investigation of Mathematics Self-Efficacy, the Sources of Mathematics Self-Efficacy, and Mathematics Achievement Among Primary School Students in Trinidad and Tobago

Purpose of the Study This dissertation addressed two problems in the literature. Firstly, while many study findings have highlighted the critical role of self-efficacy in students\u27 achievement, additional research was needed about the four hypothesized sources that influence the improvement of students\u27 mathematics self-efficacy. Many studies on self-efficacy sources were conducted with measures not closely tied to social cognitive theory and have not demonstrated sufficient reliability. Using the Sources of Mathematics SelfEfficacy Scale, Usher and Pajares (2009) addressed this problem. They suggested several recommendations for future research (Usher & Pajares, 2008b, 2009), including exploring the validity of their scale in different contexts, examining changes in students\u27 self-efficacy across significant transition periods, and clarifying gender differences in the sources of self-efficacy. The very first part of my dissertation addressed each of those recommendations. This scale was validated with pupils in Standards 4 and 5 (Grades 5-6) because this context has gained less attention in studying mathematics self-efficacy sources. Gender and other demographic differences in pupils\u27 scores on the sources of Middle School Mathematics Self-Efficacy Scale were analyzed, and the independent contribution of each source to predicting mathematics self-efficacy. Method Data were collected from 277 primary school students in four North Eastern Education District schools in Trinidad. Two survey instruments and a mathematics achievement test were used to gather the data. The surveys were analyzed through descriptive statistics, structural equation modeling (SEM), exploratory factor analysis, confirmatory factor analysis, and Pearson correlation coefficient statistical programs. Exploratory factor analysis on a content-specific mathematics skills self-efficacy scale showed a two-factor scale. The scale had content validity and acceptable reliability. A four-factor confirmatory factor model demonstrated the best fit for the SMMSE scale for the primary school samples. As predicted, mastery experience was the strongest predictor of mathematics skills self-efficacy. Slight or moderate differences were observed between gender and age groupings. The analysis results verified the factor structure of the Sources of Middle School Mathematics Self-Efficacy with a new primary school sample. Contrary to previous research, neither mathematics skills self-efficacy nor any of the sources of mathematics self-efficacy were statistically significant predictors of mathematics achievement. Results Student perceptions of their ability to perform basic math operations were positive (M=3.74, SD=0.53). Student perceptions of using math concepts were also positive (M=3.2, SD=1.63). Pairwise comparison using the Bonferroni procedure suggested that 11-year-olds (M=16.79, SD=3.64) reported significantly higher mastery experience than 12-year-olds (M=14.88, SD=4.09) and 13-14-year olds (M=14.27, SD=3.67). A comparison of the means suggested that males (M=17.82, SD=4.83) reported significantly higher physiological states than females (M=15.05, SD=5.46). There were no statistically significant predictors of mathematics achievement. Conclusion This study demonstrated that the surveys for mathematics skills self-efficacy and the Sources of Middle School Mathematics Self-Efficacy scale could be considered valid and reliable measures of those concepts among a Trinidad primary school population. Previously, research on the sources of mathematics self-efficacy focused on middle school students in the United States. This structural equation modeling found neither mathematics skills self-efficacy nor any of the sources of self-efficacy were statistically significant in predicting mathematics achievement among the primary school sample. These findings substantially contribute to the knowledge of mathematics achievement among primary school students in Trinidad and Tobago

The influence of mathematics anxiety on pupils' choice of mental calculation strategies for two-digit addition and subtraction.

The ability to calculate mentally is a core skill in mathematics and is now a required feature of mathematics teaching. Mathematics anxiety is an established affective construct, associated with mathematical outcomes. The focus of this research is on the affective construct of mathematics anxiety and this may influence a pupil's choice of mental calculation strategy for two digit addition and subtraction. The main study (preceded by a pilot study) was divided into two parts and focused solely on Year 5 pupils; background data with permission, was obtained for each pupil. In the first part, pupils were given a mental calculation assessment, the Myself As Learner Scale (Burden, 1998) and the Mathematics Anxiety Scale for Children (Chiu Henry, 1990; Beasley, Long Natali, 2001). In the second part, the mental calculation strategies of pupils with either high or low mathematics anxiety was explored individually through a series of two digit addition and subtraction questions. Pupil responses were recorded, transcribed and classified. Strategy classification particularly distinguished pupils partitioning both two digit numbers and only one of the two digit numbers. Pupils with high mathematics anxiety tend to use lower order (less effective) strategies, whereas pupils with low mathematics anxiety tend to use higher order (more effective) strategies. No gender differences were found regarding strategy use. When controlled for mathematical competence, low mathematics anxious pupils produced more accurate mental calculation, whereas high mathematics anxious pupils produced less accurate mental calculations. Implications for Educational Psychologists and teachers in schools are discussed

Values and Valuing in Mathematics Education

This engaging open access book discusses how a values and valuing perspective can facilitate a more effective mathematics pedagogical experience, and allows readers to explore multiple applications of the values perspective across different education systems. It also clearly shows that teaching mathematics involves not only reasoning and feelings, but also students’ interactions with their cultural setting and each other. The book brings together the work of world leaders and new thinkers in mathematics educational research to improve the learning and teaching of mathematics. Addressing themes such as discovering hidden cultural values, a multicultural society and methodological issues in the investigation of values in mathematics, it stimulates readers to consider these topics in cross-cultural ways, and offers suggestions for research and classroom practice. It is a valuable resource for scholars of mathematics education, from early childhood through to higher education and an inspiring read for all mathematics teachers. ; Features the intellectual work of researchers from different ethnicities and nationalities Offers an alternative perspective of complementing cognition and affect Presents a comprehensive collection of values and valuing in mathematics educatio

Students' difficulties, conceptions and attitudes towards learning algebra : an intervention study to improve teaching and learning

The skills necessary to identify and analyse errors and misconceptions made by students are needed by teachers of all levels especially at the lower secondary school level in Malaysia. If students are to be successful in tackling mathematical problems later in their schooling, the one prerequisite is the mastery of basic concepts in algebra. Despite the best efforts of the teachers, students still develop algebra misconceptions. Is it possible to reduce or eliminate these misconceptions? The research involved a survey of 14 year-old students in Form 2 (Grade 8) in the Penampang district of Sabah, East Malaysia. The focus of this study lies in students’ difficulties, conceptions and attitudes towards learning algebra in the framework of conceptual change. A possible way to help students overcome their learning difficulties and misconceptions is by implementing diagnostic teaching involving conflict to foster conceptual change. The study involved evaluating the efficacy of a conceptual change instructional programme involving cognitive conflict in (1) facilitating Form 2 students’ understanding of algebra concepts, and (2) assessing changes in students’ attitudes towards learning mathematics, in a mixed quantitativequalitative research design.A 24-item Algebra Diagnostic Test and a 20-item Test of Mathematics-Related Attitudes (TOMRA) questionnaire were administered as a pretest and a posttest to 39 students in each of a heterogeneous high-achieving class and a below-average achieving class. In addition 9 students were purposefully selected to participate in the interview.The results of the study indicated that students’ difficulties and misconceptions from both classes fell into five broad areas: (1) basic understanding of letters and their place in mathematics, (2) manipulation of these letters or variables, (3) use of rules of manipulation to solve equations, (4) use of knowledge of algebraic structure and syntax to form equations, and (5) generalisation of rule for repetitive patterns or sequences of shapes.The results also showed that there was significant improvement in students’ achievement in mathematics. Further, students’ attitude towards inquiry of mathematics lessons showed significant positive improvement. Enjoyment remained high even though enjoyment of mathematics lesson showed no change. Also, changes in students’ understanding (from unintelligible to intelligible, intelligible to plausible, plausible to fruitful) illustrated the extent of changes in their conceptions.Different pedagogies can affect how conceptual change and challenge of misconceptions occurs. Therefore, knowledge of the origin of different types of misconceptions can be useful in selecting more effective pedagogical techniques for challenging particular misconceptions. Also, for teachers to create an effective learning experience they should be aware of and acknowledge students’ prior knowledge acquired from academic settings and from everyday previous personal experiences. Since all learning involves transfer from prior knowledge and previous experiences, an awareness and understanding of a student’s initial conceptual framework and/or topic can be used to formulate more effective teaching strategies. If this idea is taken a step further, it could be said that, because misconceptions comprise part of a conceptual framework, then understanding origins of misconceptions would further facilitate development of effective teaching strategies.Further research is needed to help teachers to understand how students experience conflict, how students feel when they experience conflict, and how these experiences are related to their final responses because cognitive conflict has both constructive and destructive potential. Thus, by being able to interpret, recognise and manage cognitive conflict, a teacher can then successfully interpret his/her students’ cognitive conflict and be able to make conceptual change more likely or help students to have meaningful learning experiences in secondary school algebra

Students' difficulties, conceptions and attitudes towards learning algebra : an intervention study to improve teaching and learning

The skills necessary to identify and analyse errors and misconceptions made by students are needed by teachers of all levels especially at the lower secondary school level in Malaysia. If students are to be successful in tackling mathematical problems later in their schooling, the one prerequisite is the mastery of basic concepts in algebra. Despite the best efforts of the teachers, students still develop algebra misconceptions. Is it possible to reduce or eliminate these misconceptions? The research involved a survey of 14 year-old students in Form 2 (Grade 8) in the Penampang district of Sabah, East Malaysia. The focus of this study lies in students’ difficulties, conceptions and attitudes towards learning algebra in the framework of conceptual change. A possible way to help students overcome their learning difficulties and misconceptions is by implementing diagnostic teaching involving conflict to foster conceptual change. The study involved evaluating the efficacy of a conceptual change instructional programme involving cognitive conflict in (1) facilitating Form 2 students’ understanding of algebra concepts, and (2) assessing changes in students’ attitudes towards learning mathematics, in a mixed quantitativequalitative research design.A 24-item Algebra Diagnostic Test and a 20-item Test of Mathematics-Related Attitudes (TOMRA) questionnaire were administered as a pretest and a posttest to 39 students in each of a heterogeneous high-achieving class and a below-average achieving class. In addition 9 students were purposefully selected to participate in the interview.The results of the study indicated that students’ difficulties and misconceptions from both classes fell into five broad areas: (1) basic understanding of letters and their place in mathematics, (2) manipulation of these letters or variables, (3) use of rules of manipulation to solve equations, (4) use of knowledge of algebraic structure and syntax to form equations, and (5) generalisation of rule for repetitive patterns or sequences of shapes.The results also showed that there was significant improvement in students’ achievement in mathematics. Further, students’ attitude towards inquiry of mathematics lessons showed significant positive improvement. Enjoyment remained high even though enjoyment of mathematics lesson showed no change. Also, changes in students’ understanding (from unintelligible to intelligible, intelligible to plausible, plausible to fruitful) illustrated the extent of changes in their conceptions.Different pedagogies can affect how conceptual change and challenge of misconceptions occurs. Therefore, knowledge of the origin of different types of misconceptions can be useful in selecting more effective pedagogical techniques for challenging particular misconceptions. Also, for teachers to create an effective learning experience they should be aware of and acknowledge students’ prior knowledge acquired from academic settings and from everyday previous personal experiences. Since all learning involves transfer from prior knowledge and previous experiences, an awareness and understanding of a student’s initial conceptual framework and/or topic can be used to formulate more effective teaching strategies. If this idea is taken a step further, it could be said that, because misconceptions comprise part of a conceptual framework, then understanding origins of misconceptions would further facilitate development of effective teaching strategies.Further research is needed to help teachers to understand how students experience conflict, how students feel when they experience conflict, and how these experiences are related to their final responses because cognitive conflict has both constructive and destructive potential. Thus, by being able to interpret, recognise and manage cognitive conflict, a teacher can then successfully interpret his/her students’ cognitive conflict and be able to make conceptual change more likely or help students to have meaningful learning experiences in secondary school algebra

Understanding High School Students\u27 Motivation and Amotivation to Read in and Outside of School: A Phenomenology

The purpose of this phenomenological study was to describe the motivation and amotivation to read of 9th-12th grade adolescents in a large semi-urban high school in southwestern North Carolina. The principal theory guiding this study is Self-Determination Theory (Deci & Ryan, 1985, 1991, 1994, 2000) as it explicates three universal human needs underpinning adolescent motivation to read. This investigation was guided by the following principal research question: How do high school students in southern North Carolina describe their motivation to read? General education high school students (n=12), balanced for gender, ethnicity, race, socioeconomic status, and initial reading motivation, were observed, interviewed in a focus group, and interviewed individually during one semester (15 weeks). Students were enrolled in a semi-urban high school in southwestern North Carolina. Phenomenological reductionism (Schutz, 1970) primarily informed data analysis through bracketing out of personal biases and bracketing in of essential commonalities. Participants offered multiple layers and interpretations of motivations and amotivation to read. Most importantly, students read or do not read primarily through interest, choice, and desire/enjoyment, i.e. autonomy. Students want to read materials that they choose out of personal interest; realizing their own interest is often the first barrier. Further research should be conducted on the following: programs or instruments that facilitate interest-creation, case studies with recorded literacy conversations from homes, and a longitudinal ethnography on personality changes over two to three years and the effects on reading motivation

Insights Into the Beliefs and Practices of Preservice Elementary Mathematics Teacher Educators: A Naturalistic Inquiry

The purpose of this naturalistic inquiry was to explore and analyze aspects of the reported beliefs and practices of a group of preservice elementary mathematics teacher educators. Until now, researchers have had little understanding of beliefs and practices of teachers in elementary mathematics methods classrooms, despite the fact that teacher educators’ beliefs and practices have profound effects on what happens in thousands of classrooms every day. The qualitative research in this study offered insights with the potential to inform higher educational practice in regard to the preparation of elementary mathematics teachers and mathematics teacher educators. Participants were six professors and instructors of elementary math methods courses at six different colleges and universities. A series of 18 in-depth interviews, three with each participant, allowed context, nuance, and detail to be closely examined. Typological analysis led to the emergence of six themes. They dealt with consistency, challenge, content, methods, resources, and reasons. Details related to those themes helped to illuminate what the working experience of a preservice elementary mathematics teacher is like. Study conclusions indicated (a) general consistency, with some exceptions, between reported beliefs and reported practices; (b) some common challenges faced by most participants, particularly in regard to limited elementary classroom experience, and perceived time constraints; (c) wide variation in content and methods despite agreement on teaching philosophy; (d) perceived student needs as the main reported basis of participant teaching decisions, and; (e) some indication of the extent of influence of curricular and pedagogical reform as elementary mathematics teacher educators sought to enact generally constructivist inspired teaching visions. Recommendations for educators, researchers and policy makers stemming from these conclusions have potential benefits for elementary mathematics teacher preparation

Educational performance of young immigrants in Hong Kong, Macao and Vancouver

The influx of school-age Chinese immigrant children to Hong Kong, Macao and Vancouver In recent years has caused a concern to local schools and educators. The change of learning environment and how it relates to school performance is a topic useful for explaining school success or failure among the groups of immigrant children. One way to explore the factors affecting school performance is to adopt a system model with variables under a four-domain design. The individual, family, school, and peer effect are major factors that cause school performance variations. The first aim of this study was to determine if any of the four domains could be related to school performance. The results of simple correlation indicated that there were four variables (future aspiration, school attachment, after-school activity participation, and peer influence) significantly associated with school performance of the three groups of immigrant children. Family variables were all insignificantly associated with school performance. The second aim of this study was to determine if the variables under the four domains could predict school performance. The results of the multiple regression indicated that there were six variables (gender, future aspiration, intention of stay, school attachment, after-school activity participation, school or other trip participation) that predicated school performance. The third aim of this study was to determine if there was a significant difference between different groups of immigrant children. The results of the t-test indicated that there was no significant difference between the mean school performance scores of groups with entrance examination and those that did not have entrance examination. Another t-test also revealed that there was no significant difference between the mean school performance scores of groups that entered to preferred class after migration and those that entered to not-preferred class. A one-way AN OVA test of three groups assigned to different grade upon arrival, moreover, found insignificant mean school performance among the groups in lower, just-right or higher grade. The fourth aim of this study was to examine the difference of school performance in the two surveys of the three cities. The results of t-test indicated no significant difference between the mean school performance scores of the two surveys in the Hong Kong and Vancouver but a significant difference in the Macao sample. The fifth aim of the study investigated the difference of selected variables among the three cities in the two surveys. Vancouver group achieved the highest median value in school performance scores in the first survey. Macao group outperformed Vancouver and obtained the first place in the second survey. Among the three, Vancouver group again obtained the highest median value in the two surveys of school attachment. Additional qualitative data from the Macao group also revealed other effects on school performance that quantitative data did not uncover. The effects were grouped into "feeling happy", "feeling unhappy", and "future educational expectation" domains. A culturally-based explanation of school performance of immigrant children was suggested for future evidence seeking activity

The Role of Mathematics in Engineering Practice and in the Formation of Engineers

This research investigated the role of mathematics in engineering practice and whether there is a relationship between students’ experiences with school mathematics and their choice of engineering as a career. The study was inspired by the observation that there is a lacuna in the scholarly literature concerning the nature of mathematics’ role, if any, as a significant cause of the declining number of students entering professional engineering courses. Additionally there is currently no broad picture of the mathematical expertise required or used by practising engineers. The population of interest in this study comprises professional engineers practising in Ireland. A sequential explanatory mixed methods design, where the subsequent collection and analysis of interview data builds on the survey findings, is employed. Engineers’ use of mathematics is considered in three parts: curriculum mathematics, mathematical thinking, and engaging with mathematics. Curriculum mathematics usage is measured by a derivation of de Lange’s mathematics assessment pyramid and with reference to three dimensions: mathematics domain, usage type, and academic level. Thinking usage relates to mathematical modes of thinking. Engaging usage is the motivation to take a mathematical approach. Engineers’ experiences of school mathematics, factors that contributed to their engagement with school mathematics and the impact of their feelings about mathematics on their choice of engineering careers are investigated. The findings show that (i) engineers’ feelings about mathematics are a major influence on their choice of engineering as a career; (ii) teachers, affective factors and sociocultural influences are the main contributors to engineers’ interest in and learning of mathematics; (iii) while almost two thirds of engineers use high level curriculum mathematics in engineering practice, mathematical thinking has a greater relevance to engineers’ work compared to curriculum mathematics; (iv) professional engineers’ curriculum mathematics usage is dependent on the interaction of engineering discipline and role and their mathematical thinking usage is independent of discipline and role; (v) engineers show high affective engagement with mathematics and their usage of mathematics in engineering practice is influenced by the value given to mathematics within their organisation; and (vi) the focus on “objective” solutions at the expense of tacit knowledge in mathematics education reduces the value of mathematics in engineering practice