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Teachers' confidence and beliefs and their students' attitudes to mathematics
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This paper reports some initial results of a project that involved profiling middle school mathematics teachers and their students. Survey data concerning the teachers' confidence in relation to the mathematics topics that they teach, their beliefs about numeracy and effective teaching of mathematics, students' attitudes to mathematics, and their perceptions of the frequency of various events in their mathematics classrooms contribute to a picture of many teachers and their students working in traditional classrooms, believing in the importance of mathematics, but struggling with the conceptual demands of the subject and with finding relevance for the material. Recent and ongoing curriculum reform in Tasmania has emphasised the importance of being numerate rather than of simply knowing mathematics. The definition that underpins the Being numerate key element of the Essential Learnings (ELs) Framework (Department of Education, Tasmania (DoET), 2002, p. 21) acknowledges the centrality of the discipline of mathematics along with the role of affect. It includes the following: Being numerate involves having those concepts and skills of mathematics that are required to meet the demands of everyday life. It includes having the capacity to select and use them appropriately in real life settings. Being truly numerate requires the knowledge and disposition to think and act mathematically and the confidence and intuition to apply particular principles to everyday problems.
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... Confidence has been defined as how sure a person is to perform well on a particular task (Fennema & Sherman, 1976). Confidence has been positively linked to the quality of pedagogy, acting partly through the interaction of confidence in discipline knowledge and self-efficacy, that is, a belief that their teaching will succeed (Bandura, 2006), and has been linked to more effective classroom practice (Beswick, Watson, & Brown, 2006;Graven, 2002;Lazarides, Buchholz, & Rubach, 2018). As with knowledge, there has been little empirical data on Australian middle years teachers' confidence. ...
... As with knowledge, there has been little empirical data on Australian middle years teachers' confidence. Beswick et al. (2006) found low levels of confidence with respect to critical aspects of pre-service teacher knowledge of middle school mathematics in their relatively small sample (N = 42) of primary and middle school teachers. ...
... A further difference between this study and earlier studies involving confidence and self-efficacy is that earlier studies tended to be much more generic with respect to what the subjects were confident about doing, for example, "I am sure I can learn the mathematics" or "I am a self-reliant person" (Sherer et al., 1982, p. 666). In this study participants were asked how confident they are in doing 31 very specific middle school mathematics tasks; such specificity is consistent with that modelled by Beswick et al. (2006). ...
... The workshops were designed to provide the necessary cross curricular training to promote increased statistical literacy levels of learners (North & Zewotir, 2006). Some studies focusing on teachers' confidence levels in the teaching of statistics found that teachers' confidence in teaching statistical ideas was not uniform across concepts (Begg & Edwards, 1999;Beswick et al., 2006Beswick et al., , 2012Harrell-Williams et al., 2015). Beswick et al. (2006) conducted a study with 42 middle school mathematics teachers about their confidence in relation to the mathematics topics they teach. ...
... Some studies focusing on teachers' confidence levels in the teaching of statistics found that teachers' confidence in teaching statistical ideas was not uniform across concepts (Begg & Edwards, 1999;Beswick et al., 2006Beswick et al., , 2012Harrell-Williams et al., 2015). Beswick et al. (2006) conducted a study with 42 middle school mathematics teachers about their confidence in relation to the mathematics topics they teach. Their findings revealed the teachers were most confident about teaching Measurement and Space, and least confident about Pattern and Algebra. ...
... The statistics also provided strong evidence to support the three dimensions in their model. The notion of dimensionality of instruments measuring teachers' self-efficacy has been investigated by other studies (Beswick et al., 2006;Beswick et al., 2012;Yim et al., 2007). On the one hand, studies showed that teachers' confidence in teaching statistical ideas was not uniform across concepts (Callingham & Watson, 2014). ...
The purpose of this study is to explore the expressions of confidence by a group of South African mathematics teachers about teaching mathematics and statistics concepts from various perspectives. The participants were 75 mathematics teachers who were teaching Grades 4 to 12 in KwaZulu-Natal (KZN) schools. They then were asked to express their opinion on their level of confidence in teaching using 17 confidence items on a 5 point Likert scale, graded from very low to very high. The study drew upon factor analysis, Rasch analysis as well as regression analysis. The findings suggest that teachers’ confidence in teaching mathematics concepts is quite different from their confidence in teaching statistics concepts and those which require connections across topics. Furthermore, the study has also found differences in teachers’ confidence level by gender during the middle teaching years as well as a significant interaction between phases of teaching and whether or not teachers completed additional professional qualifications.
... Misalignment between beliefs and practices may occur at the conscious or subconscious level, vary in degree, and are based on internal and external factors (Cross Francis et al., 2015;Buehl & Beck, 2015). In some instances, teachers articulate that they believe they should be using reform practices, but they find it difficult to effectively implement certain normative beliefs well into pedagogical practice because of a lack of content and/or pedagogical knowledge (Stein, Grover, & Henningsen, 1996;Henningsen & Stein, 1997;Beswick, Watson, & Brown, 2006;NRC, 2012). In such instances, the disconnect is at the conscious level, attributed to the internal lack of knowledge. ...
... Are the beliefs of entering PTs similar, more traditional, or more reform-based than those ITs that might represent their former teachers 3 ? Related to how and what mathematics should be taught, literature on middle and secondary ITs examining similar belief constructs and utilizing similar methodologies revealed that at the normative level, persistent reform beliefs included: teachers should be fascinated with student insights; slight frustration by students can lead to a productive struggle resulting in deep learning; student-generated ideas should not be ignored; justifications to solutions are an important part of mathematics; and students should develop inquiry skills when doing mathematics (Lloyd et al., 2016;Beswick, Watson, & Brown, 2006). Reform discursive claims included the assigning of problems that could be solved in multiple ways, using multiple representations and the sharing of varying solution strategies among peers (Lloyd et al., 2016). ...
... Collaboration was a major N-D disconnect; teachers believed that collaboration, theoretically, was a valuable pedagogical practice, but claimed that it was challenging to implement. Interestingly, though ITs reported both at the normative and discursive level the reform belief that mathematical processes were just as significant as answers, they also very traditionally indicated that teacher-centered, expository teaching with a procedural focus was important to effective mathematics teaching and learning (Lloyd et al., 2016;Beswick, Watson, & Brown, 2006), putting into question if the mathematical processes they valued as much as the solutions were the mathematical procedures that were taught through direct instruction. ...
... Additional to students' interest loss and heightened perceptions of mathematics as difficult through secondary schooling (Beswick et al., 2006;Watt, 2004), their selfconcepts and valuing of mathematics as useful are important influences on their subsequent mathematical enrolments and mathematics-related career aspirations (Watt et al., 2012). These also decline through adolescence, although boys rate their self-concepts and interest higher, and difficulty of mathematics lower, despite similar measured achievement (Watt, 2004). ...
... Ingram et al., 2018;Sullivan, 2011) often describes such practices. Educational psychologists and mathematics educators alike have noted the decline in students' engagement with mathematics as they progress through the years of schooling (Beswick et al., 2006;Watt et al., 2004). Our findings have identified clusters of students with differing mathematical engagement, along with the antecedents of cluster membership, suggesting specific factors that require attention from primary school onwards to maintain engagement. ...
This study examined the extent to which boys fell into clusters comprised of different levels of motivations and costs. In turn, the antecedents of these clusters and associations with engagement and wellbeing outcomes were considered. Based on survey responses from 168 students across Years 5, 7 and 9 from an all-boys' school in Sydney, Australia, three clusters were identified: Positively Engaged, Disengaged , and Struggling Ambitious . Performance-approach and avoidance achievement goals, mastery classroom goal structure, perceived peer valuing of mathematics and teacher enthusiasm differentially predicted profile membership. Clusters were also found to differ in terms of both wellbeing and engagement, such that students within maladaptive profiles evidenced the most negative outcomes. The study reaffirms prior work, holds implications for addressing student motivation in mathematics, and adds to understanding of the interplay of individual and classroom goal structures in relation to students’ mathematics expectancies, values and resultant outcomes.
... Confidence has further been defined as a firm trust or belief, faith in oneself and self-reliance (Callingham and Watson 2014). Beswick, Watson, and Brown (2006) contended that confidence was important due to its association with knowledge. In general, teachers who knew more middle school mathematics tended to be more self-confident. ...
... In this regard, the present results add to the findings of earlier authors who have commented on secondary school teacher confidence in Australia (e.g. Beswick, Watson, and Brown 2006;Callingham and Watson 2014). The very different confidence that participants recorded for different levels of questions supports the practice of asking about confidence within narrow content domains. ...
It is generally assumed that in order to teach mathematics effectively, middle years teachers ought to have a high degree of knowledge of mathematics and confidence in their ability to do the mathematics as well as self-efficacy to teach it. This study examines the content knowledge, mathematics confidence and self-efficacy of 99 graduate-entry pre-service teachers in an Australian school of education. The findings indicate that, in general, their mathematical content knowledge was not strong. Further, the participants expressed different levels of confidence and self-efficacy for specific concepts, so, while the scale used had high Cronbach’s alpha coefficients, its internal consistency was relatively weak. That is, confidence and self-efficacy were found to be content specific. Further, the participants tended to have confidence and self-efficacy scores that, while low, were inconsistent with their ability to do the mathematics; they tended to overestimate their mathematics competency. The findings with respect to pre-service teachers’ deficit of relevant mathematical knowledge, confidence and self-efficacy have implications for teacher preparation to teach mathematics in the study institution and potentially more broadly in the West.
... Making assumptions about Australian PSTs' knowledge of mathematics has been cautioned (e.g., The consensus is that considerable portions of primary Australian PSTs have low levels of confidence that can manifest as anxiety about learning and teaching primary mathematics (e.g., Grootenboer 2008;Norton, 2017). The relationship between confidence and self-efficacy and subsequent classroom effectiveness has been well documented (e.g., Ball, Lubienski, and Mewborn 2001;Beswick, Watson, and Brown 2006;Hattie 2009) with confident teachers exhibiting greater flexibility in pedagogy and being more effective in supporting higher achievement. ...
The purpose of this paper is to document pre-service primary school teachers’ responses to manifestations of genericism in mathematics teacher preparation. Specifically, it documents their responses to curriculum units that focus on developing mathematical content knowledge and specific mathematical pedagogical knowledge. Contextualised in an Australian initial teacher education program, the pre-service teachers (n = 789) were surveyed at the commencement of their units to gain insights into what they considered important to learn in their forthcoming mathematics curriculum units. Qualitative responses to the survey were categorised using thematic analysis and then used to guide the development of tailored units. The mathematics curriculum units focused on attempting to ensure depth of school mathematics content knowledge and specific pedagogy associated with this mathematics. A second survey, administered through post-course evaluations (n = 405), suggests that pre-service teachers overwhelmingly valued the modelling of specific pedagogies and scaffolding of the teaching and learning of school mathematics concepts. The results have implications for the teaching of mathematics in initial teacher education programs, particularly in Australia but also elsewhere where there is an increasing emphasis on pre-service teachers being classroom ready at graduation. This includes a deep and connected knowledge of the mathematics and range of pedagogies for the mathematics they will soon be certified to teach.
Teachers in an education system are one of the core pillars in achieving educational goals. There is no education system that can progress and succeed to enculturate succeeding generations without teachers. Teacher quality and quality of instruction require comprehensive preservice or in-service teacher education and training programs. A teachers' training program is aimed at producing quality and effective teachers who eventually can guide students not only on academic success but also in the lifelong learning. Descriptive survey research design was adopted for the study. The target population of study comprised of Mathematics teachers in Konoin Sub County, Bomet County, Kenya. A total of 70 (89.7%) of the mathematics teachers selected participated in the study. The research instrument used was a questionnaire which consisted of five closed-ended question items. Data collected was coded and analyzed. Statistical significance was evaluated based on the Chi-square goodness-of-fit test, Fisher's exact and Freeman-Halton test (an extension of Fisher's exact test). The findings shows that majority of the mathematics teachers perceive their preservice mathematics content as not relevant to teach secondary school mathematics compared to those who perceive as relevant dependent on initial academic qualifications. Majority of teachers were not confident. High number of teachers attributed the content they teach to their secondary school mathematics teacher. Majority of teachers perceived general methods of teaching taught in college are applicable and adequate to their practice compared to those who perceived as not applicable.
This chapter backgrounds and critically reviews Australasian research in the affective domain in mathematics education from 2016–2019. It first locates the body of research within broader considerations of an affective domain and then explores the individual affective aspects of beliefs, self-efficacy, identity, attitudes, motivation and interest, feelings, anxiety and emotions, and engagement. Consideration is given to the methodologies used in research in the affective domain during this time period.
There is a chronic shortage of appropriately qualified science and mathematics teachers particularly in disadvantaged, rural and isolated communities. Less experienced and out-of-field teachers who often teach in these contexts face difficulties in accessing professional learning and mentoring. While increasing their access to quality resources is useful, these teachers need to both decide whether a resource is appropriate in their context and be able to use it confidently. This paper reports on the process used in the STEMCrAfT project to explicate the knowledge that experienced science and mathematics teachers use when selecting and using resources, and the framework that resulted.
This paper reports on the use of a profiling instrument to evaluate an in-service professional development program for teachers of middle school numeracy. Two aspects of the use of the profile are reported. One relates to the aims of the profile to reflect Lee Shulman's seven types of teacher knowledge and to measure change in teachers with respect to them. The second relates to the success of the program and how this was judged from responses to the profile. Although the providers of the program were mainly interested in this second aspect, mathematics educators more generally should be more interested in the first due to recent trends to demand evidence-based evaluations of teacher professional development programs.
The incorporation of constructivist and critical theory perspectives on the farming of the classroom learning environment led to the development of the Constructivist Learning Environment Survey (CLES). CLES enables researchers and teacher-researchers to monitor constructivist teaching approaches and to address key restraints to the development of constructivist classroom climates. CLES assesses either student or teacher perceptions of Personal Relevance, Uncertainty, Student Negotiation, Shared Control, and Critical Voice. The p plausibility of the CLES was established in small-scale classroom-based qualitative studies and its statistical integrity and robustness were validated in large-scale studies conducted in the USA and Australia.
Little consensus exists in the research literature concerning the relationship between attitude toward mathematics and achievement in mathematics. To assess the magnitude of this relationship, the researchers conducted a meta-analysis to integrate and summarize the findings from 113 primary studies. The statistical results of these studies were transformed into a common effect size measure, correlation coefficient. This relationship was found to be dependent on a number of variables: grade, ethnic background, sample selection, sample size, and date of publication. Gender did not have a significant effect on the relationship, nor were there any significant interactions among gender, grade, and ethnic background. The researchers discuss the findings in comparison to previous narrative reviews and meta-analyses, and draw implications for practice and further research.
The middle-grades mathematics related to multiplicative structures has undergone careful scrutiny over the past decade. Researchers
have identified the types of reasonings involved; the difficulties students have with the concepts and why these difficulties
might occur; and the interconnections within this content area. On the basis of this research we make four recommendations
for the preparation and professional development of teachers. The recommendations deal with different but related forms of
reasoning: quantitative reasoning, multiplicative reasoning, proportional reasoning, and reasoning with rational numbers.
Problematic issues that follow from the recommendations are discussed.
begins by considering alternative theoretical foundations for research on affect / Mandler's (1984) theory, an approach to research on affect that is based on cognitive psychology, is selected for further discussion, particularly because it illustrates how affect can be incorporated into cognitive studies of mathematics learning and teaching / presents a framework for research on affect that reorganizes the literature into three major areas: beliefs, attitudes, and emotions / research on a number of topics from the affective domain is summarized, and linked to the proposed framework / explores how qualitative as well as quantitative research methods can be used in research on affect (PsycINFO Database Record (c) 2012 APA, all rights reserved)
[discusses] psychological research and theory concerned with the way teachers affect student learning [which considers] a variety of issues germane to this research / these issues provide a context for interpreting the research presently available and for identifying an appropriate agenda for future research
addresses these issues and the relevant research in the following major sections: changing conceptions and new assumptions related to teaching, learning, and scientific research, including an overview of traditional conceptions of teaching and models of instruction; the nature of "psychological" inquiry and research; current models of teaching and learning; a summary of what is currently known (and not known) about teacher effects [and] steps that might be taken to obtain a better understanding of the teacher-learning process (PsycINFO Database Record (c) 2012 APA, all rights reserved)