Women and girls in mathematics—Equity in mathematics education

Conclusions What then can be said that is known about sex-related differences in mathematics and factors related to such differences? Certainly, when both females and males study the same amount of mathematics, differences in learning mathematics are minimal and perhaps decreasing. Many fewer females elect to study mathematics and therein lies the problem. Variables which appear to contribute to this non-election are females' lesser confidence in their ability to learn mathematics and their belief that mathematics is not useful to them. In addition, differential teacher treatment of males and females is important. All variables appear to be directly related to the stereotyping of mathematics as a male domain.There is nothing inherent (Sherman [30]) which keeps females from learning mathematics at the same level as do males. Intervention programs can and must be designed and implemented within schools which will increase females' participation in mathematics. Such programs should include male students, female students and their teachers. Only when such intervention programs become effective can true equity in mathematics education be accomplished.     

STUDY ON LATVIAN MATHEMATICS TEACHERS’ ESPOUSED BELIEFS ABOUT TEACHING AND LEARNING AND REPORTED PRACTICES

The aim of the research was to compare espoused beliefs about teaching and learning and reported practices for the teachers of mathematics in Latvia. The sample consisted of 390 teachers of mathematics from different regions of Latvia. The present research is a part of an international comparative research within the NorBa project (Nordic–Baltic Comparative Research in Mathematics Education) that makes use of a quantitative questionnaire for mathematics teachers. The results show that the espoused beliefs of Latvian teachers of mathematics on efficient teaching tend more to a constructivist approach, whilst reported practices are more oriented to a traditional approach; yet, there exist statistically significant differences for teachers of different social and demographical groups. The research outcomes may be used for the improvement of teacher further education programmes.     

Ausbildungs- und Berufserfolg im Lehramtsstudium im Vergleich zum Diplom-Studium – Zur prognostischen Validität kognitiver und psycho-motivationaler Auswahlkriterien

The basis of this study is a prognostic model derived from the theory of work and organizational psychology, from research about the selection of college students and from teaching and learning research. The model includes cognitive and psycho-motivational criteria for selecting students as well as objective and subjective indicators for study and job success. In a four-year longitudinal study with three measuring points, the prognostic validity of the selection criteria is tested (n?=?760). The basic hypotheses are that differences in the prognostic validity of the model for teacher training and subject-specific diploma students (both in the area of mathematics) exist, and that it is easier to predict study success than job success. Secondary school exit exam, classes in advanced mathematics, interest in mathematics, subject-specific study motivation and self-efficacy are the predictive indicators taken into account. Evaluative indicators for study success are study duration, intentions of dropping out, stress experiences, the results of university exit exam and students’ second state exam. Evaluative indicators for occupational success are the job status five years after graduation, job satisfaction and stress experiences. Bivariate correlations and regression analyses support the leading hypotheses.     

Not Your Usual Maths Course: critical mathematics education for adults

This article describes an action research project that investigated which features of critical theory were useful for teaching everyday mathematics in an evening course for adults. Paulo Freire's philosophy of education and Jürgen Habermas’ theory of knowledge interests are among the main influences on exponents of critical mathematics education such as Ole Skovsmose and Marilyn Frankenstein. Through the use of dialogical processes and critical reflection, students engage in social and political issues in their lives or communities and, as a result of their increased consciousness and mathematical learning, take “transforming action”. This study highlights the value of learning in a positive environment, through dialogical processes and critical questioning. Participants of the study were able to overcome barriers to learning mathematics; engage in everyday issues involving mathematics; and make changes to the way they dealt with mathematics, as a result of increased critical consciousness.     

Transfronteriza pre-service teachers managing,resisting, and coping with the demands of mathematical discourse

This article reports on a case study of a college class for pre-service teachers on the US–Mexico border in which students participated in in-depth discussion around mathematical problems every day. This pedagogical approach promotes the socialization of students into and through the specialized discourse of mathematics. The focus of this paper is on the experience of transfronterizo students in that course. Transfronterizos are Mexican residents who periodically cross the border to attend school. For these students, whose educational background in Mexico allowed them to develop proficiency in elementary mathematical discourse in Spanish, their socialization experience includes ways in which they draw on language, and other social and learning experiences in Mexico. The focus of this paper is an assignment called Thinking Logs, a genre that required the use of mathematical discourse for teaching. Drawing on data gathered from participant observation of the course, interviews, analysis of study session discourse, and genre analysis, I highlight agentive ways that each participant used in their own socialization process. I show how participants improvised writing of models, asked for clarification in the first language, and even resisted the discourse. Students who resisted the demands might incur negative effects. Furthermore, I argue that the role of the guidance from an expert (such as a professor) is imperative in a socialization process, and I offer implications for ways that teachers can guide second language writers to develop mathematics discourse.     

Does the Opportunity–Propensity Framework predict the early mathematics skills of low-income pre-kindergarten children?

Prior studies have shown that the variables described in the Opportunity–Propensity (O–P) Framework have successfully accounted for the mathematics and science achievement of students in grades 1–3 and 8–12. The two goals of the present study were to (1) determine whether the O–P Framework could also account for individual differences in the early mathematics skills of low-income, pre-kindergarten children and (2) determine whether latent variables constructed from measured variables would account for performance in the manner specified in the O–P model. The O–P Framework assumes that high achievement in mathematics is a function of three categories of factors: (a) antecedent factors, variables that operate early in a child’s life and explain the emergence of opportunities and propensities, (b) opportunity factors, variables that measure a child’s opportunity to learn mathematics content at home and school, and (c) propensity factors, variables that capture a child’s propensity for learning in terms of self-regulation, motivation, and prior cognitive skills. To test the fit of this model for low-income children during the year before they attend kindergarten, the authors conducted a secondary analysis of achievement and background data from the Early Childhood Longitudinal Study-Birth (ECLS-B) Cohort data set. Structural equation modeling indicated significant associations between the antecedent factor, opportunity factor, and propensity factor, and between the opportunity factor and pre-kindergarten mathematics achievement. The results confirmed the fit of the model and identified the kinds of learning experiences that could promote the acquisition of mathematics skills in low-income children and improve their readiness to learn in first grade and beyond.     

The influences of conceptions of mathematics and self‐directed learning skills on university students' achievement in mathematics

This study tested the mediating role of self‐directed learning skills (SDL) between students’ conceptions of mathematics and their achievement in mathematics using a structural equation model. Data were collected using the “Conceptions of Mathematics Questionnaire” and the “Self‐Rating Scale of Self‐Directed Learning”, together with students’ achievement in mathematics. A sample of 440 first year university students at King Saud University participated in the study. The findings confirm the moderating role of students’ self‐directed learning skills between their conceptions of mathematics and their achievement in mathematics. Students who have a highly fragmented conception of mathematics tended to have low SDL skills, and in turn low mathematics achievement (partial mediation), whereas students who have a highly cohesive conception of mathematics tended to have high self‐directed learning skills, and in turn high mathematics achievement (full mediation). Mathematics educators should be aware that students’ conceptions of mathematics may be influential, but not sufficient to predict achievement in mathematics. Equipping students with appropriate conceptions of mathematics and self‐directed learning skills is key to enhancing their performance in mathematics.     

Exploring Teachers’ Meta-Cognitive Skills in Mathematics Classes in Selected Rural Primary Schools in Eastern Cape,South Africa

Undoubtedly the acquisition of mathematical skills for problem solving is critically important in today’s sophisticated technological world. There is growing evidence that meta-cognition application is an important component of academic success in general and impacts on mathematical achievement in particular. Teachers’ application of meta-cognition therefore directs and reflects their teaching-practice behaviour which influences their learners’ learning with understanding in problem-solving. The purpose of the study reported on in this article was to explore teachers’ available meta-cognitive skills in class with the intention of supporting learners’ development of mathematics in problem-solving in some selected rural primary schools in the Eastern Cape, South Africa. The participants were three teachers purposefully selected from three primary schools. Interviews were conducted with the three teachers and three lessons were observed. The interviews, as an extension of observation, focused on the teachers’ knowledge or understanding of available meta-cognitive skills and how they used these skills in helping their learners’ development of mathematics problem-solving. The findings included a detailed exploration of the teachers’ acquisition and use of specific metacognitive skills, either consciously or unconsciously, during teaching and learning processes in order to develop their mathematics learners’ meta-cognitive skills as well as in solving mathematical problems. The results of the observation showed that there was evidence of teachers applying meta-cognitive skills unconsciously in assisting their learners in problemsolving in class. The interviews confirmed this evidence of available meta-cognitive skills which the teachers usually applied in assisting their learners in problem-solving in class. Recommendations have been made regarding teachers’ methods of teaching to improve the development of such skills in the lives of their mathematics learners through problemsolving.     

Pre-service and in-service teachers’ perceptions on the integration of children’s literature in mathematics teaching and learning in Ireland

The beneficial role that children’s literature plays in facilitating the meaningful integration and advancement of literacy and numeracy in the primary mathematics classroom has been well validated by research findings internationally. In Ireland, supporting the development of literacy and numeracy is a key educational priority. Consequently, a myriad of policy initiatives such as the Literacy and Numeracy for Learning and Life strategy have been introduced. All aim to address concerns about young people’s lack of basic literacy and numeracy skills and to consider new teaching and learning modalities to enhance same. Despite this, no official emphasis is given to incorporating literature in the Irish primary school mathematics curriculum. Therefore, it is pertinent and timely that this study seeks to ascertain pre-service and in-service teachers’ views on the use of literature to support mathematics teaching and learning and to investigate perceived barriers to and enablers for the integration of children’s literature in the mathematics classroom in Ireland. The analysis of the findings will be framed using Ajzen’s (Ajzen, Icek. 1991. “The Theory of Planned Behavior.” Organizational Behavior and Human Decision Processes 50 (2): 179–211) Theory of Planned Behavior (TPB) model. This research is part of a large international research collaboration (see www.mathsthroughstories.org), in which the beliefs of teachers with respect to children’s literature are investigated.     

Using Explicit and Strategic Instruction to Teach Division Skills to Students With Learning Disabilities

Students with mathematics learning disabilities (LD) exhibit difficulties with retrieval and cognitive skills that impede their ability to perform basic mathematical skills. Instruction in mathematical procedures (i.e., procedural knowledge) is necessary to help students learn and apply skills such as basic facts and whole-number computation. Division is a skill that is identified in curriculum across the grade levels; yet, it is a skill that is often taught last in instructional sequences because of its complexity and prerequisite knowledge. Reviews of research have revealed that students with LD benefit from a combined model of academic instruction that includes both explicit and strategic instructional procedures. This article presents an overview of division instruction and a sample of interventions for teaching division that include explicit and strategic instructional procedures, which are found in the combined model of teaching.     

Use of flipped classroom in the marketing career during the educational process on financial mathematics

The aim of this mixed research is to analyze the use of flipped classroom in the educational process on financial mathematics considering data science, machine learning (linear regression) and neural network. The sample is composed of 29 people who studied the career of Marketing and took the Financial Mathematics course during the 2018 school year. The results of machine learning indicate that the consultation of the English and Spanish videos before the class, the realization of the exercises collaboratively through the spreadsheet and dissemination of the answers about the exercises through Google Drive during the class and the realization of the online exams and laboratory practices after the class positively influence the development of mathematical skills about simple interest. Data science identifies 6 predictive models about the use of flipped classroom. On the other hand, the neural network identifies the aspects of flipped classroom that most influence the development of mathematical skills during the educational process on financial mathematics. Also, the students of Marketing consider that flipped classroom allows the construction of new educational spaces through the use of technology. Finally, flipped classroom is a pedagogical model that transforms the teaching-learning conditions and updates the organization of the activities before, during and after the class.

     

To Each Their Own: Students Asking Questions Through Individualized Projects

Abstract

As mathematics educators we want our students to develop a natural curiosity that will lead them on the path toward solving problems in a changing world, in fields that perhaps do not even exist today. Here we present student projects, adaptable for several mid- and upper-level mathematics courses, that require students to formulate their own questions and to begin to develop the basic research skills needed to answer these questions. These projects, where each student is given an individualized object to study, allow students to take ownership over their own learning while introducing them to the joy and challenge of discovery and research. Each student is directed to use the concepts and techniques presented in class as a set of tools to guide the investigation of their object. We discuss our experiences–both positive and negative–with these inquiry-based projects.     

Curriculum development for quantitative skills in degree programs: a cross-institutional study situated in the life sciences

Higher education policies are increasingly focused on graduate learning outcomes, which infer an emphasis on, and deep understanding of, curriculum development across degree programs. As disciplinary influences are known to shape teaching and learning activities, research situated in disciplinary contexts is useful to further an understanding of curriculum development. In the life sciences, several graduate learning outcomes are underpinned by quantitative skills or an ability to apply mathematical and statistical thinking and reasoning. Drawing on data from a national teaching project in Australia that explored quantitative skills in the implemented curricula of 13 life sciences degree programs, this article presents four program-level curricular models that emerged from the analysis. The findings are interpreted through the lens of discipline-specific research and general curriculum design theories to further our understanding of curriculum development for graduate learning outcomes. Implications for future research and to guide curriculum development practices in higher education are discussed.     

Using peer and self-assessment to develop modelling skills with students aged 11 to 16: A socio-constructive view

Eight Welsh secondary schools participated in an action research project which developed approaches to teaching and assessing mathematical thinking skills involved in practical modelling situations. The development of the metacognitive and strategic skills necessary for successful modelling is discussed from a socio-constructivist perspective as a process of acculturation as well as cognitive construction. Learning to model involves socialization into the consensual realities of a wider mathematical culture and the teacher plays a pivotal role in the generation of this consensus through the legitimization of linguistically expressed subjectivities. Assessment is an integral part of this process. Participation in peer and self-assessment was found to involve the student in a recursive, self-referential learning process which supports the explicit development of metacognitive skills.     

Socioeconomic Status and Preschoolers' Mathematical Knowledge: The Contribution of Home Activities and Parent Beliefs

Research Findings: Children from families of lower socioeconomic status (SES) enter kindergarten with less developed mathematical knowledge compared to children from middle SES families. This discrepancy is present at age 3 years and likely stems from differences in the home learning environment. This study reports SES-related differences both in the quantity and quality of mathematical support children receive in the home and in parent beliefs about early mathematical development and then compares both with children's performance on a comprehensive mathematics assessment. Participants included 90 children in their 1st year of preschool (2 years before kindergarten entry) and 88 children in their prekindergarten year (the year just prior to kindergarten entry). Both cohorts were balanced for SES and gender. The results suggested minimal SES-related variation in mathematical support received in either cohort but clear SES differences in parents’ beliefs about early mathematical development. Middle SES parents of children in both cohorts held higher expectations in terms of skills they expected children to possess by age 5, as well as a more accurate understanding of which skills are within the developmental range of most children by age 5. These differences accounted for unique variance in children's scores on the mathematics assessment. Practice or Policy: Implications are discussed.     

Model construction as a learning activity: a design space and review

Modeling is becoming increasingly important both as a way to learn science and mathematics, and as a useful cognitive skill. Although many learning activities qualify as “modeling”, this article focuses on activities where (1) students construct a model rather than explore a given model, (2) the model is expressed in a formal language rather than drawings, physical objects or natural language texts and (3) the model's predictions are generated by executing it on a computer. Most research on such learning activities has focused on getting students to successfully construct models, which they find very difficult to do. In the hope that new research can find ways to remove this bottleneck, this article attempts to list all the major ideas that have appeared in the literature and might be useful to those developing new learning activities involving model construction. The ideas are organized into a design space with five dimensions: (1) modeling language types, (2) ways for describing the systems that students should model, (3) instructional objectives and their corresponding assessments, (4) common student difficulties and (5) types of scaffolding.     

Does undergraduate education influence teachers’ perceptions of learning and teaching? The case of the Republic of Slovenia

In the first part of the paper, different models of teacher education are presented and analysed: the pre‐technocratic model or the model of training master craftsmen; the technocratic model or the model of applied science; and the post‐technocratic model or the reflexive model. In the second part of the paper, the results of the empirical research are presented. The aim of the empirical research was to determine the influence of undergraduate teacher education on teachers’ perceptions of learning and teaching and, consequently, on teachers’ actions. In Slovenia, teachers’ education was carried out following two main models: the pre‐technocratic model or model of training master craftsmen, which was typical for the Academy of Education, and the technocratic model or the so‐called model of applied science, which is used at the education faculties nowadays. Because of this dualism in teachers’ education models, there exist differences between teachers and their perception and actions as well.     

Can ‘pooling teaching tips’ be more than ‘pooling teaching tips’?

Abstract

There is increasing interest in how academic development of various kinds influences university teaching and student learning. To date the focus has been on formal, expert-led opportunities to learn how to teach. Our institution has developed a less formal, participant-led forum for teaching staff that was initially established to share ideas on teaching techniques and skills. We report here on participant-led research that explores if and how this model of group learning works, and how it might relate to other models that have been applied to tertiary teaching development. Authors adopted a self-study research framework incorporating a collaborative autoethnography. The data emphasises how participants use this forum as a community of practice, as a means for deep engagement with learning about teaching, and as a means to rationally manage their learning against a backdrop of challenges associated with learning to teach in research-led higher education.     

Teachers' Understanding of the Role of Executive Functions in Mathematics Learning

Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an online survey of teachers' views on the importance of a range of skills for mathematics learning. Teachers rated executive function skills, and in particular inhibition and shifting, to be important for mathematics. The value placed on executive function skills increased with increasing teaching experience. Most teachers reported that they were aware of these skills, although few knew the term “executive functions.” This awareness had come about through their teaching experience rather than from formal instruction. Researchers and teacher educators could do more to highlight the importance of these skills to trainee or new teachers.