History of mathematics in secondary school teachers’ training: towards a nonviolent mathematics education

In the context of mathematics teachers’ training, the concept of dépaysement épistémologique (epistemological disorientation) emphasizes that the contact with the history of mathematics, particularly with the use of original sources, pushes aside commonplace students’ perspectives about the discipline and offers them a critical look towards mathematics’s historical, social and cultural aspects. Conceptually supported by the theory of objectivation, an emergent sociocultural theory in mathematics education, this study describes the dépaysement épistémologique lived by future mathematics teachers engaged in the reading of historical texts. A phenomenological approach allowed us to clarify various meanings associated with students’ lived experiences and a dialogical perspective provides a way to get these meanings in tension through a polyphonic narration. Our reading of this polyphonic narration suggests that dépaysement épistémologique associated with the reading of historical texts encouraged empathy from students towards the authors and their future learners, opening up the possibility for a nonviolent mathematics education.     

A charity school in the nineteenth century: Old Swinford hospital school, 1815–1914

The University in Society. Edited by Lawrence Stone. 2 vols, pp. viii, 642. Princeton University Press. London: Oxford University Press, 1975. £4.75 each.

Education for National Efficiency: the contribution of Sidney and Beatrice Webb. Edited by E. J. T. Brennan. Pp. 208. London: The Athlone Press, 1975. £5.00.

Microteaching: A Programme of Teaching Skills. By G. Brown. Pp. 163. London: Methuen, 1975. £7.00 hardback, £3.60 paperback.

Heinrich Pestalozzi. Father of Modern Pedagogy. By Robert B. Downs. Pp. 147. Boston, Mass.: Twayne Publishers, Inc., 1975. $7.50 (10% higher outside U.S.).

Authority and Organization in the Secondary School. By Elizabeth Richardson. Pp. 146. London and Basingstoke: Macmillan Education Ltd., 1975. (Schools Council Research Studies). £2.25.

An Introduction to the Study of Comparative Education. By Vernon Mallinson, University of Reading, 4th ed. London: Heinemann, 1975.

The Sociology of Educational Ideas. By Julia Evetts. Pp. via, 168. London: Routledge &; Kegan Paul, 1973. £2.50.

Class, Culture and the Curriculum. By Denis Lawton. Pp. ix, 124. London: Routledge &; Kegan Paul, 1975. Cloth £3.00. Paperback £1.25.

Ideology and the Imagination. By Fred Inglis. Pp. 244. London: Cambridge University Press, 1975. £4.90 hard cover. £2.00 paperback.

Handbook on Curriculum Development. By Centre for Educational Research and Innovation. Pp. 179. Paris: OECD, 1975. £2.80.

Looking at Innovation: two approaches to educational reasearch. P. Sheldrake and S. Berry. NFER Publishing Company Ltd., 1975.

The Sciences, the Humanities and the Technological Threat. Edited by W. Roy Niblett. Pp. xiv, 168. London: University of London Press, 1975. £3.80.     

ICT use in mathematics lessons and the mathematics achievement of secondary school students by international comparison: Which role do school level factors play?

By means of an international comparison, the research presented in the article aims to identify supporting and hindering school level factors for the use of ICT in secondary school mathematics lessons. The relationship between ICT use and the performance of Grade 9 students in mathematics is examined and further integrated into a multi-level model including school level factors. Against the background of a theoretical allocation (1) the IT equipment of schools, (2) school leadership, (3) aspects of school goals and educational strategies as well as (4) teachers’ attitudes will be analyzed by means of a multi-level regression model as well as a multi-level path model including the mathematics achievement of students as measured in the context of PISA 2012. Representative school and student data from five countries, namely Australia, Germany, the Netherlands, Norway and Singapore are taken into consideration, as the integration of ICT in teaching and learning is firmly emphasized in these countries (overall 24,579 students in 1263 schools). By modeling the complex structure, school characteristics are examined with respect to their effect on the use of ICT for mathematics teaching. Moreover, the relation between different factors and students’ mathematics achievement will be synchronously assessed in the different educational systems. The results show that characteristics at school level do play a major role in the integration of ICT into teaching and learning and turn out to be relevant across the educational systems. In addition to further in-depth country-specific findings, the results point to cross-national future challenges in the field of using technologies to enhance teaching and learning.     

Teachers’ conceptions of representation in middle school mathematics

Current reform efforts call for an emphasis on the use of representation in the mathematics classroom across levels and topics. The aim of the study was to examine teachers’ conceptions of representation as a process in doing mathematics, and their perspectives on the role of representations in the teaching and learning of mathematics at the middle-school level. Interviews with middle school mathematics teachers suggest that teachers use representations in varied ways in their own mathematical work and have developed working definitions of the term primarily as a product in problem solving. However, teachers’ conception of representation as a process and a mathematical practice appears to be less developed, and, as a result, representations may have a peripheral role in their instruction as well. Further, the data suggested that representation is viewed as a topic of study rather than as a general process, and as a goal for the learning of only a minority of the students—the high-performing ones. Implications for mathematics teacher education, prospective and practicing, are discussed.     

First‐year secondary school mathematics students’ conceptions of mathematical proofs and proving

The aim of this study is to investigate students’ conceptions about proof in mathematics and mathematics teaching. A five‐point Likert‐type questionnaire was administered in order to gather data. The sample of the study included 33 first‐year secondary school mathematics students (at the same time student teachers). The data collected were analysed and interpreted using the methods of qualitative and quantitative analysis. The results have revealed that the students think that mathematical proof has an important place in mathematics and mathematics education. The students’ studying methods for exams based on imitative reasoning which can be described as a type of reasoning built on copying proof, for example, by looking at a textbook or course notes proof or through remembering a proof algorithm. Moreover, they addressed to the differences between mathematics taught in high school and university as the main cause of their difficulties in proof and proving.     

An assessment of a social–cognitive model of academic performance in mathematics in Argentinean middle school students

This study tested a set of hypotheses derived from the model of academic achievement in mathematics of the Social Cognitive Career Theory in a sample of Argentinean middle school students. To this aim, 277 students (male and female; age: 13–15 years) were assessed using the following instruments: logical–mathematical self-efficacy scale, mathematics outcome expectations, mathematics performance goals, and mathematics ability test. All of these instruments had been adapted for use in Argentinean students. Academic achievement in mathematics (i.e., grades obtained on regular school exams) was the variable to be modeled through the path analysis technique. The analysis allowed identification of interrelations among the variables and identification of direct and indirect effects. Academic achievement in mathematics was partially explained by the model. Overall, the results support the theoretical postulates of Social Cognitive Career Theory.     

The transition to secondary school geometry: can there be a “chain of school mathematics”?

Students mainly perceive the transition to secondary school as an opportunity to start their school career anew. Reality often proves them wrong, especially in the case of mathematics. In our paper, we briefly discuss children’s transition to secondary school as both an opportunity and a problem, with reference to the Greek context. In discussions about the transition to secondary school and its effect on the teaching and learning of mathematics, primary and secondary school teachers in Greece often depict school mathematics as a “chain” of concepts and procedures. With this metaphor as our reference point, we discuss how ideologies about the teaching of mathematics are enacted in both school levels. We will base our discussion on the analysis of extracts taken from dialogues in primary and secondary school mathematics classrooms in Greece. In our analysis, we employ a Peircean view of semiotics in an attempt to conceptualize students’ rushed introduction to rigor in justifying mathematical statements in secondary school. These extracts are part of a longitudinal study that aimed, on the one hand, to pinpoint discontinuities and continuities in the teaching of geometry between primary and secondary schools and, on the other, to investigate whether a set of curriculum material that we designed could serve as a link in the teaching of geometry between the two school levels.     

Development of low-stakes mathematics and literacy test scores during lower secondary school – A multilevel pattern-centered analysis of student and classroom differences

The development of students’ learning and test-taking behavior may derive from the social context and the group of peers they associate with daily for years. Consequently, it is assumed that students’ academic achievements are to some degree affected by their classmates and the composition of the classroom. The present study provides evidence on how Finnish students (N = 5071) from different classrooms (N = 435) develop distinct patterns regarding their mathematics and literacy achievement during lower secondary school. We analysed longitudinal large-scale educational assessment data using a multilevel latent profile analysis (MLPA) to investigate the impact of classroom effect on students’ achievement patterns, that is, on the development of students’ low-stakes mathematics and literacy test scores from 7th to 9th grade. The results demonstrated the added value of modelling the multilevel structure inherent in educational assessment data: we identified four student achievement patterns that displayed different distributions across the school classes. More precisely, besides individual characteristics, the development of students’ low-stakes mathematics and literacy test scores was associated with class-level factors and some of the classrooms seemed to have a stronger effect on students’ test scores. These results suggest that classroom context is associated with students’ achievement patterns, especially regarding the worst achieving students. The findings may reflect a combination of class placement practices as well as classroom and peer effect. Although the differences between Finnish schools have been one of the lowest in the OECD countries, the findings of the present study suggest that the classroom membership may create class level quality differences in both the preconditions and the development of learning.     

What were the processes and outcomes of involving secondary school pupils transitioning from primary to secondary school in pre-arrival shared-reading? A case study

ABSTRACT

Coombe Boys’ School in New Malden worked with Kingston University to establish a ‘Big Read’, a scheme of pre-arrival shared-reading for boys transitioning from local primary schools into year 7 of the Coombe Boys’ secondary school. A novel was chosen for shared-reading, and all arriving pupils were given a copy at their Induction Day (at the end of the summer term). Copies were also made available to all staff. The book was the basis of group-based activities during the school’s Summer School (three weeks before of the start of the autumn term) and of cross-curricular individual and group-based activities during the early teaching weeks of the new school year. Outcomes were monitored using online surveys of pupils, staff and parents/guardians, and through face to face interviews with individuals from representative groups. Here outcomes are reported, both direct and indirect, comparisons made with similar schemes within higher education, and recommendations are made for how the scheme might be adapted for greater effectiveness in future.     

Who makes it to secondary school? Determinants of transition to secondary schools in rural India

Despite considerable progress made, a significant proportion of children continue to drop out before reaching secondary school in India. This study investigates factors influencing parental decision-making with regard to children's secondary schooling in the context of a rural area of Uttar Pradesh. The study finds that cost, distance to the nearest secondary school, membership in traditionally marginalised social groups, and being a girl child have a significant effect on a child's chance of transition. It also finds that factors influencing participation at the primary level may influence the transition decision, having key implications for education policy formulation across education levels.     

Photovoice: understanding high school females’ conceptions of mathematics and learning mathematics

Photovoice is a participatory action research tool that is grounded in the literature for critical consciousness (Wang & Burris, 1997). Four creative high school girls who reported struggles with mathematics were given cameras and asked to take photographs to answer the following questions: (1) What is mathematics? (2) What is your ideal learning environment? (3) What things impede your learning of mathematics? Within-case and cross-case analyses of the photographs and interview responses were conducted. Each individual case was analyzed using the work of Belenky, Clinchy, Goldberger, and Tarule (Women’s Ways of Knowing, 1986) who investigated women’s epistemological perspectives. The girls were either silenced (disconnected from the mathematical knowledge of the teacher), received (lacked confidence to do mathematics independently), or “fragily” subjective (viewed mathematical knowledge as personal rather than imparted by the teacher) knowers of mathematics. The use of photovoice has the power to facilitate the nurturing of silence as it moves toward the “roar which is on the other side of silence” (Belenky et al., 1986, p. 4).     

High school students’ acceptance and use of mobile technology in learning mathematics

The purpose of this research is to investigate factors affecting the acceptance and use of mobile technology in learning mathematics based on the Unified Theory of Acceptance and Use of Technology 2 (UTAUT2) model. The study group comprised of 1640 students attending different types of high schools and grade levels. The results of the study revealed both direct and indirect effects of exogenous variables on Behavioral Intention and Use Behavior in mobile technology acceptance of high school students in learning mathematics. It was also found that the theoretical model was confirmed adequately based on the regression coefficients, the significance of the regression coefficients, and the goodness of fit indices obtained from the SEM analysis. The strongest predictors of Behavioral Intention were Hedonic Motivation and Habit, respectively. Exogenous variables of the study together explained 76% of the variance in Behavioral Intention and 13% of the variance in Use Behavior.

     

A content analysis of school anti‐bullying policies: progress and limitations

Schools in England are legally required to have an anti‐bullying policy, but the little research so far suggests that they may lack coverage in important areas. An analysis of 142 school anti‐bullying policies, from 115 primary schools and 27 secondary schools in one county was undertaken. A 31‐item scoring scheme was devised to assess policy. Overall, schools had about 40% of the items in their policies. Most included improving school climate, a definition of bullying including reference to physical, verbal and relational forms, and a statement regarding contact with parents when bullying incidents occurred. But many schools did not mention other important aspects, and there was low coverage of responsibilities beyond those of teaching staff; following up of incidents; management and use of records; and specific preventative measures such as playground work and peer support. There was infrequent mention of homophobic bullying, and of cyberbullying. There was little difference between policies from primary and secondary schools. Findings are discussed in terms of national policy, and ways to support schools in maximising the potential of their policies for reducing bullying.     

Elementary school teachers’ uses of mathematics curricular resources

With the adoption of new content standards, teachers are often left without adequate curriculum resources. This study examined how educators used their curricular resources to teach new mathematics standards in the USA. Analyses of open-ended survey responses from 257 teachers and teacher–leaders in Grades 3 through Grade 5 indicated that every educator reported supplementing their districts’ or schools’ primary curricular resources with other materials. These supplements primarily included resources found for free on websites and resources that claimed to be aligned to the new standards, but varied in terms of alignment to national standards for effective mathematics curriculum. Implications for this study include further research on how teachers make decisions regarding curriculum resources as well as increasing teachers’ access to quality curriculum materials that can support students’ mathematical learning.