Secondary Mathematics Classrooms Research Articles

Cultural capital and the perception of feedback

This study draws on the concept of cultural capital to determine whether the cultural capital of students is related to their perceptions of classroom interactions, specifically teacher–student feedback practices. The analysis of new data in ‘Feedback and Cultural Capital,’ a Danish survey of feedback practices among 14-year-old and 15-year-old students (N = 1101), showed a positive and practically linear relationship between the cultural capital of the students and the amount of feedback they perceived in lower secondary mathematics classrooms. Drawing on Bourdieu’s theory of cultural reproduction in education, I argue that this inequality stems from either or both of two mechanisms: differences in treatment by teachers and/or differences in the perceptions of students. I link both mechanisms to the cultural capital of the students. Furthermore, the results indicate that the relationship was stronger for boys than for girls. The implications of the findings for practice and policy are discussed.

Epistemic issues in classroom mathematical activity: There is more to students’ conversations than meets the teacher’s ear

We report on a comparative investigation of student mathematical activity in two settings of a secondary mathematics classroom: peer interaction in small group and group interaction with the teacher. Our framework draws on the understanding of school mathematics as activity in between the historicity of knowledge and the situatedness of norms. We propose the term epistemic issue to refer to instances of knowledge about the construction and justification of school mathematics knowledge whose use is traceable in student activity. A major finding points to the presence of a number of epistemic issues during peer work and their omission in the communication of this work to the teacher; a phenomenon we call epistemic shift. To illustrate this finding and the methods of analysis, we take data from a group of students during a lesson of probability and the lesson-based video stimulated recall interview. We finish by discussing some implications for the development of the mathematical culture of the classroom.

Secondary students’ proof constructions in mathematics: The role of written versus oral mode of argument representation

Prior research showed that many secondary students fail to construct arguments that meet the standard of proof in mathematics. However, this research tended to use survey methods and only consider students presenting their perceived proofs in written form. The limited use of observation methods and the lack of consideration of students presenting their perceived proofs orally—in tandem with their written proofs for the same claims—might have resulted in a skewed picture of the potential of students’ constructed proofs, and this raises concern about the validity of research findings. The research reported in this article substantiates this concern. Using data from a design experiment in two secondary mathematics classrooms (14–15‐year‐olds), I explored the role of the written versus the oral mode of argument representation in students’ proof constructions. Findings from the comparison between the written arguments (perceived proofs) that the students produced during small group work and the oral arguments that the students presented in front of the class for the same claims showed that the oral mode of representation is more likely than the written mode to be associated with the construction of arguments that meet the standard of proof. Thus if a study had analysed students’ written arguments only (as in survey research), it would have reported a less favourable picture of the potential of students’ constructed proofs than another study that would focus only on students’ oral arguments (as in observational research). Implications for methodology, research and practice are discussed in light of these findings.

Mathematical sense-making through learner choice

This article explores a conceptual relationship between learner choice and mathematical sense-making. It argues that when learners can exercise choice in their mathematical activities, mathematical sense-making can be enhanced. The literature around mathematical modelling suggests a link between sense-making and learner choice. A three-tiered conceptual analysis allowed ‘purposiveness to thinking’ from the author through engagement with selected literature. Research questions related to a three-tiered analysis: generic, context-specific, and conditional accounts of sense-making in mathematics classrooms were formulated. The analysis resulted in a framework showing how sense-making may be constrained or enhanced in mathematics classrooms through learner choice. This article may add to our holistic understanding of sense-making in mathematics classrooms. It may contribute to mathematics teacher education by proposing that teachers are resourced to facilitate learners’ conceptual and procedural choice in primary or secondary mathematics classrooms.

Effects of response options on the mathematics performance of secondary students with emotional or behavioral disorders

ABSTRACTThis study examined the effects of three response options (traditional responding, response cards, and response systems) on the mathematics performance, participation, and time on-task of secondary students with emotional or behavioral disorders (EBD). A three-way crossover design was utilized to evaluate the efficacy of response options in secondary mathematics classrooms. Thirty-three students with EBD attending an urban high school and their teachers served as participants. Results indicated that the use of response cards (white boards) or response systems (ActivResponders) significantly increased students’ mathematics performance, participation, and time on-task when compared to traditional responding. Further, the use of response cards resulted in significant increases in performance and response accuracy over the increases found when using response systems. Social validity data indicated that students and teachers felt they benefited from the use of response cards and systems. Limitations, discussions, and implications for practice and future research are presented.

Pitfalls of Autonomy: the Overlooked Challenges of Teaching Locally Developed Mathematics in Ontario High Schools

Streaming students in secondary mathematics classrooms is a common practice in the province of Ontario, although there is conflicting evidence of its benefits. In this province, three streams of mathematics are available in grade 9. One of these streams, termed “locally developed,” is based on the idea that school boards and teachers would have some flexibility in the curriculum, based on differing student needs. As such, these courses fall outside the realm of the standardized provincial tests, and hence less is known about these courses, and their students’ and teachers’ needs. Teachers in one school were interviewed in order to provide a baseline case study, in order to examine their perceived challenges, needs, and views about the courses and the students in them. Recommendations for further study are included.

The Power of Interactive Whiteboards for Secondary Mathematics Teaching: Two Case Studies

Interactive whiteboard offers a high-potential innovative tool in mathematical educational environments, in which teachers’ modeling processes and students’ exploring activities can easily be executed. Nevertheless, these affordances are not self-evident. There is a gap between the potential claims of the tool and its actual use in the classrooms. This study investigated, through two parallel case studies, the interactive whiteboard potential in view of optimizing the exploitation of the interactive whiteboard, improving conceptual understanding, and fostering interactivity in secondary mathematics classrooms. Two main patterns for a productive interactive whiteboard use emerged: (a) a problem-solving pattern consisting of interactive whiteboard supporting problem-solving activities and (b) an organizer pattern consisting of using interactive whiteboard as a kind of advanced organizer and stimulating students’ reflection and mathematical contributions. The two patterns were used to design and teach lessons that were analyzed through the instrumental orchestration framework elaborated by Drijvers, Tacoma, Besamusca, Doorman, and Boon. Analysis showed how the interactive whiteboard acted as a useful instrument for students’ discussion and collective construction of mathematical knowledge.

Mathematics teachers’ views about the limited utility of real analysis: A transport model hypothesis

In the United States and elsewhere, prospective teachers of secondary mathematics are usually required to complete numerous advanced mathematics courses before obtaining certification. However, several research studies suggest that teachers’ experiences in these advanced mathematics courses have little influence on their pedagogical practice and efficacy. To understand this phenomenon, we presented 14 secondary mathematics teachers with four statements and proofs in real analysis that related to secondary content and asked the participants to discuss whether these proofs could inform their teaching of secondary mathematics. In analyzing participants’ remarks, we propose that many teachers view the utility of real analysis in secondary school mathematics teaching using a transport model, where the perceived importance of a real analysis explanation is dependent upon the teacher’s ability to transport that explanation directly into their instruction in a secondary mathematics classroom. Consequently, their perceived value of a real analysis course in their teacher preparation is inherently limited. We discuss implications of the transport model on secondary mathematics teacher education.

Examining Mathematics Classroom Interactions: Elevating Student Roles in Teaching and Learning

<p style="text-align:justify">This article introduces a model entitled, “Responsive Teaching through Problem Posing” or RTPP, that addresses a type of reform oriented mathematics teaching based on posing relevant problems, positioning students as experts of mathematics, and facilitating discourse. RTPP incorporates decades of research on students’ thinking in mathematics and more recent research on responsive teaching practices. Two classroom case studies are presented. A high school unit on functions is explored utilizing individual research on the part of the teacher to enact RTPP lessons. A middle school teacher enacts a RTPP lesson on proportions and utilizes this model to bridge students’ incorrect additive reasoning strategies with correct multiplicative reasoning strategies. The results showed that both teachers were able to elevate students’ roles in classroom discussions through implementation of RTPP. Individual research conducted by the high school teacher informed his RTPP approach while participation in professional development sessions with a classroom embedded component influenced the middle school teacher’s enactment of RTPP lessons. Both teachers used specific teacher moves within RTPP to relinquish their role as mathematics experts in order to elevate their students’ roles in classroom discussions. The RTPP cycle is offered as a potential model for studying mathematics teaching and learning across a variety of secondary mathematics classrooms.</p>

A snapshot of the role of the textbook in English secondary mathematics classrooms

The role and function of the mathematics textbook has been widely discussed since its inclusion in the Trends in International Mathematics and Science study (TIMSS) in the late nineties. They are a common feature in many classrooms worldwide and have been identified as important vehicles for the promotion of curricula. However, there has also been much debate about the role of a mathematics textbook and as a result there is anecdotal evidence to suggest a decline in the use of mathematics textbooks in England. This paper reports on an examination of the current role of mathematics textbooks in secondary and middle schools in the North-West of England based on teachers self-reported use of mathematics textbooks. The data indicates that for all teachers in this sample who used a mathematics textbook, there is a positive correlation between the number of years teaching experience a teacher has and the amount of their classroom time that is 'textbook driven' and a negative correlation between the number of years' experience a teacher has and the likelihood that they will use a mathematics textbook as their key resource for planning. These teachers also identified as having access to a range of different resources to supplement their use of mathematics textbook and using textbooks in varied ways such as to set reading tasks.

Use of comics to enhance students’ learning for the development of the twenty-first century competencies in the mathematics classroom

This paper discusses the use of comics in teaching mathematics in the secondary mathematics classroom. We explicate how the use of comics in teaching mathematics can prepare students for the twenty-first century competencies. We developed an alternative teaching package using comics for two lower secondary mathematics topics. This alternative teaching package consists of (1) several sets of comic strips expounding all related mathematical concepts in a lively way; (2) tiered practice questions for learning reinforcement; and (3) a set of proposed lesson outlines with suggestions on how to use the comics for mathematics teaching. We also report how one of the teachers in our study used this teaching package in her mathematics lessons. Her lessons were video-recorded and 11 students were interviewed to help us understand how the mathematics comics lessons were enacted and the students’ perception of comics as instruction. We identified instances in which the teacher tweaked the provided resource to further enhance student learning and incorporated elements of the twenty-first century competencies during her lessons. Through selected student interviews, we also identified instances in which students commented on their gain from the new approach from the perspective of the twenty-first century competencies.

Writing in the secondary mathematics classroom

Writing in the secondary mathematics classroom

Exploring the use of 3D Computer-Aided Design and 3D Printing for STEAM Learning in Mathematics

This snapshot explores the use of 3D computer-aided design (CAD) and 3D printing for teaching about the volume of solids in junior secondary mathematics classrooms. An open-ended class project involving the design (in a CAD environment), calculation (on paper) and printing of 3D objects (using a 3D printer) was offered to students aged 13 to 15 in three mathematics classes. Qualitative data was collected in the form of video recordings of the students’ communications (while working both with and away from the computers), and in the form of students’ calculations and written reflections (as part of their projects). These observations revealed that the students developed a discourse about volume of composite solids that was inextricably linked to the 3D CAD environment, and that the 3D printing technology enabled an integrated STEAM learning experience for the students. Implications about task design and extensions are discussed in relation to STEAM learning.

Graphing Calculators in the Secondary Mathematics Classroom

Graphing Calculators in the Secondary Mathematics Classroom

Smart girls traversing assemblages of gender and class in Australian secondary mathematics classrooms

ABSTRACTI examine experiences of former Australian schoolgirls in relation to mathematics during secondary school. This research scrutinises misunderstandings about success and impact on subject choice that can result in post-schooling trajectories that limit what girls can do in their lives beyond school. I examine ways affective relationality, as a sense of embodied belonging, may influence participation in subjects. I frame the discussion using the Baradian concept of intra-action, a co-production that engages an ethic of non-coincidence. For these participants, a reductive high-stakes testing environment and aspirations to become a master subject evoke a powerful not good enough assemblage. The responsibility to achieve enough success incites a soliciting of a particular self in affective regulation. The dread of not excelling in mathematics was often too much to endure thus participants chose to discontinue studying mathematics. They understood this as a sensible solution to prevent vulnerability, as not good enough.

New Standards Require Teaching More Statistics

Mathematics teacher education programs often need to respond to changing expectations and standards for K-12 curriculum and accreditation. New standards for high school mathematics in the United States include a strong emphasis in statistics. This article reports results from a mixed methods cross-institutional study examining the preparedness of preservice secondary mathematics teachers to teach statistics and identifying factors and experiences that influence their preparedness. Our results suggest that the cohort of teachers entering secondary mathematics classrooms in 2015-2016 were not well prepared to teach statistics. Specific suggestions are given for how teacher education programs must rise to the challenge of preparing their graduates to teach statistics.

Learning to notice important student mathematical thinking in complex classroom interactions

Noticing students' mathematical thinking is a key element of effective instruction, but novice teachers do not naturally engage in this practice. Prospective secondary school mathematics teachers were engaged in an intervention grounded in analysis of minimally edited video from local secondary school mathematics classrooms; the goal was to support their ability to notice important student thinking within the complexity of instruction. Evidence of participants' learning in five iterations of the intervention is discussed, including their focus on student mathematical thinking, their ability to discuss the mathematics in that thinking, and their ability to notice particular high-leverage instances of student thinking.

Theorizing Participation, Engagement and Community for Primary and Secondary Mathematics Classrooms

Student engagement and participation in mathematics learning is increasingly mentioned in Australian policy and curriculum documents that focus on ways to improve student achievement. However, such ways are not always made clear, nor is what constitutes participation, engagement and community in primary and secondary mathematics classrooms. These elements are theorised and discussed to identify their meaning and their influences on teacher and student engagement in mathematics learning.

Examining the Relationship between Secondary Mathematics Teachers’ Self-efficacy, Attitudes, and Use of Technology to Support Communication and Mathematics Literacy

The rich language surrounding mathematical concepts often is reduced in many classrooms to a narrow process of memorizing isolated procedures with little context. This approach has proven to be detrimental to students’ ability to understand mathematics at deeper levels and remain engaged with this content. The current generation of students values technology as a natural, and often preferred method, for communication. These preferences provide teachers a unique opportunity to extend mathematics communication beyond the classroom. This study sought to understand secondary mathematics teachers’ use of communication technology and the relationship between variables that may contribute to a teacher’s decision to integrate technology for this purpose. Using a descriptive quantitative approach, the research investigated the relationship between teachers’ self-efficacy, attitudes, and the use of communication technology in secondary education mathematics classrooms. A total of 90 teachers in grades 7-12 participated. Results revealed a significant relationship between teachers’ attitudes toward using technology for communication and personal self-efficacy (p < .05), yet few reported using technology in this way. An important recommendation from this study is to investigate why teachers who demonstrate key positive indicators for technology integration are not capitalizing on the potential that communication technology provides to cultivate mathematics communication and literacy.

Building Bridges: Barriers to Parent Engagement Faced by Secondary Mathematics Teachers

Although parent engagement is widely supported by research, it is largely absent in the secondary mathematics classroom. Limited preservice teacher education and perceptions surrounding teacher professionalism are discussed as barriers to engaging parents. Math teachers are additionally inhibited by the antagonistic portrayal of parents in the literature and in the media, e ectively alienating parents in the minds of teachers. We suggest a shift in the language used to discuss math education and the positioning of parents regarding knowledge as a way to enable parent engagement and build relationships of trust, which can transform otherwise di cult exchanges between teachers and parents.