Indicators of middle school students' mathematics enjoyment and confidence

A study involving 916 students spanning grades 5–8 was conducted to investigate indicators that may contribute to enjoyment and confidence in mathematics. For this group of middle school students, mathematics enjoyment, mathematics confidence, and attitudes toward school were found to generally decline across grade levels. Mathematics enjoyment and confidence were also found to differ significantly based upon student preferences for future careers. Gender differences as well as similarities regarding predictors of mathematics enjoyment and confidence were identified. Specifically, the best predictor for end of year mathematics enjoyment for males was beginning of year attitude toward school, while the most significant predictor of end of year enjoyment for females was beginning of year dispositions toward mathematics (semantic perception). A strong relationship between mathematics enjoyment and confidence overall was found, with indications that activities that increase mathematics enjoyment contribute to increased confidence, and also that activities that increase mathematics confidence contribute to increased enjoyment.     

Three modes of STEM integration for middle school mathematics teachers

Of the four subjects in an integrated science, technology, engineering, and mathematics (STEM) approach, mathematics has not received enough focus. This could be in part because mathematics teachers may be apprehensive or unsure about how to implement integrated STEM education in their classrooms. There are benefits to integrated STEM in a mathematics classroom though, including increased motivation, interest, and achievement for students. This article discusses three methods that middle school mathematics teachers can utilize to integrate STEM subjects. By focusing on open‐ended problems through engineering design challenges, mathematical modeling, and mathematics integrated with technology middle school students are more likely to see mathematics as relevant and valuable. Important considerations are discussed as well as recent research with these approaches.     

Centripetal and centrifugal language forces in one elementary school second language mathematics classroom

Research on the learning and teaching of mathematics in contexts of language diversity has highlighted a number of common tensions that arise in a variety of contexts. These tensions can be explained by Bakhtin’s characterization of two sets of forces that are present in any utterance: centripetal forces represent the drive for unitary language, standardisation and linguistic hegemony; centrifugal forces represent the presence of heteroglossia, stratification and decentralisation. In this paper, I use this theoretical perspective to examine ethnographic data from a study of a second language mathematics classroom in Canada, in which the students are almost all speakers of Cree, one of the original languages of Canada. My analysis highlights three situations in which the tension between centripetal and centrifugal forces is particularly salient: the students’ use of Cree; working on mathematical word problems; and producing mathematical explanations.     

Conceptions of Turkish mathematics teachers about the effectiveness of classroom teaching

This study investigated how Turkish mathematics teachers evaluate the effectiveness of classroom teaching in terms of improving students’ mathematical proficiency. To this purpose, teachers were asked to evaluate a mathematics lesson as presented them in a vignette. By means of cluster analysis, the participants’ evaluations of the lesson were described in five thematic dimensions, which could be further assembled into two overriding categories: students’ understanding of the subject, and teachers’ classroom practices. The overall aim of the current paper is to propose a preliminary model of the framework that Turkish mathematics teachers use to evaluate a mathematics lesson.     

Investigations and explorations in the mathematics classroom

In Portugal, since the beginning of the 1990s, problem solving became increasingly identified with mathematical explorations and investigations. A number of research studies have been conducted, focusing on students’ learning, teachers’ classroom practices and teacher education. Currently, this line of work involves studies from primary school to university mathematics. This perspective impacted the mathematics curriculum documents that explicitly recommend teachers to propose mathematics investigations in their classrooms. On national meetings, many teachers report experiences involving students’ doing investigations and indicate to use regularly such tasks in their practice. However, this still appears to be a marginal activity in most mathematics classes, especially when there is pressure for preparation for external examinations (at grades 9 and 12). International assessments such as PISA and national assessments (at grades 4 and 6) emphasize tasks with realistic contexts. They reinforce the view that mathematics tasks must be varied beyond simple computational exercises or intricate abstract problems but they do not support the notion of extended explorations. Future developments will show what paths will emerge from these contradictions between promising research and classroom reports, curriculum orientations, professional experience, and assessment frameworks and instruments.     

Visualization and art in the mathematics classroom

In this paper we summarize our concepts and practice on computer-aided mathematical experimentation, and illustrate them byMathematica projects that we have developed for our research and the courses “Computer-aided mathematical modelling” and “Computer Algebra I–II” held for students of life sciences at University of Szeged and computational engineering at TFH Berlin, University of Applied Sciences.     

Ancient accounting in the modern mathematics classroom

Florida State University owns a collection of twenty-five cuneiform tablets, acquired from Edgar J Banks in the 1920s. We describe their rediscovery, present an edition of one of them (a twenty-first century BC labour account from the Sumerian city of Umma), and discuss their potential for use in undergraduate mathematics education.1 ¹We are very grateful to Steve Garfinkle, Denise Giannino, John Larson, Lucia Patrick, Plato L Smith II, and Giesele Towels for their help in the research and writing of this article.      

Experimental mathematics and proofs in the classroom

Experimental mathematics is a serious branch of mathematics that starts gaining attention both in mathematics education and research. We given examples of using experimental techniques (not only) on the classroom. At first sight it seems that introducing experiments will weaken the formal rules and the abstractness of mathematics that are considered a valuable contribution to education as a whole. By putting proof and experiment side by side we show how this can be avoided. We also highlight consequences of experimentation for educational computer software.     

Implementing a flipped classroom approach in a university numerical methods mathematics course

This paper describes and analyses the implementation of a ‘flipped classroom’ approach, in an undergraduate mathematics course on numerical methods. The approach replaced all the lecture contents by instructor-made videos and was implemented in the consecutive years 2014 and 2015. The sequential case study presented here begins with an examination of the attitudes of the 2014 cohort to the approach in general as well as analysing their use of the videos. Based on these responses, the instructor makes a number of changes (for example, the use of ‘cloze’ summary notes and the introduction of an extra, optional tutorial class) before repeating the ‘flipped classroom’ approach the following year. The attitudes to the approach and the video usage of the 2015 cohort are then compared with the 2014 cohort and further changes that could be implemented for the next cohort are suggested.     

Working at scale to initiate ongoing validation of learning trajectory-based classroom assessments for middle grade mathematics

The paper reports on the design and validation argument for classroom assessments within a digital diagnostic assessment system built on learning trajectories (LTs). It consists of a learning map of nine big ideas, 25 relational learning clusters, and 62 LTs for grades 6−8 mathematics. Students take cluster assessments, and teachers use the data to adapt instruction. An ongoing validation process is presented with data for an algebra cluster. Validation among practitioners, learning scientists, and psychometricians is conceptualized as examining and adjusting inter-level, intra-level, and construct-irrelevant variation in measures of item difficulty and deploying item response theory modeling followed by sequential regressions. Using data from 37,000 assessments collected over three years at 3 middle schools, 167 potentially non-conforming items of the 676 calibrated items (24 %) were identified and revised. The paper discusses how the trajectories and map were refined through a combination of data analysis and feedback from practitioners.     

Pre-service mathematics teachers become full participants in inquiry investigations

Research is described concerning the effectiveness of inquiry-based laboratory environments created in US mathematics/science education programme courses. Laboratory projects were conducted using a framework that allowed pre-service teachers to explore, analyse, and communicate ‘investigable’ realms of physical phenomena. Goals were for pre-service teachers to experience the value of learning in an inquiry-enhanced environment and to engage in contextualized mathematics so they would utilize this instruction in their future classrooms. It is proposed that inquiry-based laboratories are needed within the mathematics classroom in order to allow students the opportunity to contextualize, to connect to other disciplines, and to experience mathematical concepts. Pre-service teachers were expected to pursue conjectures, collect data, think critically, and communicate findings. This qualitative research shows how the use of inquiry can complement the learning of mathematical content and educational strategies for pre-service teachers. Results provide detailed information for teacher educators regarding instructional design of contextualized mathematical inquiry.     

Using narrative inquiry for investigating the becoming of a mathematics teacher

This article presents narrative inquiry as a method for research in mathematics education, in particular the study of how pre-service teachers’ views of mathematics develop during elementary teacher education. I describe two different, complementary approaches to applying narrative analysis, one focusing on the content of a narrative, the other focusing on the form. The examples discussed are taken from interviews with and teaching portfolios compiled by four pre-service teachers. In analysing the content of the students’ narratives, I use emplotment to construct a retrospective explanation of how one pre-service teacher’s own experiences at school were reflected in the development of her mathematical identity. In analysing the form of the narratives, I also look at how the students told their stories, using linguistic features, for example, to identify core events in the accounts. This particular focus seems to be promising in locating turning points in the trainees’ views of mathematics.     

The mathematics of medical imaging in the classroom

The article presents an integrated exposition of aspects of secondary school mathematics and a medical science specialty together with related classroom activities. Clinical medical practice and theoretical and empirical literature in mathematics education and radiology were reviewed to develop and pilot model integrative classroom topics and activities. The techniques of computer-axial tomography (CT) and positron emission tomography (PET) are discussed, followed by a presentation of accessible mathematical applications in numeration and linear algebra for use in a high school classroom. This discussion of the mathematics of a medical speciality, and the related activities, might not only offer teachers and students specific examples of the connections between their everyday study and a professional discipline, but also might foster further investigation into the importance and relevance of mathematics in other technology-based careers.     

A survey of advanced mathematics topics: a new high school mathematics class

The number of students pursuing undergraduate degrees in mathematics is decreasing. Research reveals students who pursue mathematics majors complained about inadequate high school preparation in terms of disciplinary content or depth, conceptual grasp, or study skills. Unfortunately, the decrease in the number of students studying advanced mathematics occurs at a time when the world's technological drive demands students have improved critical thinking and problem-solving skills. This paper suggests one solution for this alarming problem: a high school class offered to seniors as a means of preparing them for the rigours of college level mathematics while simultaneously increasing their motivation to pursue advanced mathematics. This paper provides the course scope, goals, structure, and analysis of how the curriculum aligns to professional standards. Although this programme has not currently been field tested, the authors are convinced of its impact. Once implemented and properly taught, the proposed Survey of Advanced Mathematics Topics class could increase the quantity and quality of students pursuing studies in mathematics at the university level.     

Potential scenarios for Internet use in the mathematics classroom

Research on the influence of multiple representations in mathematics education gained new momentum when personal computers and software started to become available in the mid-1980s. It became much easier for students who were not fond of algebraic representations to work with concepts such as function using graphs or tables. Research on how students use such software showed that they shaped the tools to their own needs, resulting in an intershaping relationship in which tools shape the way students know at the same time the students shape the tools and influence the design of the next generation of tools. This kind of research led to the theoretical perspective presented in this paper: knowledge is constructed by collectives of humans-with-media. In this paper, I will discuss how media have shaped the notions of problem and knowledge, and a parallel will be developed between the way that software has brought new possibilities to mathematics education and the changes that the Internet may bring to mathematics education. This paper is, therefore, a discussion about the future of mathematics education. Potential scenarios for the future of mathematics education, if the Internet becomes accepted in the classroom, will be discussed.