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.     

An Investigation of Relationships between Seventh-Grade Students' Beliefs and Their Participation during Mathematics Discussions in Two Classrooms

As mathematics teachers attempt to promote classroom discourse that emphasizes reasoning about mathematical concepts and supports students' development of mathematical autonomy, not all students will participate similarly. For the purposes of this research report, I examined how 15 seventh-grade students participated during whole-class discussions in two mathematics classrooms. Additionally, I interpreted the nature of students' participation in relation to their beliefs about participating in whole-class discussions, extending results reported previously (Jansen, 2006) about a wider range of students' beliefs and goals in discussion-oriented mathematics classrooms. Students who believed mathematics discussions were threatening avoided talking about mathematics conceptually across both classrooms, yet these students participated by talking about mathematics procedurally. In addition, students' beliefs about appropriate behavior during mathematics class appeared to constrain whether they critiqued solutions of their classmates in both classrooms. Results suggest that coordinating analyses of students' beliefs and participation, particularly focusing on students who participate outside of typical interaction patterns in a classroom, can provide insights for engaging more students in mathematics classroom discussions.     

Capitalizing on Emerging Technologies: A Case Study of Classroom Blogging

The challenge many teachers face is how to incorporate new technology into their classrooms that strengthens classroom learning by capitalizing on students’ media literacies. Blogs, a new and innovative technological tool, can be used in math and science classrooms to support student learning by capitalizing on students’ interests and familiarity with on‐line communication. This study explores the emerging blogging practices of one high school mathematics teacher and his class to explore issues of intent, use, and perceived value. Data sources for this case included one year's worth of blog content, an interview with the facilitating teacher, and students ‘perceptions of classroom blogging practices. Findings indicate that (1) teachers’ intentions focused on creating additional forms of participation as well as increasing student exposure time with content; (2) blogs were used in a wide variety of ways that likely afforded particular benefits; and (3) both teacher and students perceived the greater investment to be worthwhile. The findings are used to critically consider claims made in the literature about the potential of blogging to effectively support classroom learning.     

Influence of gender,single-sex and co-educational schooling on students’ enjoyment and achievement in mathematics

This research investigates the influence that gender, single-sex and co-educational schooling can have on students’ mathematics education in second-level Irish classrooms. Although gender differences in mathematics education have been the subject of research for many years, recent results from PISA (Programme for International Student Assessment) show that there are still marked differences between the achievement and attitude of male and female students in Irish mathematics classrooms. This paper examines the influence of gender in more detail and also investigates the impact of single-sex or co-educational schooling. This is a follow on study which further analyses data collected by the authors when they designed a pedagogical framework and used this to develop, implement and evaluate a teaching intervention in four second-level Irish schools. The aim of this pedagogical framework was to promote student interest in the topic of algebra through effective teaching of the domain. This paper further analyses the quantitative data collected and investigates whether there were differences in students’ enjoyment and achievement scores based on their gender and whether they attended single-sex or co-educational schools.     

Motivations and meanings of students' actions in six classrooms from Germany, Hong Kong and the United States

This article presents an analysis of about 100 interviews with students from eight-grade classrooms in Berlin, Hong Kong and San Diego that reconstructs student motivations and the meanings they attribute to classroom activities. The data of the six classrooms were produced in the Learner's Perspective Study (LPS). The LPS is an international collaboration of researchers investigating practices in eighthgrade mathematics classrooms in 13 countries. Although not the central focus of the research, the case study of six classrooms revealed a variety of students' beliefs and perceptions, which are the focus of this article. These correspond to the possibilities the classroom practices offer. The study also reveals some similarities among student motives and concerns across classrooms. The findings are an important reminder that basing a curriculum upon an alternative vision calls for changing mathematical content as well as the social relations that are established through teaching methods and principles of evaluation.     

A study of early career teachers’ practices related to language and language diversity during mathematics instruction

The role of language in mathematics teaching and learning is increasingly highlighted by standards and reform movements in the US. However, little is known about teachers’, and especially early career teachers’ (ECTs) practices and understandings related to language in mathematics instruction. This multiple case study explored the language-related understandings and practices of six ECTs in diverse elementary classrooms. Using iterative cycles of analysis, we found that all ECTs regularly attended to students’ mathematical vocabulary use and development. Yet, there was variability in ECTs’ focus on how to teach mathematical vocabulary, expectations for students’ precise use of mathematical terminology, and the use of multiple languages during instruction. These findings indicate that ECTs need more targeted support during teacher preparation and early career teaching in order to better support all students’ language development in the mathematics classroom.     

Geometry‐Related Children's Literature Improves the Geometry Achievement and Attitudes of Second‐Grade Students

Use of mathematics‐related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi‐experimental study of two second‐grade classrooms assessed whether daily inclusion of geometry‐related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the hypothesis, only the students in the classroom with a strong emphasis on geometry‐related children's literature showed a significant improvement in their attitudes about geometry over time. While both classes improved their geometry performance over the 4 weeks of the study, the class with a strong emphasis on geometry‐related literature improved significantly more (51.2%) than the control class (33.47%). Children's literature can provide a useful and interesting context in which students can develop their understanding of geometry.     

Measuring Reform Practices in Science and Mathematics Classrooms: The Reformed Teaching Observation Protocol

The National Science Foundation has funded 22 Collaboratives for Excellence in Teacher Preparation. Despite the remarkable allocation of resources to this effort, it has proven exceptionally difficult to demonstrate the effectiveness of collaborative reform. In large part, this has resulted because of the difficulty of defining and measuring reform. The Reformed Teaching Observation Protocol (RTOP) was designed by the Evaluation Facilitation Group of the Arizona Collaborative for Excellence in the Preparation of Teachers (ACEPT). It is a 25‐item classroom observation protocol that is (a) standards based, (b) inquiry oriented, and (c) student centered. This instrument has provided the definition for reform and the basis for evaluation of the ACEPT collaborative. The data upon which this report is based were collected over a period of more than 2 years from 153 public school, college, and university mathematics and science classrooms. A trained team of observers consisting of two faculty members and seven graduate students was able to achieve exceptionally high levels of interrater reliability. Internal consistency, as estimated by Cronbach's alpha, was also remarkably high. Correlation coefficients ranging from 0.88 to 0.97 between RTOP scores for classrooms, and mean normalized gain scores for students in those classrooms on achievement measures demonstrate that reform, as defined by ACEPT and measured by the RTOP, has been effective.     

Studies of argumentation in primary mathematics education

The participation of students in processes of collective argumentation is seen as a fundamental condition for enabling mathematics learning in classroom settings. Using data from a finished research project on argumentation in primary mathematics classrooms it will be shown, that in elementary education these processes are of a narrative character.     

Middle School Mathematics Teachers Learning to Teach With Calculators and Computers

This paper reports the results of a project in which experienced middle grades mathematics teachers immersed themselves in calculator and computer use for both doing and teaching mathematics and prepared themselves as leaders for communicating their knowledge to colleagues. Project evaluation included formal observation of students while they used technology in learning mathematics. Classroom observation data suggested that computers hold somewhat more attraction for students than calculators. Overall, students in all 13 classes, independent of the type of technology used, were observed to be off-task 3% of the time. These data suggested a classroom environment in which the teacher worked hard to engage students in mathematical activity. The fact that students were observed off-task so little is encouraging. The difference in off-task behaviors for calculators versus computers suggests that different technologies will indeed have different effects on students. It appears that the introduction of technologies in classrooms altered the ways teachers taught.     

Talking mathematically: An analysis of discourse communities

Discourse has always been at the heart of teaching. In more recent years, the mathematics education community has also turned its attention towards understanding the role of discourse in mathematics teaching and learning. Using earlier classifications of discourse, in this paper, we looked at three types of classrooms: classrooms that engage in high discourse, low discourse and a hybrid of the two. We aimed to understand how the elements of each discourse affected classroom learning, relationships between teachers and students, and participatory structures for students. Overall, our findings highlight the important relationship between cognitively demanding tasks and mathematical talk, and the power of discourse as a “thinking device” as opposed to mere conduit of knowledge. Our work also points to the under-theorized nature of hybrid discourse in mathematics classrooms, thereby providing some directions for pedagogy and further research.     

Cultural distance and identities-in-construction within the multicultural mathematics classroom

In this paper we present and exemplify our interpretation of some theoretical constructs that have proved useful to our understanding of the complexity of multicultural mathematics classrooms. Constructs such as culture, cultural distance, cultural conflict and identities-in-construction have oriented our study of the complexity of highly multicultural mathematics classrooms in Barcelona. The purpose of this paper is to discuss how cultural distance arising from the different meanings that students, being local or immigrant, inevitably bring to the mathematics classroom may turn into cultural conflicts when cultural interaction is not facilitated through classroom discourse. The lack of cultural interaction and communication may give rise to strong negative feedings and refusal to participate on the side of the students. Students' nonparticipation can be understood as an active response to cultural distance and negative opinions in order to safeguard the identities they (wish to) construct within a context that they perceive as hostile.     

Characterizing exemplary mathematics instruction in Japanese classrooms from the learner’s perspective

This paper aims to examine key characteristics of exemplary mathematics instruction in Japanese classrooms. The selected findings of large-scale international studies of classroom practices in mathematics are reviewed for discussing the uniqueness of how Japanese teachers structure and deliver their lessons and what Japanese teachers value in their instruction from a teacher’s perspective. Then an analysis of post-lesson video-stimulated interviews with 60 students in three “well-taught” eighth-grade mathematics classrooms in Tokyo is reported to explore the learners’ views on what constitutes a “good” mathematics lesson. The co-constructed nature of quality mathematics instruction that focus on the role of students’ thinking in the classroom is discussed by recasting the characteristics of how lessons are structured and delivered and what experienced teachers tend to value in their instruction from the learner’s perspective. Valuing students’ thinking as necessary elements to be incorporated into the development of a lesson is the key to the approach taken by Japanese teachers to develop and maintain quality mathematics instruction.     

An “inverse” relationship between mathematics identities and classroom practices among early career elementary teachers: The impact of accountability

This qualitative case study guided by portraiture examines the relationships between three early career elementary teachers’ beliefs about themselves in relation to mathematics (mathematics identities) and their classroom practices. Through autobiographical inquiry, reflective practice, classroom observations, interviews, and artifacts, findings show that all three second grade teachers appeared to have an “inverse” relationship between their mathematics identities and their classroom practices. In this relationship, as negative as they felt about themselves with regards to mathematics, they expended that much more effort to ensure that their students would have positive experiences with it and not be stigmatized by it as they had been. Accountability to schools, students, and parents, to increase student achievement appeared to play an important role in this relationship. Implications for preservice teacher education, inservice professional development, and research on beliefs and practices are discussed.     

Sociocultural Factors Influencing Students' Learning in Science and Mathematics: An Analysis of the Perspectives of African American Students

The voices of African American students reveal sociocultural factors that influence their achievement in science and mathematics classes. Using a sociocultural theoretical framework ( Mercer & Covey, 1980 ), this ethnographic study interpreted the perspectives of five African American students as they discussed their learning experiences in science and mathematics classrooms. This framework acknowledges the vulnerability of the educational system to societal influences that inevitably assert cultural values and norms. The students' discussions provided insight into their beliefs about the varied ways in which sociocultural factors impact their learning in science and mathematics classrooms.     

The Effects of Self-Regulation,Motivation, Anxiety,and Attributions on Mathematics Achievement for Fifth and Sixth Grade Students

For this quantitative study, a total of n = 761 students (58.1% female) from selected fifth- and sixth-grade mathematics classrooms in Alabama were surveyed in order to investigate the relationships between self-regulated learning, motivation, anxiety, attributions and achievement in mathematics. Data analyses revealed that significant contributions are made by motivation and anxiety on both test score and mathematics grade for fifth grade students. Specific factors (e.g., self-efficacy, worry, other, and failure) were related to academic performance while failure attribution was significantly related to mathematics grade. As for sixth grade students, data analyses showed relationships exist between motivation, anxiety and academic performance with specific factors (i.e., self-efficacy, intrinsic value, and worry) significantly predicting both test score and mathematics grade for sixth graders. The findings underlie the importance of motivation and anxiety for students and how these constructs interact to facilitate self-regulation over the course of developing expertise in a domain, such as mathematics.     

The Influence of an Internet‐Based Formative Assessment Tool on Primary Grades Students’ Number Sense Achievement

This study examined primary grades students’ achievement on number sense tasks administered through an Internet‐based formative assessment tool, Assessing Math Concepts Anywhere. Data were analyzed from 2,357 students in teachers’ classrooms who had participated in a year‐long professional development program on mathematics formative assessment, 1,427 students from teachers who had participated in the program in the year prior, and 9,783 students whose teachers had not participated at all. Analyses indicated that all students in the treatment group demonstrated growth, and that student achievement was influenced by the number of times the assessment was used to collect data and make instructional decisions. Further, there was a relationship between districts’ socioeconomic status and growth, meaning students from impoverished backgrounds grew more than their peers.     

Mathematics achievement and interest in mathematics from a differential perspective

In this article, we present results of an empirical study with 500 German students of grades 7 and 8. The study focussed on students' mathematics achievement and their interest in mathematics as well as on the relation between these two constructs. In particular, the results show that the development of an individual student's achievement between grade 7 and grade 8 depends on the achievement level of the specific classroom and therefore on the specific mathematics instruction Interest in mathematics could be regarded a predictor for mathematics achievement Moreover, our findings suggest that the students show hardly any fear of mathematics independent of their achievement level.     

“Mathematicians Would Say It This Way”: An Investigation of Teachers' Framings of Mathematicians

Although popular media often provides negative images of mathematicians, we contend that mathematics classroom practices can also contribute to students' images of mathematicians. In this study, we examined eight mathematics teachers' framings of mathematicians in their classrooms. Here, we analyze classroom observations to explore some of the characteristics of the teachers' framings of mathematicians in their classrooms. The findings suggest that there may be a relationship between a teachers' mathematics background and his/her references to mathematicians. We also argue that teachers need to be reflective about how they represent mathematicians to their students, and that preservice teachers should explore their beliefs about what mathematicians actually do.