Elementary School Teachers’ Use of Technology During Mathematics Teaching

Various educational technologies have been advanced as potential vehicles to transform teaching and learning. Still, research studies have documented that primary school teachers struggle to integrate technology in meaningful ways. This article presents the findings of a year-long study in which the author frequently observed three primary school teachers’ enactments of technology into their mathematics teaching. Each teacher was observed between 25 and 30 times during the school year. The types of technologies used as well as the types of mathematical tasks and problems that participants posed while teaching with technology were inductively analyzed. Inductive qualitative analyses indicated that participants’ technology use focused on presentation technologies such as the document camera or interactive whiteboard more than computer-based technologies or interactive activities. Further, teachers varied widely in their enacted pedagogies while integrating technology, and two participants demonstrated more frequent enactments of learner-centered pedagogies toward the end of the school year. Implications for researching teachers’ use of technology in the future are also shared.     

Middle School Teachers’ Use of Mathematics to Make Sense of Student Solutions to Proportional Reasoning Problems

Mathematics teacher education aims to improve teachers’ use of mathematical knowledge to support teaching and learning, an aspect of pedagogical content knowledge (PCK). In this study, we interviewed teachers to understand how they used mathematics to make sense of student solutions to proportional reasoning problems. The larger purpose was to find accurate ways of categorizing teachers’ ability to do this vital aspect of teaching and thereby to inform assessment, teacher education, and professional development. We conjectured that teachers’ PCK for proportional reasoning could be reliably described in terms of attention to quantitative meanings in story problem contexts and in terms of understanding naïve forms of proportional reasoning. Instead, our findings reveal that individual teachers used a variety of means to make sense of (1) cognitively similar student solutions to different tasks and (2) mathematically related steps of a student solution within a single task. These findings illustrate the complexity of PCK for the topic of proportional reasoning and suggest the limits of what can be inferred about teacher knowledge from teachers’ evaluations of student solutions. We discuss implications for teacher education and assessment.     

Preservice Middle and High School Mathematics Teachers’ Strategies when Solving Proportion Problems

The purpose of this study was to investigate eight preservice middle and high school mathematics teachers’ solution strategies when solving single and multiple proportion problems. Real-world missing-value word problems were used in an interview setting to collect information about preservice teachers’ (PSTs) reasoning about proportional relationships. An explanatory case study methodology with multiple cases was used to make comparisons within and across cases. Analysis of the semi-structured interviews with each PST revealed that using practical problems, in which plastic gears and a mini balance system were provided, and multiple proportion problems facilitated the PSTs’ recognition of the proportional relationships in their solutions. Therefore, they avoided using cross-multiplication and erroneous strategies in those problems. Among the strategies that the PSTs used in solving single and multiple proportion problems, the ratio table strategy was the most frequent and effective strategy. The ratio table strategy enabled the PSTs to recognize the constant ratio and product relationships more than the other strategies. The results of this study illuminate how PSTs reason about proportional relationships when they cannot rely on computation methods like cross-multiplication.     

Using Variables in School Mathematics: Do School Mathematics Curricula Provide Support for Teachers?

This study employed content analysis to examine 3 popular middle-grades mathematics curricula in the USA on the support they provide for teachers to implement concepts associated with variables in school mathematics. The results indicate that each of the 3 curricula provides some type of support for teachers, but in a varied amount and quality. More specifically, whereas the University of Chicago School Mathematics Project (UCSMP) curriculum provides support for teachers on several aspects of using variables in school mathematics, the support found in the Connected Mathematics 2 and the Math Connects curricula focused mainly on one conception of variables—namely, the use of variables as quantity that varies in the Connected Mathematics 2 curriculum and the use of variables as specific unknowns in the Math Connects curriculum. Overall, the UCSMP curriculum provides the most support for teachers, followed by the Connected Mathematics 2 curriculum, with the Math Connects curriculum recording the least support for teachers to enact variable concepts. It is worth pointing out that, although the 3 curricula collectively provide guidance for teachers to implement variable ideas within meaningful real-world contexts, the supports identified in the respective curriculum were not sufficient in addressing all of the areas that are essential for teaching the many concepts associated with variables in school mathematics effectively. Recommendations for curriculum developers and for international researchers with interest in the roles of variables in school mathematics are provided.     

Prospective Early Childhood and Elementary School Mathematics Teachers’ Concept Images and Concept Definitions of Triangles

International Journal of Science and Mathematics Education - This study presents a characterization of prospective early childhood teachers’ (ECEPTs) and prospective elementary school...     

Middle School Students’ Reasoning in Nonlinear Proportional Problems in Geometry

In this study, we investigate sixth, seventh, and eighth grade students’ achievement in nonlinear (quadratic or cubic) proportional problems regarding length, area, and volume of enlarged figures. In addition, we examine students’ solution strategies for the problems and obstacles that prevent students from answering the problems correctly by using a mixed method research design. A total of 935 middle school students were given a paper-pencil test and 12 of them were interviewed. Findings indicated that achievement of the participants were low and that students used a limited number of strategies for solving the problems. In addition, these strategies were found to have lacked the argument of the linear proportional and nonlinear proportional relationships among length, area, and volume concepts for most of the participants’ answers. Moreover, analysis revealed that the confusion of linear proportional and nonlinear proportional relationships and misinterpretation of additive and multiplicative relationships were serious obstacles while solving the nonlinear proportional problems related to the area and volume of enlarged figures.     

The Progression of Prospective Teachers’ Conceptions of School Science Content

The purpose of the present work is to describe the progression in the conceptions of prospective primary teachers about school science content while they were participating in three teacher education courses following the same constructivist oriented strategy. The participants’ written output was analyzed in various categories—selection of content, types of content and their relationships, levels of complexity, and presentation of content to pupils. There was evidence for some progress in their conceptions of the content from a traditional view to another that we termed intermediate since it did not reach the vision that we consider to be the most complex. Finally, we present a General Itinerary of Progression on school content that could serve as a referent for initial teacher education.     

Dynamic Changes in Peer Victimization and Adjustment Across Middle School: Does Friends’ Victimization Alleviate Distress?

Although some adolescents are chronically bullied throughout middle school, others may only experience peer victimization temporarily. This study examined the effects of time-invariant (average level) and time-varying (year-to-year) victimization experiences across middle school on adolescents’ depressive symptoms, somatic complaints, and self-blame. A key question was whether friends’ victimization buffered students from their victimization-related distress. The diverse sample (n = 5,991) was surveyed four times between sixth and eighth grade (M_age at sixth grade = 11.54 years). Three-level multilevel models revealed both time-invariant and time-varying effects of victimization on adjustment, but these maladaptive associations were attenuated when adolescents’ friends experienced more victimization across middle school. The results suggest that even temporarily victimized youth may have unmet mental health needs, and sharing social plight with friends can protect victims.     

Prospective Teachers’ Difficulties in Interpreting Elementary Phenomena of Electrostatic Interactions: Indicators of the status of their intuitive ideas

Student teachers were tested before and after a teaching unit on electrostatic interactions in an attempt to consider their intuitive ideas and concept development. A study was made of students’ explanations of basic interactions: those between two charged bodies, and those between a charged body and a neutral body. Two indicators of the cognitive status of the explanations were investigated: “context dependence” and “certainty or confidence index”. This allowed cognitive comparisons to be established between the explanations of different electrostatic interactions, and between the degrees of difficulty they represent for satisfactory conceptual evolution. The greatest difficulties were found with explanations of the phenomena of electrostatic induction. The sample consisted of 52 students in primary school teacher education who participated in a teaching unit designed to overcome these obstacles.     

An Investigation of Pre-service Middle School Mathematics Teachers’ Ability to Conduct Valid Proofs,Methods Used,and Reasons for Invalid Arguments

The purposes of this study are to investigate Turkish pre-service middle school mathematics teachers’ ability in conducting valid proofs for statements regarding numbers and algebra in terms of their year of enrollment in a teacher education program, to determine the proof methods used in their valid proofs, and to examine the reasons for their invalid arguments. A proof questionnaire containing three proof statements was administered to 115 pre-service middle school mathematics teachers in a large state university in Ankara, Turkey. The results showed that more than half of the pre-service teachers were able to conduct valid proofs for the given statements. In terms of year levels, it was seen that the seniors were the least successful group in conducting valid proofs for each statement. When pre-service teachers’ valid proofs were analyzed, it was concluded that mathematical induction and direct proof were the mostly used methods for the given statements. When pre-service teachers’ invalid arguments were analyzed, it was seen that “inserting numbers to verify the given statement” and “rewriting the givens in the statement” were the common reasons for stating invalid arguments.     

Middle School Science Teachers’ Confidence and Pedagogical Practice of New Literacies

Due to the rapid advancements of information and communication technologies (ICTs), educational researchers argue that multimodal and new literacies should become common practices in schools. As new ICTs emerge and evolve, students need the new literacies skills and practices to successfully participate fully in the civic life of a global community. Are teachers prepared to integrate ICTs in the classroom to develop students’ new literacies skills? The purpose of this study is to suggest a new literacies framework that guides ICTs integration and supports scientific inquiry, as well as investigate middle school teachers’ confidence to practice new literacies in science classrooms. The study adopted mixed-methodology design, surveyed 32 middle school science teachers’ ICTs and new literacies skills, and randomly observed 15 teachers’ new literacies practices in the classrooms. The results revealed that even though teachers have high confidence in using ICTs, the meaningful technology integration and new literacies practices were scarcely observed in their classroom practices.     

Preservice Mathematics Teachers’ Selective Attention and Professional Knowledge–Based Reasoning About Students’ Statistical Thinking

International Journal of Science and Mathematics Education - This study examined preservice mathematics teachers’ selective attention and knowledge-based reasoning as they viewed a statistics...     

Investigating Upper Secondary School Teachers’ Conceptions: Is Mathematical Reasoning Considered Gendered?

This study examines Swedish upper secondary school teachers’ gendered conceptions about students’ mathematical reasoning: whether reasoning was considered gendered and, if so, which type of reasoning was attributed to girls and boys. The sample consisted of 62 teachers from six different schools from four different locations in Sweden. The results showed that boys were significantly more often attributed to memorised reasoning and delimiting algorithmic reasoning. Girls were connected to gamiliar algorithmic reasoning, a reasoning type where you use standard method when solving a mathematical task. Creative mathematical founded reasoning, which is novel, plausible and founded in mathematical properties, was not considered gendered.

     

Commitment to Teach in Under-Resourced Schools: Prospective Science and Mathematics Teachers’ Dispositions

In this exploratory study, we sought to gain an understanding of what motivates prospective teachers who are Noyce Scholars at a research-intensive southeastern US university to commit to teaching secondary level science or mathematics in school districts that have a high proportion of students who come from low-socioeconomic households. An interpretive methodology revealed three themes associated with Noyce Scholars’ motivations to teach (1) awareness of educational challenges, (2) sense of belonging to or comfort with diverse communities, and (3) belief that one can serve as a role model and resource. The paper describes and compares the significance of each theme among six prospective teachers who identify with the schooling experiences of students who came from low-income or poor households and nine prospective teachers who identify with the schooling experiences in a middle-income school or district. The implication of this study supports the importance of recruiting prospective science and mathematics teachers who have knowledge of and a disposition to work with learners from low-income or poor households, even if those prospective teachers are not themselves the members of under-served populations.     

Investigating Upper Secondary School Teachers’ Conceptions: Is Mathematical Reasoning Considered Gendered?

This study examines Swedish upper secondary school teachers’ gendered conceptions about students’ mathematical reasoning: whether reasoning was considered gendered and, if so, which type of reasoning was attributed to girls and boys. The sample consisted of 62 teachers from six different schools from four different locations in Sweden. The results showed that boys were significantly more often attributed to memorised reasoning and delimiting algorithmic reasoning. Girls were connected to gamiliar algorithmic reasoning, a reasoning type where you use standard method when solving a mathematical task. Creative mathematical founded reasoning, which is novel, plausible and founded in mathematical properties, was not considered gendered.     

Middle School Science Teachers’ Discursive Purposes and Talk Moves in Supporting Students’ Experiments

Science & Education - The paper reports qualitative findings from a study about how science teachers enacted discursive purposes and talk moves to support the students’ experiments....     

Prospective and In-Service Mathematics Teachers’ Attention to a Rich Mathematics Task While Planning its Implementation in the Classroom

International Journal of Science and Mathematics Education - This study explores secondary mathematics teachers’ attention to the three components of Jaworski’s (1992) “teaching...