Strategy diversity in early mathematics classrooms

Strategic processes are a form of procedural knowledge in which a child knows how to enact a given strategy that improves their capability in problem solving or learning. The solution strategies children use are critical components of their learning, especially in mathematics. Children vary substantially in their knowledge and use of different strategies, and much research has focused on intraindividual strategy variability. However, we do not know if classrooms that evince a broader variety of strategies across children are related to higher mathematics achievement. We investigated the diversity of arithmetical strategies within classrooms and examined the relations between strategy diversity and mathematical achievement as children moved from preschool to kindergarten and first grade. These analyses were applied to data from a large-scale experiment involving 1305 children from 42 schools and 106 classrooms. We created and applied a new method of measuring classroom strategy diversity and related this measure to children’s concurrent and subsequent math achievement. We found that early strategy diversity was strongly related to achievement, but in subsequently, less diversity was so related. We compared these results to the predictions of three theoretical categories and found that our results mainly supported one.     

Affinity spaces,literacies and classrooms: tensions and opportunities

Building communicative competence in textual and multimodal literacies has become a linchpin of learning, of engagement with the world, and of participation in online and blended spaces. Young creators now compose online and with digital tools, often in what we call “user‐generated content affinity spaces” – interest‐based spaces that focus on creating and sharing self‐made content. Such spaces focus on processes of developing users' creations and sharing the products with an audience. These spaces have been inspirations for teachers to reinvigorate classroom practices and expose students to learning opportunities for creation and critique. But questions remain about models of participation in such spaces, especially those that idealise youth who are the most highly engaged while ignoring those whose participation is less visible. Here, we share three experiences of bringing user‐generated content affinity spaces into more formal learning environments and reflect on the tensions emerging from these efforts. We end by outlining steps to develop theory and interventions to navigate tensions and propel the field forward.     

Gender interaction in mathematics classrooms: Reflection and transformation

In this article, studies done on gender in Botswana's classrooms at the junior secondary level, are reported. The initial studies were more quantitative in nature, and dealt with questioning as part of classroom interaction. The studies revealed other gender related issues however, which were observed in more detail later. With the participating teachers, the findings were discussed and a plan for reform in their teaching was drawn up.     

Professional development for practicing mathematics teachers: a critical connection to English language learner students in mainstream USA classrooms

This article examines the effects of changing teacher self-efficacy on student achievement. Results from a quantitative study of mathematics teachers in a USA mid-Atlantic state showed that teachers experienced reduced self-efficacy when working with English language learner students (ELLs) relative to non-ELLs. Further, the article explores professional development opportunities for strengthening teachers’ effectiveness with ELLs. The study utilized a four-part survey instrument based on the Teacher Sense of Efficacy Scale (TSES). All participants (n = 181) were mathematics educators from the highlighted state, and 94 % of them were preK-12 public school practicing classroom teachers. Study results indicate that teachers’ participation in professional development on ELL instruction is positively correlated to their heightened sense of self-efficacy. This finding points to continuing education as a potentially viable approach to reducing academic challenges for ELL students in mainstream mathematics classrooms by developing ever more effective practicing teachers.     

Cogenerated understandings of mindfulness-based breathing in elementary mathematics classrooms

Bringing an awareness of emotions to the fore through mindfulness-based breathing and providing a space to discuss them is a way of promoting teacher and student agency in collectively developing structures specific to their learning environment. The authors explore students', teachers', and researchers' collective sensemaking through cogenerative dialoguing (cogen) about a mindfulness-based breathing practice at the start of mathematics lessons in an elementary classroom. They found that the power of cogen as hybridized space enabled the generation of collective understanding and the potential for all cogen participants to become engaged in an authentic and transformative way in discussing classroom life. The authors argue that the mindfulness-based breathing practice itself acted as a heuristic for thinking about learning environments and, during the reflexive process of thinking about the breathing practice, new forms of classroom culture unfolded both expanding classroom structures and the practice itself, and laying bare otherwise taken-for-granted practices.     

Problem solving strategies of girls and boys in single-sex mathematics classrooms

This study examines patterns in middle-grade boys’ and girls’ written problem solving strategies for a mathematical task involving proportional reasoning. The students participating in this study attend a coeducational charter middle school with single-sex classrooms. One hundred nineteen sixth-grade students’ responses are analyzed by gender according to the solution strategy they used to arrive at their final response to the task. The categories of solution strategies include non-response, purely additive, purely procedural, transition, novice, and mature. The proportions of girls and boys classified as mature in their strategies were essentially equal. However, more than half of girls’ responses were considered purely procedural or purely additive—a proportion double that of boys thus classified.     

Events in learning mathematics: Insights from research in classrooms

In this paper, it is contended that in order to understand individual student's learning in the complexity of the mathematics classroom it is necessary to examine the events that occur before, during, and after learning. To illustrate, the process by which two children each construct new mathematical meanings is examined in this manner. The detailed analyses of each of these events provides insight into the processes by which individual students construct mathematical meanings in classroom settings. The investigation also reveals that the underlying social norms differ from those found in traditional classes, and that this creates different opportunities for learning. It is contended that it is the differences in the norms that have been established in their respective classes that distinguishes between the events in learning for the two children.Preparation of this paper was supported by the National Science Foundation (RED 9254939) and while the author was the Snodgrass Scholar in the School of Education Purdue University. The final draft was completed at the Mathematics Education Research Centre, Oxford University. All opinions are those of the author.     

让角色扮演与模拟走进外语课堂

角色扮演是一种能够较长时间自由使用语言的有效课堂交际活动，它有助于学生在课堂上把所学语言运用到模拟的实际生活。把角色扮演与模拟两种交际活动形式引进外语课堂，旨在鼓励学生通过自如地交谈，达到有效培养口语交际能力的目的。     

Using digital technology to enhance formative assessment in mathematics classrooms

In this paper, which is based on research from the EU-funded project Improving Progress through Formative Assessment in Science and Mathematics Education, we explore how iPads are used within formative assessment processes by six mathematics teachers and their classes in two secondary comprehensive schools in the Midlands of England. A design research approach is first used to develop and trial six lessons in which iPads are used in different ways within formative assessment processes. Through lesson observations, video analysis and teacher interviews we then examine how iPad technology contributes to these processes, the functions it performs and the distribution of activity between the main actors (teacher, technology and student). An analytic approach is developed which captures the interactions in visual representations, showing how the technology is often used as a form of communication but also performs more active functions which affect the role taken by the teacher in formative processes. The study offers insight into ways in which iPad technology contributes to effective student learning through formative assessment and introduces an analytic approach that may be useful for further studies.     

大学英语教师在多媒体课堂中的语言艺术

在多媒体英语课堂教学中教师的话语量减少了,但是不是不用重视教师的课堂语言艺术了呢?本文通过分析多媒体英语课堂教学中教师课堂语言艺术的特点和作用,来说明大学英语多媒体课堂中教师语言艺术的重要性,并指出大学英语教师在多媒体课堂中教师的课堂语言艺术应注意的几个方面。以求达到更佳的教学效果     

Measuring language learning environments in secondary science classrooms

The purpose of this study was to explore a new learning environment instrument which could be used by teaching practitioners and other educators to measure the language learning environment in the secondary science classroom. The science teacher is central in creating science classrooms conductive to the language needs of students and should be promoting the learning of language in the science curriculum and in the teaching strategies with English as second language learners. The data in this study were collected using a structured self-administered survey with a sample of 240 secondary school students from eight science classrooms. Factor analysis identified five dimensions, namely, Teacher Support, Vocabulary Development, Assessment, Motivation and Language for Learning Science. These five dimensions explained 56.9% of the variance in the language learning environment instrument. The internal reliability of the dimensions using Cronbach’s α ranged from 0.603 to 0.830. The study revealed significant differences in the dimensions of the language learning environment between what the students perceived to actually be occurring to what they would prefer. Implications from this preliminary research include the ability for measuring the language learning environment in the secondary science class and the potential for practitioners to use the information to develop teaching strategies conducive to learning for all students.     

Evolving strategies for using interactive video resources in mathematics classrooms

In order to understand the role of interactive video (IV) in mathematics classrooms, teachers were given a set of IV resources which were very mixed in character and style, and from which they could freely select. These were used in lessons over an extended period, in some cases two years or longer. By interviewing and by observing lessons, it has been possible to draw some tentative conclusions about the relative merits of different styles of IV in mathematics classrooms. IV resources are often managed in a similar way to computers and this similarity seems to have influenced teachers' opinions and choices. However, the affective impact of video was also evident in teachers' choices. A complex picture emerges with no one style dominating.     

Social representations as mediators of mathematics learning in multiethnic classrooms

Drawing on socio-cultural theory, we understand the norms regulating the practices within the mathematics classroom as resulting from the social representations of the socially dominant groups and of the school culture related to what constitutes learning mathematics. Immigrant studients, having their own personal histories as members of particular social groups, and having been in school traditions other than the one predominant in the host society, have their own images of what mathematics in school is about. Individuals interacting in the classroom are all re-interpreting the different episodes from the perspective of the social representations of the larger groups with which they identify themselves. In multiethnic classrooms different re-interpretations of the same norms clash. The lack of negotiation gives rise to obstacles to immigrant students’ participation in the mathematical conversations and, therefore, interferes with the students’ learning process.     

Pre-service teacher planning for differentiation of instruction in mathematics classrooms

This study investigated how 46 pre-service teachers (PSTs) planned for differentiation of instruction in mathematics. Content analysis was utilized to explore the differentiation strategies included and student characteristics considered in PST plans and how PSTs used differentiation strategies and student characteristics to differentiate lesson content, process, product, and environment. In addition, a rubric was designed and utilized to analyze the level of detail PSTs provided in their plans. Results indicated that overall, PSTs were developing in their planning for differentiation of instruction, using general terms to describe the modifications they would make to meet student needs. Moreover, results revealed that PSTs included strategies to differentiate lesson content and environment most often in their plans and frequently considered student readiness levels when planning for differentiation. Findings also revealed that PSTs need support in learning how to plan for differentiation based on student cultural backgrounds. Implications for mathematics teacher preparation are discussed.

     

Navigating privacy tensions when responding to online aggression at postsecondary institutions

Postsecondary institutions have a legal responsibility to ensure that students have access to a safe learning environment. While institutions adopt policies and hire administrators to protect students from harm, many are underprepared to support students when these harmful incidents happen online. This is of increased concern now that online aggression is pervasive across universities worldwide. While faculty, administrators and students agree that online aggression is a significant issue and that institutions ought to provide prevention and response services, there is concern that these efforts might violate privacy norms. We used the theory of privacy as contextual integrity (CI) to explore the tensions that postsecondary students and staff perceive regarding student privacy when responding to incidents of online aggression. To do so, we conducted focus groups with undergraduate students and student affairs administrators from a Historically Black College and University (HBCU) in the Mid-Atlantic USA. Our analysis surfaced three considerations that inform students' and staff's decision to report an incident of online aggression: their closeness to the person making the post, their perception of the online post content as a real threat and their knowledge of an authority figure who could help resolve the situation. We used CI theory to explain how these considerations can inform institutional policy, practice and future research.

Practitioner notes

What is already known about this topic

• Online aggression is a pervasive issue at postsecondary institutions worldwide that can contribute to psychological, academic and developmental issues.
• Postsecondary students and staff are unsure of how to respond to incidents of online aggression.
• There is a gap in policies and procedures for responding to online aggression at postsecondary institutions.

What this paper adds

• A novel use of Nissenbaum's (2010) theory of contextual integrity to understand students' and staff's perceptions of privacy.
• Students' and staff's decisions to intervene or report an online aggression incident are determined by their relationship to the perpetrator, the severity of the social media post and their knowledge of who to tell on campus.
• Students and staff are reluctant to inform the police out of fear of violence against the perpetrator.

Implications for practice and/or policy

• Raise awareness about responding to online aggression incidents.
• Implement online bystander intervention training programs to increase awareness and self-efficacy to intervene in unclear situations.
• Develop clear policies regarding online aggression, as well as a trustworthy procedure for how to respond.

     

Methods of analysis and overall mathematics teaching quality in at-risk prekindergarten classrooms

Research Findings: This study analyzed the quality of teacher–child interactions across 10 videotaped observations drawn from 5 different prekindergarten classrooms delivering the same mathematics curriculum: MyTeachingPartner–Math. Interactions were coded using 2 observational measures: (a) a general measure, the Classroom Assessment Scoring System (CLASS); and (b) a math-specific measure, the Classroom Observation of Early Mathematics–Environment and Teaching (COEMET). Practice or Policy: High correlations were found between the 2 measures, suggesting that the CLASS may serve as a sufficient metric to determine the quality of mathematics instruction in prekindergarten, though the COEMET may provide finer grained detail about teachers’ practice. Results indicate that the quality of mathematics instruction provided by teachers generally fell in the low- to medium-quality range and did not differ significantly across curriculum-related contextual factors.     

Some characteristics of mathematics teaching in Zimbabwean infant and primary school classrooms

The purpose of this paper is to highlight some observations made in a recent study aimed at describing the nature of current practice in the teaching of mathematics in Zimbabwean infant and primary school grades. It has been observed that the teaching is characterized by, among other things, a preponderance of chorus responses, non‐questioning pupils, lack of problem solving, teaching more than mathematics, more product and less process orientation, and small group work with group leaders. It is proposed that if teachers wish to improve the quality of their teaching then an appropriate starting point is that of apprehending and understanding what they currently do in their classrooms. Such an understanding can be developed through deliberate and serious observation of and reflection on their own current practice. This paper is intended to stimulate that process. It is also suggested that the observations described here can be turned into research questions for investigations that can provide insights into ways of increasing effectiveness of mathematics teaching and learning in primary schools.