Exploring the impact of written reflections on learning in the elementary mathematics classroom

The authors examined the implementation of written reflections in a Grade 4 mathematics classroom over the course of 8 weeks. Students in this case study engaged in a workshop modeled after Calkin's Writers' Workshop and within this workshop the use of writing as a reflective tool in mathematics was introduced. The authors explore how students used writing to evaluate their learning and how the teacher used the students' written reflections as a formative assessment for instructional purposes. Students' written reflections were coded and these codes were used to conduct an inductive thematic analysis. Analysis of written reflections via constant-comparison analysis was used for further differentiation. The findings show students' ability to accurately self-evaluate their problem-solving skills and highlighted students' confidence level with certain mathematical concepts. Teachers were able to use students' reflections as a place to begin conferring with a student for further clarification. The written reflections aided in instructional decisions and increased individual instruction when needed. The authors include implications for teacher practice and areas for future research.     

Aspects of Teaching and Learning Science: What students' diaries reveal about inquiry and traditional modes

We present an analysis of students' reflective writing (diaries) of two cohorts of Grade 8 students, one undergoing inquiry and the other traditional science teaching. Students' writing included a summary of what students had learned in class on that day and their opinions and feelings about the class. The entries were analysed qualitatively and quantitatively. This analysis of students' first-person accounts of their learning experience and their notes taken during class was useful in two ways. First, it brought out a spectrum of differences in outcomes of these two teaching modes—conceptual, affective and epistemic. Second, this analysis brought out the significance and meaning of the learning experience for students in their own words, thus adding another dimension to researchers' characterisation of the two teaching methods.     

The challenge of self-regulated learning in mathematics teachers' professional training

This study investigated mathematics teachers' professional knowledge among elementary school teachers exposed to a professional training program that either supported self-regulated learning (SRL) or offered no SRL support (no-SRL). The SRL support was based on the IMPROVE metacognitive self-questioning method that directs students' attention to understanding when, why, and how to solve problems (Kramarski and Mevarech, Am Educ Res J 40:281–310, 2003). Sixty-four Israeli elementary teachers participated in a month-long professional development program to enhance mathematical and pedagogical knowledge. The course was part of a 3-year professional development program sponsored by the Israeli Ministry of Education. This mixed-method study included quantitative assessments of teachers' professional knowledge in mathematical problem solving for an authentic task based on Program for International Student Assessment's framework (Program for International Student Assessment, 2003) and in lesson planning, as well as qualitative interviews and videotaped observations of two teachers. Results indicated that teachers in the SRL program outperformed those in the no-SRL program on various problem solving skills (e.g., reflection and conceptual mathematical explanations) and lesson planning (e.g., task demands and teaching approach). Videotaped observations of actual teaching indicated that the SRL-trained teacher demonstrated more teaching practices that aimed to promote students' understanding and better supported students' regulation of their own learning, compared to the no-SRL-trained teacher. We discuss educational and practical implications.     

Student Perceptions of the Use of Writing in a Differential Equations Course

The use of writing to learn mathematics at the university-level is a pedagogical tool that has been gaining momentum. The setting of this study is a second-year differential equations class where written assignments have been incorporated into the course. By analyzing survey results and students' written work, we examine the extent to which students view writing as an effective learning strategy, as well as their beliefs about the relationship between mathematical writing and communication. We also discuss what students' narratives reveal about their past mathematical experiences.     

Effects of Guided Journal Writing on Students' Story Understanding

Abstract

The authors investigated the effects of guided journal writing on students' understanding of themes and main characters in a complex novel. Three English 12 classes were randomly assigned to 1 no-writing condition and 2 writing conditions—character clues and general-response questions. The results from 2 posttests consistently indicated that students who wrote significantly surpassed students who did not write. Student self-ratings data indicated that the students believed that the writing activities helped them with story understanding. Student interview data indicated that students believed that the writing made them think more deeply about the story. The results support the contributions of writing to student literary learning and the research of J. Marshall (1987) and G. E. Newell (1994, 1996).     

The effect of levels of cooperation within physical science laboratory groups on physical science achievement

The purpose of this study was to investigate the effect of the levels of group cooperation on students' achievement during a series of physical science laboratory activities. Six intact seventh-grade physical science classes taught by two teachers, with each teacher instructing three classes, were selected from two middle schools. For each teacher, one of the classes was taught with a traditional approach (no cooperative goal structure). The other two classes were assigned to a cooperative goal structure (role assignment and nonrole assignment). For the role assignment class, each student was assigned a specific role, but students in both traditional and nonrole assignment classes were not assigned roles. The Classroom Observation Instrument in Science Laboratory Activity (COISLA), which includes investigative skills (i.e., managing, manipulating, observing, reading, writing, and reporting); social skills (i.e., discussing, encouraging) and nonlearning behaviors (i.e., waiting, off-task), was used to measure the levels of group cooperation. The grades on lab reports and lab quizzes of students who were taught by the same teacher were compared to assess the effects of the different learning conditions. No significant differences on the students' final achievement were found with respect to the three instructional approaches followed by each teacher. The teacher effect was more significant than either instructional approach on managing, manipulating, observing, reading, and writing behaviors. No significant teacher effect was found for the other behaviors. Only one treatment effect was significant, writing behavior. Overall, the teacher effect was more influential than instructional approach on students' behaviors. In teacher A's classes, reading behavior predicted 21% of students' achievement. However, no significant correlations existed between the 10 collaborative behaviors and students' achievement in teacher B's classes.     

A window into thinking: Using student writing to understand conceptual change in science learning

This study, conducted in an inner-city middle school, followed the conceptual changes shown in 25 students' writing over a 12-week science unit. Conceptual changes for 6 target students are reported. Student understanding was assessed regarding the nature of matter and physical change by paper-and-pencil pretest and posttest. The 6 target students were interviewed about the goal concepts before and after instruction. Students' writing during lesson activities provided qualitative data about their understandings of the goal concepts across the science unit. The researcher constructed concept maps from students' written statements and compared the maps across time to assess changes in the schema of core concepts, complexity, and organization as a result of instruction. Target students' changes were studied in detail to determine patterns of conceptual change. After patterns were located in target students' maps, the remaining 19 students' maps were analyzed for similar patterns. The ideas that students identified in their writing showed changes in central concepts, complexity, and organization as the lessons progressed. When instructional events were analyzed in relation to students' demonstrated ideas, understanding of the goal conceptions appeared in students' writing more often when students had opportunities to explain their new ideas orally and in writing.     

‘Shoot for the moon!’ Students' identities as writers in the context of the classroom

A study of students' identities as writers was carried out in the classroom of a New Zealand primary teacher who had been formally identified by a national body of teachers as having excellent practice in supporting literacy acquisition. The researchers, Professor Janice Wearmouth, from the University of Bedfordshire, Mere Berryman, from the University of Waikato, New Zealand, and Lisa Whittle, from the Department of Conservation, Wellington, New Zealand, aimed to compare high and low literacy achievers' identities as writers within the context of this teacher's pedagogy and the learning environment of her classroom. The researchers concluded that all students, both high and low achievers, were developing very positive writing identities in a context where the teacher's method of supporting her students' writing was very well planned through a process‐writing approach. This teacher had a very high degree of subject and pedagogical content knowledge and an acute awareness of her students' literacy learning needs. Her approach had an immediacy of responsiveness in relation to every student's learning and, above all, had recognition of the overwhelming importance of positive relationships in the classroom, teacher to student and peer to peer.     

Teacher support and its influence on students' intrinsic value and effort: Dimensional comparison effects across subjects

While positive influences of teacher support on students' motivational development have been widely shown, existing research has not yet considered that students' school experiences are interrelated across classrooms and subjects. The aims of this study were, thus, twofold: (a) To investigate the effects of teacher support on the development of students' intrinsic value and effort; and (b) based on dimensional comparison theory, to examine potential cross-subject contrast effects of teacher support in one subject on students' intrinsic value and effort in another subject. Using a sample of 1155 German students assessed in Grade 5 and 6, multilevel latent change models revealed positive within-subject associations between teacher support and intrinsic value and effort. Furthermore, support for contrast effects was found. Higher levels of teacher support in one subject were related negatively to intrinsic value and effort in another subject, calling for the examination of students' classroom experiences as interrelated across subjects.     

Programming and Mathematics in an Upper-Level University Problem-Solving Course

We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs, etc.), offers simulation and experimentation, invites discussions about structure, requires logic and testing strategies, and handles mathematics objects with an added feeling of reality. Focusing on novice and inexperienced programmers, we look for answers to the practice-oriented question, “How do students reason through their difficulties when using programming to explore a mathematics problem?” Following literature review and methodology, we build the programming model, which we use to study students' experiences as they approach a mathematical problem by writing computer code. Our research is based on analyzing students' in-class work and class notes, author's observations of students working on their computers, and his interactions with students in class and elsewhere. In the four case studies that we present we touch upon students' difficulties in working with complex conditional statements and recurrence relations. As well, we discuss cases where resolving a programming issue demands posing and answering mathematical questions.     

“Tjaa,I Do Have Ears,But I Do Not Hear”: New Literacy Studies and the Awakening of a Hearing Teacher

To address the low literacy achievement of minority students, the sociocultural movement of the New Literacy Studies (NLS) encourages us to expand on current understandings of literacy. Instead of thinking of literacy as a neutral set of skills transferable from one setting to another, NLS researchers encourage us to contextualize literacy within individuals’ social and cultural realms. In this view, there are multiple literacies. As a literacy teacher of students who are deaf, I have witnessed students struggling with school-based literacy learning. As I began to examine what I was doing within the classroom, I realized that my assumptions about literacy instruction were the main source of students' struggles. In this study I explore how I used the theoretical perspective of the NLS to expand my understanding of literacy. The findings suggest that, in order to base literacy instruction on students' resources, teachers need to learn to negotiate conflicting educational Discourses on reading and writing, to create a space within the classroom for students to bring in their literacy practices, and to recognize and preserve students' agency and identity in their learning. Findings also indicate the vital role of writing in deaf students' learning of Icelandic.     

Exploring the Metafictive in Elementary Students' Writing

Although some researchers have examined students' literary understandings of and responses to books with metafictive characteristics, few have explored how elementary students incorporate metafictive devices into their writing. In this article I analyse the stories and books created by a class of Grade 5 students and discuss the metafictive devices evident in their work. In addition to considering how the literature students read and how the classroom interpretive community influenced the students' stories/books, I discuss some broader issues about the significance of students reading and writing metafictive texts.     

Differential effects of three professional development models on teacher knowledge and student achievement in elementary science

To identify links among professional development, teacher knowledge, practice, and student achievement, researchers have called for study designs that allow causal inferences and that examine relationships among features of interventions and multiple outcomes. In a randomized experiment implemented in six states with over 270 elementary teachers and 7,000 students, this project compared three related but systematically varied teacher interventions—Teaching Cases, Looking at Student Work, and Metacognitive Analysis—along with no‐treatment controls. The three courses contained identical science content components, but differed in the ways they incorporated analysis of learner thinking and of teaching, making it possible to measure effects of these features on teacher and student outcomes. Interventions were delivered by staff developers trained to lead the teacher courses in their regions. Each course improved teachers' and students' scores on selected‐response science tests well beyond those of controls, and effects were maintained a year later. Student achievement also improved significantly for English language learners in both the study year and follow‐up, and treatment effects did not differ based on sex or race/ethnicity. However, only Teaching Cases and Looking at Student Work courses improved the accuracy and completeness of students' written justifications of test answers in the follow‐up, and only Teaching Cases had sustained effects on teachers' written justifications. Thus, the content component in common across the three courses had powerful effects on teachers' and students' ability to choose correct test answers, but their ability to explain why answers were correct only improved when the professional development incorporated analysis of student conceptual understandings and implications for instruction; metacognitive analysis of teachers' own learning did not improve student justifications either year. Findings suggest investing in professional development that integrates content learning with analysis of student learning and teaching rather than advanced content or teacher metacognition alone. © 2012 Wiley Periodicals, Inc. J Res Sci Teach 49: 333–362, 2012     

The effects of cooperative learning on enhancing Hong Kong fifth graders' achievement goals,autonomous motivation and reading proficiency

Research indicates that cooperative learning with teacher‐guided instruction is more effective in helping young children to learn than cooperative learning with minimal guidance. In the present study, two different cooperative learning activities (jigsaw and drama) and a control condition (a traditional teacher‐led approach) were compared. The participants were 279 Grade 5 Hong Kong students located in nine classrooms. The two experimental conditions emphasised teachers' cognitive support in helping students to understand a text through both teacher‐led and student‐led activities. Post‐test data included a reading comprehension test and three questionnaires that investigated students' goal orientations, initial level of relative autonomy and perceptions of instructional practices. Findings indicate that students in the jigsaw group outperformed students in both the drama group and the control group in the reading comprehension test. The implications of conducting cooperative learning activities with well‐planned teacher guidance are discussed.     

Synergy Between Teacher Practices and Curricular Scaffolds to Support Students in Using Domain-Specific and Domain-General Knowledge in Writing Arguments to Explain Phenomena

We investigated how 2 different curricular scaffolds (context-specific vs. generic), teacher instructional practices, and the interaction between these 2 types of support influenced students' learning of science content and their ability to write scientific arguments to explain phenomena. The context-specific scaffolds provided students with hints about the task and what content knowledge to use in or incorporate into their writing. The generic scaffolds supported students in understanding a general framework (i.e., claim, evidence, and reasoning) regardless of the content area or task. This study focused on an 8-week middle school chemistry curriculum that was enacted by 6 teachers with 578 students during the 2004–2005 school year. Analyses of identical pre- and posttests as well as videotapes of teacher enactments revealed that the curricular scaffolds and teacher instructional practices were synergistic in that the effect of the written curricular scaffolds depended on the teacher's enactment of the curriculum. The context-specific curricular scaffolds were more successful in supporting students in writing scientific arguments to explain phenomena, but only when teachers' enactments provided explicit domain-general support for the claim, evidence, and reasoning framework, suggesting the importance of both types of support in successful learning environments.     

issues in Portfolio Assessment: Assessing Writing Processes From Their Products

We investigated the ways that portfolio evidence of students' competencies with writing processes was created and interpreted in 4 classrooms. Our study was conducted during preliminary classroom trials of California Learning Assessment System portfolios, when teachers and students were challenged with the new task of preparing portfolios that demonstrated students' competency with the "dimensions of learning." Drawing data from teacher and student interviews as well as portfolios, we considered three issues regarding the meaning of portfolio indicators of writing processes (a) Students' opportunities to learn to use a range of resources, processes, and standards in ways that enhance the effectiveness of their writing; (b) students' opportunities to produce "hard copy" evidence of their uses of processes; and (c) students' capacities to analyze their writing processes. Further research is needed to understand how participants in a large-scale portfolio assessment program develop shared understandings of the ways that evidence of writing processes is considered in the scoring and how the programmatic needs for comparability of evidence can be reconciled with the personal needs of young writers, whose uses of processes will vary with the purposes and contexts of their writing.     

Writing in Math: A Disciplinary Literacy Approach

Mathematics teachers often resist generic literacy strategies because they do not seem relevant to math learning. Discipline-specific literacy practices that emerge directly from the math content and processes under study are more likely to be embraced by math teachers. Furthermore, national and state-level mathematics standards as well as Common Core standards provide frameworks for situating literacy practices squarely within the disciplines. A disciplinary literacy approach to writing in math requires teachers to develop innovative strategies and practices that link writing to particular mathematical processes and tasks. An example is shared of a math writing approach developed by a middle school teacher used to prompt her students' critical thinking and problem solving processes during the study of algebra. She designed a template that when completed can serve as a reflective tool for her students and provide the teacher useful feedback on their learning. The example of teaching with the template as a guide for working through steps to solve a story problem demonstrates what disciplinary writing can look like in a typical middle school classroom.     

Preparing future teachers for diverse schools in an online learning community: Perceptions and practice

This study provides an example of one institution's efforts to design coursework that meets the simultaneous challenges of supporting the aims of increasing access to online courses and simultaneously better preparing teachers to work in diverse classrooms. Based on online pre- and post-surveys and monthly open-ended writing prompts administered to students in an introductory teacher preparation course, the study sought to discover students' motivation to select online or blended courses, student perspectives on the benefits and challenges to taking this course online, characteristics of the learning environment that promoted or interfered with students' learning, instructor's perspective of learners' reaction to topics addressing K-12 classroom diversity, and the impact of an online format on students' discussions of issues related to learner diversity. Findings suggest that online courses should include a classroom placement component in which students experience a diverse classroom in order to best prepare students for diverse teaching assignments. Thus, the best online teacher preparation courses maybe those that blend virtual and face-to-face interaction rather than being strictly online.     

Understanding teaching or teaching for understanding: Alternative frameworks for science classrooms

We came to this study with a set of beliefs about good science teaching that had been heavily influenced by the constructivist literature of the past decade. In this article we reexamine some of our own assumptions about good teaching by exploring the classroom practices of an experienced physics teacher. This teacher did not fit the mold of the constructivist teacher and, yet, there was much to suggest that he was meeting the needs of the students in his class. His methods were almost entirely whole class—focusing mainly on physics content, examination technique and algorithm practice. Our close observation of this teacher in his Grade 11 classroom over several months suggests an alternative framework for examining his work. We examine this framework through a number of themes: teacher confidence, the structure of the discipline, student motivation, trust, and the cultural context of learning. We argue for a broader view of good science teaching than that proposed by the constructivist literature, one that takes into account teachers' and students' understandings of science in relation to their social and cultural contexts.