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1.
AbstractIn this article, we share a model of flipped instruction that allowed us to gain a window into our students’ mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be used to design experiences that help students make sense of mathematics during class sessions. 相似文献
2.
Formative assessment practices for secondary mathematics have been advocated as valuable for students, but difficult for teachers to learn. There have been calls in the literature to increase the emphasis on formative assessment in mathematics teacher preparation courses. This study explored the use of peer-assessment strategies for helping pre-service secondary mathematics teachers (PSTs) cultivate formative assessment principles and practices for assessing school students. Twenty-seven PSTs participated in a peer-assessment cycle comprised of: sourcing a rich mathematics task; constructing an assessment rubric for it; and collecting and analysing a selection of secondary student responses to the task. Each PST then provided written and verbal feedback to a peer on his/her rubric and student solution assessments. We draw on theoretical conceptions of Teacher Assessment Literacy in Practice to characterize the PSTs’ perceptions of their experience of formative assessment processes for learning to assess school students, in terms of cognitive and affective dimensions of their conceptions of assessment. The cohort evidenced a wide range of levels of confidence with the various aspects of formative assessment practices but on average less confidence in assessing school student task responses themselves than in assessing peer work. In addition to highlighting specific changes to different types of assessment knowledge, the PSTs also evidenced an awareness of shifts in their attitudes, in coming to view student task responses with more appreciation and humility. 相似文献
3.
This article aims to describe a type of formative assessment, MAP Classroom Challenge, which has been introduced in mathematics classrooms in recent years. MAP, or the Mathematics Assessment Project Classroom Challenges (formerly known as Formative Assessment Lessons), are developed by teams of math educators from the Shell Centre for Mathematical Education at the University of Nottingham and the University of California, Berkeley, with the support from the Bill & Melinda Gates Foundation. The overarching goal of Classroom Challenges is to support teachers in administering effective formative assessment by identifying student misconceptions of main mathematical ideas and helping students develop better understanding. The design of Classroom Challenges stems from the Common Core State Standards in Mathematics and it is based on the seamless fusion of the standards for mathematical content and the standards for mathematical practices. Furthermore, this article demonstrates the positive impact one Classroom Challenge had on revealing and subsequently eliminating student misconceptions related to certain fundamental algebraic concepts. 相似文献
4.
This article reviews literatures on mathematics education in China in the last decade. It focuses on papers that were published
after 2000, and Chinese Social Science Citation Index (CSSCI). Some influential journals in the field of mathematics education,
such as the Journal of Mathematics Education and the Mathematics Instruction were also reviewed. The author shares in this article with international scholars the most recent research in the field of
Chinese mathematics education. Mathematics education in China mainly focuses on the essence of mathematics classroom instruction,
student learning of mathematics, mathematics teacher education, and its curriculum reforms. 相似文献
5.
Three mathematics scoring methods are being used or explored in large-scale assessment programs: item-by-item scoring, holistic scoring, and "trait" scoring. This study investigated all 3 methods of scoring on 3 mathematics performance-based assessments. Mathematics assessment tasks were selected from a pool of pilot tasks because they could be scored using all 3 methods. Results of the study suggest that holistic scoring and item-by-item scoring methods provide similar information; however, trait score for conceptual understanding and mathematics communication tapped into different aspects of student performance. Implications for the validity of scoring methods now in use for performance-based mathematics assessments are discussed. 相似文献
6.
Every student who enrols in a degree programme involving service mathematics in the University of Limerick in Ireland is given a mathematics diagnostic test. The diagnostic test was developed due to mathematics lecturers’ anxiety regarding students’ mathematical competency levels. Students receive the 40 question paper-based test in their first service mathematics lecture without prior notification. Initial analysis of students’ work revealed that many students were having difficulties with basic algebra and arithmetic in particular [Gill, O. 2006. “What Counts as Service Mathematics? An Investigation into the ‘Mathematics Problem’ in Ireland.” PhD diss., University of Limerick]. Further research highlighted the significant decline in diagnostic test performance and the changing profile of service mathematics students between 1998 and 2008 [Faulkner, Fiona, Ailish Hannigan, and Olivia Gill. 2010. “Trends in the Mathematical Competency of University Entrants in Ireland by Leaving Certificate Mathematics Grade.” Teaching Mathematics and Its Applications 29 (2): 76–93]. One of the most notable changes to the student profile over time was the increase in mature students (non-standard students) entering service mathematics programmes. Although non-standard students had a lower mean performance in the diagnostic test, they were found to have a higher mean performance in some cases in service mathematics compared to standard students. This paper explores some of the possible reasons for such findings. 相似文献
7.
AbstractA number of trends are converging to drive the need for more informed teacher data use. These include advocacy for formative assessment and the need for teachers to account for student learning. In this context, assessment literacy and data literacy have emerged as a focus in research and professional development. Problematically, research signals that developing assessment/data literacy is challenging with evidence that teachers may not have mastered relevant aspects of mathematics and statistics. This paper reports lecturer, student teacher and school leader views of the role and requirements of data literacy using data from a larger study into how to foster student teacher mathematical thinking for the breadth of teacher professional work. Data were generated via interviews, surveys and document analysis. Findings suggest a concern and opportunity to develop assessment/data literacy as this calls on mathematical and statistical understanding. 相似文献
8.
ABSTRACTDrawing inferences about the extent to which student performance reflects instructional opportunities relies on the premise that the measure of student performance is reflective of instructional opportunities. An instructional sensitivity framework suggests that some assessments are more sensitive to detecting differences in instructional opportunities compared to other assessments. This study applies an instructional sensitivity framework to compare student performance on two different mathematics achievement measures across five states and three grade levels. Results suggest a range of variation in student performance among teachers on the same mathematics achievement measure, variation between the two different mathematics achievement measures, and variation between grade levels within the same state. Findings highlight initial considerations for educators interested in selecting and evaluating measures of student performance that are reflective of instructional opportunities. 相似文献
9.
Mathematical modeling is a high-leverage topic, critical for college and career readiness, participation in STEM education, and civic engagement. Mathematical modeling involves connecting real-world situations, phenomenon, and/or data with mathematical models, and in this way applies across various STEM disciplines, including mathematics, engineering, and science. Although research has begun to explore mathematical modeling instruction in the elementary grades, questions remain about how to assess student learning at the elementary level. We addressed this need by designing an assessment of mathematical modeling competencies for students in grades 3 through 5. Informed by international research, our assessment includes a hybrid structure to assess mathematical modeling competencies holistically (as students engage in the complete modeling process) and atomistically (as students engage in different components of the modeling process, including making sense of phenomena and real-world situations, setting up and operating on mathematical models, and interpreting results in relation to the real-world context). We conducted student interviews, followed by two rounds of pilot testing to inform item development and ensure acceptable psychometric properties. The final assessment included 13 items (9 multiple choice, 3 open-response, and 1 complete modeling task). We describe our assessment development process, and provide sample assessment items and detailed coding rubrics. We summarize quantitative analyses which established high reliability and low standard error for our assessment, supporting its use for grades 3 to 5. Implications of our framework and assessment for mathematical modeling instruction and future research on STEM learning are discussed. 相似文献
10.
This paper focuses, empirically, on the developments seen in a group of South African early grades’ mathematics teacher educators in the course of a university-provincial education department partnership project. This project sought to support the district Mathematics Subject Advisers to support, in turn, teachers to implement an intervention consisting of a sequence of four lessons focused on multiplicative reasoning. Outcomes based on pre- and post-tests administered by the Subject Advisers suggested substantial pre- to post-test improvement at the student level. Subject Adviser observations and reflections pointed to successes in engendering more dialogic conversations between mathematics teachers and mathematics teacher educators focused on mathematics and its teaching and learning. The ‘double move’ of increasing overlap between the subject adviser and teacher communities, coupled with evidence that implementing the intervention had enabled the Subject Advisers to develop their mathematical and pedagogical understandings, provides a useful way of considering development in the capacity of mathematics teacher educators to support mathematics teaching and learning. 相似文献
11.
ABSTRACT The authors describe results from a study of a middle school mathematics formative assessment strategy. They employed a randomized, controlled design to address the following question: Does using our strategy improve student performance on assessments of key mathematical ideas relative to a comparison group? Eighty-five teachers and 4,091 students were included. Students took a pretest and a transfer measure at the end of the year. Treatment students completed formative assessments. Treatment teachers had exposure to professional development and instructional resources. Results indicated students with higher pretest scores benefited more from the treatment compared to students with lower pretest scores. In addition treatment students significantly outperformed control students on distributive property items. This effect was larger as pretest scores increased. Results, limitations, and future directions are discussed. 相似文献
12.
Item stem formats can alter the cognitive complexity as well as the type of abilities required for solving mathematics items. Consequently, it is possible that item stem formats can affect the dimensional structure of mathematics assessments. This empirical study investigated the relationship between item stem format and the dimensionality of mathematics assessments. A sample of 671 sixth-grade students was given two forms of a mathematics assessment in which mathematical expression (ME) items and word problems (WP) were used to measure the same content. The effects of mathematical language and reading abilities in responding to ME and WP items were explored using unidimensional and multidimensional item response theory models. The results showed that WP and ME items appear to differ with regard to the underlying abilities required to answer these items. Hence, the multidimensional model fit the response data better than the unidimensional model. For the accurate assessment of mathematics achievement, students’ reading and mathematical language abilities should also be considered when implementing mathematics assessments with ME and WP items. 相似文献
13.
AbstractInquiry is promoted as a way to engage students so that they learn more deeply; inquiry is also an end in itself, introducing students to the research process and the behaviors of a mathematician. This article reflects on an individual exploratory project used in a sophomore-level number theory course, examining how it supported student inquiry and integrated with departmental efforts to encourage productive mathematical dispositions. Additional attention is given to the choice of topics, focus on process rather than product, and student reflections in supporting the goal of student inquiry. 相似文献
14.
This study analyses the potential of a learning analytics (LA) based formative assessment to construct personalised teaching sequences in Mathematics for 5th-grade primary school students. A total of 127 students from Spanish public schools participated in the study. The quasi-experimental study was conducted over the course of six sessions, in which both control and experimental groups participated in a teaching sequence based on mathematical problems. In each session, both groups used audience response systems to record their responses to mathematical tasks about fractions. After each session, students from the control group were given generic homework on fractions—the same activities for all the participants—while students from the experimental group were given a personalised set of activities. The provision of personalised homework was based on the students' errors detected from the use of the LA-based formative assessment. After the intervention, the results indicate a higher student level of understanding of the concept of fractions in the experimental group compared to the control group. Related to motivational dimensions, results indicated that instruction using audience response systems has a positive effect compared to regular mathematics classes. Practitioner notes What is already known about this topic - Developing an understanding of fractions is one of the most challenging concepts in elementary mathematics and a solid predictor of future achievements in mathematics.
- Learning analytics (LA) has the potential to provide quality, functional data for assessing and supporting learners' difficulties.
- Audience response systems (ARS) are one of the most practical ways to collect data for LA in classroom environments.
- There is a scarcity of field research implementations on LA mediated by ARS in real contexts of elementary school classrooms.
What this paper adds - Empirical evidence about how LA-based formative assessments can enable personalised homework to support student understanding of fractions.
- Personalised homework based on an LA-based formative assessment improves the students' comprehension of fractions.
- Using ARS for the teaching of fractions has a positive effect in terms of student motivation.
Implications for practice and/or policy - Teachers should be given LA/ARS tools that allow them to quickly provide students with personalised mathematical instruction.
- Researchers should continue exploring these potentially beneficial educational implementations in other areas.
相似文献
15.
Teachers of mathematics orchestrate opportunities for interactions between learners and subject matter. Therefore, mathematics
teachers need rich, multidimensional content knowledge for teaching mathematics, which incorporates knowledge of the subject
matter, students, and teaching. Studying this mathematical knowledge for teaching (MKT) necessitates more than a unidirectional
assessment. In this study, the mathematical knowledge for teaching reasoning and proving of two secondary mathematics teachers
was investigated through classroom observations and clinical assessments. Results indicate that using MKT as a frame for examining
classroom practice, in addition to assessing the MKT a teacher possesses in a clinical setting, provides an in-depth and innovative
method for investigating MKT. The comparison of the two cases also identifies student positioning as a key mediating factor
between MKT and opportunities to learn. Implications for using MKT as a lens for examining practice in teacher education are
discussed. 相似文献
16.
This longitudinal study examines growth in teacher knowledge as measured by two popular assessments—Learning Mathematics for Teaching (LMT) and Diagnostic Teacher Assessments in Mathematics and Science (DTAMS). Using data collected from 24 teachers, we compare the extent to which each assessment captured teacher learning during a K-8 mathematics content/pedagogy hybrid course and a general mathematics content course. Teachers made large gains on both measures, but the LMT better captured gains made during the hybrid course, whereas DTAMS better detected gains during the mathematics course. Patterns in teacher performance suggest substantive differences between specialized mathematical knowledge for teaching and everyday mathematics knowledge. The theoretical and practical implications of these findings are discussed. 相似文献
17.
This study examines the influence of a year-long mathematics professional development program on Kindergarten teachers’ beliefs, content knowledge, instructional practices, and their students’ achievement. The professional development program is grounded in the theoretical construct of learner-centered professional development and focuses on supporting teachers’ integration of standards-based pedagogies aligned with the Common Core State Standards in Mathematics. Data analysis included examining 15 Kindergarten teachers’ mathematics content knowledge, their beliefs about mathematics, their enactment of student-centered pedagogies, and student achievement on curriculum-based assessments. Findings indicated that teachers adopted more student-centered pedagogies and embraced more student-centered beliefs about mathematics teaching during their time in the project. Further, Kindergarten teachers also demonstrated gains in their mathematical content knowledge, and those content knowledge gains were linked to gains in student achievement. 相似文献
18.
Abstract In the present study the relationship between teaching and learning was examined using a conceptual framework that links dimensions of instructional tasks with gains in student learning outcomes. The greatest student gains on a performance assessment consisting of tasks that require high levels of mathematical thinking and reasoning were related to the use of instructional tasks that engaged students in the “doing of mathematics” or the use of procedures with connections to meaning. In addition, student performance gains were greater for those sites whose tasks were both set up and implemented to encourage the use of multiple solution strategies, multiple representations, and explanations. Whereas, student performance gains were relatively small for those sites whose tasks tended to be both set up and implemented in a procedural manner and that required a single solution strategy, single representations, and little or no mathematical communication. 相似文献
19.
数学是人类科学发展的重要工具,然而对数学的学习却成为成人高校学生的头疼之事,传统的教育模式造成教师难教、学生难学、学习的收获微小等问题。因此,成人高校的数学教育工作成为我们成人教育工作者应该研究的课题。文本探讨了在成人高校的数学教育中引入数学文化知识,紧密结合实际应用问题讲授数学课、传授数学文化、提高学生的数学素质的必要性与可行性。 相似文献
20.
This paper explores the nature of prospective teachers’ noticing of students’ understanding as they analyze and discuss middle school students’ understandings of trapezoids in micro-case videos in the context of geometry. In this exploratory study, the data were obtained from eight prospective middle school mathematics teachers through individual video analysis, reflection papers, and group discussions. The results indicated that the use of purposeful micro-case video designs based on prospective teachers’ background knowledge of quadrilaterals allowed them to be productive in video analyses and discussions. In individual video analyses, prospective teachers attended to various mathematical elements to identify students’ responses but did not always use them to make interpretations of each student’s understanding of trapezoid. In the group discussions of the micro-case videos, in contrast, prospective teachers could provide alternative interpretations of students’ understanding by identifying links between the mathematical elements in students’ responses and the characteristics of students’ understandings. In the group discussions, they provided more detailed and specific instructional actions to support each student’s understanding of trapezoid than their individual video analyses. This study suggests practical implications for teacher education programs on how to use video cases (e.g., firstly, working individually and then having group discussions about the videos) to explore prospective teachers’ professional noticing skills. Considering prospective teachers’ background knowledge of related mathematical contents, this study can also inspire future studies on how to design effective videos about students’ mathematical understanding. 相似文献
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