Building Conceptual Understanding of Multiplicative Reasoning Content in Third Graders Struggling to Learn Mathematics: A Feasibility Study

This formative study of a multiplicative reasoning (MR) intervention explored the intervention's potential for improving the ability of third-grade struggling students’ ability to reason with multiplicative concepts and procedures. The feasibility of the study was examined in a school setting before a randomized control trial was conducted. Students who scored between the 10th and 35th percentile on a district-administered math screening test received the MR intervention from their teachers. We developed intervention units to build a conceptual foundation in a student-centered approach to Tier 2 instruction that included opportunities for students to engage in critical thinking as they generalized big ideas, participated in classroom discourse, and modeled multiplicative relationships with multiple representations. Preliminary data demonstrate the potential of the intervention to promote students’ MR skills. Instructional implications are discussed in terms of opportunities for these students to engage in grade-level mathematics content.     

A capstone mathematics course for prospective secondary mathematics teachers

This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered pedagogical and assessment strategies. Examples show how students teach the class, complemented by excerpts from student journals containing students?? perceptions of their learning. Preliminary research indicates the effectiveness of this course for preparing future mathematics teachers.     

Comparative analyses of discourse in specialized STEM school classes

ABSTRACT

The authors detail the discourse patterns observed within mathematics and science classes at specialized STEM (science, technology, engineering, and mathematics) high schools. Analyses reveal that teachers in mathematics classes tended to engage their students in authoritative discourse while teachers in science classes tended to engage students in dialogic discourse. The authors examined variations in the type of discourse in relationship to the discipline being taught, the educational level of the teacher, and course requirements were also explored.     

Rethinking Mathematical Concepts with the Lens of the History of Mathematics: An Experiment with Prospective Secondary Teachers

In this paper we present the main lines of a course on the history of mathematics for prospective secondary school (students’ age range 14–19) mathematics teachers, enrolled on a 2-year postgraduate teacher preparation program. In order to integrate the historical objectives with the educational objectives of the program we adopted the following strategy: on the one hand we focused on some important concepts taught in upper secondary school that required the prospective teachers to reflect on the difficulties linked to these concepts; on the other hand we proposed original sources intended to enhance the students’ reflection through challenging some existing beliefs on these concepts. We informed the prospective teachers that they were participating in a research project. This fostered a collaborative atmosphere and an active involvement that guided our students towards the final step of the course, where they were requested to outline a teaching sequence for presenting the concepts in the classroom.     

Student participation in whole-class discourse: individual conditions and consequences for student learning in primary and secondary school

Students’ participation in whole-class discourse is an important feature of classroom learning. Within socio-cultural research, two explanations for this connection can be emphasised: students’ engagement and teacher-student verbal interaction. We suggest a video-based coding scheme that can be specifically connected with each theoretical strand by distinguishing between student-guided and teacher-guided participation. The aim is to explore the conditions (student characteristics) and consequences (student learning) of both types of classroom participation. The results of two video studies with standardised pre- and post-assessments – one in secondary school mathematics (932 students, 40 classes) and one in primary school science (681 students, 35 classes) – emphasise both the relevance of students’ prior knowledge for participation in whole-class discourse and the role of student-guided participation in learning.     

微课教学技术支持下的中职数学教学反思

数学是中职教育阶段一门非常重要的基础学科,由于长期以来人们对中职教育存在错误的认识,中职院校的生源普遍基础很差,因此,在数学知识的学习方面很多学生都感到压力很大。文章通过对中职数学教学中存在问题的反思,提出利用微课技术这种新的教学方式改善中职数学教育的方法,以此来提高中职数学教学的质量。     

Talking About Teaching Episodes

This paper examines two types of discourse in which teachers engage when discussing case studies based on classroom episodes, and the ways in which the availability of video data of these episodes may motivate a shift in the mode of discourse used. We interviewed two pairs of secondary school mathematics teachers after they had read a case study based on a 16-minute mathematics classroom episode taped in a secondary school in the United States. During each interview, a multimedia version of the case study, including video of the original episode, was available to the participants. We identify two modes of discourse engaged in by the teachers during the interviews: Grounded Narrative and Evaluative Discourse. We examine and identify the characteristics of the two discourse forms, drawn from both video and textual analysis. These characteristics are self-reflective talk, perspective, ethics, and linguistic patterns. The identification of two modes of discourse is relevant for researchers and teacher educators using case studies or video recordings. In addition, the findings provide insight into how teachers are “seeing” classroom events in a video case study.     

试论新课改下小学数学教学的创新

随着新课程改革的不断深入,小学数学教师也应转变传统的教学观念,创新数学教学方法,以达到新课程改革对小学阶段数学教学目标的新要求。小学阶段的数学教学能为学生未来更好地学习数学知识打好理论基础,在这一段时间内培养学生的良好学习习惯能使学生的学习达到事半功倍的效果。因此抓住这一关键期对学生进行教育,对帮助学生形成数学思维、提高学生运用数学知识解决实际问题的能力有重要作用。基于此,本文将研究在新课改背景下小学数学教学方法的几种创新形式。     

TIMSS 2019数学评价的框架、结果与启示

TIMSS 2019数学评价发现,中小学生的数学学习成绩正在逐渐提高,达到国际基准的比例也在提高,并存在区域、性别、领域和认识差异。同时,家庭与学校环境、师生教学准备、学生数学学习态度和数学课程与教学等背景因素都影响数学学习。为了促进我国数学教育的健康发展,我们要继承中华优秀教育传统,吸收先进教育理念,更新数学课程内容,优化教育教学评价,培养积极学习态度。     

Examining the use of multiple writing and discourse tasks in 5th grade mathematics

Abstract

The purpose of this study is to examine how fifth grade students were impacted by the infusion of multiple writing tasks in mathematics. In this study, writing tasks provided opportunities for students to communicate prior knowledge, share ideas to construct and justify arguments, for reflection, and assessment. In this deductive qualitative study, students’ work samples were analyzed. Findings indicated that students grew in their understanding of mathematics and ability to self-reflect and self-evaluate through multiple opportunities to write for a variety of purposes. The opportunities for constructing mathematical understanding with activities that included writing and discourse also fostered learning between peers. The findings suggest a variety of opportunities to write and engage in mathematics discourse encouraged reflection, evaluation, and learning. Implications for future research include the need to examine the impact of these activities on students’ mathematics understanding as measured by assessments or an analysis of student work samples.     

Teachers’ beliefs and practices related to mathematics instruction

Beliefs and practices related to mathematics were assessed for 21 fourth- through sixth-grade teachers. At the beginning and the end of the school year teachers’ beliefs about (1) the nature of mathematics (i.e., procedures to solve problems versus a tool for thought), (2) mathematics learning (i.e., focusing on getting correct solutions versus understanding mathematical concepts), (3) who should control students’ mathematical activity, (4) the nature of mathematical ability (i.e., fixed versus malleable), and (5) the value of extrinsic rewards for getting students to engage in mathematics activities were assessed. (6) Teachers self-confidence and enjoyment of mathematics and mathematics teaching were also assessed. Analyses were conducted to assess the coherence among these beliefs and associations between teachers’ beliefs and their observed classroom practices and self-reported evaluation criteria. Findings showed substantial coherence among teachers’ beliefs and consistent associations between their beliefs and their practices. Teachers’ self-confidence as mathematics teachers was also significantly associated with their students’ self-confidence as mathematical learners.     

Providing written feedback on students’ mathematical arguments: proof validations of prospective secondary mathematics teachers

Mathematics teachers play a unique role as experts who provide opportunities for students to engage in the practices of the mathematics community. Proof is a tool essential to the practice of mathematics, and therefore, if teachers are to provide adequate opportunities for students to engage with this tool, they must be able to validate student arguments and provide feedback to students based on those validations. Prior research has demonstrated several weaknesses teachers have with respect to proof validation, but little research has investigated instructional sequences aimed to improve this skill. In this article, we present the results from the implementation of such an instructional sequence. A sample of 34 prospective secondary mathematics teachers (PSMTs) validated twelve mathematical arguments written by high school students. They provided a numeric score as well as a short paragraph of written feedback, indicating the strengths and weaknesses of each argument. The results provide insight into the errors to which PSMTs attend when validating mathematical arguments. In particular, PSMTs’ written feedback indicated that they were aware of the limitations of inductive argumentation. However, PSMTs had a superficial understanding of the “proof by contradiction” mode of argumentation, and their attendance to particular errors seemed to be mediated by the mode of argument representation (e.g., symbolic, verbal). We discuss implications of these findings for mathematics teacher education.     

Analysing the correlation between secondary mathematics curriculum change and trends in beginning undergraduates’ performance of basic mathematical skills in Ireland

The phenomenon in which students enter university under-prepared for the mathematical demands of their undergraduate courses, regularly referred to as the ‘Maths Problem’, has been widely reported in Ireland, UK, Australia, and the US. This issue has been of particular concern in Ireland recently, with beginning undergraduates’ performance of basic mathematical skills showing signs of significant decline in recent years. New mathematics curricula, commonly referred to as ‘Project Maths’, were gradually introduced into the Irish secondary school education system from 2010 onwards. These new curricula aim to place greater emphasis on student understanding of mathematical concepts, use of contexts, and applications of mathematics. This study analyses, through mathematics diagnostic test data gathered between 2008 and 2014, the change in the basic mathematical skills of beginning undergraduates over the time period in which the new mathematics curricula were introduced to secondary education in Ireland. It was found that students’ basic mathematical skills have declined over the time period during which the new mathematics curricula were introduced. Significant declines in beginning undergraduates’ performance of basic mathematical skills were observed during the period 2008–2014, particularly among students who have achieved Higher Level C grades and Higher Level D grades.     

Self‐Regulation and Mathematics Instruction

Abstract The purpose of this article is to provide an overview of research‐based interventions that incorporate self‐regulation strategies to improve mathematics performance of students with learning disabilities (LD). Self‐regulation is a metacognitive function essential to academic success. Students with LD are notoriously poor at self‐regulation and must be taught explicitly to monitor and control their cognitive activities as they engage in academic tasks such as mathematical problem solving. This article describes intervention studies that use self‐regulation strategies to improve mathematics performance of students with LD at the elementary, middle, and secondary school levels. Several techniques to facilitate effective implementation of self‐regulation instruction in the classroom are presented.     

First‐year secondary school mathematics students’ conceptions of mathematical proofs and proving

The aim of this study is to investigate students’ conceptions about proof in mathematics and mathematics teaching. A five‐point Likert‐type questionnaire was administered in order to gather data. The sample of the study included 33 first‐year secondary school mathematics students (at the same time student teachers). The data collected were analysed and interpreted using the methods of qualitative and quantitative analysis. The results have revealed that the students think that mathematical proof has an important place in mathematics and mathematics education. The students’ studying methods for exams based on imitative reasoning which can be described as a type of reasoning built on copying proof, for example, by looking at a textbook or course notes proof or through remembering a proof algorithm. Moreover, they addressed to the differences between mathematics taught in high school and university as the main cause of their difficulties in proof and proving.     

Making the invisible visible: a methodological and a substantive issue

This article discusses the issue of ‘making the invisible visible’ from a methodological and a substantive viewpoint. The ideas emerged from a doctoral research study into individual target setting with middle ability students in an English secondary school. The students involved had been identified by assessments as ‘average’ and by their teachers as quiet, unnoticed children. It is suggested that the methods used by the researcher to elicit the students' perceptions could also be used by teachers in order to engage these quiet students in a learning discourse.     

核心素养下的初中数学教学策略

随着新的教育理念的更新发展,对于数学教学的要求也不再是让学生学习基础的数学知识,而是要求培养学生的核心素养,切实培养学生应用数学知识解决实际问题的能力,为学生的全面发展奠定良好的教育基础。为此,初中教师需要结合学生的特点,主动转变教育理念,坚持以学生为主体,相信学生并且在教学时以核心素养为标准科学选择教学方法。