Mathematics Classroom Instruction Research Articles

Differentiating Instruction: Development of a Practice Framework for and with Secondary Mathematics Classroom Teachers

This article outlines an approach to bridging the gap between the theory and practice of differentiated instruction. Differentiated instruction has long been suggested as a pedagogical approach to cater for student individuality and diversity, particularly in mixed-ability classrooms. Although the theory of differentiated instruction has been applied widely, such instruction has not been taken up widely in teaching practice. The first part of the article explores the relationship of theory and practice of differentiated instruction in relation to pedagogical content knowledge, teacher efficacy, formative assessment, teacher confidence and competence and professional learning. This exploration uses exemplar cases from mathematics teaching to pave the way for an outline, in the second part of the article, of how differentiated instruction could be implemented for the mixed-ability groupings increasingly engaged in the Australian secondary mathematics classroom. A protype practice framework for teachers is presented as part of a project being conducted in regional Australia, with the overall aim of assisting teachers in developing and implementing strategies for differentiated instruction in secondary mathematics classrooms.

The contribution of online mathematics games to algebra understanding in Grade 8

This study explores how online mathematics games contribute to Grade 8 learners’ understanding of basic principles and more sophisticated aspects of algebra. This project documents the trajectory of a purposive sample of 30 Grade 8 learners doing mathematics and one mathematics educator. The study is premised on the argument that learners with the guidance of the teacher can grasp algebraic concepts better and learn to manipulate these imaginatively and independently, by integrating new online mathematics games into standard classroom teaching of mathematics. The study was located within the interpretive qualitative research paradigm and used a case study approach. Data were collected by means of (1) lesson observations, (2) questionnaires and (3) semi-structured interviews. The data collected were analysed through the lens of the sociocultural theory, social constructivism and the activity theory. This study supports the view, set out in the literature reviewed, that the way in which resources are utilised can substantially improve the teaching and learning of algebraic concepts. Teachers should encourage learners to venture into the world of online mathematics games to learn algebra because they help learners to be creative, look for patterns, make conjectures, collect data, express their own thoughts, accept the ideas of others and establish structured forms of cooperation. The teacher’s role is to show and guide the learners how to use online mathematics games to solve mathematics problems. This study’s main recommendation, among others, is a revision of the curriculum to integrate online mathematics games into all subjects in classrooms at all levels.

Research on Mathematics Classroom Teaching Based on the Model of Hierarchical Teaching Management

With the implementation of nine-year compulsory education, and our school is located at the border of urban and rural areas, there are many children in rural areas and the quality of students varies. The problems of mathematics learning in our school have come to the fore. Some do not learn at all, and some cannot learn. Coupled with the traditional thinking that mathematics is a “big problem” in students’ minds, students’ learning initiative and self-consciousness are generally higher. Poor, it was difficult to improve at one time. On the other hand, limited by students’ large classes, number of class hours and 45 minutes of class time, classroom teaching can provide students of different levels with limited participation opportunities. Therefore, as a mathematics teacher in actual work, they will constantly try to use better methods. To change the problem of student differences in class teaching mode. By analyzing the status quo of mathematics teaching in the middle school, studying the reform practice of mathematics teaching at home and abroad, it is decided to conduct experimental research of layered teaching in mathematics classroom teaching of our school. Hierarchical teaching conforms to the dialectical theory of materialism, the theory of pedagogy, the learning psychology of students, and the principles of teaching students in accordance with their aptitude in the teaching theory. It has a broad theoretical foundation.

Activity systems analysis of classroom teaching and learning of mathematics: a case study of Japanese secondary schools

Activity systems analysis of classroom teaching and learning of mathematics: a case study of Japanese secondary schools

Responsiveness and intellectual work: Features of mathematics classroom discourse related to student achievement

ABSTRACT Background: This study considers the moment-by-moment mathematics discourse of teachers and students and the relationship of these discourses to student learning. I focus on the discursive constructs of responsiveness to students’ mathematical thinking and the intellectual work in teacher and student discourse. Responsiveness to students’ mathematical thinking is the extent to which one acknowledges, elicits, takes up, or builds on student thinking in-the-moment. Intellectual work reflects the cognitive work set in motion or performed by a speaker within a given turn of talk. Methods: I developed analytic frameworks that accounted for different levels of responsiveness and intellectual work during whole-class instruction in seventh-grade mathematics classrooms. These frameworks captured variation in responsiveness and intellectual work which was linked to student achievement using MLM. Findings: Analyses revealed a significant positive relationship between teachers’ responsiveness to student thinking and student learning. Additionally, the intellectual work requested by the teacher was related to the level of intellectual work students provided, acting as an upper bound on students’ mathematical activity. Contributions: The analytic frameworks developed for this study identified forms of responsiveness (High Exploring moves) that were most effective for student learning and specified the relationship between a teacher’s and her students’ levels of intellectual work.

A Brief Discussion on How to Evaluate Students in Mathematics Classroom Teaching Activities of Lower Grades in Rural Primary Schools

A Brief Discussion on How to Evaluate Students in Mathematics Classroom Teaching Activities of Lower Grades in Rural Primary Schools

On the Art of Establishing Doubt in Mathematics Classroom Teaching

On the Art of Establishing Doubt in Mathematics Classroom Teaching

Design and Research of Mathematics Teaching Intelligent Classroom Based on PCA-NN Algorithm.

With the increasing importance of mathematics in basic education, how to evaluate and analyze the intelligent effect of mathematics teaching classroom through scientific methods has become one of the indicators to evaluate the intelligent classroom. This paper studies the design and application of mathematics teaching intelligent classroom based on the PCA-NN (principal component analysis-neural network) algorithm. Firstly, this paper briefly describes the current research status of mathematics teaching intelligent classroom design and PCA-NN algorithm. Secondly, combined with the key factors of mathematics teaching, it formulates specific standards and puts forward an adaptive strategy of intelligent and personalized intelligent mathematics teaching classroom. Finally, the algorithm is verified by experiments. The results show that, for students with different mathematics basic levels, the mathematics teaching intelligent classroom based on the PCA-NN algorithm can effectively improve the quality of mathematics classroom teaching. Through the research on the factors such as teaching quality, effect, and interaction mode involved in the process of mathematics teaching classroom design, the intelligent classroom design factors affecting teaching quality are determined. This paper analyzes and studies the system from different angles. The research results provide some help for the current quality evaluation of classroom teaching and use the PCA-NN algorithm to make quantitative analysis and multivariate verification of mathematics classroom teaching effect.

小学数学课堂教学中语言艺术的应用策略

小学数学课堂教学中语言艺术的应用策略

The Reform of High School Mathematics Classroom Teaching

The Reform of High School Mathematics Classroom Teaching

Exploration of Mathematics Classroom Teaching Practice in Middle School under the Concept of Core Mathematics Literacy

With the rapid development of the social economy, people pay more and more attention to receiving education. The traditional duck-filling teaching model is contrary to the quality education concept of the new curriculum reform and does not conform to the trend of the times. With the deepening of the new curriculum reform, people-oriented teaching ideas have gradually become prominent, teachers in various subjects are trying their best to explore new teaching methods and find differentiated teaching methods. Mathematics is an important setting for middle school courses, and it takes a large proportion in the entrance examination. The core literacy of mathematics is formed in mathematics knowledge skills, but it is higher than mathematics knowledge skills. Based on the background of contemporary education, this article analyzes the value of core literacy and the guiding role of strengthening the core literacy of mathematics in an attempt to add benefits to the effective development of mathematics teaching in middle schools.

The comprehensive evaluation method of mathematics classroom teaching based on AHP

The comprehensive evaluation method of mathematics classroom teaching based on AHP

A framework for designing mathematics instruction using comics at the primary school level

Developing primary school students’ interest in and getting them motivated to learn mathematics has been a perennial focus of educators. The use of comics for classroom instruction is an area gaining more attention from educators. In this paper, we review some existing education literature on the impact of comics on students’ cognitive and affective learning needs. We also propose a TSCT (Theme, Storyline, Character, Text) framework for educators to design instructional material using comics for mathematics instruction in the primary mathematics classroom. With the TSCT framework, we demonstrate the design of one comics mathematics lesson on the topic of Fraction.

Enhancing the Teaching and Learning of Basic Arithmetic Through Subitizing

This paper examines how subitizing (recognizing a quantity and naming it without having to count the objects individually) can help develop students’ understanding of basic arithmetic and how teachers’ and students’ actions can inform one another. Studies suggest that subitizing is underused in teaching and can be harnessed to enhance the learning of subtraction and addition because of its deep links to visualization. Pairing research that points to possibilities of using subitizing to teach arithmetic with an enactivist view of teaching, this research examines how teachers’ and students’ actions co-adapt. Data from short, seven- to eight-minute addition and subtraction lessons in a Grade 2 classroom were collected and analyzed with an enactivist view of teaching actions as triggers. Actions included verbal prompts, movement of small circular objects that represent numbers and hand gestures above the objects. In these lessons, teachers and students arranged small circular objects to guess/identify one another’s computational strategies to arithmetic questions. Our findings suggest that teacher actions triggered and were triggered by students’ subitizing capabilities and occasioned making connections between number (de)composition and operations. Teachers’ actions were contingent on students’ actions as they repeated, enhanced or changed their actions. Triggered by teachers’ actions, students were able to use subitizing to describe their computation strategies instead of counting to combine and/or form large values and to (de)compose, add or subtract values. This research recommends the use of subitizing to make arithmetic strategies visual and calls for more research on the co-emergence of teaching and learning in mathematics classrooms.

Experiencing active mathematics learning: Meeting the expectations for teaching and learning in mathematics classrooms

Active learning mathematics classrooms incorporate meaningful activities that emphasize reasoning, thinking and active interaction with mathematics. Current mathematics standards and curricula recommend that Mathematics Teacher Educators (MTEs) use elements of active learning in their mathematics content courses specifically designed for Prospective Teachers (PTs) as they prepare PTs to learn and teach mathematics. However, it can be very difficult for PTs to shift their pedagogical dispositions towards instruction associated with active learning because they typically have not experienced mathematics taught in this way. This article focuses on two instructional practices for MTEs to use with PTs. First, selecting tasks that promote reasoning and problem solving. This includes practices to open tasks for multiple entry points or solution strategies, tasks that allow for analysis of examples and counterexamples, and tasks that evaluate multiple strategies. Second, facilitating meaningful mathematical discourse. This includes practices for whole class and small group discourse. When MTEs use active learning strategies with PTs in their mathematics content courses, PTs begin their journey in shifting their beliefs and understandings about what it means to teach and learn mathematics. By offering PTs valuable active learning experiences during their mathematics content courses and highlighting how these experiences can enhance both PTs’ own understanding and their future students’ mathematical understanding, MTEs will provide a valuable foundation for PTs to meet the expectations for teaching and learning in mathematics classrooms.

A systematic review of the literature regarding socially assistive robots in pre-tertiary education

With rapid advances in Artificial Intelligence (AI) over the last decade, schools have increasingly employed innovative tools, intelligent applications and methods that are changing the education system with the aim of improving both user experience and learning gain in the classrooms. Even though the use of AI to education is not new, it has not unleashed its full potential yet. Much of the available research looks at educational robotics and at non-intelligent robots in education. Only recently, research has sought to assess the potential of Socially Assistive Robots (SARs), including humanoids, within the domain of classroom learning, particularly in relation to learning languages. Yet, the use of this form of AI in the field of mathematics and science constitutes a notable gap in this field. This study aims to critically review the research on the use of SARs in the pre-tertiary classroom teaching of mathematics and science. Further aim is to identify the benefits and disadvantages of such technology. Databases' search conducted between January and April 2018 yielded twenty-one studies meeting the set inclusion criteria for our systematic review. Findings were grouped into four major categories synthesising current evidence of the contribution of SARs in pre-tertiary education: learning gain, user experience, attitude, and usability of SARs within classroom settings. Overall, the use of SARs in pre-tertiary education is promising, but studies focussing on mathematics and science are significantly under-represented. Further evidence is also required around SARs' specific contributions to learning more broadly, as well as enabling/impeding factors, such as SAR's personalisation and appearance, or the role of families and ethical considerations. Finally, SARs potential to enhance accessibility and inclusivity of multi-cultural pre-tertiary classroom is almost unexplored.

Investigating the Perception of Senior Secondary School Students on the Role of Classroom Engagement in Mathematics Problem Solving

This study was designed to investigate the perception of students on the role of classroom engagement in student’s problem solving in mathematics. Specifically, the study investigated the perception of 6 students taught by 4 mathematics teachers in 2 secondary schools in Nigeria for a period of 2 years. Two research objectives were developed to guide the study. Research journal and video recordings were used to document the focus group discussions and classroom observations. The findings of the study suggested that the mathematics teachers made positive effort to use the engagement strategy as a tool to increase students problem solving abilities during mathematics classroom instruction. In addition, the result of the study suggested a positive increase in students’ problem-solving skills. This was evident in students’ engagement in collaboration, participation, increase in positive relationships that existed between students and their teachers. The study also suggested that the mathematics teachers created positive classroom atmosphere for students’ participation in classrooms problem solving. It also suggests that teachers provided inclusive support for students’ problem solving in mathematics and provided evidence of general traditional teacher centred learning in mathematics as opposed to student-centred learning among the students.

Classroom Management as a Response to Challenges in Mathematics Education: Experiences from a Province in South Africa

This paper reports on an investigation into management in Mathematics classrooms. Classroom management is contextualised in terms of the managerial actions required to manage classrooms effectively and the extent to which effective classroom management responds to contextual challenges. Relevant literature is reviewed, and theoretical perspectives with investigative value for classroom management are examined. Data was collected using individual semi-structured interviews with four Mathematics department heads and with five teachers per school, for the four focus group interviews. The interviews were audio-taped, transcribed and the data analysed using a process of abductive data analysis as suggested by McMillan and Schumacher (2010; Research in education: Evidence-based inquiry, 4th ed., Pearson Education). The participants in this study supported the use of different overlapping management styles. Teachers apply these styles by introducing useful and suitable management actions in their classroom practice. It was found that organising group work and motivating learners are actions that encompass the majority of functions related to the management of teaching and learning in Mathematics classrooms. Contextual influences like teachers’ professional competencies, curriculum implementation, the maintenance of facilities and the availability of resources and learning materials were highlighted as factors that both support and constrain the effectiveness of classroom management.

Characterising the Pedagogical Practices in Mathematics Lessons among Selected Malaysian Primary Schools

This study aims to characterise the pedagogical practices of 45 observed primary mathematics lessons taught by 24 mathematics teachers in six national primary schools (SK) and six Chinese vernacular primary schools (SJKC). The data were collected using two video cameras, one focused on the teacher while the other camera focused on the pupils’ activities. The qualitative data were analysed based on two main activities in the classroom, which are teacher’s activities and pupils’ activities. The findings show that mathematics lessons conducted by SK teachers tended to engage the pupils in individual seatwork so as to assess pupils’ understanding. Conversely, SJKC teachers were focused more on explaining mathematical concepts to help the pupils build up their conceptual understanding. By characterising the pedagogical practices of mathematics lessons in various schools, the researcher hopes that the findings of this study will contribute to better understanding of the teaching and learning process in SK and SJKC mathematics classrooms. The results serve as a documentation of pedagogical practices in Malaysia to enable implementation of suitable programmes to help in improving teachers’ pedagogical practices from different types of primary schools. While the results are interesting and provide some directions, a much larger study would be needed to determine if the results are due to the teachers’ enthusiasm, geographical differences, cultural or social differences, or what is known as the Hawthorne Effect.

The derailing impact of content standards–an equity focused district held back by narrow mathematics

Many school districts strive to achieve high mathematics achievement and equitable outcomes. This study examines the work of Gateside district, an urban district that had made great progress in the enactment of equity minded policies such as de-tracking and the availability of high-level mathematics to all students. A detailed, case study of teaching and learning in the high school mathematics classrooms showed that the equity focused work of the teachers and district leaders was compromised by the narrow mathematics standards that informed the tasks used in classrooms. The prevalence of narrow tasks led students to develop binary perceptions of each other, revealing a fundamental tension between narrow content standards and equitable outcomes.