Effective Mathematics Teaching Research Articles

Careful Co-Planning for Effective Team Teaching in Mathematics

This paper reports on a semester-long co-teaching investigation in which three mathematics teacher educators in the USA themselves enacted a co-plan/co-teach credentialing model in the context of a mathematics content course for future elementary teachers. The mathematics teacher educators sought to examine the co-planning practices for improving the team teaching co-teaching strategy. Data were collected from the mathematics teacher educators over fifteen weeks, including twice-weekly journal entries and classroom observation protocols. Utilizing a first-person research study design, the mathematics teacher educators found that a co-planning strategy could be used to maximize resources and improve lesson cohesion during team taught lessons. In particular, the mathematics teacher educators used co-planning meetings to divide lesson responsibilities by learning goal or by task. In this novel approach to mathematics teacher educator training, we describe the co-planning strategy along with its expansion, implementation, benefits, and limitations, and argue for its use in co-teachers’ co-planning repertoire.

Developing Student Teachers’ Skills at Eliciting Students’ Mathematical Thinking Using the Coaching Cycle

Eliciting students’ thinking is a key component of effective student-centered mathematics instruction, and research demonstrates promising approaches to developing this skill in pre-service teachers [PSTs] during methods courses. However, few studies have provided insight into how PSTs can be supported in continuing to develop the skill of eliciting thinking during student teaching internships. This case study describes the development of two PSTs as they worked to fully elicit their students’ thinking during their internship, with the support of a coach. The PSTs’ development generally aligned with an emergent trajectory synthesized from the literature; however, additional specificity was needed to fully interpret the data. Both PSTs learned to effectively probe the thinking of students who provided correct answers to initial prompts but made less progress in probing students’ incorrect answers. The article concludes with an analysis of the learning opportunities presented by the coaching moves, as well as missed opportunities.

Factors that cause students to develop math anxiety and strategies to diminish

This research aimed to determine the factors that cause elementary school students to feel fear and anxiety about mathematics and to identify the strategies that the teachers can use to reduce and eliminate these factors. For this purpose, a case study method based on qualitative approach was used in the study. Researchers created an online questionnaire and collected the data from randomly selected 65 classroom teachers working in various primary schools of Northern Cyprus in the 2019-2020 Academic Year. The questionnaire was finalized in line with the literature search, feedback from the field experts and the pilot study to ensure the reliability of the study. In the first part of the questionnaire, there are questions to determine the demographic features of the participants. In the second part, there are questions to determine the opinions of the teachers about the factors that may cause students to develop 'fear and anxiety towards mathematics (student, teacher, parent, and other factors). The third part of the questionnaire comprises a question to identify the strategies that the teachers use to reduce and eliminate the factors that cause anxiety development towards maths. The study is thought to contribute to the classroom teachers and the literature as it is a research aimed at identifying the factors that prevent effective mathematics teaching and the data will help teachers rethink and redesign the math courses based on data obtained.
 
 Key words: Anxiety, Effective Teaching, Teachers, Mathematics, Primary School, Total Quality Management

Bearing/Distance Problems in Mathematics: Teachers’ Construction Efficacy in the Secondary School in Plateau State, Nigeria

<p style="text-align:justify">In Nigeria, most teachers among other things lack the necessary teaching skills, and mastery of subject matter for effective teaching of mathematics at the secondary school level. These deficiencies have often resulted in high and repeated failure rates in national and standard mathematics examinations. The present study investigated the ability of mathematics teachers to construct practical and realistic word problems in bearing and distance toward mitigating the deficiencies. The research methods adopted were exploratory and descriptive surveys due to the need to explore and analyze the abilities using quantitative techniques. Sample consisted of 292 (35.48%) mathematics teachers who took part in the in-service training workshop organized by the Mathematical Association of Nigeria (MAN) in Plateau state, Nigeria. Purposive sampling technique was used to select the sample that involved the workshop participants only. The instrument ‘construction of practical and realistic word problems in bearing and distance test (CPRWPBDT)’ was used for data collection while the analysis was carried out using simple percentages, mean scores and one-way ANOVA. The findings of the study among other things revealed that the mathematics teacher participants constructed practical and realistic word problems in bearing and distance within 91.67% completion rate, 70.45% of the problems constructed were within the context, at least 75% rate of correctness with little difficulties/errors was observed in sketching (65.90%), and reality (40.90%). The variations observed within the participants in the construction of the problems were statistically not significant. Thus it was recommended among other things that mathematics teachers should undergo regular in-service workshop training to help in developing essential skills themselves for constructing practical/realistic word problems in bearing and distance; and should avoid unnecessary errors for meaningful teaching and learning of bearing and distance.</p>

Instructional videos: an intervention to an effective mathematics instruction

This study attempted to (1) identify the learners? level of understanding of the different Mathematics concepts, (2) devise instructional videos, (3) identify the learners? perception of the instructional videos in terms of its (a) purpose, (b) content and (c) video quality and to (4) ascertain whether there is a significant difference in the learners? level of understanding before and after the intervention. This employed an experimental approach of research that made use of the devised instructional videos, achievement test and survey questionnaire. The respondents were one hundred (100) learners of Buenavista Integrated National High School. It is determined that the use of the instructional videos gives a highly significant difference in the improvement of the learners? understanding. Also, the feedback survey questionnaire also gained highly favourable results. With regards to the instructional videos? purpose, it was generalized that it was very helpful to achieve the standards set by the department. Meanwhile, it was also found out that in terms of the content of the tool, the learners noted that the activities, examples, and exercises are appropriate and suits all types of learners with varying backgrounds. Moreover, the video is identified to be in high resolution and quality, not affecting its performance while being presented and watched. Overall, the impact of the instructional videos to the learners? attitude towards learning and its effect on the achievement of the competencies are highly favourable.

Forty Years of Mathematics Education: 1980-2019

The purpose of this study is to establish the evolution and expose the trends of research in mathematics education between 1980 and 2019. The bibliometric analysis of the articles in Web of Science database indicated four-clustered structure. The first cluster covers the items related to the theoretical framework of mathematics education whereas the second cluster has the terms defining the methods for effective mathematics instruction. The third cluster includes the concepts interrelated to mathematics education while the fourth cluster encloses the studies about international mathematics assessments. The earlier studies look mathematics education mostly in students’ perspective and investigates generalization, restructuring, interiorization and representation. Between 1995 and 2010, curriculum and teacher-related factors were dominant in mathematics education studies. After 2010, the articles investigated specific topics and carried the traces from all stakeholders in mathematics education. The investigation on the trends of mathematics education would provide gain insight about the areas that need more research, contribute to the researchers, teachers, students and policy makers in this field and light the way ‎for further studies.

Preparing Pre-Service Teachers for Mathematics Teaching at Primary Schools in Vietnam

This article aims to identify the professional competencies that primary school teachers in Vietnam need for effective mathematics teaching and the extent to which teacher-training colleges prepare pre-service teachers with those competencies. A mixed method approach with an explanatory sequential design was employed. Questionnaires were sent to 493 pre-service teachers and interviews were conducted with 20 teacher trainers from five major teacher-training colleges in Vietnam. The findings indicated that Vietnamese pre-service teachers were adequately trained in terms of mathematical content knowledge yet were less ready in terms of mathematical teaching pedagogies. Mathematical pedagogical content knowledge was reportedly an often-neglected area at teacher-training colleges and was subsumed under general pedagogical content knowledge. The study has both theoretical and practical contributions to the development of professional qualities for primary school teachers teaching mathematics at primary school in Vietnam.

Teaching Classroom Mathematics: Linking Two Pedagogical Models for Promoting Student Engagement and Conceptual Connections

This paper explains how an original conceptual framework model for mathematics pedagogy, the Australian Curriculum Conceptual Rubric (ACCR), has continued to be used successfully by the author in pre-service and in-service teacher education programs over the past ten years or more. Now further enhanced by a deeper reflection upon Peter Sullivan’s Six Principles (2011) for the effective teaching of classroom mathematics, the ACCR is based on four preparatory “big questions” that the teachers may ask of themselves and their students. The model is also a sequenced system of conceptual “rubrics” whose aim is to encourage, in new teachers especially, a beginning sense of hierarchical mathematics concept building and connectedness. Using Sullivan’s Principles for corroboration, the ACCR presents some useful ideas for helping teachers to keep track of the important elements of practical, effective teaching, and to use engaging and meaningful language in their classrooms.

A network case of knowledge brokering

PurposeThe purpose of this paper is two-fold: (1) to offer a conceptual understanding of knowledge brokering from a sociometric point-of-view; and (2) to provide an empirical example of this conceptualization in an education context.Design/methodology/approachWe use social network theory and analysis tools to explore knowledge exchange patterns among a group of teachers, instructional coaches and administrators who are collectively seeking to build increased capacity for effective mathematics instruction. We propose the concept of network activity to measure direct and indirect knowledge brokerage through the use of degree and betweenness centrality measures. Further, we propose network utility—measured by tie multiplexity—as a second key component of effective knowledge brokering.FindingsOur findings suggest significant increases in both direct and indirect knowledge brokering activity across the network over time. Teachers, in particular, emerge as key knowledge brokers within this networked learning community. Importantly, there is also an increase in the number of resources exchanged through network relationships over time; the most active knowledge brokers in this social ecosystem are those individuals who are exchanging multiple forms of knowledge.Originality/valueThis study focuses on knowledge brokering as it presents itself in the relational patterns among educators within a social ecosystem. While it could be that formal organizational roles may encapsulate knowledge brokering across physical structures with an education system (e.g. between schools and central offices), these individuals are not necessarily the people who are most effectively brokering knowledge across actors within the broader social network.

Использование веб-технологий в эффективном обучении математике в вузе

The article describes the role of web technologies in effective teaching of mathematics at universities. The advantages of the use of WebQuests are defined. This study aims to examine the effect of WebQuests used in instruction on students’ academic achievements and the student and teacher opinions on WebQuests.

Mathematics teacher educator noticing: examining interpretations and evidence of students’ thinking

Noticing is a skill that is not overtly observable yet is consequential to effective mathematics instruction. Researchers have found that prospective and practicing teachers can learn to notice, but little focus has been given to those who teach teachers to notice. The purpose of the study was to characterize mathematics teacher educators’ noticing and their ability to interpret students’ thinking and connect interpretations to evidence. Participants in the study included 16 mathematics teacher educators who took part in a course designed to support noticing. Results indicate the mathematics teacher educators noticed at varying degrees and improved their noticing and incidence of connections between interpretations and evidence. Findings indicated that 19% of participants had no shift in their noticing because they were at the highest level of noticing to begin with (Robust with Strong Evidence), which was considered advanced noticing. Twenty-five percent of the participants did not shift in their noticing at all and remained at Limited, which is considered an intermediate level of noticing. The remaining 56% of the participants improved their noticing. The results of the study reveal that at the end of the course a majority of the participants were able to connect interpretations with evidence. These findings are important because they describe mathematics teacher educators’ interpretations and evidence as they notice.

Factor analysis and psychometric evaluation of the mathematical modeling attitude scale for teachers of mathematics

The effective teaching and learning of mathematics through mathematical modeling and connecting mathematics to the real world has gained rapid growth at various educational levels all over the world. The growth in modeling practices in the United States of America (US) and the international community is the result of the development and implementation of new mathematics standards and curricula across the world. In this article, we report on the development and use of a quantitative instrument aimed at assessing teachers of mathematics attitudes toward mathematical modeling practices. Based on the responses of 310 practicing teachers of mathematics from the US, the mathematical modeling attitude scale was evaluated using item analysis, exploratory factor analysis, confirmatory factor analysis, and other psychometric properties. The scale isolated four dimensions: constructivism, understanding, relevance and real-life, and motivation and interest. These 4 factors accounted for 59% of the variation in the 28-item measure. Cronbach’s alpha coefficient for the overall scale was .96, and that for the subscales was .93 for constructivism, .81 for understanding, .88 for relevance and real-life, and .89 for motivation and interest. The findings suggest a psychometrically useable, reliable, and valid scale for studying teacher’s attitudes toward mathematical modeling. We discuss the instrument’s merit for research and teaching, and implications for teacher education, professional development, and future research.

Understanding the Concept of Language of Mathematics for Effective Teaching and Learning of Mathematics in a School System

The paper deals with understanding the concept of language of mathematics for effective teaching and learning of mathematics in a School System. It as well looked at the causes of students’ failure in mathematics in internal and external examinations to include lack of understanding of mathematics language. The persistent poor performance of students in internal and external examinations in mathematics has become an issue of concern to Mathematics educators, and relevant stakeholders. Findings of recent research studies in mathematics education have identified inadequate understanding of mathematics language to translate word problems into mathematical form as one of the factors responsible for poor performance. Hence, this paper examined the language of mathematics and its understanding. Specifically, the paper discussed the algebraic language; the language of basic operations; the language of set theory; the language of functions; the language of relations; the logical language and the language of differential calculus. The paper further examined the usefulness of variables; difficulties in learning mathematical language and made some recommendations among many others to include that mathematics teachers should teach the mathematical language instruction in mathematics before proceeding to the topic proper to enhance better performances of students in mathematics.

Adopting Mathematics as A Desired Insrtument for The Reduction Of Corruption In Nigeria

This paper discussed that mathematics is a valuable subject, as such, it is vital in inculcating good and acceptable behaviours and values among different categories of students in Nigeria. Since corruption is not an acceptable behaviour and there is the need to avoid and prevent it in the society, it was argued that with effective mathematics teaching and learning, students will acquire the knowledge and inherent values of mathematics towards cultivating good and acceptable behaviours. This will help Nigeria to produce well-behaved citizens and to develop in a healthy manner. Some vital concepts in mathematics through which good and acceptable behaviours and values can be inculcated into students discussed in this paper include the critical roles of formulas, logic and mathematical games. The paper concluded that, besides the acquisition of knowledge, mathematics is useful in cultivating good behaviours in students for good the society. It was thereof, recommended that all mathematics teacher should be encouraged to teach the subject very well through the use of practical examples in order to make its learning simple, realistic and interesting for the students. Also, in the course of teaching, they need to give examples of how specific aspects of mathematics could be used to help in moulding the behaviours of students positively

Effective Teaching and Evaluation of Mathematics by Secondary School Mathematics Teachers in the North West Region of Cameroon

The study set out to examined the extent to which secondary school mathematics teachers implement the principles of effective teaching and evaluation of mathematics as put forward by the National Council of Teachers of Mathematics – NCTM; principles which when effectively implemented will enable learners to construct knowledge thereby doing away with mathematics phobia, and consequently performing better in mathematics. The study adopted a descriptive survey research design. The population of the study was made up of 600 public and private secondary school mathematics teachers serving in the North West Region of Cameroon. Using the Taro Yamane’s formula, 240 mathematics teachers selected through simple random sampling, constituted the sample of the study. Two research questions and two hypotheses guided the study. A questionnaire whose Cronbach alpha reliability was found to be 0.87 was used to collect relevant data. The data collected was analysed using mean to answer the research questions and t-test to test the hypotheses at the 0.05 level of significance. The findings of the study revealed that the level of implementation of the principles of effective teaching and evaluation of mathematics by secondary school mathematics teachers in the North West Region of Cameroon is significantly low. Furthermore, male and female mathematics teachers do not differ significantly in their implementation of the principles of effective teaching and evaluation of mathematics. It was recommended among other things that secondary school mathematics teachers should embrace the NCTM principles of effective teaching and evaluation of mathematics with finesse and incorporate them within their instructional programs and practices.

The Challenges of South African Teachers in Teaching Euclidean Geometry

The current study identifies challenges confronting teachers in the teaching of Euclidean geometry in schools. This qualitative case study purposefully selected ten schools situated in the Motheo District of Education, Free State, South Africa. Data was generated using classroom observations and focus group interviews. The findings revealed that the majority of the teachers lacked mathematical subject content knowledge as well as pedagogical content knowledge to teach geometry effectively. In many cases, redeployment of teachers led to teachers being ill-equipped to teach specific subjects, such as mathematics. Recommendations have been made to enhance effective teaching and learning of mathematics (geometry in this case) in schools. https://doi.org/10.26803/ijlter.19.8.16

Efficacy of the Bar Model Method of Teaching Mathematics to Year 7 Students: Case Study of Teachers in Brunei Darussalam

Mathematics is a subject that challenges many Brunei secondary school students. The Bar Method of instruction uses visual or pictorial representations to make mathematics easier to understand. The survey participants consisted of 127 randomly selected teachers (24 males and 103 females). Male teachers had significantly higher negative attitudes toward the BMM strategy than their female counterparts. The predictor variables that were significantly related to effective teaching of mathematics using the BMM included gender, age, Experience in using the BMM, Positive opinions on BMM, and district of residence. Evidence from the present study showed that the BMM was not much used by many school teachers. Only a small number or percentage of teachers used the BMM strategy when instructing students in mathematics most likely due to lack of skills and experience in using the method. However, both genders expressed the desire to use the BMM strategy in future, an indication of the degree to which the BMM is rapidly gaining popularity. Further large scale mixed-methods research employing interview probes was recommended to gain additional insights.

Effective mathematics teaching in tertiary technological education: The case of ASPETE

In this mixed methods study, we draw upon a systemic perspective to investigate the way that effective mathematics teaching is constructed in the ASPETE (School of Pedagogical and Technological Education) learning system. We focused on the perspectives of the first-year students (through questionnaires), of the lecturer who taught the course (through interviews), as well as of the research team (through observations). We considered both the pragmatic level (what they actually experienced) and the desired level (what they would prefer to experience). The results of the conducted analyses support the proposed research approach, revealing convergences and divergences in the mapped perspectives, which identify the mathematics teaching effectiveness of the subsystem of the mathematics class in ASPETE as an emergent, systemic phenomenon. The pedagogical implications are discussed, with respect to the planifications of teaching and learning mathematics in the ASPETE learning system.

Teaching the mathematics that teachers need to know: Classroom ideas for supporting prospective elementary teachers’ development of mathematical knowledge for teaching

The goal of this article is to articulate aspects of mathematical knowledge for teaching (MKT) that should be addressed in college mathematics content courses for prospective teachers (PTs), and to make research- and practice-based recommendations of class activities, materials, and strategies in support of developing this knowledge. We describe class activities that engage PTs in problem solving as a means of making sense of the content that they will later teach and that immerse them in the mathematics practices that they will later need to foster with their own students. We also provide examples of how mathematics manipulatives, school curriculum materials, and samples of children’s thinking can be integrated as instructional tools in content courses. In developing these activities, we were guided by the research regarding the depth and breadth of knowledge required for the effective teaching of mathematics at the early childhood and upper elementary levels, and by the recommendations of professional organizations for math teacher education.

Learning about Active Learning While Actively Learning: Insights from Faculty Professional Development

ABSTRACT With knowledge in hand that teaching mathematics through active engagement leads to better learning outcomes for students, the field of mathematics is now tasked with researching effective facilitation of professional development for faculty. Our university embarked on an initial year of active learning professional development for mathematics faculty, implementing and researching a variety of professional development formats. We conjectured that effective faculty professional development, like effective mathematics instruction of students, would engage faculty in active learning experiences. Initial results indicate that effective professional development for faculty is tightly aligned with effective classroom instruction of students. This paper provides a framework of professional development practices for faculty, informed by a subset of mathematics instructional practices.