Mathematics Subject Knowledge Research Articles

How might a mastery style of teaching in mathematics lead to deeper understanding and sustained levels of attainment?

ABSTRACT The ‘mastery’ approach for the teaching of mathematics in primary schools has been advocated by the UK government stating it will develop deeper understanding and sustained learning for pupils. The approach, emulated from countries that have scored highly in international testing, has seen varied implementation in England. This research aims to compare the understanding of the mastery approach and its implementation in two English primary schools to the approach to teaching mathematics in Shanghai. The findings suggest that the implementation must be supported by relevant and ongoing training in both subject and pedagogical knowledge in mathematics for all practitioners.

유아교사의 수학적 상호작용에 대한 수학지원지식의 영향

Objectives In this study, it was verified whether the moderating effect of teaching creativity on the effect of early childhood teachers' play teaching efficacy and mathematics pedagogical content knowledge on mathematical interaction was significant.
 Methods For this purpose, 300 nursery class teachers working at daycare centers and kindergartens in the metropolitan area were selected. As a measuring tool for the mathematical interaction of early childhood teachers, Kim and Kwon (2022)'s tools and early childhood teachers' mathematics subject pedagogical knowledge tool developed by Hong and Jeong (2012) were used to find out mathematics pedagogical content knowledge. In order to measure teaching creativity, the ‘teacher's creative teaching-learning test tool’ developed by Cropley (2004) was modified and adapted by Baek and Kim (2008) and validated and verified. For data analysis, frequency, percentage, average, reliability analysis, partial correlation analysis, multiple regression analysis for moderating effect analysis, and moderating effect analysis were conducted using the SPSS 22.0 program. At this time, a hierarchical multiple regression analysis was conducted after injecting the status of tenure and training, career, number of times of use of study materials, and the number of homeroom teachers as control variables.
 Results The effect of mathematics pedagogical content knowledge on the mathematical interaction of early childhood teachers was regulated by teaching creativity.
 Conclusions This study found that the early childhood teacher's teaching creativity plays a role in regulating the effect of mathematics pedagogical content knowledge on mathematical interaction, and thus the role of teaching creativity is important in the variables that affect mathematical interaction. Therefore, it was revealed that educational and institutional support for improving teaching creativity is needed first.

Lärarstudenters förutsättningar att utveckla yrkesspecifika kunskaper

This study aims to investigate how the courses in didactics of mathematics in preschool and primary teacher education create conditions for preservice teachers to develop professional knowledge in an interactive learning process that integrates the knowledge domains of mathematical subject knowledge and pedagogical mathematical knowledge. An analysis of 20 course documents and 8 focus group interviews with students have been done. The results show that the intentions in the documents create conditions for the students to develop mathematical subject knowledge. Still, they were given inferior conditions for pedagogical mathematical knowledge. In the focus groups, perceptions emerged among the participants about a changed view of mathematics during the education, from being an abstract theoretical subject to a subject to be explored and discovered through various practical exercises and activities. As support for transferring their newly discovered perception, it is important that the students participate in core practices to bridge the gap between theoretical and practical knowledge in teacher education. The continued development of such core practices, in which student teachers can integrate professional knowledge and skills into their education, is an important implication of this study.

Competency Level of Teachers’ Subject Matter Knowledge as a Compulsory for Teaching Secondary School Mathematics: A Case Study on Postgraduate Diploma Trainee

The purpose of this paper is to assess the status of mathematics subject matter knowledge competency of student teachers and show the role of subject matter knowledge in teaching secondary school mathematics. This study involved 70 student teachers attending postgraduate diploma training program of teacher training modality. An achievement test was used to collect the data from the participant. The result has shown that the overall subject matter knowledge competency of the trainee is remarkably low. However, algebra received relatively higher competency with a mean score of 2.2, and mathematics as communication and reasoning competency was considerably lower with a mean score of 0.56. In addition to these, a comparison among subject matter knowledge competency areas identified shows that there is a significant difference between algebra (higher competency) and the remaining 12 selected subject matter knowledge competency areas. This study concluded that student teachers have a deficiency in mathematics subject matter knowledge competency in general and lack uniformity within selected mathematics subject matter knowledge competency areas. Based on the findings, it is recommended that subject matter knowledge is particularly required for secondary school mathematics teaching needed in the teacher training program and the teacher training program needs amendment toward the direct purpose.

PROBLEM OF PROFESSIONAL TRAINING OF FUTURE TEACHERS OF MATHEMATICS: DOMESTIC CONTEXT OF RESEARCH

The article, based on the analysis of scientific sources and the results of author’s own research, considers the problem of professional training in general and highlights the features of professional training of future teachers of mathematics in particular. It has been established that today there is a wide range of research on the solution of above-mentioned problematic issue, in particular, there is no ambiguity regarding the definition of the professional training of the future teacher. Ukrainian scientists consider professional training as: a purposeful process; a system of corresponding measures; a system of professional training; the goal and result of activity; the acquisition of professional education, as a set of special knowledge, abilities and skills already acquired by a person, as well as a personal achievement on the way to the formation of readiness for the realization of personality in the future professional activity. It was found that the essence of the concept of "professional training of a teacher" should be specified by the peculiarities of pedagogical activity, thus the differences in subject specialization should be accounted for, and, among the priority tasks of professional training, the formation of professional competence in future mathematics teachers is defined. The analysis carried out made it possible to formulate the following: the professional training of a future teacher of mathematics is a purposeful, specially organized educational process that ensures the achievement of the appropriate level of pedagogical and mathematical (subject) knowledge, abilities, skills, as well as the development of personal qualities of future specialists with the aim of forming in them a professional competence. In the structure of professional competence of future teachers of mathematics, key, basic and specialized subject competences, as well as mathematical, methodical, communicative, informational and psychological-pedagogical components are highlighted. It is substantiated that only a high level of development of each component can ensure the formation of professional competence of future specialists. It has been established that due to the modernization processes in education, special importance is now attached to methodical competence, which includes the teacher's assimilation of new methodical and pedagogical ideas, approaches to teaching mathematics. However, at present, all aspects of the problem cannot be considered to have been finally solved. Prospects for further research are outlined in the development of theoretical and methodological foundations of professional training of future teachers of mathematics in the conditions of graduate education.

Mathematical Knowledge for Teaching in Further Education and Training Phase: Evidence from Entry Level Student Teachers’ Baseline Assessments

This paper investigates entry-level student teachers' mathematical knowledge for teaching in the Further Education and Training phase (FET) through Baseline Assessment. The study employed a quantitative research technique. The data collection instrument was a mathematics subject knowledge test (Baseline Assessment) for FET phase student teachers. Purposive and convenient sampling methods were employed in the study. The study enlisted the participation of 222 first-year mathematics education student teachers from a rural Higher Education Institution (HEI) specialising in FET phase mathematics teaching. One hundred and seventy-five (175) student teachers completed the Baseline Assessment for all grades in this study (10, 11, and 12). The Baseline Assessment findings were examined using descriptive statistics. The results revealed that student teachers have a moderate knowledge of mathematics topics in the FET phase at the entry-level. In addition, an adequate level of understanding for teaching Grades 10 and 12 Patterns, Functions, Algebra, Space and Shape (Geometry), and Functional Relationships. While the elementary level of understanding for teaching grade 10 Measurement, Grade 11 Patterns, Functions, Algebra, and Trigonometry and Grade 12 Space and Shape (Geometry). There is no level of understanding for teaching FET phase Data and Statistics and Probability. The paper suggests that student teachers must develop a comprehensive understanding of the mathematics curriculum with the assistance of teacher educators in HEIs.

Teaching Process and Emotional Reactions in Mathematics

Teachers are increasingly required to have mathematical subject knowledge described as lists of facts, skills and competencies. Different emotional reactions are present in the classroom every day. Emotional reactions are most often divided into positive and negative, and negative emotional reactions are most often related to the evaluation process. Teaching mathematics at all stages and levels of education is often a challenge for students. It is known that mathematics is not very popular and one often hears this misconception: "common sense and mathematics do not go together". Unfortunately, statements such as "not for me", "I don't know math" and "my mom is not a mathematician" can often be heard from students. The popularity of mathematics is on the scale of less popular subjects in schools, although teachers are forcing the teaching of mathematics, and even the curriculum offers more math classes than some other subjects.

Migrant Maths Teachers: Deficit, Translanguaging, and Growing Authority

This article draws from a longitudinal case study of trainee (the term used in official documentation related to Initial Teacher Training (ITT) in England and with some reservations throughout this paper) and early-career teachers (ECT) of mathematics. The sample represents migrant teachers that the Immigration Act of 2020 seeks to attract to the UK to address national shortages identified by the Migration Advisory Committee (MAC). The analysis examines how multimodal semiotic repertoires of language, bodies and pedagogical practices are entangled in classroom encounters. It shows how the ideology of Standard English can create an uncomfortable sense of different deficits amongst multilingual professionals and evidences how these can be addressed through a model of authority in which teachers get the right mix of mathematical subject knowledge (epistemic authority), the use of school practices and expectations (practical authority), and individual biography (personal authority). It uses translanguaging spaces to examine how teachers use communicative repertoires to orchestrate semiotic resources and manage their identity positions in ways that promote intercultural competencies during the daily encounters of teachers and their pupils.

Online Baseline Assessment in Mathematics: Initial Teacher Education Entry-Level Student Performance

This article describes a part of an online and technological intervention at a rural South African Higher Education Institution focused at improving the mathematical knowledge of first-year Senior Phase and Further Education Training (SP& FET) Bachelor of Education student teachers. As part of the interventions in an ICT integrated Mathematics Education and Research Centre, the student teachers were subjected to write an online baseline assessment on the content knowledge in Grade 7 mathematics, which is the first year in Senior Phase in South African Schools. A total of 193 student teachers wrote the online baseline test with 20 items in an invigilated computer laboratory environment. The test items were from the online Computer Aided Mathematics Instruction (CAMI) program which is aligned to the Grade 7 CAPS curriculum of South Africa. The data were analysed by the CAMI system and were further analysed using Microsoft Excel 2016. The result of the test showed an average performance of 38,67% (Variance: 0,66% and SD: 0,81%). This sheds light into the disturbingly limited mathematics subject content knowledge the student teachers enter the HEI with. The programme structure of the Senior Phase mathematics content module of the HEI was also analysed. The authors of this paper recommend that student teachers need to be thoroughly engaged in learning the content during their training as future mathematics teachers. This paper contributes to the ongoing research on ITE programmes at HEIs that prepare teachers for their mathematics teaching role in the senior Phase classrooms. 
 
 Received: 21 September 2021 / Accepted: 11 December 2021 / Published: 3 January 2022

Does Teacher Subject Knowledge Contribute to Student Academic Performance in Developing and Least Developed Countries?

AbstractLittle is known about the causal impact of teacher knowledge on student performance. In this research paper we intend to approach the potential causal effect (i.e. going beyond correlation) of sixth grade teachers’ knowledge on their students’ academic achievement for three Sub‐Saharan African countries. To achieve this, we have used the heterogeneity of teachers’ subject knowledge and students’ correspondent academic achievement within‐student between‐subjects using student fixed effects. Concretely, our work is based on previous research by Bietenbeck, Piopiunik and Wiederhold. Compared to them, we do not use countries that lack representative information after keeping only those students taught by the same teacher for the subjects under analysis. This enables us to obtain more reliable results on this issue. Our results indicate that teacher subject knowledge in reading and mathematics does not have a significant influence on student academic achievement in these subjects for the countries under scrutiny. Many robustness checks have corroborated this conclusion, which contrasts with the positive effect found by Bietenbeck, Piopiunik and Wiederhold.

Needs analysis for the implementation of a complementary course in Mathematics education for teachers of Mathematics in Namibia

After the introduction of the Basic Education Teacher Diploma (BETD) in Namibia, a number of studies were conducted on how teachers, lecturers, stakeholders and the Namibian public perceived the BETD program and its implementation. However, very few studies focused specifically on mathematics subject content knowledge and pedagogical content knowledge in the BETD. This paper reports on a study which investigated the need for a complementary course for mathematics teachers to address the perceived lack of mathematical content and pedagogical knowledge in the Namibian BETD. The study involved five mathematics school teachers, two former mathematics college lecturers in the Kavango educational region and a professor of mathematics education at the University of Namibia. These participants were purposefully selected because of their knowledge and experiences with various aspects of the BETD program. And the data was collected by means of two methods namely documents analysis and semi-structured interviews. These methods complemented each other and also provided a degree of cross checking of claims.

Special education and subject teachers’ self‐perceived readiness to teach mathematics to low‐performing middle school students

Educational reforms during the last decade have led to a more inclusive environment for students with different needs and have placed demands on teachers’ readiness to instruct diverse students in the general classroom. Previous research has ascertained that student achievement is correlated with teacher quality and teachers’ efficacy beliefs. Today, basic competence in mathematics is more important than ever for managing routine day‐to‐day activities and therefore, identifying and educationally supporting students with low performance in mathematics is necessary. The aim of the study was to investigate the perceived teacher efficacy beliefs of special education and mathematics teachers when teaching mathematics to low‐performing middle school students. Results indicated that special education teachers had higher teacher efficacy beliefs than mathematics teachers. Teacher experience, certification or gender had no effect on teachers’ efficacy beliefs. Furthermore, subject teachers reported high pedagogical knowledge for teaching low‐performing students, and special education teachers reported having moderate mathematical subject knowledge.

Special education pre-service teachers' interest, subject knowledge, and teacher efficacy beliefs in mathematics

Teacher efficacy beliefs is an important characteristic to predict instructional quality and the level of cognitive activation and educational support. Since teacher efficacy beliefs are context and domain specific, this study focuses on how special education pre-service teachers' individual interest and subject knowledge in mathematics predict their efficacy beliefs in teaching mathematics. Data were collected from 57 special education pre-service teachers. The results indicated that the individual interest of pre-service teachers has a strong effect on teacher efficacy beliefs, while subject knowledge has only an indirect effect.

Relationships between teachers’ background, their subject knowledge and pedagogic efficacy, and pupil achievement in primary school mathematics in Hong Kong: An indicative study

This study investigates how teacher background, subject knowledge and pedagogic efficacy affect Grade 4 children’s (aged 9–10) mathematical achievement in 10 primary schools in Hong Kong. Mathematics teachers were selected for their strong commitment to teaching mathematics and their pupils’ consistently high international mathematics performance. Teacher measures (i.e. level of mathematics education, teaching experience, mathematics subject knowledge, performance in mathematical operations and pedagogic efficacy) were checked for factor consistency and assessed against age-appropriate pupil mathematical achievement. The results showed that teachers were secure in their subject knowledge, and that such knowledge was related to their performance of mathematical operations, but it was high levels of pedagogic efficacy and the ability to perform age-appropriate mathematics operations (rather than subject knowledge) that positively affected their pupils’ achievement. These findings contradict ongoing international calls for the enhancement of primary school teachers’ mathematical subject knowledge, as they show pedagogic efficacy to be more strongly associated with pupil achievement.

Teaching Proficiency and Preparedness of Pre-service Secondary Mathematics Teachers: its Implications to Actual Practice

Teacher training institutions in the Philippines offering Bachelor of Science in Education major in Mathematics like the MUST aimed to produce globally competitive graduates ready for the challenge in becoming the next breed of excellent secondary mathematics educators in the field. However, are the prospective secondary mathematics teachers indeed ready for the challenge? This study would answer this question aimed at identifying the level of competence of these soon-to-be mathematics teachers. It would attempt to examine the pre-service mathematics subject matter knowledge (SMK), expertise in lesson planning activities, classroom management skills, instructional strategies and motivation, communication and questioning skills and professionalism from the cooperating teachers (CT’s) perspective. Data collected were analyzed using frequency count, percentage, mean and standard deviation. Result revealed that the level of SMK of the prospective mathematics teachers was proficient and the rest of the competence indicators were on the approaching proficiency level which implies that although they were proficient with mathematics content, these prospective mathematics teachers are not fully equipped with all the necessary teaching skills. The trainings they received from the university during their academic years was adequate but not sufficient. The researcher then recommends that the university may consider designing an intensive professional development training program to be included in the curriculum for these prospective mathematics teachers before they will be deployed in the field.

EQUIP-Tanzania Impact Evaluation. Briefing Note 1: Teacherss Knowledge, Behaviour and Support in Some of the Most Disadvantaged Districts in Tanzania

This briefing note presents evidence on early grade teachers’ professional capacity and support in 17 of the most disadvantaged districts in Tanzania. The results come from a rigorous mixed-methods baseline study for an impact evaluation of the Education Quality Improvement Programme in Tanzania. The key findings on teachers from the impact evaluation study reveal some important strengths including the fact that most teachers are trained and have good early grade subject knowledge in Kiswahili and mathematics. The research also identifies four major constraints to good teaching in these disadvantaged districts. The challenges associated with these constraints are: improving curriculum and subject knowledge; improving pedagogical skills; getting teachers into the classroom; and providing monitoring and support to teachers.

Addressing prospective elementary teachers’ mathematics subject matter knowledge through action research

There is international dissatisfaction regarding the standard of mathematics subject matter knowledge (MSMK) evident among both qualified and prospective elementary teachers. Ireland is no exception. Following increasing anecdotal evidence of prospective elementary teachers in one Irish College of Education (provider of initial teacher education programme) demonstrating weaknesses in this regard, this study sought to examine and address the issue through two cycles of action research. The examination of the nature of prospective teachers’ MSMK (as well as related beliefs in the main study) informed the design and implementation of an intervention to address the issue. A mixed method approach was taken throughout. In both cycles, Shapiro's criteria were used as a conceptual framework for the evaluation of the initiative. This paper focuses on the perceived and actual effects of the intervention on participants’ MSMK. As well as its contribution at a local and national level, the study provides an Irish perspective on approaches taken to address the phenomenon internationally.

‘Walking in a Foreign and Unknown Landscape’: Studying the History of Mathematics in Initial Teacher Education

This article develops the argument that students in initial teacher education benefit in terms of who they are becoming from developing awareness of and engagement in the history of mathematics. Initially, current school mathematics practices in the UK are considered and challenged. Then the role of teachers’ relationship to mathematical subject knowledge and of teachers’ engagement in critical thinking are considered. Connections are made between these concerns and studying the history of mathematics in initial teacher education classrooms. I then draw on the perspectives and practices of the mathematics teacher educators at one institution to understand these connections better and to exemplify them. Issues of equity are threaded throughout.

The challenges facing initial teacher education: Irish prospective elementary teachers’ mathematics subject matter knowledge

Given the acknowledged relationship between teachers’ knowledge, their teaching and pupil learning, teachers’ mathematics subject matter knowledge (MSMK) has received increased attention internationally. As children's early mathematics experiences have been recognized as a critical stage, elementary teachers’ MSMK has become a focal point among researchers and policy makers alike. International research findings have uncovered that in many cases, there is a mismatch between what is perceived to be an appropriate MSMK for teaching elementary mathematics and that demonstrated by many qualified and prospective elementary teachers. Following repeated incidences of weak MSMK during interactions with prospective elementary teachers in one Irish College of Education (provider of initial teacher education programme for elementary teachers), this study sought to examine and address the issue purposefully through two cycles of action research. This article focuses on the data collected prospective teachers’ MSMK in the initial stage (reconnaissance) of these cycles, i.e. pre-test findings. While considerable differences were evident among the pre-test population, the findings suggest that prior to the intervention stage many participating prospective teachers; regardless of previous mathematics achievements or the level of mathematics study; demonstrate weaknesses and gaps in their ‘common’ MSMK. Particular difficulties were evident in relation to pre-test items requiring knowledge of rational numbers, conceptual understanding or problem solving. These findings highlight the inadequacy of previous mathematics achievements and indeed minimum entry requirements as predictors of MSMK for teaching. As well as its contribution at a local and national level, the findings provide an Irish perspective on this international issue.

Student primary teachers improving their mathematics subject knowledge: cognition and affect intertwined

This paper describes a study conducted with a random sample of 80 student primary teachers drawn from all four years of the Bachelor of Education (BEd) programme at a teacher education institution in Scotland, with a view to determining why there were such differing levels of engagement with an online maths assessment. The assessment was created in an attempt to address deficiencies in subject knowledge in order to reduce the amount of time spent on mathematics remediation, and to raise awareness of the levels of mathematics competence required in the primary classroom. Study of the reasons behind the differing patterns of engagement with the assessment revealed that two thirds of the group were able to reach a competence threshold and often to improve upon it by some way; a worrying third of the students, however, made little attempt to use the tool to improve their subject knowledge. A further finding indicated that students who engaged with the online assessment reported improving levels of confidence in mathematics.