Good Mathematics Teaching Research Articles

How Pre-Service Teachers Define “Good” Mathematics Teaching and Learning

Mathematics self-efficacy (beliefs about oneself as a learner of mathematics) and mathematics teaching efficacy (beliefs about oneself as a mathematics teacher) are important constructs that influence pre-service teachers’ (PTs’) learning and teaching (Bandura 1986). However, less is known qualitatively about how PTs define good teaching and learning when they make efficacy judgments such as, “I am good at learning mathematics” or “I am good at teaching mathematics.” This qualitative case study used journaling to examine 23 elementary PTs’ definitions of being good at doing and teaching mathematics. Our findings suggest PTs define being good at mathematics in a variety of ways, including receiving good grades, being fluid (quickly and successfully doing procedures), and having the ability to apply mathematics to new contexts. PTs also held a variety of definitions of good mathematics teaching, including focusing on student understanding, using group work and manipulatives, and having passion. These results have implications for researchers studying self-efficacy and teaching efficacy as well as for teacher educators hoping to engage PTs fully in their classrooms.

Teaching mathematics in post-Apartheid South Africa: the perspectives of teachers of black students

ABSTRACT Using a critical race theoretical lens, we examine how South African secondary mathematics teachers of Black students characterised their preparation in the post-apartheid era, how they portrayed good mathematics instruction, and what challenges they identified as barriers to becoming a good mathematics instructor. We found that teachers characterised their preparation in terms of their students’ achievement, often talked about the importance of teaching their students mathematical skills and procedures, identified challenges associated with using English as the language of instruction, and engaged in student blaming. Implications from this study include prioritising quality professional development for mathematics teachers of Black students that focuses on developing teachers specialised mathematical knowledge. Professional development should also strengthen South African mathematics teachers’ abilities to teach the mathematics register in English and support teachers to examine the detrimental effects of student blaming.

Examination of Pre-service Teachers' Error Analysis Skills in Teaching Differential Calculus

Error analysis has been considered indispensable in teaching mathematics in classrooms worldwide. One of the greatest skills in mathematics teaching has been recognised as the ability to model learners’ misconceptions through error analysis. The use of error analysis in the classroom has therefore made tremendous contribution to mathematics teacher knowledge. However, despite the acclaims about error analysis in teaching mathematics, researchers and teachers lack a detailed understanding of mathematics teacher knowledge as it is used in error analysis and the use of error analysis is still regarded as challenging for most teachers. This qualitative study therefore explored eight purposively selected pre-service teachers’ ability to identify, interpret and remediate learners’ error patterns as a result of misconceptions in differential calculus. The pre-service teachers’ analyses were re-analysed by the researcher to ascertain their ability to handle learners’ errors in mathematical calculus. The study established that though some pre-service teachers portrayed knowledge of the differentiation content as reflected by their ability to identify the errors made, most of them failed to identify the possible causes of the errors as well as provide appropriate instructional strategies that could be used to remediate learners’ error patterns. This finding illustrates that the pre-service teacher’s ability to diagnose, interpret and correct errors in learners’ work, with targeted instruction is an essential and necessary skill for good mathematics teaching.

When Students’ and Teachers’ Views on Good Mathematics Teaching Limit Co-teaching in Mathematics

The empirical material in this paper is from a Swedish upper secondary school where the mathematics lessons over the last two years have been co-taught. Co-teaching implies that two teachers are most often present in the classrooms during the mathematics lessons. Despite this additional support, students’ performance in mathematics remained low and this is why a professional development program was initiated. The aim of the professional development program was to find new ways to increase the number of approved students. At the start of this professional development program, classroom observations and a questionnaire were conducted with teachers and students. The results indicate that teachers’ and students’ views on good mathematics teaching became a limitation for the design of the co-taught lessons. Thus, to increase the number of approved students, teachers’ and students’ views on good mathematics teaching ought to be the focus of the professional development program.

Pre-service Special Education Teachers' perceptions on 'Good Mathematics Instruction' for Students with Disabilities

Pre-service Special Education Teachers' perceptions on 'Good Mathematics Instruction' for Students with Disabilities

현직수학교사와 예비수학교사들의 좋은 수학 수업을 위한 지식 및 능력에 관한 인식조사

Mathematics teachers' knowledge and abilities for effective mathematics teaching has been discussed by many mathematics educators and researchers. This study surveyed the perspectives on the knowledge and abilities for good mathematics teaching of inservice and preservice teachers based on their teaching experiences. The perspectives of the two teacher groups about teachers' knowledge and abilities for teaching mathematics are very different. The results from this study are expected to give information on developing teacher education curriculum and programs.

학습 전이에 있어서 유추 거리와 지식의 영향

본 연구는 유추 거리 및 수학적 지식과 학습의 전이 사이의 관계를 규명하기 위해 수행되었다. 구체적으로 유추적 거리에 따라 구분된 세 가지 전이 문제 해결에서 차이를 보이는지, 그리고 각 전이 문제를 성공적으로 해결하는데 기여하는 수학적 지식은 무엇인지를 분석하였다. 분석 결과 세 가지 종류의 전이 문제 해결에서 통계적으로 유의한 차이를 보였으며 유추 거리가 증가할수록 성공률은 점차적으로 감소하였다. 또한 사실 지식 보다는 개념적 지식이 전이 문제를 해결하는데 긍정적으로 기여하였다. 이상의 결과를 토대로 본 연구는 학습의 전이를 위해 수학 수업은 어떠한 점에 초점을 맞추어야 하는지, 그리고 유추 거리라는 새로운 구인을 찾고 그것이 전이에 미치는 영향을 실증적으로 규명했다는 점에서 의의를 찾을 수 있었다. The purpose of this study is to analyze whether analogy distance and mathematical knowledge affect on transfer problems solving with different analogy distance. To conduct the study, transfer problems were classified into multiple categories: mathematical word problem based on rates, science word problem based on rates, and real-life problem based on rates with different analogy distance. Then analysed there are differences in participants' transfer ability and which mathematical knowledge contributes to the solution on over the three transfer problem. The study demonstrated a statistical significant difference(.05) in participants' three transfer problem solving and a gradual decrease of the participants' success rates of on transfer problems solving. Moreover, conceptual knowledge influenced transfer problem solving more than factual knowledge about rates. The study has an important implications in that it provided new direction for study about transfer of learning, and also show a good mathematics instruction on where teachers will put the focus in mathematical lesson to foster elementary students' transfer ability.

What are the Important Attributes of Good Mathematics Teaching?

What are the important attributes of good mathematics teaching? The answer depends on whom you are asking. Teachers, researchers, policymakers, administrators, and parents usually provide their own view on what they consider the important attributes of good mathematics teaching. The purpose of this study was to determine what beginning teachers report as being the most important attributes at the secondary level. This research explored whether there was a relationship between the demographics of the participants and the attributes of good teaching. A quantitative analysis was used to gather information from the research participants regarding their beliefs and classroom practices of good mathematics teaching. The three most important attributes in good teaching were classroom management, motivation, and strong in content knowledge. One interesting finding was the discovery of four groups of beginning teachers, and how they were associated with specific attributes of good mathematics teaching according to their demographics.

Factors that Influence the Understanding of Good Mathematics Teaching

This study explored the factors that influenced the understanding of good mathematics teaching. A mixed methodology was used investigate the beliefs of beginning secondary teachers on good mathematics teaching. The two research instruments used in this study were the survey questionnaire and an interview. Beginning teachers selected Immediate Classroom Situation, Mathematical Beliefs, Pedagogical Content Knowledge, and Colleagues as the top four factors from the survey analysis that influenced their understanding of good mathematics teaching. The study’s results have implications on investigating specific mathematical content knowledge that is important for classroom instruction at the secondary level. Furthermore, this study can be used as a reference for teacher education programs to improve the effectiveness of the pedagogical courses in mathematics education.

예비 초등 교사의 좋은 수학 수업에 대한 인식

Prospective teachers need to have an opportunity to critically examine their initial perception with regard to effective mathematics instruction during the teacher education period. This study analyzed the perception in relation to good mathematics instruction by a total of 265 prospective teachers from four institutes for elementary teacher education using a survey. The results of this study showed that the pre-service teachers regarded learner, teaching and learning method, selection of content, and construction of curriculum as important for high-quality mathematics instruction. However, they revealed relatively low levels of agreement against the importance of instructional materials, classroom environment and atmosphere, and assessment. On the basis of teachers' perception on each element of effective mathematics instruction, this paper raises issues for discussion and includes some implications for teacher education.

좋은 수학수업과 교사 전문성 개발에 대한 현직수학교사 인식 조사 - 학교급 및 교육경력에 따른 차이 조사 -

This study investigated elementary and secondary mathematics teachers' views on: (1) Requirements for good mathematics teaching (2) what professional development programs and supports are needed for these requirements. In particular, this study analyzed the common and difference between school levels and teaching experiences. For it, we developed questionnaire and the questionnaire was anonymously answered by one-hundred-five elementary and secondary mathematics teachers. We suggested implications related to professional development programs for mathematics teachers based on common and difference between school levels and teaching experiences.

Inside the UTeach Program: Implications for Research in Mathematics Teacher Education

As the national impetus to advance education continues to look toward improving the teachers sent into the classroom, more research needs to be done to in the area of mathematics teacher education. A number of recent studies have summarized, synthesized, and developed useful information about what should be viewed as important in mathematics teacher training. This paper looks at some of these claims from current research and uses the UTeach program from the University of Texas at Austin as a means of elaborating on how some theoretical issues might be addressed in practice. A number of implications are proposed in response to the discussion, one in particular addressing a gap in current research about understanding when beginning mathematics teachers learn the attributes helpful for good mathematics instruction.

Searching for good mathematics instruction at primary school level valued in Taiwan

In this article, we aim to provide a glimpse of what is counted as good mathematics instruction from Taiwanese perspectives and of various approaches developed and used for achieving high-quality mathematics instruction. The characteristics of good mathematics instruction from Taiwanese perspectives were first collected and discussed from three types of information sources. Although the number of characteristics of good mathematics instruction may vary from one source to another, they can be generally organized in three phases including lesson design before instruction, classroom instruction during the lesson and activities after lesson. In addition to the general overview of mathematics classroom instruction valued in Taiwan, we also analyzed 92 lessons from six experienced teachers whose instructional practices were generally valued in local schools and counties. We identified and discussed the characteristics of their instructional practices in three themes: features of problems and their uses in classroom instruction, aspects of problem–solution discussion and reporting, and the discussion of solution methods. To identify and promote high-quality mathematics instruction, various approaches have been developed and used in Taiwan including the development and use of new textbooks and teachers’ guides, teaching contests, master teacher training program, and teacher professional development programs.

Good mathematics instruction in South Korea

There have been only a few studies of Korean mathematics instruction in international contexts. Given this, this paper describes in detail a sixth grade teacher’s mathematics instruction in order to investigate closely what may be counted as high-quality teaching and learning in Korea. This paper then discusses several key characteristics of good mathematics instruction along with some background information on Korean educational practice. This paper concludes with remarks that good mathematics instruction may be perceived differently with regard to underlying social and cultural norms.

Card Sorts, State Tests, and Meaningful Mathematics

“Data-driven decision making” is a phrase that is now commonplace in educational conversations. It is used when school districts discuss strategies to help meet the needs of all students while closing the achievement gap between subgroups of students. Within mathematics education, there is a growing need to educate prospective and practicing mathematics teachers about No Child Left Behind accountability measures and corresponding data within a given state in a way that emphasizes meaningful mathematics instruction that is consistent with national recommendations (NCTM 2000). Given pressures that teachers face within high-stakes teaching environments, it is important to analyze assessment tools, such as state-mandated tests, in an efficient, enlightened manner. A goal of such an analysis is to acknowledge accountability through constructive discourse while continuing to emphasize good mathematics teaching. Such discourse about accountability can take on many forms (Chauvot 2006). This article shares card-sorting activities that use items from state-mandated tests with prospective and practicing mathematics teachers. These activities give teachers tools to further accountability measures while exploring reformminded mathematics instruction.

The Myth of the Good Mathematics Teacher

One of the most publicly celebrated figures in mathematics teaching during the last century was Jaime Escalante (dramatized in the film Stand and Deliver). The Escalante story aptly fulfills three prevailing myths about effective teachers: the Teacher is self-made, the Teacher is the expert, and everything depends on the Teacher. These myths are so predominant in our culture that we can also see their representation in recent legislative actions such as No Child Left Behind and the American Competitiveness Initiative. This demonstrates the strength that the myth has in reflecting, influencing, and legalizing our perceptions of good mathematics teaching.

What Constitutes Good Mathematics Teaching and How it Develops: Nine High School Teachers’ Perspectives

Scholars of decades past, current researchers, and various reform documents all deal, directly or indirectly, with the question of what constitutes good mathematics teaching. Often good teaching is situated in the context of broader educational goals, such as preparing literate citizenry. Researchers generally define good teaching implicitly with attention to various processes such as reasoning and problem solving. In a series of three interviews, we examined nine experienced and professionally active teachers’ views of good mathematics teaching and how it develops. The interviews were couched in the context of the teachers mentoring student teachers. In general, these teachers thought good teaching requires a sound knowledge of mathematics, promotes mathematical understanding, engages and motivates students, and requires effective management skills. Furthermore, the teachers felt that good teaching is developed from experience, education, personal reading and reflection, and interaction with colleagues. Experience was considered the primary contributor. The article compares and contrasts the teachers’ notions of good teaching with those of various scholars and researchers and positions stated in various reform documents.

Characteristics of the College Geometry Course for Preservice Secondary Teachers.

Based on 30 syllabi and 108 questionnaire responsesfrom randomly selected U.S. colleges and universities,college geometry courses were analyzed with respect tocontent, pedagogy, and assessment. About 40% of thecourses start with elementary axioms and emphasizeEuclidean geometry or a mix of Euclidean andnon-Euclidean geometry; 23% employ a survey approach;and 20% employ an analytic or projective geometryapproach. In about 63% of the courses, the instructorlectures most or all of the time; in 36% of thecourses a substantial amount of class time is devotedto group work; and about 27% of the courses reflectnearly all the characteristics of good mathematicsteaching as defined by the NCTM Professional TeachingStandards. In most courses, in-class examinations,homework, and a final examination are the primaryevaluation tools; in about half of the courses atleast one alternative assessment contributes to thefinal grade. Common characteristics are evident butwide diversity exists also. A typical geometry coursedid not emerge from the data.

Contra a ditadura da escola

Este texto, escrito em 1995, busca colocar em questão certas compreensões quase ingênuas do que seja fazer (ou tornar) uma escola indígena. Por isso é ainda atual, quando a discussão dos currículos das escolas está em pauta. O texto aponta o desafio de se conquistar uma "escola indígena" e sugere que a educação escolar indígena faria muito (e melhor) se fosse capaz de apenas duas coisas: um bom ensino de matemática e a formação efetiva de leitores.

Implementing the “Professional Standards for Teaching Mathematics”: Applying the Standards to the College Mathematics Classroom: Ideas and Obstacles

This assumption that how teachers teach mathematics is fundamentally connected with how they learned it underlies the first standard of the “Standards for the Professional Development of Teachers of Mathematics.” This standard, Experiencing Good Mathematics Teaching, focuses on the role of the college and university mathematics professors in the process of reforming school mathematics teaching. It is essential that mathematics teacher educators invite and encourage college-level mathematics faculty to join them in implementing the teaching standards. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) and Professional Standards for Teaching Mathematics (1991) present a new vision of school mathematics. Mathematics courses and programs of study in colleges and universities should share in this vision.