Factors that Influence the Understanding of Good Mathematics Teaching (original) (raw)
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The effectiveness of lesson study on mathematical knowledge for teaching
of mathematical thinking; Derivative approaches that are controlled in more or less directive ways. As a consequence teachers are focused on preparing for the exams. Individual teachers may reflect on and improve their practice in the isolation of their own classrooms. The complexity of their daily work rarely allows them to converse with colleagues about what they discover about teaching and learning (Cerbin & Kopp, 2006). If it is possible to share their ideas about teaching and learning, it likely takes the form of knowledge they develop from their experiences in the classroom (Verhoef & Terlouw, 2007). This type of knowledge seems immediately useful, but it tends to be tied to concrete and specific contexts and is not always in a form that can be accessed and used by others (Hiebert, Gallimore & Stigler, 2002). This suggests that practitioner knowledge should preferably be made public, shareable, and verifiable so that it may become professional knowledge. It is recommend to improve teaching practice in their fields, leading to the formation of a professional knowledge base. 1.1 Mathematical knowledge for teaching Mathematical knowledge for teaching is strongly related to Pedagogical Content Knowledge (PCK) which "identifies the distinctive bodies of knowledge for teaching. It represents the blending of content and pedagogy into an understanding of how particular topics, problems or issues are organized, represented, and adapted to the diverse interests and abilities of learners, and presented for instruction" (Shulman, 1987, p.4). The work of Shulman and his colleagues expanded ideas about how knowledge might matter to teaching, suggesting that it is not only knowledge of content but also knowledge of how to teach such content that conditions teachers' effectiveness (Borko,
Cognition and Instruction, 2008
This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' mathematical knowledge for teaching (MKT), which includes both the mathematical knowledge that is common to individuals working in diverse professions and the mathematical knowledge that is specialized to teaching. We use a series of five case studies and associated quantitative data to detail how MKT is associated with the mathematical quality of instruction. Although there is a significant, strong, and positive association between levels of MKT and the mathematical quality of instruction, we also find that there are a number of important factors that mediate this relationship, either supporting or hindering teachers' use of knowledge in practice. This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. Such claims stem originally from the "educational production function literature," or research that examines the contribution of student, teacher, and school resources to student learning. As far back as the Equality of Educational Opportunity study (Coleman, 1966) scholars identified a unique contribution of teacher knowledge to student achievement (in mathematics, see also Hanushek,
Journal of Social Sciences, 2013
In this paper, as a case study, the teachers' Pedagogical Content Knowledge (PCK) was determined by analyzing how teachers taught a topic on mathematics and their responses to the questions on the same topic. Data was collected using face-to-face interview schedules with short-answer and multiple-choice type items. A one sample t-test was used to analyze the collected data. The items that were open ended were compiled to generate quantitative data which were then subjected to quantitative analysis. The findings showed that many teachers had no adequate PCK to understand well the characteristics of the problems tackled, solutions obtained by different methods, their interpretation and lack of understanding of students' problems in learning. It was concluded that teachers needed improvement in their mathematical PCK for effective teaching of the subject.
Good Mathematics Teaching: Perspectives of Beginning Secondary Teachers
2012
What is 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 is good mathematics teaching and what is not. The purpose of this study was to determine how beginning teachers define good mathematics teaching and what they 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. In addition, factors that influence the understanding of good mathematics teaching were explored. A mixed methodology was used to gather information from the research participants regarding their beliefs and classroom practices of good mathematics teaching. The two research instruments used in this study were the survey questionnaire and a semi-structured interview. Thirty-three respondents who had one to two years of classroom experience comprised the study sample. They had graduated from a school of education in an eastern state and had obtained their teacher certification upon completing their studies. The beginning mathematics teachers selected these four definitions of good teaching as their top choices: 1) have High Expectations that all students are capable of learning; 2) have strong content knowledge (Subject Matter Knowledge); 3) create a Learning Environment that fosters the development of mathematical power; and 4) bring Enthusiasm and excitement to classroom. 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. 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. Teacher education programs should provide more opportunities for their students to investigate and practice classroom management skills in the real classroom settings.
Developing mathematical content knowledge for teaching elementary school mathematics
In this paper the authors present three design principles they use to develop preservice teachers' mathematical content knowledge for teaching in their mathematics content and/or methods courses: (1) building on currently held conceptions, (2) modeling teaching for understanding, (3) focusing on connections between content knowledge and other types of knowledge. The authors share results of individual research projects and teaching approaches focusing on helping preservice elementary teachers develop such knowledge. Specific examples from different content areas (whole number, fractions, angle, and area) are discussed. (Contains 8 figures.)
Strategies for assessing mathematical knowledge for teaching in mathematics content courses
2020
In their practice, teachers must not only know how to solve mathematics problems; they must also be able to make sense of students’ mathematical thinking, understand the organization and intent of curricular materials, and select contexts to motivate and highlight mathematical ideas. Similarly, mathematics content courses for prospective teachers (PTs) should not only seek to convey mathematical content; they should prepare PTs to use mathematical knowledge in ways that enhance school teaching and learning of the subject. Accordingly, mathematics teacher educators (MTEs) should assess not only the mathematics that PTs know but also whether this mathematical knowledge is organized in ways that are likely to support their teaching. In this article, we present some of the existing research on the assessment of mathematical knowledge for teaching and discuss ways in which MTEs can draw upon the work of elementary school teaching to help assess PTs’ content knowledge and habits of mind. ...
Toward a framework for the development of mathematical knowledge for teaching
Journal of Mathematics Teacher Education, 2008
Shulman (1986, 1987) coined the term pedagogical content knowledge (PCK) to address what at that time had become increasingly evident—that content knowledge itself was not sufficient for teachers to be successful. Throughout the past two decades, researchers within the field of mathematics teacher education have been expanding the notion of PCK and developing more fine-grained conceptualizations of this knowledge for teaching mathematics. One such conceptualization that shows promise is mathematical knowledge for teaching—mathematical knowledge that is specifically useful in teaching mathematics. While mathematical knowledge for teaching has started to gain attention as an important concept in the mathematics teacher education research community, there is limited understanding of what it is, how one might recognize it, and how it might develop in the minds of teachers. In this article, we propose a framework for studying the development of mathematical knowledge for teaching that is grounded in research in both mathematics education and the learning sciences.