The development of mathematical knowledge of prospective primary teachers in a lesson study

PurposeTo understand how lesson study (LS) can promote the development of pedagogical content knowledge (PCK) of prospective primary teachers. More specifically, to know what PCK prospective primary teachers develop during LS and how this development occurs.Design/methodology/approachFollowing a qualitative approach, this study took place in a teacher education institution where a LS was carried out during the last semester of the academic year with the participation of two prospective teachers, a teacher educator, a cooperating teacher and a researcher.FindingsThe results suggest that prospective teachers may develop PCK when they participate in LS, regarding lesson planning (goals and lesson plan), task design, students' difficulties and solving strategies, whole-class discussions and observation of student learning. This development occurs through the engagement in LS activities that allow prospective teachers to deepen their knowledge.Originality/valueThis study investigates how the development of prospective teachers' PCK occurs during LS, providing knowledge about how different activities of the LS help develop different aspects of PCK.

The study aims to investigate the mathematics anxiety-apprehension of prospective primary school teachers and its causes. The mathematics anxiety-apprehension of the prospective primary school teachers was analyzed using a number of variables. The prospective teachers were asked to provide written answers to open-ended questions about the causes of their mathematics anxiety. The study used mixed method research design. The quantitative data for the prospective teachers’ mathematics anxiety-apprehension were collected using the Mathematics Anxiety-Apprehension Scale developed by Ikegulu (1998) and translated into Turkish with validity-reliability analyses by Ozdemir and Gur (2011). The qualitative part of the study used the phenomenological method, and the prospective teachers’ metaphors for aspects of mathematics were collected as data. The participants in the study were third- and fourth-grade prospective teachers studying in the Primary Education Department of the Necatibey Faculty of Education at Balikesir University. They were chosen by simple random sampling. The independent samples t-test was computed to analyze the quantitative data, and descriptive statistics were used for the qualitative data. The study found that the mathematics anxiety-apprehension of prospective primary school teachers who were Anatolian high school graduates was significantly lower. Mathematics anxiety-apprehension did not vary by gender, and the third-grade prospective teachers had significantly higher mathematics anxiety-apprehension. The causes of the prospective primary school teachers’ mathematics anxiety-apprehension were found to be related to teachers, prospective teachers, the examination system, mathematics program-related and school facilities-related causes. The prospective primary school teachers often used metaphors such as life, crossword puzzle, game and human for each sub-theme, and 166 metaphors for mathematics were identified. The themes with the highest number of metaphors were basic principles of mathematics teaching, basic mathematical skills and mathematical knowledge, respectively.

Background:Previous research points to two different frameworks: Knowledge Quartet provided the field to assess the (prospective) teachers’ mathematical knowledge in teaching. Teacher perspectives framework contributed to the field to examine (prospective) teachers’ pedagogical principles underlying their mathematical knowledge in teaching. The field mostly focuses on what (prospective) mathematics teachers know and/or lack. Thus, there is need to investigate both what they know and why they know in terms of their mathematical knowledge in teaching.Materials and methods:Classroom teaching experiments (Cobb, 2000) was conducted for a total of eleven weeks during both a methods and the seminar part of a practice-teaching course. Data shown in this study included prospective teachers’ lesson plans, practice-teachings and self-reflection papers. All the lessons within the methods and practice teaching courses as well as the prospective teachers’ practice-teachings were videotaped and then transcribed. Prospective teachers wrote reflection papers after watching their videotaped lessons.Results:Results showed that prospective teachers holding a progressive incorporation perspective (PIP) had demonstrated all the codes in the Knowledge Quartet Framework during their practice-teaching.Conclusions:There is need to investigate coherency between other teacher perspectives and what they reveal in teaching in terms of their mathematical knowledge.

(ProQuest: ... denotes formulae omitted.)Relevant LiteratureProspective teachers go through teacher training programs and take many courses that partially or mostly address teacher knowledge categories (as detailed later in the article) at different universities in the world. Thus, they gain experience in contentspecific and generic knowledge types and in pedagogical reasoning that will shape their future teaching. prospective teachers bring to those courses or to their programs is as important as what they are taught in those courses (Ball, 1988; Goulding, Rowland, & Barber, 2002) and the experiences they gain from their programs. they bring to courses is crucial because of the two following reasons: (1) They are likely to operate from that knowledge in their future classrooms, which may not be parallel to the type of teaching that is expected of them when they graduate from those programs and enter the teaching practice. (2) This factor is also important to inform the field about the needs of teachers and teacher education programs. Such information may help us to revise and enhance teacher education programs and the teaching of those future teachers.As Ball (1988, p. 46) mentioned,How can teacher educators productively challenge, change, and extend what teacher education students bring? Knowing more about what teachers bring and what they learn from different components of and approaches to professional preparation is one more critical piece to the puzzle of improving the impact of mathematics teacher education on what goes on in elementary mathematics classrooms.Related information on this matter can be obtained through analyses of teachers' knowledge levels as they go through the programs using certain measurement instruments (e.g., Hill, Schilling, & Ball, 2004; Toluk Ucar, 2011; Turnuklu, 2005) or through analyses of teachers' actual teaching approach (e.g., Rowland, Turner, Thwaites, & Huckstep, 2009; Haciomeroglu, 2012). Our study falls into the latter category because we also believe that an investigation of teacher knowledge as they teach is informative in identifying teachers'needs and the nature of teaching knowledge. Such information can be obtained through investigations of in-service or prospective teachers. The current study strictly focuses on actual teaching of prospective teachers and deliberates the methods/ways of teaching, which we call prescriptions that guide these teachers' mathematics teaching. We pursued the following research question: teaching methods (prescriptions) guide prospective middle school mathematics teachers in their teaching of mathematics? The relevant literature that oriented us in pursuing this question and the rationale for the study is detailed below.The relevant literature suggests that mathematics teachers draw on various resources in teaching mathematics. One of these resources is mathematics teacher knowledge (Ball & Forzani, 2009), which has a special feature specific to mathematics teaching (Ball, Thames, & Phelps, 2008). Identification of the core of (mathematics) teacher knowledge is pursued extensively in mathematics education literature (e.g., Hill et al., 2004; Rowland, Huckstep, & Thwaites, 2005; Shulman, 1986). Revealing how and in what ways teacher knowledge guides, limits, or shapes teachers' teaching approach is as important as understanding the nature of teacher knowledge. An articulation of the factors that affect the teaching of mathematics teachers may inform decisions as to what should be focused on in teacher education programs and policy development. The current study aims to contribute to such knowledge base through investigating prospective teachers' teaching.Our search in the relevant literature also reveals the following questions that many researchers have struggled with for the last few decades: What kind of knowledge do teachers need to teach effectively? is the nature of the knowledge that is specific to teaching? …

Improving prospective mathematical teachers’ lesson planning skills is a very crucial task in teacher preparation programs. The purpose of this study is to examine how a lesson study approach implemented in a method course could develop prospective mathematical teachers’ lesson planning skills from the perspective of Mathematical Knowledge for Teaching (MKT). Thirty-nine prospective teachers (PTs) enrolled in the course “Instructional Skills of Mathematics” participated in the program of developing lesson planning skills at a public university. Participants experienced an adapted lesson study cycle concentrating on lesson planning. Data included 39 PTs’ lesson plans, 8 groups’ revised lesson plans, and group reflections. The framework of MKT was used to capture the weakness of PTs’ existing knowledge and the progress they made from the initial to the revised lesson plans. The analysis of the initial 39 lesson plans showed 18 different types of problems regarding planning a lesson. About 75% of the problems fell in the domain of pedagogical content knowledge. After experiencing the lesson study process, the participants demonstrated significant improvement in thinking about learning objectives, analysis of content and students, anticipating students’ solutions, and sequencing mathematics tasks. Their reflections further confirmed their gains from the process. This study indicated that lesson study is an effective way to enhance PTs’ teaching cognition and lesson planning skills.

This case study explores the degree to which mathematical knowledge for teaching can be developed by prospective teachers in a multi-site teacher education context. The majority of the article focuses on a description of the target middle level mathematics endorsement program, including distance-based instructional norms, community building efforts, and tasks and activities intended to support the generation of mathematical knowledge for teaching. All preservice teachers enrolled in the program were invited to participate in the study. Means on Likert-scale survey items were calculated at three points in time over one year to determine changes. Open-ended survey items and focus group interviews were analyzed qualitatively to supplement the quantitative findings. These data support the result that middle level preservice teachers’ mathematical knowledge for teaching can be positively impacted by a middle level mathematics teacher education program. Two broader implications are provided: 1) teacher education experiences can have positive impact on prospective teachers’ development, and 2) this development is possible in a multi-site teacher education setting. Possible implications on international teacher education efforts are provided.

Features of two lesson study contexts, one with prospective secondary teachers engaged in microteaching lesson study and one with prospective elementary teachers engaged in field experiences, were investigated for providing US prospective teachers with opportunities for growth as teachers of mathematics. In both contexts, the prospective teachers (PTs) exposed their knowledge, beliefs and practices to the scrutiny of peers and other experts, developing and reconsidering their thinking and practices through the shared teaching experiences. Similarities and differences in features of the two contexts are discussed with respect to PT learning. Similarities included the importance of negotiation during teaching cycles as catalysts for PT learning, the value of the cooperative nature of the experiences for sharing varying ideas and perspectives among PTs, the merits of overarching student learning goals for PT lesson planning, and the contributions of the group products (written or oral reports of the lesson study) to the learnercenteredness of the experiences. Differences influencing prospective teacher learning included the extent of focus on mathematics knowledge, extent of focus on classroom processes and management, use of videotaped lessons as part of formative feedback, and participation of knowledgeable advisors during or at the end of the cycles.

IntroductionElementary teachers need a solid understanding of so that they can teach it as a coherent, reasoned activity and communicate its elegance and power (Conference Board of Mathematical Sciences [CBMS], 2001, p. xi}. However, research studies on prospective teachers' knowledge have shown that many possess a limited knowledge of in key content areas as number (e.g.. Ball, 1990a; Thanheiser, 2009; Tobias, 2013}. This is particularly true in case of which, along with ratio and proportion, Lamon (2007} calls, the most protracted in terms of development, most difficult to teach, most mathematically complex, most cognitively challenging, most essential to success in higher and science, and one of most compelling research sites (p. 629}.The National Mathematics Advisory Panel (2008} affirmed that with fractions is a major goal for K-8 education because such proficiency is foundational for algebra and, at present time, seems to be severely underdeveloped (p. xvii}. Therefore, developing proficiency in prospective elementary teachers (PTs} is a critical task for educators. As authors of Mathematical Education of Teachers, Part 1 suggest, The key to turning even poorly prepared prospective elementary teachers into mathematical thinkers is to work from what they do know (CBMS, 2001, p. 17}. Thus, in order to design courses for prospective teachers that will help them to develop solid understanding of mathematics called for by Conference Board of Mathematical Sciences (2001}, including a deep understanding of and with fractions, we must begin by determining what it is that PTs know. In this paper, we discuss main findings from a research summary of existing studies on prospective elementary teachers' fraction knowledge to identify directions for future research.Theoretical FrameworkIn looking at teacher knowledge, we begin by examining work of Shulman (1986], who proposed three categories of content knowledge for teachers: (a] subject matter content knowledge, (b] pedagogical content knowledge, and (c] curricular knowledge. For Shulman, subject matter content knowledge includes knowing a variety of ways in which the basic concepts and principles of discipline are organized to incorporate its facts and truth or falsehood, validity or invalidity, are established (p. 9]. Pedagogical content knowledge refers to knowledge of useful forms of representations (e.g., analogies, illustrations, explanations] of subject-matter ideas that make it understandable to others, as well as an understanding of conceptions and preconceptions students bring to learning processes. third type of knowledge, curricular knowledge, includes knowledge of a full range of programs designed for teaching of particular subjects and topics at a given level, variety of instructional materials available in relation to those programs, and set of characteristics that serve as both indications and contraindications for use of particular curriculum or program materials in particular circumstances (p. 10].Shulman's ideas on pedagogical content knowledge sparked a huge interest in knowledge for teaching, eliciting over a thousand studies (Ball, Thames, & Phelps, 2008] throughout a number of content areas, with a large number of these studies focusing on teachers' knowledge of (e.g., Ball et al., 2008; Davis & Simmt, 2006; Hiebert, 1986; Ma, 1999]. Deborah Ball and her colleagues introduced term mathematical knowledge for teaching (MKT) (e.g., Ball & Bass, 2002), which focused on work that teachers do when teaching mathematics.Building on Shulman's (1986) categories of knowledge, Ball, Thames, and Phelps (2008) introduced a framework for mathematical knowledge for teaching. …

This study sheds light on prospective primary teachers’ understanding of rational numbers. This is an experimental study that aims to evaluate prospective primary teachers’ mathematical and didactic knowledge of rational numbers through online formative assessment. The participants were 38 prospective primary teachers from a primary teacher education study program at a public university in Pekanbaru, Riau, Indonesia. This study indicates that the prospective teachers have insufficient knowledge of rational numbers, and they possess better mathematical than didactic knowledge. This study also reveals a significant increase in prospective teachers’ mathematical and didactic scores from the first test to the second test.

Differentes recherches ont etabli l'influence des enseignants sur la qualite de l'apprentissage des enfants. La question est de savoir ce qui rend un enseignant plus performant qu'un autre. Quatre indicateurs, etudies par les AA., peuvent etre utilises dans ce but : les acquisitions pedagogiques des enseignants, leurs participations dans les programmes d'etudes, leurs connaissances des matieres enseignees et leurs strategies pedagogiques

This paper explores the education of prospective teachers with regard to the Theory of Didactical Situations when they engage in lesson study. We particularly focus on studying how a lesson study process oriented towards the Theory of Didactical Situations contributes to increasing prospective teachers’ self-efficacy to plan and teach lessons based on such theory, reducing the gap between theory and practice. Prior to the study, we will discuss how the theoretical postulates assumed in lesson study affect crucial aspects of the process. The study is implemented with 47 prospective early childhood education teachers. We also consider another group of 47 prospective teachers that were engaged in practicum at the time the lesson study process took place. Using a quasi-experimental methodology based on a questionnaire developed ad hoc that captures the particularities of the didactic paradigm assumed, the results of our study show that both lesson study and practicum lead to a statistically significant increase in future teachers’ self-efficacy to plan and teach lessons in line with the paradigm assumed. However, size effect measures show that the increase observed in the lesson study group is significantly higher, which supports the benefits of lesson study in initial teacher education. We discuss what the features of lesson study are that could be related to this increase. Finally, we sketch new lines of research connected with the benefits of lesson study versus other teacher education experiences like practicum, as well as with links between self-efficacy and knowledge growth in lesson study.

Prospective teachers' beliefs have a beneficial effect on their knowledge and actions. Furthermore, teachers' pedagogical content knowledge is an essential contributor to teachers' impact on students' academic outcomes. However, examining how prospective teachers' beliefs influence their pedagogical content knowledge is still unclear. The current study investigates prospective mathematics teachers' beliefs and pedagogical content knowledge. We recruited three undergraduate students in the mathematics department consisting of one male and two female participants in this study. By assigning two interviews, a test, and observation, we examined three prospective mathematics teachers' pedagogical content knowledge and their beliefs about the nature of mathematics, mathematics learning, and mathematics teaching. Prospective mathematics teachers' test, interview, and observation results were analyzed in three stages: data condensation, presentation, and conclusion drawing and verification. The findings point out that traditional beliefs (instrumentalist and platonist views) are more dominant in prospective teachers' beliefs about the nature of mathematics. Moreover, the more sophisticated prospective teachers' beliefs about the nature of mathematics, mathematics learning, and mathematics teaching are, the higher one's content knowledge and pedagogical content knowledge levels are. Implications of this study, mathematics teacher educators should assist and foster prospective teachers in developing constructivist or problem-solving beliefs.

The main purpose of this study is to determine prospective teachers’ metacognitive awareness levels of reading strategies. A quantitative surve method was used. Participants consisted of 150 prospective primary teachers and 150 prospective Turkish language teachers from Necmettin Erbakan University in Turkey. The data were collected through Metacognitive Awareness of Reading Strategies Inventory during the spring semester of the 2014–2015 academic year. Results show that prospective teachers’ global reading and problem solving strategies levels are high while their support reading strategies level is medium. Female participants’ metacognitive awareness level was found to be higher compared to males. Prospective Turkish language teachers’ problem solving strategies level is higher than that of prospective primary teachers. Prospective primary teachers preferred historical and psychological books more while prospective Turkish Language teachers favoured all types of books equally. The metacognitive awareness levels of participants reading book everyday and sometimes are significantly higher than those of reading book never.
 
 Keywords: Metacognitive awareness, reading strategies, prospective teachers.

The main purpose of this study is to determine prospective teachers’ metacognitive awareness levels of reading strategies. A quantitative surve method was used. Participants consisted of 150 prospective primary teachers and 150 prospective Turkish language teachers from Necmettin Erbakan University in Turkey. The data were collected through Metacognitive Awareness of Reading Strategies Inventory during the spring semester of the 2014–2015 academic year. Results show that prospective teachers’ global reading and problem solving strategies levels are high while their support reading strategies level is medium. Female participants’ metacognitive awareness level was found to be higher compared to males. Prospective Turkish language teachers’ problem solving strategies level is higher than that of prospective primary teachers. Prospective primary teachers preferred historical and psychological books more while prospective Turkish Language teachers favoured all types of books equally. The metacognitive awareness levels of participants reading book everyday and sometimes are significantly higher than those of reading book never.Keywords: Metacognitive awareness, reading strategies, prospective teachers.*

This paper presents a teacher education experiment that was conducted in an algebra course based on an exploratory approach and articulating content and pedagogy. We investigate the contribution of analysing teaching and learning situations, namely student answers and episodes of classroom work, in developing the mathematical and teaching knowledge of prospective primary school teachers. We use a design research methodology to probe the prospective teachers’ development after having participated in an experiment in their third year of a primary education degree program. The results show that the prospective teachers’ understanding of algebra and grasp of how to use different representations and strategies grew considerably. The results also show that their didactical knowledge regarding tasks, classroom organization, attention to students’ reasoning, and teacher’s questions grew as well. The variety of tasks proposed to the prospective teachers during the course was of vital importance to this outcome, as was the opportunity to reflect, work with elements of real practice, and participate in whole class discussions.