The introduction part of The Evolution of Research on Teaching Mathematics by Manizade, Buchholtz and Beswick, the editors, explains the background, objectives and structure of the book. The lack of a systematic scientific overview of the complete chain of effects between teacher characteristics, activities and students’ learning processes served as the impetus for writing this book. This book examined the present state of research on teaching mathematics and explored the likely direction of future research development. This book adapts Medley’s (1987) framework process-product research, which has been updated to presage process-product research (see Figure 1) by taking into account additional variables that emerged from recent advances in technology and research methodology in the digital era.Although this book focuses only on Western culture, it also mentioned other countries from other continents (e.g. Africa and Asia), especially Japan, which is quite often mentioned. From the reviewers’ perspective (i.e. Indonesia), some of the theories are or have been developed. One of them is RME, wherein some Scopus-indexed journals in Indonesia explicitly call for original research articles on the subject (e.g. Journal on Mathematics Education and Infinity Journal). The Indonesian readers can certainly consider other theories by taking socio-cultural aspects into account and, if required, making adjustments. According to the curriculum document, Indonesian teachers should, in theory, determine learning goals before considering how to teach them when developing lesson plans. Additionally, Indonesia’s most recent curriculum, known as “Kurikulum Merdeka” or the Independent Curriculum, has already integrated technology, including introducing programming as a specific discipline. However, like in England, which is described in this book, it only regulates the content without providing adequate pedagogical guidance for teachers.This book is divided into two parts. The first part consists of six chapters that explain each online variable, which are units of analysis of research that can be under the control of mathematics teachers, including Type F to Type A. The second part consists of four chapters that explain each offline variable, which are units of analysis that are not under the direct control of teachers, including Type J to Type G. A final chapter in this book outlines the direction of the evolution of mathematics education research in the future.Chapter 1, “Pre-existing mathematics teacher characteristics,” by Olive Chapman discusses the Type F unit. Pre-existing mathematics teacher characteristics (PTMCs) include prospective teachers of mathematics' (PTs') knowledge and skills, pedagogical knowledge and abilities and beliefs at the beginning of their mathematics teacher education (MTE), which reflect the nature of their background knowledge or ability related to their school experiences with mathematics. PTs’ pre-existing mathematical knowledge of various content areas and problem-posing skills was hampered by a low conceptual understanding. PTs’ pedagogical abilities have many shortcomings related to the ability to observe and draw appropriate conclusions or offer suggestions regarding instruction, to notice and provide solid evidence to support students’ reasoning, to recognize the potential of tasks or difficulties students may encounter and to classify a high level of complexity problem. PTs’ beliefs are dominated by the Platonist and absolutist perspective of mathematics, the traditional perspective or “teacher-centered” perspective of teaching and learning mathematics, narrow mathematical conceptions, PS and multiple representations and a lack of understanding of the use of technology to support students’ learning and to develop concepts.Future research should focus on PTMC for PTs at the point of entry into MTE; the types of PTMC within and beyond the previously mentioned categories; addressing affective factors such as PTs’ attitudes and what they value and PTs’ ability to reflect on types of beliefs. Furthermore, research should focus on the impact of technology and culture on the PTs’ PTMC at the point of entry into MTE; conceptualizing PTMC in relation to teacher education, technology and culture and exploring PTMC at the point of entry to MTE, which requires different or better instruments and analysis and uses a more rigorous mixed-methods research design with more rigorous statistical analysis and use of technology.Chapter 2, “The evolution of research on mathematics teachers’ competencies, knowledge, and skills,” by Buchholtz, Kaiser and Schwarz discusses the Type E unit. The narrative reviews in this chapter present how Type E variables encountered paradigm shifts and how these paradigms are critiqued. Medley’s process-product paradigm took over in the 1960s as a result of the deficiency of the personality or traits paradigm, which did not explain how to measure personality traits. Since the mid-1980s, the focus of the research based on this paradigm has been on the more complex structures of instructional quality or the combination of multiple variables and on teachers’ cognition, which underlies Shulman’s work. However, Shulman had a static understanding of knowledge, and the idea of “transforming” or “translating” subject matter into pedagogical forms amounted to a routine, mechanistic transmission. Thus, the expert paradigm sparks and holds that teachers are considered experts because of their ability to successfully manage a highly specialized, complex task such as school teaching due to the students’ behavior.Future research should address how suitable instruments can be used to survey content knowledge (CK), pedagogical content knowledge (PCK) and general pedagogical knowledge in connection to teaching practice, particularly leading to situation-specific teacher competencies observation and measurement based on the expert paradigm; expanding studies that used Medley’s paradigm that was strongly influenced by cognitivism by including several cognitive perspectives and advancing methodology by critically analyzing the validity of measuring instruments.Chapter 3, “The research on mathematics teaching and planning: theoretical perspectives and implications of teachers’ pre-post classroom activities,” by Manizade, Moore and Beswick discusses the Type D unit. Observable Type D actions produced by the decision-making process that reflect how teachers’ thinking – based on the Type E elements they possess – determines the effectiveness of the Type C implementation and the degree to which the teaching purpose is met. In designing lesson plans, teachers might choose to focus on the process of student learning – then it is less likely that they will think of students’ conceptual development, and lessons can become more prescribed and rigid – and discovery of concepts or on specific content outcomes – would drive teachers to likely consider common student challenges, typical questions or difficulties students might experience based on their developmental levels, as well as strategies to deal with those.The most important part is the literature review of theoretical perspectives for teaching mathematics that are present in Type D, which includes eight epistemological perspectives: situated learning theory (SLT), behaviorism, cognitive learning theory, social constructivism (SC), structuralism, problem solving (PS), culturally relevant pedagogy and project and problem-based learning (PBL). Definitions, teaching goals, examples from the literature and pros and cons of each perspective are explained. This chapter also explains their respective cultural contexts and the implications of Type D for lesson planning.Future research should address the theory-practice gap that can be seen as an attempt to link Type E variables directly to Type C variables with insufficient attention to Type D variables. When this gap is successfully overcome, it should be possible to trace a coherent theoretical perspective along the chain of Type E-C-D variables, influenced and constrained by Type I-J variables. Future research should also focus on some theoretical perspectives that have not been researched well (e.g. SLT and PBL); investigate the potential of digitalization for improving teachers’ practice of lesson planning, assessment and reflection and investigate the theoretical perspective through which the teacher views the teaching goals.Chapter 4, “Interactive mathematics teacher activities,” by Beswick, Rawlings-Sanaei and Tuohilampi discusses the Type C unit. Large-scale international surveys, particularly TIMSS and PISA, provide information including teaching mathematics resources, instructional practices and teachers' use of technology. Regarding teaching resources, lack of time constrains the kind of students’ activities and impedes the adoption of innovative practices. Regarding instructional practices, there was increased practice of computational skills and decreased practice of PS, contrary to current trends that emphasize reasoning and PS as the teaching goals. Additionally, time limits resulted in structured teaching practices – explicitly stating learning goals, allowing students to practice until they understand and providing summaries – as the most frequently used – and the use of project work was less frequent. Regarding the use of technology, the majority of students reported that they never or almost never do computer activities to support learning that resulted in their low achievement. Teachers also face challenges to use new technologies and engage in higher-order pedagogical tasks.Those findings are similar in atypical teaching practices. Student-centered approaches are not widely used, and on the other hand, it was hard to find an innovative perspective on behaviorist approaches. Teachers seemed to struggle to shift from procedural knowledge-developing pedagogies to ones that facilitate robust understanding (Schoenfeld, 2018; Schoenfeld et al., 2020).During an intervention from the researcher, teachers may adopt the new practice; however, future research should document what happened before and after these interventions. Researchers' beliefs constrain their study, resulting in a mismatch between the teacher behaviors that researchers advocate and the pedagogies that students most commonly report experiencing. This raises questions about how a teacher’s practice can be influenced. Future research should also document how teachers have reacted to the recent opportunities due to the growing digital world and fully identify the COVID-19 pandemic’s effects.Chapter 5, “Student mathematics learning activities,” by Timmerman discusses the Type B unit. Over the last 3 decades, there has been a shift in focus toward student thinking needed to develop a mathematical conceptual understanding and identify how students should experience solving mathematical problems. However, teaching practices (Type C) that support student learning with understanding were missing. Historical reviews also address the dilemma of balancing between the needs of mathematics and the learner; if either side dominates too much, then the entire curriculum is disrupted. Thus, curriculum frameworks should examine student engagement in learning activities (Type B), including technological environments, that have evolved in both cognitive and affective aspects as students become mathematics knowers and doers.This chapter provides three theoretical perspectives that explain student engagement in learning activities to develop mathematical CK with understanding. The first theory is Hackenberg’s (2010) scheme theory, which defined mathematical learning as a process in which people make accommodations in schemes in continuous interaction with their experiential world. According to Simon, perturbations in scheme theory do not demonstrate how learning happens, and scheme theory does not explain what a learner “attends to” in order to achieve a learning goal. Thus, learning through activity (LTA), which is a research model, examines how learners engage in learning activities to develop mathematical concepts (Simon et al., 2016, 2018). Reflective abstraction is now understood as a construction of higher-level concepts based on lower-level actions, rather than as a chronological sequence of actions for developing a new concept. A concept in LTA consists of a goal and an action that develop in two stages. The first stage is participatory or initial reflective abstraction; a learner engages in activity and uses existing concepts to start developing new knowledge. The second stage is anticipatory, only when a learner can call upon an earlier abstraction (concept) in different contexts. PS activities may provide an opportunity to examine LTA’s theory in terms of providing a more detailed explanation of how teachers can promote a transition between the two stages beyond individual students to small- and whole-group work methods in the classroom.Liljedahl’s (2016) AHA! Experience is the theory in which encouraged changes in students’ behaviors and dispositions; that is, engagement in learning activities of PS and perseverance. This chapter explains three kinds of perseverance based on Liljedahl’s theory: (1) productive disposition – viewing mathematics as sensible, useful and worthwhile, coupled with belief in diligence and one’s own efficacy; (2) productive struggle – intellectual effort students do to understand difficult concepts that are within their reasoning capabilities and (3) productive failure – students’ initial individual PS attempts were unsuccessful in finding correct solutions and became productive when supported with appropriate classroom instruction.Future research should attribute to transitioning from past theories and methods of measuring procedural student performance goals to a vision of measuring conceptual student learning goals; provide evidence of the effect of students’ engagement in learning activities CK and student to some of PS with a new for analyzing students’ and examine students’ productive (Type and (Type an appropriate Additionally, new areas of research are needed with a focus on the complexity of the learning and teaching process – the between teachers, mathematical curriculum content and the effect of technology.Chapter “Student mathematics learning by discusses the Type A unit. From the to the there was a shift in focus with mathematical learning outcomes from knowledge and understanding of content and a of procedural skills to PS and beyond computational theoretical frameworks have been used to mathematical and the idea shifts from a cognitive The framework eight competencies into two aspects of with and in mathematics and with and mathematical and However, the framework did not consider affective and et al., as a – a combination of that are and the include action The last frameworks in this chapter are TIMSS and PISA, from the TIMSS two the content which is the subject matter to be and the cognitive which is the thinking processes to be the other hand, mathematical as a mathematics framework from contexts in which were The mathematical content and the processes were to in the assessment is to that for an understanding of how students to use mathematics (Type in different social and how to that them better (Type However, of assessment does not assessment to teaching and learning assessment to determine an individual has a level of Large-scale such as and about a rather than an a new understanding of students’ competencies, goals and the for research should what student outcomes and to mathematics, understand the of factors in the of especially their existing and a or framework in assessment and and theories in the use of and and the teacher’s in improving mathematics learning by discusses the Type unit. education the general mathematics teachers are now for learners with intellectual are three of student mathematics learning are in the with some by factors (e.g. developmental and which the understanding of and reported develop new through However, to the mathematics learning is not mathematics learning which are not in the student by affective characteristics or school students and task this low due to and mathematics learning which are related to their school learners from mathematics it should be from developing in the first should focus on learning that can be design for learning which as many learning support needs as possible in a lesson provides multiple of with content (e.g. use PS tasks that can engage and learners with a and is for and for and of teachers can make the are or other methods might be used to design curriculum purpose is to with the curriculum for the and then specific learning needs through adjustments. might also students with writing difficulties can be or their and students with can be through making However, additional into the use of digital to the learning of students with intellectual is research should more about Type variables and their effect on Type particularly in mathematics Furthermore, there is to about how teachers develop by on the between learner variables, student activities and student student contexts and for mathematics teaching and by and discusses the Type unit. Mathematics is a that and is by social includes students’ construction of and of mathematics that is and is cognitive processes to understand mathematics in the were influenced by However, for the past several decades, constructivism has is not a process of and pre-existing mathematics does not of the of the views about the nature of mathematics are by their experiences as students that are as Type C and Type their experience from a traditional perspective mathematics is seen as a static they will that mathematics is about is and and is a of Thus, teachers should support productive to understand as learners are with affective processes including mathematics and is important to become to students’ belief in at which to and provides to understand the complexity of students’ can which can in performance and the can also research should the of research perspectives on student consider theoretical approaches in of student and of student and student performance in that are to and in develop of the nature of of and the of social contexts of are in experiences and understand students’ and social contexts in a of technological learning and understand and in student to important online learning digital as of the mathematics teachers’ by and discusses the Type unit. This chapter focuses on Type variables in the digital including both the and various aspects of teachers’ (e.g. This Type variables to Type variables. Research on has from the use in the classroom to how use digital curriculum to support teacher design and classroom practices. studies that to practice due to and technology has become an in studies have curriculum it pedagogical Furthermore, teachers are at a on how to the quality of and how to design or Research has produced various for digital the to to consider new for and to teachers as of their own curriculum (Type variables, because design both and Research on teachers’ has from a technology to complex of digital This was with the of theoretical frameworks and new of digital In a students develop as learners with teachers as knowledge Teachers new including their perspective on mathematics (e.g. programming as an part of have both the potential and of teachers’ research should focus on relevant to the of digital curriculum and the between teacher and of the to teachers with education and quality of specific (e.g. for mathematical including digital assessment developing from to complex digital students can and teaching at levels, and to and digital for teacher (Type J framework for the of of by and discusses the Type J unit. Mathematics teacher includes activities at and for are a intervention that teaching In mathematics, on teachers’ CK and has a effect than only on The process teachers to recognize new and innovative approaches that they use in the Thus, the competencies of are a new presage in the This chapter to provide a complete of the competencies by to through a that and teachers with experience in continuous along with the et al., The result to the for Mathematics Education framework four areas of the competencies for the of from the perspective of mathematics and competencies at the level and competencies at the classroom research should identify the of from the to the student develop instruments needed to measure competencies in the framework which be researched in more regarding taking into account the of competencies and develop quality for and in different countries with as well as them to the of book with chapter evolution of research on teaching and exploring methods for research on teachers, teaching and by and The includes that have become more some examples of research methods that offer new of thinking about research questions and presage process-product research in the research was used in However, research are particularly appropriate for a teaching and learning paradigm that on knowledge from the expert to the The of socio-cultural and theories has research a research Since became a within the some researchers use and methods methods to better understand the in the learning the other hand, technological can make research analysis more robust and The statistical and that have emerged in the last several decades, including theory, and are particularly important for This chapter then four methods that provide new perspectives on the nature of the variables for teaching and teacher research, activity theory and The and and examples of each are this chapter provides three examples of how technology has the kind of researchers may and the questions that they can and other and and examples of each are book is at suitable to be by and, this book provides a general idea for them to develop lesson plans, them in the classroom and design This Type variables. this book provides an overview of how Western countries have and how technology might be into them and – – explains of the offline variables that be directly by teachers by they might from this book in writing a research the introduction the can consider which are most to if they are in Type A and Type B variables, this book provides a literature review about the lack of PTs’ pre-existing mathematical knowledge and abilities as in to researchers might draw attention to the findings in 2, which that teachers’ is to their However, when it to student teachers’ was more than their In this Type J may also be into account by researchers as a for Type A and Type B variables. the past and current research development, researchers can at the on the suggestions by the for This would be an appropriate research the theoretical framework this book and explains a of theories and 3 various theoretical perspectives for teaching mathematics, different frameworks for students’ mathematics learning In order to and between theories and the and their respective Thus, researchers are to the suitable as the framework and the from Regarding the in theoretical perspectives for teaching mathematics, the explains that SLT is different from in that it does not that knowledge is by an than a knowledge is and Furthermore, the also explain that the perspective on the existing mathematical the perspective on exploring to students’ own concepts from a are to about and do not use that because the concept is own However, the of the in constructivism is not in this book et al., for the methodology researchers to the last chapter to they they can choose the most appropriate with their research Indonesian which is This book several on it that the framework for teacher knowledge by three different of knowledge. However, then it only two different the there are only two Additionally, several without the the for continuous However, would this book because of do not think
Saifurrisal et al. (Fri,) studied this question.