No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Teaching mathematics in seven countries: Results from the TIMSS 1999 video study
Abstract
The Third International Mathematics and Science Study (TIMSS) 1999 Video Study sampled eighth grade mathematics lessons in seven countries including Australia. As well as describing teaching in these countries the study aimed to : develop objective, observational measures of classroom instruction to serve as appropriate quantitative indicators of teaching practices in each country; compare teaching practices among countries and identify similar or different lesson features across countries; describe patterns of teaching within each country; and develop methods for communicating the results of the study, through written reports and video cases, for both research and professional development purposes. The results in this report are presented from an international perspective.
... Developing tasks, evaluating their quality, and monitoring their implementation is a very important activity for mathematics educators (Kieran et al., 2015;Shimizu et al., 2010). This is mainly due to the fact that in mathematics lessons, a large part of the learning time is used to solve tasks (Hiebert et al., 2003;Reusser & Pauli, 2003) and that the didactic quality of tasks is a predictor of successful learning processes Hiebert et al., 2003Hiebert et al., , 2005Sullivan et al., 2015). Thus, tasks in mathematics are regarded as a "vehicle" (Stein et al., 1996, p. 455) of teaching quality (Bardy et al., 2021;Baumert et al., 2010;Kunter et al., 2013;Shimizu et al., 2010;Sullivan et al., 2015;Stein et al., 1996). ...
... Developing tasks, evaluating their quality, and monitoring their implementation is a very important activity for mathematics educators (Kieran et al., 2015;Shimizu et al., 2010). This is mainly due to the fact that in mathematics lessons, a large part of the learning time is used to solve tasks (Hiebert et al., 2003;Reusser & Pauli, 2003) and that the didactic quality of tasks is a predictor of successful learning processes Hiebert et al., 2003Hiebert et al., , 2005Sullivan et al., 2015). Thus, tasks in mathematics are regarded as a "vehicle" (Stein et al., 1996, p. 455) of teaching quality (Bardy et al., 2021;Baumert et al., 2010;Kunter et al., 2013;Shimizu et al., 2010;Sullivan et al., 2015;Stein et al., 1996). ...
... Level 1-Potential of tasks and intentions of the task constructor (intended curriculum): task-related research takes place here, for example, in the form of didactic analyses of tasks, task types, or task systems in the context of the explicit or implicit curricular intentions of the task constructors (see Hiebert et al., 2003;Jordan et al., 2008). ...
Classification of mathematics tasks has long been an important part of classroom assessment. The classification systems used in this context are based on different approaches and often make use of different categories of analysis. Comprehensive studies that examine these aspects in terms of their interrelationships, and thus shed light on the contribution of classification systems to research and practice, are of great benefit. The present study provides a systematic overview of classification systems for mathematics tasks (search period: 1956–2023; worldwide distribution). It includes 17 such classification systems developed between 1963 and 2019. These systems are analyzed with the help of a model developed here. On the one hand, this model focuses on the aspects of the use of the classification systems; on the other hand, it considers the theoretical basis and the components of the classification systems. The results show that early attempts to classify mathematics tasks were largely based on Bloom’s work. These classification systems were used to analyze test items from large-scale studies and were related to mathematical content. Since the 1990s, there has been a shift in emphasis in the use of classification systems, with a greater focus on tasks used in learning processes on the one hand, and on mathematical activities on the other. At the same time, there has been an increasing differentiation of the classification systems, allowing different aspects of mathematics learning to be captured.
... In classrooms around the world, teachers dedicate most of their teaching time to interacting with the entire class (Alexander, 2008(Alexander, , 2020Hiebert et al., 2003;Pauli, 2010;cf. Schnitzler et al., 2021). ...
... The high demands of conducting dialogic classroom discussions are evident in everyday school practice. The TIMSS international video study revealed that teachers had significantly more talk time than students in all surveyed countries (Hiebert et al., 2003). Teachers' contributions were generally longer, with over 70% of their statements exceeding five words, while students' responses were mostly brief (1-4 words). ...
... By creating "interactional spaces in which students are positioned as contributors whose inputs are recognized and credited" (Lipponen & Kumpulainen, 2011, p. 813), students become accountable agents in meaning-making processes in classroom discourse. Thus, the roles of all participants differ from those generally observed in whole-class discourse (Hiebert et al., 2003). ...
This article examines the characteristics of meaning-making during classroom discourse using data from a study regarding a yearlong teacher professional development (TPD) program intended to promote dialogic discourse in whole-class practice.The in-depth, video-based case analyses of two whole-class discussions in history classes (two classes/teachers, N = 46 students) at the end of the TPD integrate multi-semiotic and content-bound perspectives. The analyses show how the students adopt an active role in shaping the dialog and contribute to the direction of the discourse, while both teachers assume a moderating stance. Concurrently, the findings highlight the inherent tension teachers face while ensuring student participation and compliance with disciplinary norms. In addition, the results reveal new student roles and asymmetries due to altered responsibilities in student-owned classroom discourse, which are particularly elucidated through nonverbal interactions. This contributes to existing research by highlighting novel, critical elements for consideration in TPD.
... Research on the quality of mathematics teaching is a crosscultural endeavor, as is evident (for example) in the TIMSS videostudy (Hiebert et al., 2003) and in work on Mathematics Classroom around the World (Kaur, 2017;Kaur et al., 2013;Shimizu et al., 2010). However, it would go beyond the scope of this article to present and duly acknowledge all the diverse and numerous findings from around the globe. ...
... We therefore concentrate in this section on the presentation of central results that stem from the tradition of Germanlanguage as well as U.S. empirical research. In these two regions, the question of the quality of (mathematics) teaching has been discussed particularly intensively-mainly based on broad empirical studies such as the COACTIV project in Germany or the Pythagoras study (Klieme et al., 2009) in Germany and Switzerland, and in the US context the international TIMSS videostudy (Givvin et al., 2005;Hiebert et al., 2003) or the TEDS-M research program (Blömeke et al., 2022;Kaiser & König, 2020)-with quite different accentuations 1 which might be fruitful to combine. These studies had a strong influence on the discussion of quality in mathematics education, in particular with their linking to learning and instruction (Klieme et al., 2009;, their relation to teachers' skills and competences (Baumert & Kunter, 2013a, b), and their examination of the quality of applied tasks in mathematics education (Adleff et al., 2023;Jordan et al., 2006;Neubrand et al., 2013;Shimizu et al., 2010). ...
... Several studies show differences in mathematics teaching and teaching practices when cultural background is considered (e.g., Hiebert et al., 2003). But in what ways does the quality of mathematics teaching depend on cultural beliefs and values (e.g., Dreher et al., 2018;Gasteiger et al., 2021;Hiebert et al., 2003;Kaur, 2017;Kaur et al., 2013;Leung, 2002Leung, , 2017Zhu & Kaiser, 2019)? ...
In this survey paper we focus on aspects of the quality of teaching mathematics from several perspectives. We differentiate between effective aspects that are empirically proven and more normative ones that constitute “good teaching” but that are highly dependent on context. High quality of mathematics teaching includes characteristics from a generic point of view as well as those that rely upon more subject- and topic-specific features. In the paper we draw upon examples of the research traditions in Germany and in the US—where the discussion regarding quality of mathematics teaching has been particularly intensive—to provide a short overview about empirical key findings. We then describe open questions in this research field and conclude by proposing a conceptualization of high quality mathematics teaching that foregrounds the relationship between generic and topic-specific and also considers different possibilities for the measurement of the quality.
... For instance, Grossman et al. [11] argue that effective teaching requires a dynamic interplay between teachers' content knowledge, pedagogical knowledge, and knowledge of students' thinking. Teachers must continually reflect on their practice and refine their instructional approaches to meet the diverse needs of their students [12]. In conclusion, mathematics teachers' knowledge of the four strands of Algebra, Geometry and Measurement, Data, and Number, as well as their understanding of Bloom's Taxonomy cognitive domains, is essential for providing comprehensive and effective instruction. ...
... the coefficients to be estimated,12 , ,..., k x xx are the independent variables, log is the natural logarithm function.i y is the observed count for the i th observation. ...
In the field of mathematics education, it is essential to grasp teachers' competence in recognizing cognitive domains, as it plays a pivotal role in elevating teaching methods, evaluation techniques, and ultimately enhancing student academic achievements. This study examines the proficiency of basic school teachers in Ghana in identifying the cognitive domains of mathematics questions using Bloom's Taxonomy. A sample of 338 teachers from across the regions of Ghana participated, selected through random sampling. Teachers were assessed using a set of 50 Basic Education Certificate Examination (BECE) past questions spanning a decade (2010-2022), covering Algebra, Geometry and Measurement, Data, and Number strands. Participants categorized each question according to Bloom's Taxonomy. Poisson regression analysis and Confirmatory Factor Analysis were employed to evaluate teachers' proficiency. Results indicated a statistically significant intercept term, suggesting a baseline performance level among teachers. Significant interaction effects between demographic and professional characteristics (Class:category, Class:SchTyp, TeachEx:SchTyp, 42 TeachEx:Domain, and the main effect of Domain) influenced teachers' ability to identify mathematics domains. Teaching experience positively influenced scores, while school type had a negative impact. The model demonstrated high discriminatory power and strong predictive performance with an AUC of 0.996. Dependency analysis revealed that understanding Bloom's taxonomy domains influenced the identification of mathematics strands. Primary level teachers' consistently demonstrated higher proficiency compared to Junior High School (JHS) level teachers. Additionally, experienced and qualified professionals performed better than pupil teachers. These findings highlight the importance of targeted interventions and professional development programs to enhance teachers' competency in identifying mathematics domains, thus improving mathematics education in Ghana.
... Existing empirical studies on mathematics teaching show a methodological divide or -put it another way -paradigmatic divide, with some applying quantitative analyses to often 80 to 100 'stand-alone' lessons per nation (e.g., the TIMSS Video Studies and the most recently TALIS Video Study: Hiebert et al., 2003;OECD, 2020;Stigler & Hiebert, 1999) and others applying qualitative interpretation of characteristics of stand-alone or consecutive lessons (e.g., the Learner's Perspective Study: Clarke et al., 2006). ...
... Findings from existing studies on maths teaching were based on either quantitative (QUAN) or qualitative (QUAL) methods. These include the widely known TIMSS Video Studies (QUAN) (Hiebert et al., 2003;Stigler & Hiebert, 1999), the Learner's Perspective Study (QUAL) (Clarke et al., 2006), and the recent TALIS video study (QUAN) (OECD, 2020). We have made the best use of both QUAN and QUAL methods, which makes the study much needed in methodological terms and both rich and robust in terms of findings, implications and contributions. ...
This practical guide invites teachers to take a journey towards masterly mathematics teaching using the experiences and lessons learnt across five Chinese provinces, Anhui, Beijing, Jiangsu, Jiangxi and Tianjin.
On this journey, you will gain a thorough understanding of: (1) the quality and characteristics of master mathematics teachers’ teaching, (2) the quality of mathematics learning they have nurtured amongst their students in affective, metacognitive and cognitive dimensions and (3) the teaching-learning mechanisms that underpin excellent performance in the three dimensions. Alongside the quantitative and qualitative evidence on educational excellence, you will also delve deep into the trajectories and processes of professional development that generate professional excellence amongst master mathematics teachers and their peers within and across primary schools, up and down China.
Building on data collected with 70 master mathematics teachers and 3,178 students and from teaching research events at the school, municipal, provincial and national levels, the Master Mathematics Teachers (MasterMT) project is, to date, the first that has looked at the legendary tribe of master mathematics teachers in China at such a large scale, and with such breadth and depth. The book offers invaluable insights for any teacher or teacher educator who wants to improve mathematics teaching and learning and generate educational and professional excellence in primary schools and beyond.
... Designing lesson plans that incorporate teachers' goals and are focused on "students' anticipated learning" (Akyuz et al., 2013, p. 94) has been the focus of key reform-based documents, including Adding It Up . Further, Hiebert et al. (2003) emphasized the importance of developing teachers' Type D: "[T]eachers need to design lessons with clear goals in mind, monitor their implementation, collect feedback, and interpret the feedback in order to revise and improve future practice" (p. 206). ...
... The 1999 lessons have also been examined in terms of lesson structure, mathematical content, and instructional practices, and to discern differences in mathematics classroom activity in different countries. Hiebert et al., (2003) observed that while there were some similar features in the relatively higher achieving countries, there were also distinct differences. For example, eighthgrade lessons in all participating countries included both whole-class work and individual/small group work. ...
Mathematics teaching is subject to cultural and temporal conditions. Not only do
school and societal conditions shift, and with them the composition of the student
body, but also curricular regulations and new mathematical and pedagogical insights
determine the content to be taught and the approach to learning used in mathematics classes. To reflect on mathematics teaching in a changing world, there is a need for continuous scientific research into this process of teaching mathematics. Results of this research also have a retrospective impact on mathematics teacher education insofar as the conditions of education need to be continuously adapted to the professional requirements of teachers in practice. Research on teaching mathematics thus bears a great responsibility and is a constantly evolving field of research for scholars around the globe.
This book comes at the time when the world is facing an ongoing global pandemic
and experiencing violence and unrest due to active war. This publication symbolizes a professional commitment and international collaboration par excellence apropos
teaching mathematics. The editors from three different continents and researchers
who represent sixteen institutions and eight countries worked constructively and
collaboratively with utmost respect for each other, with intentions to reflect on
existing research knowledge and to create new knowledge that can be shared and
used by other educators and researchers across the world.
In preparation for this book, our international group of researchers shared current
issues related to the evolution of research on teaching mathematics. We examined
the present state of research on mathematics teaching and discussed the theoretical and methodological challenges associated with it, including issues related to conceptualization, instrumentation, and design. Additionally, we explored the likely direction of future research developments. In our literature review and discussions on this project, it became evident that studies on teaching frequently establish direct relationships between units of analysis that, at first glance, cannot be assumed to be directly related in a chain of effects. There are examples of studies presented in this book that directly relate teacher competencies to student achievements using empirical measurement models in a causal or relational way. Without criticizing these studies across the board, however, it seems reasonable to consider moderating or intermediate variables in this chain of effects (Baron & Kenny, 1986), such as the initiated student learning activities observable by teachers in the classroom, aspects of instructional quality (e.g., classroom management or cognitive activation), or corresponding student variables such as attention and cooperation in class or students’ prior knowledge (e.g., Fig. 1).
Although there are researchers who do indeed study mediating variables (e.g.,
Blömeke et al., 2022), it became clear to us that there is a lack of a systematic
scientific overview of the complete chain of effects between teacher characteristics, activities, and students’ learning processes. Overviews of precisely these aspects of research on teaching and respective studies are scarce, which inspired this book.
... Designing lesson plans that incorporate teachers' goals and are focused on "students' anticipated learning" (Akyuz et al., 2013, p. 94) has been the focus of key reform-based documents, including Adding It Up . Further, Hiebert et al. (2003) emphasized the importance of developing teachers' Type D: "[T]eachers need to design lessons with clear goals in mind, monitor their implementation, collect feedback, and interpret the feedback in order to revise and improve future practice" (p. 206). ...
... The 1999 lessons have also been examined in terms of lesson structure, mathematical content, and instructional practices, and to discern differences in mathematics classroom activity in different countries. Hiebert et al., (2003) observed that while there were some similar features in the relatively higher achieving countries, there were also distinct differences. For example, eighthgrade lessons in all participating countries included both whole-class work and individual/small group work. ...
In this chapter we investigate the evolution of research in mathematics education related to digital resources as an essential element of the external context for mathematics teachers’ professional activity. In the relevant research literature, we identified different themes and different kinds of evolution. We investigate the evolution of research with respect to educational policies related to digital resources, and to teacher integration of digital resources, including digital assessment. We also analyze the evolution of research concerning the quality of digital curriculum resources, and discuss emerging research questions related to mathematics and programming; to collective dimensions of teachers’ work with digital resources; and about the COVID-19 pandemic consequences. The different kinds of research developments are a result of evolution in the external context, or from more general trends in the research in mathematics education. We finally discuss possible directions for future research.
... Designing lesson plans that incorporate teachers' goals and are focused on "students' anticipated learning" (Akyuz et al., 2013, p. 94) has been the focus of key reform-based documents, including Adding It Up . Further, Hiebert et al. (2003) emphasized the importance of developing teachers' Type D: "[T]eachers need to design lessons with clear goals in mind, monitor their implementation, collect feedback, and interpret the feedback in order to revise and improve future practice" (p. 206). ...
... The 1999 lessons have also been examined in terms of lesson structure, mathematical content, and instructional practices, and to discern differences in mathematics classroom activity in different countries. Hiebert et al., (2003) observed that while there were some similar features in the relatively higher achieving countries, there were also distinct differences. For example, eighthgrade lessons in all participating countries included both whole-class work and individual/small group work. ...
Lesson planning, assessment, and reflection constitute the key actions that teachers perform when students are not present in the classroom (henceforth, “Type D” variable). These “pre- and post-”actions are the most direct ways through which teachers shape their observable teaching work as mediated by their goals for their teaching. These goals are representations of teachers’ epistemological commitments apropos of teaching mathematics, whether those commitments be consciously espoused or unconsciously reproduced due to constraints within which they work. In this chapter, we survey the literature on lesson planning, assessment, and reflection according to eight epistemological paradigms that are widely known in the field of mathematics teaching. These epistemological paradigms are: Situated Learning Theory, Behaviorism, Cognitive Learning Theory, Social Constructivism, Structuralism, Problem Solving, Culturally Relevant Pedagogy, and Project- and Problem-Based Learning. We situate other perspectives on learning theory, which are derivatives of these prevailing paradigms, within this overarching frame. Our literature search revealed that some of the theoretical perspectives are well-reported in the literature whilst others have not received the same amount of attention from researchers. We detail each perspective, providing a definition, goals for teaching, pros and cons, and examples from the literature. We posit that, with the advent of the digital era of mathematics education, researchers must engage more explicitly with the theoretical perspectives we identified as underserved and must reckon with their own epistemological commitments more intentionally when reporting on studies regarding Type D.
... Tilknytningen til dagliglivet er et annet eksempel. Resultatene fra TIMSS 1999 Video Study viste at det var store forskjeller på tvers av land i hvilken grad matematikken ble knyttet til en hverdagslig eller realistisk kontekst (Hiebert et al., 2003), og det ser også ut til at norske laerere har ulike oppfatninger og praksis om dette -selv om norske laereplaner har lagt vekt på en tilknytning til dagliglivet (Mosvold, 2006). På bakgrunn av dette, vil vi ikke i denne sammenheng avgjøre hvorvidt konkrete undervisningsoppgaver bør legges til eller trekkes fra listen over matematiske undervisningsoppgaver, men vi vil peke på at dette er en sammensatt diskusjon som i stor grad er knyttet til synet på undervisning. ...
Denne artikkelen bidrar til studier og begrepsfesting av det profesjonelle lærerarbeidet i matematikk ved å analysere diskusjoner mellom erfarne matematikklærere. Gjennom slike analyser forsøker vi å komme nærmere et svar på hvilke matematiske undervisningsoppgaver de fremhever som sentrale i sitt lærerarbeid. Utgangspunktet for diskusjonene er en liste med sentrale matematiske undervisningsoppgaver presentert i forskningslitteraturen. Resultatene viser at de erfarne lærerne mener at: 1) listen over matematiske undervisningsoppgaver trenger finpuss og presisering, 2) listen må omstruktureres, og 3) listen mangler matematiske undervisningsoppgaver som er viktige i en norsk kontekst. Vi konkluderer med at studier av erfarne læreres syn på hva som er sentrale matematiske undervisningsoppgaver for matematikklærere kan bidra til videreutvikling av den praksisbaserte teorien om undervisningskunnskap i matematikk.
... Comparison can be made at different levels and with different foci. For instance, largescale studies such as Third International Mathematics and Science Study (TIMSS) (Hiebert et al., 2003) and Programme for International Student Assessment (PISA) (OECD, 2004) inform about students' achievement, curriculum and systems. They present national images, which are often eye-catching and sometimes get quick responses from policy-makers (Ainley, 2004). ...
The aim of this paper is to illustrate how the topic of fractions can be taught differently by making a comparison between two cultures. We have studied mathematics teaching in classrooms in Hong Kong and Sweden. One of our basic assumptions is that the way in which the content is taught in a classroom has an important implication for what students may possibly learn. With reference to the framework of Variation Theory, two different spaces of learning are delineated. The Hong Kong lesson demonstrated a pattern of many juxtaposed variations, whereas the Swedish lessons presented a pattern of sequential and wide spreading character.
... Consequently, we argue that not only large-scale cultural differences between areas, such as Western Europe and Southeast Asia, can exist, but also two neighbouring countries with similar school systems can differ regarding specific topics. These differences became even more visible through the lens of cross-cultural comparison, in line with suggestions from Hiebert (2003). ...
Solving linear equations is a cornerstone in the learning of algebra. There are two main strategies for solving a linear equation, ‘swap sides swap signs’ (SSSS) and ‘do the same to both sides’ (DSBS). While SSSS can often be more efficient for solving equations, DSBS has been shown to better promote the learning of algebra. Thus, the preference of SSSS or DSBS might depend on the purpose of solving equations. Since both approaches are common, mathematics teachers, and thus also pre-service teachers (PSTs), must be familiar with both SSSS and DSBS. This study draws on data from 161 Swedish and 146 Norwegian PSTs. They were given a correct but short and unannotated solution to the linear equation x + 5 = 4x − 1. The PSTs were invited to explain the provided solution for a fictive friend. Of the Norwegian PSTs, 2/3 explained the additive steps in the solution by SSSS, while only 1/3 of the Swedish PSTs applied SSSS. Consequently, DSBS was more frequent among the Swedish PSTs regarding the additive steps. However, in the final, multiplicative step, 3/4 of the Norwegian PSTs invoked DSBS. On the contrary, among the Swedish PSTs, the proportion applying DSBS for the multiplicative step decreased, and it was common to provide an incomplete explanation of the final operation. We also analysed how mathematics textbooks for secondary school presented how to solve linear equations. In Sweden, all textbooks utilised DSBS through the whole solution for all years in secondary school. This also applied for Norwegian textbooks for the first two years of lower secondary school. However, in last year of lower secondary school, they changed their approach and promoted an SSSS strategy in additive steps, while DSBS was still suggested for multiplicative steps. This might explain the differences between the two countries regarding the PSTs’ preferences of solution strategies. We suggest that these results can be useful for teacher education, since increased awareness of PSTs’ pre-knowledge is beneficial to support their development of teaching linear equations.
... This difference in performance, which has been attributed to general factors such as differences in SECIs or a more equitable education system (I.N.E.E., 2023), could also be due to the use of textbooks. Books are the most used didactic resource used by teachers to teach problem solving to their students in the classroom (Hiebert et al., 2003;Mullis et al., 2008). Moreover, the variety and level of difficulty of the problems that children face from books influence their ability to solve them (Siegler and Oppenzato, 2021), with the semantic-mathematical structure of these problems being one of the variables that most influences their level of difficulty (Carpenter and Moser, 1984;Greer, 1992;Vergnaud, 1991). ...
The results of mathematics achievement assessments such as the TIMSS, in which problem-solving is the cornerstone, show that the performance of students in Castile and Leon is significantly greater than that of students in Andalusia. These differences seem to be due to some aspects pointed out by the TIMSS (such as the social and economic index), although they could also be due to certain elements of the teaching-learning process, such as the textbook, since they are used intensively in the classroom. In fact, the books used in countries with more proficient students in mathematics include more problems and more varied and difficult problems than books from other countries. The aim of the present work is to determine whether the primary mathematics textbooks used in Castile and Leon are different from those used in Andalusia in terms of learning verbal arithmetic problem solving. For this purpose, in the first study, we determined which books are most frequently used in each autonomous community, and in the second study, we analysed 3rd grade primary school books from the most widely used textbooks in each autonomous community in relation to the number of tasks aimed at solving problems and the variety and level of semantic-mathematical difficulty of these problems. The results indicated that although the most frequently used books in both communities belong to different publishing projects, the most-used books in Castile and Leon and Andalusia were very similar with respect to the variables analysed, the only difference being a greater number of problems in the Castilian-Leonese books. These results contrast with those obtained in international comparisons of textbooks and point to a greater influence of other variables on differences in student performance in both autonomous communities.
... Tasks play a central role as learning opportunities in mathematics classrooms (Brod, 2024;Bromme, 1981;Chapman, 2013;Hiebert et al., 2003a;Johnson et al., 2017;Thanheiser, 2017). They specify the topic of a learning situation and strongly contribute to the subsequent learning processes (Hiebert et al., 2003b;Stein et al., 1996). ...
The selection of tasks based on the evaluation of task features can be considered a core practice of teaching and a relevant component of teaching quality. This is typically part of teachers’ preparation for their classroom teaching, which prompts the following question: What are the characteristics of the tasks that teachers use when selecting tasks for differentiated teaching? To answer this question, we analyzed systematic differences in the focus of 78 in-service high school and lower secondary school teachers during the evaluation of task features. The teachers had to select eight tasks about the practice of fractions with respect to their differentiation potential—operationalizing their adaptive teaching competence from a mathematics educational perspective. To analyze the differences, we performed a cluster analysis of the task features that the teachers drew upon. Three groups of teachers could be identified with variations in their focus on directly or indirectly relevant, domain-specific or domain-general task features. Taking into account such variations may explain differences in teaching quality and student outcomes and may be relevant when designing teacher professional development programs.
... Insbesondere in der empirischen Schul-und Unterrichtsforschung besitzen videogestützte Beobachtungsverfahren eine lange Tradition, beispielsweise zur Dokumentation von Lehr-Lernprozessen im Unterricht (Gröschner, 2019;Häusler et al., 2019;Janik & Seidel, 2009 1970er Jahre in den Studien von Jacob Kounin (Kounin, 2006). Für die Etablierung und Verbreitung der Videoforschung im deutschsprachigen Raum spielte insbesondere die Third International Mathematics and Science Study (TIMSS-Videostudie) in den 1990er Jahre eine wichtige Rolle (Hiebert et al., 2003 (Gold & Holodynski, 2017) und professionelle Unterrichtswahrnehmung (Keskin et al., 2024) (Helmke, 2014;Seidel, 2014 ...
Der Beitrag beschäftigt sich mit der Video- und Audio- analyse als empirische Methode für die interprofessionelle Bildungsforschung. Ausgehend von der Beschreibung grundlegender Merkmale werden zunächst die zentralen Forschungsfelder der Video- und Audioanalyse im Kon- text des Lehrens und Lernens vorgestellt. Hieran schließt sich die Darstellung des methodischen Vorgehens der video- und audiogestützten Datenerhebung sowie -analyse an. Es werden etablierte Techniken und Gütekriterien für Video- und Audioaufnahmen präsentiert und sowohl quantitative als auch qualitative methodische Zugänge für die Analyse des Video- und Audiomaterials bespro- chen. Der Beitrag schließt mit einem Ausblick auf die Perspektiven und Potenziale video- und audiogestützter Forschungsvorhaben im Feld der interprofessionellen Bildungsforschung.
... Bokhove (2016) also argues the importance of dynamic social network analysis (SNA) in modeling and exploring in-class interactions, especially "verbal utterings". The research project builds on six videos from the TIMSS study (Hiebert et al., 2003) and observations of classrooms in South England and harnesses Lesson Note which is an iPad application observing the classroom interactions. ...
Technology in the classroom comes in many shapes to differentiate
instruction, create meaningful learning experiences, actively engage the
learners, or inform about classroom exchanges. Video recordings are no
exception. They facilitate the investigation of classroom interactions and the
collection of audio-visual data that provide further insights into the teaching
practice and classroom dynamics. Previous education research has almost
turned a blind eye to uncovering the intricacies of elementary classroom
behavior and interactions through the medium of modern technologies. Only
scattered attempts have brought to bear the issue. To this end, this paper
presents an overview of the salient role of digital technologies, mainly video
materials, in clarifying the different interactions that take place within the
confines of the classroom, including teacher-to-teaching assistant (TA)
relationships, teacher-aide-to-pupil interactions, and peer-to-peer interaction
drawing on an ongoing data collection from elementary schools around
Hradec Králové (HK) region in the Czech Republic. Classroom recordings
might be a fountainhead for detailed, reflective analysis, enhanced
communication among all participants, and better teaching-learning practice
if used properly. The first part of the paper reviews some related definitions
based on several previous theoretical grounds. Then, it highlights the peculiar
classroom interactions aided by various analytic angles. Deeply rooted in
education research, these dynamics are indebted to the presence of audio
and visual records. Most importantly, the paper is built around the research
endeavor by researchers at the University of HK, mainly the Faculty of
Education, that aims at getting down to brass tacks of TAs interactions by
means of technological intervention in data collection (video recordings) and
measurement (Flanders et al. – FIAS)
... In this study, we explore the relationship between teachers' pedagogical practices and ILEs. We focused on the 3rd to 5th graders' mathematics teaching, as it has been found that, in mathematics, traditional teacher-led methods are predominantly used (Hiebert et al., 2003;OECD, 2009). Thus, the aim of our study was to gain more knowledge of the pedagogy that teachers use in ILEs and the factors influencing teachers' use of ILEs while teaching mathematics. ...
New school buildings are often designed for flexible innovative learning environments (ILEs) to support learning future skills better than before. However, little is known about the relationship between environment and pedagogy. This article examines the relationship between the environment and pedagogy from the perspective of primary school teachers in the context of teaching mathematics. We interviewed 26 teachers from 10 Finnish ILEs and did a thematic analysis. The relationship between the environment and pedagogy forms a complex network of entangled tensions between teacher's inner space, community's social space and physical space. When the tensions between these spaces were resolved in a positive way, ILEs enabled pedagogy that diversified mathematics education, improved student cohesion and teachers' well‐being at work. However, the ILEs' transformation process often appears to be left unfinished, leading to unsuccessful resolution of tensions. Further, our findings highlight the importance of four‐dimensional environmental competence in exploiting the affordances enabled by ILE.
... (2008) zeigten anhand der Analyse von Aufgaben, die Lehrpersonen für die an den PISA-Erhebungen 2003 und 2004 beteiligten Schulklassen auswählten, dass der Anteil kognitiv aktivierender Aufgaben im Mathematikunterricht eher gering ist. Kommen Aufgaben mit Potenzial zur kognitiven Aktivierung zum Einsatz, werden sie oft reduziert eingesetzt, indem sie hinsichtlich ihrer Problemhaltigkeit verringert werden (Hiebert et al., 2003). ...
Im Artikel wird mit KOSI – Kognitiv aktivierende Gespräche im Mathematikunterricht digital simulieren ein Projekt vorgestellt, dass durch digitale Selbstlerneinheiten Grundschullehramtsstudierende auf eine kognitiv aktivierende Gesprächsführung vorbereiten möchte. Kern der Selbstlerneinheiten bilden Dialogsimulationen, die als interaktive Übung ein echtes Gespräch mit einem Kind nach-ahmen. Im Folgenden werden ausgehend von Herausforderungen einer kognitiv aktivierenden Gesprächsführung im Unterricht das Projekt und der erwartete Mehrwert vorgestellt. Das Projekt wird im Rahmen des Programms „Fellowship für Innovationen in der digitalen Hochschullehre“ durch den Stifterverband und das Thüringer Wissenschaftsministerium gefördert.
... Based on the main objective of MATH 101 stated above, the vast experience of our faculty, and the instructional coherence [10,11] of our mathematics curriculum, we made a careful selection of each of the topics covered in this course. Unlike traditional remedial courses, MATH 101 focuses only on those subjects that are the cornerstone of our first engineering mathematics course, namely MATH 201. ...
... Thus, the countries participating in the exam can follow their own developments on the one hand, they have the opportunity to compare their results with other countries on the other (MoNE, 2016). Countries also have the opportunity to review their curricula and shape education reforms accordingly (Hiebert et al., 2003;Johansson & Hansen, 2019;MoNE, 2016). As a matter of fact, it can be claimed that the content of international exams is taken as criteria in the structuring of learning domains and learning outcomes while adapting the curricula by the Ministry of National Education [MoNE] in Türkiye (MoNE, 2018). ...
... Das Schulfach Mathematik (nicht die Wissenschaft Mathematik!) scheint sich wie kein anderes um die Bearbeitung von Aufgaben herum zu organisieren. Für die Praxis berichten Hiebert et al. (2003), dass etwa achtzig Prozent der Zeit im Mathematikunterricht mit der Bearbeitung von Aufgaben verbracht wird. Für die Forschung spiegelt sich das an dem internationalen Interesse an Theorie, Konstruktion und Nutzung von Aufgaben in den oben genannten unterschiedlichen Funktionen wider (aktuelle Monographien: Shimizu et al. 2010;Sullivan et al. 2013;Watson et al. 2013). ...
... This owes in no small part to theoretical advances in education research writ large that overcame prior focus on the individual characteristics of teachers or on the generic behaviors of teachers in the classroom and put more emphasis on the activity of instruction (Cohen et al., 2003;Hiebert & Stigler, 2017). International studies like TIMSS have addressed that question across countries for a given level of schooling (Hiebert et al., 2003;Stigler & Hiebert, 1999). As a contribution to our community's understanding of what kind of practice mathematics teaching is, we demonstrate how to investigate differences in mathematics teaching practice across different levels of schooling. ...
This paper investigates how mathematics instructors' recognition of the professional obligations of mathematics teaching varies based on their institutional environment, specifically whether they teach high school or college mathematics. Using an instrument that measures instructors’ recognition of four hypothesized professional obligations, we surveyed 471 US high school mathematics teachers and 239 university mathematics instructors to measure the extent to which they recognized professional obligations when evaluating the appropriateness of certain instructional actions. After testing measurement invariance of four item sets, each of which measures one of the four hypothesized professional obligations—disciplinary, institutional, interpersonal, and individual obligations-, we compared the instructors’ recognition of each of the four obligations between the two groups. We found that university instructors recognized the institutional obligation more than high school teachers, while recognizing the individual and interpersonal obligations significantly less. This investigation provides insight into the variation in the nature of mathematics teaching practice across different levels of schooling.
... The 1999 lessons have also been examined in terms of lesson structure, mathematical content, and instructional practices, and to discern differences in mathematics classroom activity in different countries. Hiebert et al., (2003) observed that while there were some similar features in the relatively higher achieving countries, there were also distinct differences. For example, eighthgrade lessons in all participating countries included both whole-class work and individual/small group work. ...
The focus of this chapter is on interactive mathematics teacher activities (Type C). That is, the activities in which teachers engage in the presence of students.
... Some assessed more than one lesson: For example, SINUS for primary schools recorded one to three lessons (Dalehefte and Rieck 2014), and the Pythagoras video study recorded three lessons (Drollinger-Vetter 2011). The well-known TIMSS video study (1999), in contrast, recorded one lesson to measure dimensions of instructional quality (Hiebert et al. 2003). Recent results suggest that content-independent dimensions of instructional quality (e.g., classroom management) can be observed accurately based on one recording (Praetorius et al. 2014). ...
Productive classroom talks provide a variety of learning opportunities including the collaborative construction of mathematical meaning. To support the orchestration of productive classroom talk, teachers can use specific conversational strategies called “talk moves”. Positive relations between the number of productive talk moves, discourse quality, and learning success have been demonstrated, but mostly at the secondary school level and in English-speaking countries. There are very few findings from elementary school in German-speaking countries. The present study makes the first step towards closing this gap by analyzing classroom talk in mathematics second grade classes in Switzerland ( n = 22). The dataset includes recordings of mathematics lessons as well as students’ pretest and posttest performance in mathematics. The results show that teachers varied in their use of productive talk moves and that some talk moves such as reasoning moves were preferred, depending on the teacher. In addition, the number of productive talk moves was positively related to both the number of justifications students provided and their learning success. Implications for the use of productive classroom talk in elementary school mathematics lessons are discussed.
... The incongruency between beliefs and practice, as seen in Mr. B, has been noted in other studies that have found similar inconsistencies [37,42,92,108,109]. This misalignment among individual teachers perpetuates the prevalence of a transmissive, teacher-directed approach to teaching mathematics on a global scale [110]. The teacher's dominant presence within math classes undermines the envisioned ideal of co-constructing knowledge advocated by proponents of math reforms. ...
The dynamic interplay between teachers’ beliefs and practices significantly impact the quality of instruction and the trajectory of talent development in young students. This case study explores the beliefs and practices of two elementary teachers instructing gifted ELs in mathematics. The constant comparison method was used to analyze data collected from classroom observations, semi-structured interviews, and field notes. Three factors were found to affect the (in)consistency between teachers’ expressed beliefs and observed practices: compatibility among core and peripheral beliefs, knowledge about evidence-based practices, and classroom management skills. Students exhibit higher levels of participation, communication, and engagement in critical thinking skills when their teacher embraces constructive perspectives in teaching mathematics, demonstrates pedagogical expertise, and employs a proactive classroom management approach. Conversely, students encounter restricted opportunities to independently construct their own understanding of mathematics when their teacher holds maladaptive beliefs about teaching mathematics, has limited knowledge of evidence-based practices, and has an authoritarian classroom management style. These findings underscore the need for a new approach to professional development (PD) that encourages teachers to critically examine the connection between their beliefs and instructional practices and their impact on the student’s mathematical talent development.
... Mathematics textbooks, as already known, are a common feature of many mathematics classrooms all over the world, and their content and structure play an important role in students' learning and understanding of the subjects. Research done by Hiebert et al. (2003) found that teachers in many countries rely heavily on mathematics textbooks or worksheets of some kind in which they used mathematics textbooks in at least 90 percent of their lessons. Furthermore, most of the research on mathematics textbook analysis focused on the content and structure of the text. ...
[English]: This article investigates the nature of probability problems presented in mathematics textbook using the socio-political perspective and critical discourse analysis drawn from well-known critical linguists Norman Fairclough. Specifically, the paper analyzed how the students are positioned by the problems presented in the text, to find out the role of authors and student readers, and to gain insight about the possible consequences for students. Drawing on Fairclough's three-dimensional model for critical discourse analysis as a framework for studying the relationship between the written text of probability problems in the textbook, the associated discursive practices, and the social practice to which the discursive practices form part, the article argues that the textbook authors tend to be authoritative by directing students about what to do and how to do the probability (mathematical) activities. The analysis also shows that the use of real-word problems in the text points out the attempts of the authors to present the probability concepts more relevant and accessible to the student readers. The article demonstrates the usefulness of Fairclough's three-dimensional model as a framework for analyzing probability problems presented in the mathematics textbook. [Bahasa]: Artikel ini menyelidiki sifat masalah peluang yang disajikan dalam buku teks matematika dengan menggunakan perspektif sosio-politik dan analisis wacana kritis yang diambil dari ahli bahasa kritis terkenal Norman Fairclough. Secara khusus, makalah ini menganalisis bagaimana siswa diposisikan oleh masalah yang disajikan dalam teks, untuk mengetahui peran penulis dan siswa sebagai pembaca, serta untuk mendapatkan wawasan tentang konsekuensi yang mungkin terjadi pada siswa. Merujuk pada model tiga dimensi Fairclough untuk analisis wacana kritis sebagai kerangka kerja untuk mempelajari hubungan antara teks tertulis dari masalah peluang dalam buku teks, praktik diskursif yang terkait, dan praktik sosial yang merupakan bagian dari praktik diskursif, artikel ini menunjukkan bahwa penulis buku teks cenderung otoriter dengan mengarahkan siswa tentang apa yang harus dilakukan dan bagaimana melakukan kegiatan berkaitan dengan konsep peluang (matematika). Analisis juga menunjukkan bahwa penggunaan masalah berbasis kehidupan sehari-hari dalam teks menunjukkan upaya penulis untuk menyajikan konsep peluang yang lebih relevan dan dapat diakses oleh siswa. Artikel ini menunjukkan kegunaan model tiga dimensi Fairclough sebagai kerangka kerja untuk menganalisis masalah peluang yang disajikan dalam buku teks matematika.
... Their biggest concern was whether they could recall the different knowledge from previous mathematics lessons. This confirms that teaching and learning ready-made algorithms cause students to rely on memory to solve problems [42,[52][53][54]. A notable finding is that students positively evaluated task atomization because this method does not require them to learn long computational procedures. ...
The transition from arithmetic to algebra requires students to change both their thinking and the way they learn. We often observe students using arithmetic formalism also when solving algebraic problems. This formalism manifests itself primarily in the acquisition of coherent computational procedures. Students must be sufficiently aware that the computation steps are sequential transformations of the problem. This creates a problem for them in solving more complex problems. Our research investigated whether problem transformation coupled with atomization is a suitable alternative for students to learn coherent algorithms. Although atomization is not based on precise rules, it was reported by students to be a comprehensible way of solving problems and providing them with sufficient confidence. If students are motivated to understand a computational method, this understanding represents fulfilling the student’s need for security.
... All the teachers preferred to move from learner to learner particularly after assigning some work. The findings concur with Hiebert et al. (2003), whose findings across the seven countries showed that individual work and teachers talking too much than learners was common during the lesson. ...
Effective mathematics teaching and learning is crucial not only for the purposes of examination and assessment but as well for the learners’ empowerment so that they cope with the ever-changing technology and be able to solve real-life social and economic problems of the world. The study aimed at revealing the pre-service teachers’ pedagogical practices during teaching practice as well as whether they aligned their practices to the teaching approaches recommended in the mathematics syllabus. The case study involved four secondary school pre-service mathematics teachers who were purposively sampled. Documents, interviews and lesson observations were the data collection instruments. The results showed that out of the four teachers only two used both teacher-centered and learner-centered methods, whilst the other two used purely traditional teacher-centered methods. The learner-centered methods used by the two teachers were only limited to group work and pair work out of the several learner methods recommended by the syllabus. In this era of technology, none of the teachers made use of technology whilst delivering their lessons, which is also not in line with the syllabus requirements. Pre-service teachers need to be more knowledgeable in learner-centered approaches, syllabus use and interpretation as well as technology integration in the teaching and learning of mathematics.
... Moreover, video recordings were also employed to improve teaching practice and reflection [67] because it is easier for evaluators to provide an analysis of classroom events when they cannot remember them [68]. The video data enabled researchers and evaluators to re-watch the recordings [69]. ...
This study revealed the current situation and developments in teacher evaluation in primary and secondary schools by reviewing 54 articles published in the recent decade (i.e., from January 2012 to October 2022). The coding scheme was developed based on the three components of effective teacher evaluation systems: “what”, “how”, and “who”. Specifically, we investigated the frameworks used for teacher evaluation, methods of evaluation, and participants in teacher evaluation. Based on our results, most studies evaluated teachers from the dimension of Instructional Support. Evaluation through video recording became popular due to technological advancement. Further, an increasing number of schools invited external experts to conduct teacher evaluations to ensure fairness. We also identified several crucial factors for teacher development: effective use of teaching resources and technology, high-quality feedback and communication, emotional support, classroom organization, and professional responsibilities. Due to COVID-19, many schools adopted distance learning, prompting the need to develop technological skills for teachers. Through the in-depth analysis of the current situation and development trends in the various dimensions of teacher evaluation in primary and secondary education, future research directions and issues were discussed and explored in this review.
... For me, inclusion in task design could be conceptualized as considering students' prior knowledge and experience when designing tasks. In mathematics education, this includes students' prior knowledge and experience about the mathematical concepts underlying the task, their cultural identity, and real-life Previous studies in mathematics education have provided different classifications of mathematical tasks in terms of their relation to reality (e.g., Hiebert et al., 2003;Vos, 2020). For example, Vos (2020) has recently identified five different categories of mathematical tasks in terms of their relation to reality: bare task, task with mathematical context, dressed-up task, task with realistic context, and task with authentic context. ...
Task design is an important element of effective mathematics teaching and learning. Past research in mathematics education has investigated task design in mathematics education from different perspectives (e.g., cognitive and cultural) and offered a number of (theoretical) frameworks and sets of principles. In this study, through a narrative research in the form of autoethnography, I reflected on my past teaching and research experience and proposed a (theoretical) framework for task design in mathematics education. It contains four main principles: (a) inclusion, (b) cognitive demand, (c) affective and social aspects of learning mathematics, and (d) theoretical perspective(s) toward learning mathematics. This framework could be used as a tool for critically reflecting on current practices in terms of task design in teaching mathematics and research in mathematics education. It may also contribute to ongoing research in mathematics education about task design and enable or enhance opportunities for dialogue between lecturers, teachers, and researchers about how to design rich mathematical tasks for teaching and research purposes.
... International bekannt sind z.B. Dialogic Teaching (Alexander, 2020), Accountable Talk (Michaels et al., 2008) oder Academically Productive Talk Hiebert et al., 2003;Kobarg & Seidel, 2007), was meist dem "IRE-Muster" zugeschrieben wird. Demgegenüber fordern und unterstützen die im "Werkzeugkasten" der Fortbildung vorgeschlagenen Lehrpersonen-Moves bei den Lernenden eine verantwortliche Beteiligung, beispielsweise in Form von Erklärungen oder Argumenten. ...
Der Beitrag untersucht anhand einer Fallanalyse, wie sich langfristig angelegte Professionalisierungsmaßnahmen zu dialogischer Gesprächsführung auf die Sprechzeitverteilung, die Gesprächsleitung einer Geschichtslehrperson der Sekundarstufe I und den argumentativen Gehalt von Lernendenaussagen auswirkt.
... This might be a consequence of students' lack of information about mathematicians and their contributions since little emphasis is given to the history of mathematics in mathematics classrooms. TIMSS's (1999) findings support this idea that 3% of the 638 mathematics lessons included the history of mathematics, and the time devoted to the history of mathematics was limited to only 3 minutes (Hiebert et al., 2003). Similar to findings from the studies (Fasanelli, 2000;Smestad, 2000) in the international arena, Baki and Butuner (2013) also stated that the history of mathematics is generally referred to as the inclusion of mathematicians' short biographies and pictures of mathematicians in Turkish elementary mathematics textbooks. ...
... hin angenommen (Stigler & Hiebert, 1999;Reusser & Pauli, 2003). Ganz besonders in einzelnen Fächern sind kulturspezifische Untemchtsprofile deutlich auszumachen (Hiebert & Gallimore et al., 2003). Jenseits individueller Unterrichtsstile kann man sagen, dass sich Fachuntemcht oft durch ein Bündel unverkennbarer Charakteristika auszeichnet, die dem Fach in einem bestimmten Kulturraum ihr Gepräge geben. ...
Der Naturwissenschaftsunterricht der Deutschschweizer Volksschule hat ein spezielles Profil, verglichen mit den Unterrichtskulturen anderer Länder: Er ist didaktisch hoch elaboriert, zeitlich tief dotiert, inhaltlich höchst heterogen und im Fächerkanon marginalisiert. In diesem Aufsatz wird diskutiert, welche Ambivalenzen und Altlasten im curricularen, didaktischen, strukturellen und lehrerbildnerischen Bereich angegangen werden müssen, um naturwissenschaftlich-technischen Unterricht im dynamischen bildungspolitischen Umfeld neu zu positionieren, Relevanz naturwissenschaftlichen Wissens und Könnens herauszuarbeiten sowie Professionalität von Unterricht und Lehrerbildung sicherzustellen.
... Bunun nedeni olarak da matematiğin araştırmak ve anlamak için bir ilişkiler sistemi değil de ezberlenmesi gereken kurallar ve işlemler bütünü olarak görülmesinden kaynaklanmaktadır (Carpenter, Franke ve Levi, 2003). Sayı Konuşmaları, sayı hissini geliştirmek için kullanılabilecek umut verici bir yöntemdir (Boaler, 2013;Hiebert et al., 2003). Çünkü çözüm stratejilerinin paylaşılması ve tartışılması, sayı konuşmalarının önemli bir bileşenidir. ...
Matematikte bir problemi ezberlenmiş prosedürlerle çözmek ile sayılar arasındaki ilişkileri kullanarak çözmek arasında önemli bir fark vardır. Sayılar arasındaki ilişkileri kullanmak ve probleme ilişkin farklı çözüm yolları üretmek güçlü bir sayı hissi gerektirir. Sayı hissi, bir çocuğun sayılarla ilgili akıcılığı, esnekliği, sayıların ne anlama geldiği duygusu, zihinden matematik gerçekleştirme ve karşılaştırmalar yapma becerisi anlamına gelmektedir. Bu bağlamda erken yaşlarda sayı hissini güçlendirecek yöntem ve teknikler çok önemlidir. Sayı hissinin geliştirilebilir olduğunu bilmek önemlidir. Matematiksel bir öğretim uygulaması olarak Sayı Konuşmaları da öğrencilerin bir matematik problemi ile ilgili akıl yürütüp çözüm yolları geliştirerek sınıf içinde bu problemin cevabına nasıl ulaştığını açıklamasına dayanan etkili bir araçtır. İletişimi, araştırmayı, tartışmayı, düşünmeyi ve muhakemeyi teşvik eden bir sınıf ortamı oluşturulması, farklı teşvik edici sorular sorarak, tartışmalar açarak öğrencilerin strateji geliştirmeleri, problemlerin çözümünde tercih ettikleri yolları ve nedenlerini sınıf arkadaşlarıyla paylaşmaları için fırsat verilmesi Sayı Konuşmalarının avantajlarından bazılarıdır. Bu bölümde Sayı Konuşmaları tanıtılarak bileşenleri hakkında bilgi verilmiş ardından sınıf ortamında uygulama aşamaları açıklanmıştır.
In mathematics, there is an important difference between solving a problem using memorized procedures and solving it using relationships between numbers. Number sense refers to a child's fluency and flexibility with numbers, a sense of what numbers mean, and the ability to mentally perform math and make comparisons In this context, methods and techniques that will strengthen the number sense at an early age are very important. It is important to know that number sense can be improved. Number Talks, as a mathematical teaching practice, is also an effective tool based on students explaining how they came to the answer to a mathematical problem in the classroom by reasoning and developing solutions. Some of the advantages of Number Talks are creating a classroom environment that encourages communication, research, discussion, thinking and reasoning, asking different stimulating questions and opening discussions, giving students the opportunity to develop strategies, share their preferred ways of solving problems and their reasons with their classmates. In this section, Number Talks were introduced and information was given about its components, and then the application stages in the classroom environment were explained.
... ooks. A mathematical task is a set of problems or a single complex problem that focuses students' attention on a particular mathematical idea (Stein, Grover, Henningsen, 1996). Study shows that mathematical tasks influence learning (Doyle, 1988) and according to the TIMSS video study, 80% of the time in the classroom is spent on mathematical tasks (Hiebert et. al, 2003). ...
Este libro presenta la experiencia desarrollada por un grupo de docentes e investigadores implicados en la formación inicial del profesorado1, procedente de diferentes Universidades: La Universidad de Málaga y La Universidad de Cantabria en España, la Benemérita Escuela Normal Veracruzana “Enrique C. Rébsamen” en Xalapa (México) y la Universidad Nacional de Educación de Cuenca (Ecuador) en torno a dos estrategias metodológicas: La Lesson Study y el Aprendizaje y Servicio.
Una experiencia que recoge el fruto del trabajo desarrollado por la Red de Excelencia docente promovida por el Plan Propio Integral de Docencia 2019 de la Universidad de Málaga y por otros Proyectos relacionados. Un proyecto de investigación coordinado por la Universidad de Málaga y financiado por el Ministerio de Economía, Industria y Competitividad en la convocatoria de proyectos de I+D de 2017 con el título: Lesson Studies, escuela y universidad: investigando la reconstrucción del conocimiento práctico en la formación inicial del profesorado (EDU2017-86082-P), correspondientes al Programa Estatal de Fomento de la Investigación Científica, subprograma estatal de generación de conocimiento, y dos proyectos de innovación educativa: el proyecto PIE 19-108 Lesson Study y Aprendizaje-Servicio: un camino hacia la mejora de la práctica docente mediante metodologías activas de enseñanza y aprendizaje, promovido también por el Plan Propio Integral de Docencia de la UMA, y el Proyecto Innovar en la Educación Superior. Una propuesta desde el modelo Lesson and Learning Studies (2015-2017) de la III Convocatoria de Innovación Docente de la Universidad de Cantabria.
Am Beispiel der mathematikdidaktischen Forschung wird aufgezeigt, inwiefern es sich hierbei um eine notwendige vertiefende Perspektive handelt und weshalb die fachdidaktische Forschung eine Sonderrolle innehat. Die Sonderrolle wird begründet mit der Nähe zum schulischen Fachunterricht und mit dem Bezug zur fachlichen Domäne bzw. zur wissenschaftlichen Disziplin. Fachdidaktische Forschung nimmt eine fachliche Perspektive auf den Untersuchungsgegenstand ein und greift dabei auf profunde Kenntnisse des jeweiligen Unterrichtsfachs und der Inhalte zurück. Die Ergebnisse fliessen in vielfältiger Weise in die Praxis des jeweiligen Fachunterrichts sowie in die Lehrerinnen- und Lehrerbildung zurück.
Am Beispiel der mathematikdidaktischen Forschung wird aufgezeigt, inwiefern es sich hierbei um eine notwendige vertiefende Perspektive handelt und weshalb die fachdidaktische Forschung eine Sonderrolle innehat. Die Sonderrolle wird begründet mit der Nähe zum schulischen Fachunterricht und mit dem Bezug zur fachlichen Domäne bzw. zur wissenschaftlichen Disziplin. Fachdidaktische Forschung nimmt eine fachliche Perspektive auf den Untersuchungsgegenstand ein und greift dabei auf profunde Kenntnisse des jeweiligen Unterrichtsfachs und der Inhalte zurück. Die Ergebnisse fliessen in vielfältiger Weise in die Praxis des jeweiligen Fachunterrichts sowie in die Lehrerinnen- und Lehrerbildung zurück.
International assessment studies generally contribute to curriculum reform by highlighting certain aspects of curriculum needing improvement, usually attained though the recognition and application of some studies’ components. By focusing on the question “How have international studies driven school mathematics curriculum reforms?”, this chapter examines the role of international studies TIMSS (Trends in International Mathematics and Science Study) and PISA (Programme for International Student Assessment) in reforms in different countries. Emphasis is placed on examining components applied in (re)designing and implementing curriculum improvements. After presenting the global influences of TIMSS and PISA worldwide, the influences of these international studies are examined in case studies from four economically and geographically diverse countries. The chapter ends with a critical summary of the findings presented and outlines directions for further research.
DESCRIPTION
Science teaching practices have not been systematically reviewed in the scientific literature, and when they have been addressed, it has been in relation to the study of specific issues such as the implementation of pedagogical approaches, sequence design, the effects of training plans, etc. This chapter takes another view by focusing on practices and their characteristics, even if they are often the result of very different research perspectives. It thus reports the results of studies of these characteristics published in four major science education journals between 2015 and 2020. It is focused on teaching science in elementary, and middle school and physics in high school. More specifically, beyond descriptions and characterizations of practices as such, it takes stock of the relationships that practices have with student and teacher characteristics, with local or broader structures, with teacher training, with the resources available to teachers, or with the particular aspects of the taught content. The results show the great complexity and variety of science teaching practices, and allow us to understand the difficulty of grasping the expertise and ingenuity behind this human activity.
Mathematical argumentation is widely considered an important disciplinary practice, and teachers play critical roles in establishing opportunities in elementary school classrooms for students to develop, share, and evaluate mathematical arguments. In this chapter, we describe an ongoing project in which prospective teachers gain experiences participating in and facilitating small-group discussions centered on co-constructing mathematical arguments in response to complex mathematical tasks. We share our conceptualization of the primary components of mathematical argumentation in classrooms by characterizing the claims, evidence, and reasoning that individuals use as they construct arguments individually and collectively. Recognizing that traditional classroom discourse patterns limit efforts to promote mathematical argumentation among students, we argue that teachers’ and students’ classroom interactions can be enriched by explicit support from a discussion intervention. We introduce an established discussion approach, Quality Talk, which has been shown to foster students’ critical-analytic thinking across subject areas and contexts (Murphy et al., Sci Educ 102(6):1239–1164, 2018a, Quality talk: Developing students’ discourse to promote critical-analytic thinking, epistemic cognition, and high-level comprehension (Tech. Rep. No. 5). The Pennsylvania State University, 2018b, Am Educ Res J 55(5):1113–1160, 2018c). We draw attention to key Quality Talk discourse elements and scaffolding talk moves used by teachers and students during small-group discussions. Through two exemplar transcript segments from discussions involving prospective teachers and elementary students, we highlight the roles of such discourse elements in advancing the co-construction of mathematical arguments related to solving complex mathematical tasks. This chapter offers novel insights into mathematics teaching and learning by illustrating how discourse elements provide valuable tools for students’ engagement in, and teachers’ facilitation of, discussion-based mathematical argumentation. Such insights have potential to inform the work of teachers, teacher educators, and others engaged in elementary classroom contexts. Additionally, the dual lenses of mathematical argumentation and classroom discourse can further researchers’ and practitioners’ efforts to gain in-depth understandings of students’ mathematical thinking and growth.KeywordsMathematical argumentationClassroom discourseSmall-group discussionComplex mathematical taskQuestionsProspective teachersTeacher educationMethods courseElementary school
The book aims to answer whether learning tasks in Czech lower-secondary physical geography textbooks and lessons support and develop problem-solving competence. The research findings show that the analysed textbooks differ from one another in terms of both the number of learning tasks and their positioning. Regarding the requirement of forming and developing a problem-solving competence, most of the learning tasks in the observed textbooks proved to be on the lowest possible level in terms of demandingness, complexity, and systematism. The proportion of the learning tasks directly supporting forming and developing a problem-solving competence is only marginal in the textbooks (less than 5%). The findings of the analysis of the geography lessons in the video recordings prove that problem-solving tasks, as defined in the theoretical part of this book, are practically nonexistent in Czech schools. The data file identified only seven learning situations with at least partial potential to develop problem-solving competence. It must be noted that most problem-solving tasks found in the observed lessons do not integrate the highest level of systemic, complexity, and cognitive dimensions. There is an apparent contrast with the learning tasks in the textbooks we looked into, where 17 problem-solving tasks scored highest in all the dimensions mentioned above.
Zusammenfassung
In der vorliegenden Arbeit wird Bildungsmonitoring als Generierung und Verarbeitung von Daten und Informationen zuhanden bildungspolitischer Akteure mit Methoden qualitativer empirischer Sozialforschung untersucht. Die methodologischen Bezüge gehen in Richtung der qualitativ-historischen Forschung, der Politikfeldanalyse und der Hermeneutik. Ebenfalls eingesetzt werden Verfahren der Typisierung und der qualitativ-theoretischen Faktorenanalyse.
We argue that reform in curriculum and instruction should be based on allowing students to problematize the subject. Rather than mastering skills and applying them, students should be engaged in resolving problems. In mathematics, this principle fits under the umbrella of problem solving, but our interpretation is different from many problem-solving approaches. We first note that the history of problem solving in the curriculum has been infused with a distinction between acquiring knowledge and applying it. We then propose our alternative principle by building on John Dewey’s idea of “reflective inquiry,” argue that such an approach would facilitate students’ understanding, and compare our proposal with other views on the role of problem solving in the curriculum. We close by considering several common dichotomies that take on a different meaning from this perspective
By examining the premises underlying conventional approaches to teaching disadvantaged students, educators can devise more challenging content and more effective instructional methods. Some important principles include maximizing time on task, establishing high expectations and a school climate supporting academic learning, and strengthening parent involvement. Includes 22 reference. (MLH)
For α = 0.05 and 0.01 and for a range of values of ν, the number of degrees of freedom, the tables give the points above which lie a proportion , for k = 1 (1)20, and a proportion , for k = 7(1)20, of the Students distribution.
To investigate relationships between teaching and learning mathematics, the six second-grade classrooms in one school were observed regularly during the 12 weeks of instruction on place value and multidigit addition and subtraction. Two classrooms implemented an alternative to the more conventional textbook approach. The alternative approach emphasized constructing relationships between place value and computation strategies rather than practicing prescribed procedures. Students were assessed at the beginning and the end of the year on place value understanding, routine computation, and novel computation. Students in the alternative classrooms, compared with their more traditionally taught peers, received fewer problems and spent more time with each problem, were asked more questions requesting them to describe and explain alternative strategies, talked more using longer responses, and showed higher levels of performance or gained more by the end of the year on most types of items. The results suggest that relationships between teaching and learning are a function of the instructional environment; different relationships emerged in the alternative classrooms than those that have been reported for more traditional classrooms.
In the present study the relationship between teaching and learning was examined using a conceptual framework that links dimensions of instructional tasks with gains in student learning outcomes. The greatest student gains on a performance assessment consisting of tasks that require high levels of mathematical thinking and reasoning were related to the use of instructional tasks that engaged students in the “doing of mathematics” or the use of procedures with connections to meaning. In addition, student performance gains were greater for those sites whose tasks were both set up and implemented to encourage the use of multiple solution strategies, multiple representations, and explanations. Whereas, student performance gains were relatively small for those sites whose tasks tended to be both set up and implemented in a procedural manner and that required a single solution strategy, single representations, and little or no mathematical communication.
The video survey is a promising new approach for studying classrooms and teaching across cul-tures. Drawing from experience in working with two cross-cultural video surveys, the Third In-ternational Mathematics and Science Study (TIMSS) and its follow-up study (TIMSS-R), this article presents some of the challenges of studying classrooms across cultures and some of the ways that the video survey can deal with these challenges. The article begins by identifying some of the issues in cross-cultural research and classroom surveys that led to the creation of the video survey. Examples from the TIMSS and the TIMSS-R video studies are then used to illus-trate some benefits and limitations of video surveys and to share some of the lessons that were learned about studying classrooms across cultures. STIGLER, GALLIMORE, HIEBERT Studying classrooms and teaching across cultures is fraught with challenges, yet ripe with opportunity. First, this article considers the opportunities afforded by cross-cultural studies of teaching. Next, we lay out what we see as some major meth-odological challenges posed by such research and outline a new method that we are developing to address some of these challenges. This new method, which we call the video survey, evolved over the past 5 years in our work on the Third Interna-tional Mathematics and Science Study (TIMSS) and its fol-low-up study (TIMSS-R; the R stands for repeat). Using examples from these studies (the TIMSS-R is still in progress), we identify some advantages and disadvantages of video sur-veys and share some lessons we have learned about studying classrooms across cultures.
Although video has been used for small, qualitative case studies, it has almost never been used as a medium for large-scale data collection. A major reason has been the practical problems involved in the management and analysis of video information. In this chapter a new multimedia database program, vPrism™, developed for this purpose, is described. First used to manage and analyze 250 h of video for the Third International Mathematics and Science Study (TIMSS), vPrism™ is designed to manage large quantities of digital video in MPEG-1 format. The chapter discusses how to prepare video and related information for entry into vPrism™, how to link transcriptions and annotations to specific time points in the video, how to define and code categories of events that occur in the video, how to search and retrieve video, and how to export data for statistical analysis. Finally, future plans for development of the software are discussed.