Will we ever teach mathematics again in the way we used to before the pandemic?

After about two years of emergency remote teaching during the pandemic, the teaching of mathematics is slowly returning to (what used to be called) normal. However, after the period of mostly teaching online, there is uncertainty about the extent to which we will return to the way we were teaching before. In this survey paper we attempt to give some background to the impact that emergency remote teaching may have had on teaching mathematics. We examine the possible social implications and then focus on the changing mathematics classroom, focusing on the actual mathematics curriculum, learning design and assessment, the role of collaborative activities and social media, educational videos, and the role of family and parents in future. There are indicators from the literature that educators may not return to the traditional way of teaching entirely, especially in secondary and higher education. We conclude with describing some possible new research areas that have developed through emergency remote teaching, including online education for younger learners, local learning ecosystems, the role of family and parents, instructional design, and the mathematics content of curricula

Impacts of classroom teaching practices on students’ mathematics learning interest, mathematics self-efficacy and mathematics test achievements : a secondary analysis of Shanghai data from the international video study Global Teaching InSights

Teaching effectiveness is a core issue in educational research; however, there is little consensus about the most important results of classroom teaching from an international perspective. The effectiveness of teaching has remained a ‘black box’ for a long time. In the secondary study described in this paper we used empirical data for Shanghai taken from the international Organization for Economic Co-operation and Development (OECD) study Global Teaching InSights (GTI)—initially the Teaching and Learning International Survey (TALIS) Video Study—which was based on videotaped direct observations of classroom teaching. Eighty-five junior high school mathematics teachers and their students in Shanghai were observed to explore the impact of specific teaching practices on students’ interest, self-efficacy, and mathematics achievement scores. The results revealed that social-emotional support and instruction quality were the key dimensions relating to the characteristics and differences of mathematics lessons in Shanghai. While the former had a significantly positive impact on students’ general mathematics self-efficacy, the latter had a significantly positive impact on students’ mathematics interest. Although specific teaching practices had no significant direct impact on students’ mathematics achievement scores, social-emotional support and instruction quality considerably influenced students’ academic performance in an indirect way via general self-efficacy.publishedVersio

Can flipped classroom pedagogy offer promising perspectives for mathematics education on pandemic-related issues? A systematic literature review

Educators sometimes effect changes in education through the implementation of new ideas, and sometimes extraordinary circumstances force them to change their educational approaches, as during the COVID-19 crisis. Although we live in a digital age, the limited use of technology in education, particularly prior to the COVID-19 pandemic, and teachers’ insufficient experience with online or hybrid learning and teaching approaches resulted in several countries being unprepared for education during the pandemic. The flipped classroom (FC) is an innovative pedagogy with the potential to engage students in mathematics education using hybrid education combined with online and face-to-face learning, which is especially important during a pandemic. However, despite the high expectations surrounding this innovative approach, to date, no systematic literature review has discussed the opportunities and pitfalls of FCs in mathematics education regarding pandemic-related issues. In the present systematic review, we aim to bridge this gap and highlight the importance of flipping mathematics instruction during the pandemic and beyond. The results, which are based on textual analysis of 97 eligible articles, demonstrate that FC is a promising pedagogy that has numerous benefits for mathematics teaching and learning, although it is not a panacea for pandemic-related issues, as it also has several significant pitfalls. Overall, if the mechanism of mathematics education is to be crisis-ready, we should learn from experiences during the pandemic. In this regard, the current review contributes to research in mathematics education with the aim of gaining insight into successful implementations of FC pedagogy, not only during the pandemic but also beyond the crisis era of a pandemic.publishedVersio

The impact of mathematics teachers’ professional competence on instructional quality and students’ mathematics learning outcomes

Teacher quality is a critical factor that influences instructional quality and student learning outcomes. Recently, the authors have proposed broadened views of teacher competence that include dispositions, such as knowledge, and more situation-specific aspects, such as noticing, and span from the dispositions of teachers to their performance in the classroom. Mathematics-education researchers have enriched the conceptualization of teacher competence, developed new measurements, and explored effective ways to facilitate the development of teacher competence. Many empirical studies have been conducted in this field to investigate the impact of teacher professional competence on instructional quality and student mathematics learning outcomes. With this review, we intend to provide a synopsis of the state-of-the-art in this topic and outline new research perspectives.publishedVersio

Gender differences in mathematics achievement : A secondary analysis of Programme for International Student Assessment data from Shanghai

As mathematics has been seen for decades as a stereotyped male domain, gender differences in mathematics learning have received strong attention from the public and academia. In China, the issue of gender equity in education is a particularly interesting topic to most families with the implementation of the one-child policy since the late 1970s. This study aims to study in more depth the role of gender on Shanghai students’ mathematics attainment from a perspective of three societal factors (i.e., one-child status at home, socioeconomic status, and school types) via a secondary analysis of the Programme for International Student Assessment 2012 Shanghai–China mathematics data. In contrast to the official report by Programme for International Student Assessment on Shanghai–China and in line with own previous studies, the current analyses reveal that 15-year-old students in Shanghai performed significantly different on two content-related subscales (i.e., change and relationships and quantity) and two processes-related subscales (i.e., formulate and interpret). Furthermore, significant gender differences were found with students from one-child families but not multi-children families. Among schools of different types in terms of academic tracks and performance levels, the gender differences were largest in the more selective model (general) schools and then vocational schools followed by ordinary (general) schools. Given the nested structure of the Programme for International Student Assessment data, this study found that, on average, a Shanghai boy would achieve significantly higher marks than a girl in Programme for International Student Assessment 2012 mathematics test. The paper closes with discussions on societal and educational implications about these gender disparities, which are still apparent in the current school system of Shanghai.publishedVersio

Interpretation von Fehlern der Schülerinnen und Schüler als Teil der diagnostischen Kompetenz von Lehramtsstudierenden für die Grundschule

Understanding students’ thinking and learning processes is one of the greatest challenges teachers face in the classroom. Misconceptions and errors have the potential to be a rich source of information for identifying students’ thinking and reasoning processes. However, empirical studies show that pre-service teachers (PSTs) and teachers find it challenging to focus their interpretations and pedagogical decisions on students’ thinking processes when they identify students’ mathematical errors. Based on the theoretical approach of noticing, the study described in this paper examines primary PSTs’ diagnostic competence in error situations before and after they participated in a seminar sequence implemented at several Chilean universities. Our analyses focus on PSTs’ competence with regard to formulating hypotheses about the causes of students’ errors. The proposed hypotheses were categorized into those that attributed errors to students’ lack of conceptual understanding, those that explained errors in terms of lack of procedural understanding, and those that assumed a failure of instructional strategies. In addition, the relationships between PSTs’ diagnostic competence, their beliefs and university learning opportunities were examined. The results indicate that PSTs’ diagnostic competence in error situations and the changes of this competence were related to PSTs’ beliefs, practical experiences, and learning opportunities. Overall, the findings suggest that it is possible to promote changes on PSTs’ diagnostic competence during initial teacher education. The paper concludes with implications for teacher education and future research.publishedVersio

Promoting personalized learning in flipped classrooms : A systematic review study

Flipped classroom (FC) is a widely accepted, innovative pedagogy designated to enhance students’ learning by changing the paradigm of instruction. It has the potential to adapt learning to the students’ needs, interests, and mutual expectations by using the advantages of both online and face-to-face learning, which strengthens the quality of the instruction. The potential of FC to foster personalized learning (PL) has become vital in education, as individuals face different possibilities and difficulties in the learning process. To date, no systematic review study has focused on the ways in which PL occurs in FCs and the role of personalized FCs in education. The present study aims to close this gap by exploring the value of flipping instruction and strategies to support PL. We searched the literature, focusing on peer-reviewed research studies published in English that focus on PL in FCs. The key results include (a) the study characteristics, (b) the approaches developed and used in FCs to enhance PL, and (c) the role of personalized FCs in teaching and learning. Overall, this systematic review study provides insight into successful FC implementations and strategies to sustain PL.publishedVersio

Modeling from a cognitive perspective : Theoretical considerations and empirical contributions

Mathematical modeling and applications are an important part of curriculum and considered to be important for students’ current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the current thinking on modeling activities and review empirical results. Subsequently, new findings and implications for research offered by the contributions of the current special issue are described. The contributions of this special issue refer to the relation between cognitive and metacognitive modeling activities to (a) mathematical thinking during building a modeling example, (b) strategic knowledge within modeling activities, (c) solving of data-rich modeling problems and their status from a meta-perspective and (d) individual and social metacognition

Identifying and dealing with student errors in the mathematics classroom : Cognitive and motivational requirements

Introduction: Mathematics classrooms are typically characterized by considerable heterogeneity with respect to students’ knowledge and skills. Mathematics teachers need to be highly attentive to students’ thinking, learning difficulties, and any misconceptions that they may develop. Identification of potential errors and appropriate ways to approach them is crucial for attaining positive learning outcomes. This paper explores which knowledge and affective-motivational skills teachers most require to effectively identify and approach students’ errors. Methods: To address this research question within the German follow-up study of the Teacher Education and Development Study in Mathematics (TEDS-M), 131 primary school mathematics teachers’ ability to identify students’ errors was assessed based on (a) a digitalized speed test showing different students’ solutions in a written notation and (b) three video vignettes that showed different scenes from mathematics classes. These scenes dealt, among other things, with children who struggled with the lesson’s mathematical content. Teachers were asked to analyze students’ thinking and to determine how best to react. In addition, teachers’ mathematics pedagogical content knowledge, mathematical content knowledge, and beliefs were assessed in separate tests and served as predictors for teachers’ abilities to identify, analyze, and deal with students’ errors. Results: The results indicate that all components are interrelated. However, path analysis reveals that teachers’ ability to deal with students’ errors is mainly predicted by their constructivist beliefs while their ability to quickly identify typical students’ errors is largely dependent on their mathematics content knowledge. Discussion: The results show the central filtering function of beliefs. Teachers who believe that students must shape and create their own learning processes are more successful in perceiving and analyzing student errors in classroom situations. They may understand errors as learning opportunities and - thus - pay specific attention to these occurrences.publishedVersio

Mathematical modelling and discrete mathematics : opportunities for modern mathematics teaching

Discrete mathematics and mathematical modelling, along with the educational discourse surrounding these, have many connections. However, ways that the educational discourse on discrete mathematics can benefit from the inclusion of examples of mathematical modelling and the accompanying discussion are currently under-researched. In this paper, we elaborate on the educational potential of examples of mathematical modelling based on the usage of methods from discrete mathematics, with a focus on secondary education. We first describe vertex-edge graphs as possible topics of discrete mathematics that are accessible at school level within modelling lessons. Secondly, in the context of a case study, we describe modelling activities with students at the end of lower-secondary education, using a classical problem of discrete mathematics originating from the Königsberg bridge problem. The students’ solution processes for this optimisation problem based on graph theory are described. Their approaches are examined referring to the phases of the modelling cycle, using the method of qualitative content analysis. We studied in particular the extent to which students use concepts related to vertex-edge graphs in specific sub-phases of the modelling process. The analysis allows the required sub-competences of modelling to be identified and the connection of these competences with discrete mathematics to be worked out. On the basis of this analysis, educational opportunities of teaching discrete mathematics and mathematical modelling are assessed. Overall, we point out the possibilities and opportunities for using examples from the field of discrete mathematics to acquire modelling competences and to foster the linkage of mathematical modelling and discrete mathematics at school level.publishedVersio