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Mathematics teaching and classroom practice
... A teacher may ask for a student's input through enlighten details, justification, applying to similar problems, or requesting assessment from other students. These concepts are related to what Franke et al. (2007) express as access to student thinking. If teachers enlighten details, it is a request for students to explain what something means or how something happens. ...
... Sophie requested a response from both students in a pair when asking about their performed actions in GeoGebra or when specifically asking about details brought into the conversation by the students. Sophie contributed to making details in the students' mathematical reasoning explicit, thus interacting with powerful teacher moves (Franke et al., 2007) for promoting a learning environment where students actively engage in problem-solving and construction of their own understandings (Stein et al., 2008). In the teacher-student interaction with Olivia and Oscar, Sophie mainly interacted with the primary agent, Oscar. ...
This design-based research study presents results based on observations and analysis of student–student and student–teacher interactions in a Norwegian upper secondary school. The aim of this study was to examine student interactions during collaborative mathematical reasoning tasks about functions to identify insights to support collaborative problem-solving competency. The study also sought to investigate teacher actions in productive interactions and how students’ potential learning outcomes are affected by interactions. Analysis of student–student interactions and related teacher interactions revealed strategies for facilitating productive problem solving among student dyads. The productive interaction pattern—a bi-directional interaction—presents inherent learning opportunities. This study adds to the field of mathematics education by suggesting an extension of the concept of collaborative problem-solving competency (CPS) by connecting the competencies of collaboration, reasoning, and problem solving in a new model for facilitating productive interaction in mathematics classrooms. The suggested competency model has potential as an analytical tool for teacher educators and researchers to utilize in classroom studies focusing on interactional patterns in students’ mathematical problem solving.
... Children from diverse language backgrounds may think about mathematics differently, according to Chen et al.(2010), and this may affect their learning performance. Students must not only comprehend mathematical concepts, but also show that they can apply what they've learned in class to their daily lives and communicate what they've learned to others (Altieri, 2009;Franke, Kazemi, & Battey, 2007). ...
This study is to investigate the implementation of language transition in secondary school mathematics curriculum in Malaysia. Will the students' language proficiency, readiness and confidence and students' attitude in studying mathematics influences the achievement and understanding among lower secondary students? This study was conducted through questionnaire method to examine role of factors affecting on student achievement performance. The study utilized descriptive, correlation and regression analyses to answer the research objectives and to test the research hypothesis. The researchers collected the information from 100 secondary students from Sekolah Menengah Kebangsaan (SMK) from urban area in Selangor around Klang Valley. It is show that 41.7% of a student's achievement can be explained by the independent variable listed. This study found that there is strong positive relationship between relationship between students' language proficiency aspect and students' achievement in Mathematics (p-value<0.05). It shows that language proficiency is the most important aspect followed by the attitude of students in learning mathematics and the least important is students' readiness and confidence aspect. Although readiness and confidence are needed in providing students with good mathematics results, they are not important in this study. Also, it is a significant relationship between students' attitude aspect and students' achievement in Mathematics (p-value<0.05).
... Carpenter and Lehrer (1999) suggest that collaborative learning creates a learning environment where collective-public reflection can emerge. Franke, Kazemi, and Battey (2007) assert that collaborative learning creates a discursive ambiance that helps students learn mathematics better. Johnson and Johnson (2016) consider collaborative learning in relation to citizenship and democracy, as it promotes interdependence among peers and helps them to develop the values, attitudes and behaviour of engaged citizens. ...
This chapter investigates ways in which collaborative learning in
critical mathematics education can promote critical citizenship
and democracy. Drawing on necessary participatory action research
in a US high-school classroom, the article argues that the critical
mathematics education approach to collaborative learning is a
coherent alternative to neoliberal, market-driven approaches.
The results suggest that collaborative learning within critical
mathematics education should aim to transfer classrooms to
communities of learners in light of dialogic pedagogy and
inquiry-based education.
... Carpenter and Lehrer (1999) suggest that collaborative learning creates a learning environment where collective-public reflection can emerge. Franke, Kazemi, and Battey (2007) assert that collaborative learning creates a discursive ambiance that helps students learn mathematics better. Johnson and Johnson (2016) consider collaborative learning in relation to citizenship and democracy, as it promotes interdependence among peers and helps them to develop the values, attitudes and behaviour of engaged citizens. ...
... Mathematics educators have identified specific teaching practices, referred to as high-leverage practices, that address the need for ambitious teaching by improving classroom instruction and focusing on students' deep understanding of mathematics (Ball & Forzani, 2009;Grossman, 2013;Lampert et al., 2013). Examples of such practices include posing cognitively demanding mathematical tasks (Henningsen & Stein, 1997;Stein, Remillard, & Smith, 2007); promoting classroom discourse to enhance students' mathematical learning (Franke, Kazemi, & Battey, 2007;Smith & Stein, 2011); eliciting and responding to students' ideas (Jacobs, Lamb, & Philipp, 2010;Sleep & Boerst, 2012); orienting students to instructional goals (Hiebert & Morris, 2009;Sleep, 2012); supporting students' conversations about mathematics concepts (Boaler, 2006;Hufferd-Ackles, Fuson, & Sherin, 2004;Kazemi & Stipek, 2001); using and making connections among representations (Ball & Bass, 2003;Fuson, Kalchman, & Bransford, 2005;Stylianou & Silver, 2004); engaging students in productive struggle (Henningsen & Stein, 1997;Hiebert & Grouws, 2007); and questioning strategies that promote students' thinking (Herbel-Eisenmann & Cirillo, 2009). ...
... Carpenter and Lehrer (1999) suggest that collaborative learning creates a learning environment where collective-public reflection can emerge. Franke, Kazemi, and Battey (2007) assert that collaborative learning creates a discursive ambiance that helps students learn mathematics better. Johnson and Johnson (2016) consider collaborative learning in relation to citizenship and democracy, as it promotes interdependence among peers and helps them to develop the values, attitudes and behaviour of engaged citizens. ...
Creating landscapes of investigation is a primary concern of critical mathematics education. It enables us to organise educational processes so that students and teachers are able to get involved in explorations guided by dialogical interactions. It attempts to address explicit or implicit forms of social injustice by means of mathematics, and also to promote a critical conception of mathematics, challenging the assumption that the subject represents objectivity and neutrality. Landscapes of Investigation provides many illustrations of how this can be done in primary, secondary, and university education. It also illustrates how exploring landscapes of investigation can contribute to mathematics teacher education programmes.
This edited volume is the result of a collaboration established through the Colloquium in Research in Critical Mathematics Education, which took place in 2016, 2018, and 2019 in Brazil. Its twenty-eight contributors are young researchers from Brazil, Chile, Colombia, India, Mexico and the USA, who are dedicated to the further development of critical mathematics education.
Organised in eighteen chapters, the volume presents examples of engaging students from a diversity of social and economic backgrounds, age ranges, and abilities across different countries. The chapters present original findings on the social aspects of all levels of mathematics education. Landscapes of Investigation is of particular relevance to those with an interest in the potential of mathematics education to challenge social injustices.
This paper describes a Peer Leader training course that has been modified to include innovative components focusing on developing content and pedagogical knowledge, practicing rehearsals, generating action research projects, doing poster presentations, and writing a reflective letter to new Peer Leaders. Through these innovations, four types of reflection--on relevant research and theory, on students’ experiences, on peer practice, and on one’s own practice--have been incorporated into the course. The new course components promise to offer more opportunities for trainees to practice peer leading in a structured and safe environment in which immediate and supportive feedback is available, and group practice and reflection are optimized.
We compare two lessons with respect to how a teacher centers student mathematical thinking to move instruction forward through enactment of five mathematically productive teaching routines: Conferring To Understand Student Thinking and Reasoning, Structuring Mathematical Student Talk, Working With Selected and Sequenced Student Math Ideas, Working with Public Records of Students’ Mathematical Thinking, and Orchestrating Mathematical Discussion. Findings show that the lessons differ in the enactment of teaching routines, especially Conferring to Understand Student Thinking and Reasoning which resulted in a difference in student-centeredness of the instruction. This difference highlights whose mathematics was being centralized in the classroom and whether the focus was on correct answers and procedures or on students’ mathematical thinking and justifying.
The Motivational Attitudes in Statistics and Data Science Education Research group is developing a family of validated instruments: two instruments assessing students’ attitudes toward statistics or data science, two instruments assessing instructors’ attitudes toward teaching statistics or data science, and two sets of inventories to measure the learning environment in which the students and instructor interact. The Environment Inventories measure the institutional structures, course characteristics, and enacted classroom behaviors of both the students and instructors, all of which interact with the student and instructor background. This paper will discuss our proposed theoretical framework for the learning environment and its development.
The teaching and learning of mathematics in K-12 classrooms is changing. New curricula and methods engage learners in working on real problems. An essential feature of this work involves teacher and students in 'talking mathematics'. How can students learn to do this kind of talking? What can they learn from doing it? First published in 1998, this book addresses these questions by looking at the processes of formulating problems, interpreting contexts in which problems arise, and arguing about the reasonableness of proposed solutions. The studies in this volume seek to retain the complexity of classroom practice rather than looking at it through a particular academic lens.
The seminal work of Russian theorist Lev Vygotsky (1896–1934) has exerted a deep influence on psychology over the past 30 years. Vygotsky was an educator turned psychologist, and his writings clearly reflected his pedagogical concerns. For Vygotsky, schools and other informal educational situations represent the best cultural laboratories to study thinking. He emphasized the social organization of instruction, writing about the 'unique form of cooperation between the child and the adult that is the central element of the educational process'. Vygotsky's emphasis on the social context of thinking represents the reorganization of a key social system and associated modes of discourse, with potential consequences for developing new forms of thinking. This volume is devoted to analyzing Vygotsky's ideas as a means of bringing to light the relevance of his concepts to education. What does Vygotsky's approach have to offer education? Distinguished scholars from various countries and representing several disciplines discuss the essence and significance of Vygotsky's work, analyze the educational implications of his thoughts, and present applications in practice, addressing educational issues such as school organization, teacher training, educational achievement, literacy learning and development, uses of technology, community-based education, and special education.
