The role of appropriation in guided reinvention: establishing and preserving devolved authority with low-attaining students

Realistic Mathematics Education (RME) relies on the pedagogy of guided reinvention, in which opportunities for learning are created through the teacher’s orchestration of whole-class mathematical discussion towards a specific goal. However, introducing an RME approach to students who are accustomed to traditional teaching requires a substantial shift in roles, particularly with respect to the devolution of authority from teacher to student. In this study, we worked with low-attaining students, implementing RME to improve understanding of fractions. The analysis highlights how the introduction of guided reinvention is supported by extended wait time and teacher neutrality, but also by teachers’ appropriation of student strategies as a basis for supporting shared authority in the joint construction of mathematical ideas. The article considers the relationship between guided reinvention, appropriation and student agency.

Two Undergraduate Students' Reinvention of the Multiplication Principle

The multiplication principle (MP) is a fundamental aspect of combinatorial enumeration, serving as an effective tool for solving counting problems and underlying many key combinatorial formulas. In this study, the authors used guided reinvention to investigate 2 undergraduate students' reasoning about the MP, and they sought to answer the following research questions: How do students come to understand and make sense of the MP? Specifically, while a pair of students reinvented a statement of the MP, how did they attend to and reason about key mathematical features of the MP? The students participated in a paired 8-session teaching experiment during which they progressed from a nascent to a sophisticated statement of the MP. Two key mathematical features emerged for the students through this process, including independence and distinct composite outcomes, and we discuss ways in which these ideas informed the students' reinvention of the statement. In addition, we present potential implications and directions for future research.

Aspectos da Educação Matemática realística

Resumo: Neste texto, apresentamos alguns aspectos teóricos da Educação Matemática Realística, evidenciando os seis princípios, com base em um estudo de textos de autores dessa abordagem. Buscamos discutir as noções de matemática como atividade humana, matematização, conhecimento matemático, entrelaçamento entre domínios da matemática, contexto, realidade, fenomenologia didática, inversão antididática, reinvenção guiada, aprendizagem, níveis de aprendizagem e interatividade, a fim de explorar ideias que configuram a abordagem da Educação Matemática Realística.Palavras-chave: Educação Matemática; Educação Matemática Realística; Reinvenção Guiada; Matematização. Aspects of realistic Mathematics EducationAbstract: In this text, we present some theoretical aspects of Realistic Mathematics Education, evidencing the six principles, based on a study of texts of author from this approach. We persue to discss notions, as mathematics as a human activity, mathematization, mathematical knowledge, intertwining of mathematical domanis, context, reality, didactical phenomenology, antididactic inversion, guided reinvention, learning, levels in learning and interactivity, aiming to explore ideas that configure the approach of Realistic Mathematics Education.Keywords: Mathematics Education; Realistic Mathematics Education; Guided Reinvention; Mathematization.

USING GUIDED REINVENTION TO DEVELOP TEACHERS’ UNDERSTANDING OF HYPOTHESIS TESTING CONCEPTS

Statistics education reform efforts emphasize the importance of informal inference in the learning of statistics. Research suggests statistics teachers experience similar difficulties understanding statistical inference concepts as students and how teacher knowledge can impact student learning. This study investigates how teachers reinvented an informal hypothesis test for categorical data through the framework of guided reinvention. We describe how notions of variability help bridge the development from informal to formal understandings of empirical sampling distributions and procedures for constructing statistics and critical values for conducting hypothesis tests. A product of this paper is a hypothetical learning trajectory that statistics educators could utilize as both a framework for research and as an instructional tool to improve the teaching of hypothesis testing. First published May 2015 at Statistics Education Research Journal Archives

Reshaping Teachers' Mathematical Perceptions: Analysis of a Professional Development Task

As the focus of mathematics education moves from memorization toward reasoning and problem solving, professional development for in-service teachers must model these activities while simultaneously increasing participants' mathematical knowledge. We examine a representative task from a mathematics professional development course that uses rational number operation as an opportunity for problem solving and modeling. Transcripts exemplify the growth teachers make in deeply understanding the content–division of fractions–while engaging in guided reinvention and classroom discourse. We propose 4 interconnected qualities of this task that allow participants to engage in and reflect on the process of guided reinvention: (1) authentic context with multiple solution methods, including visual; (2) cognitive dissonance; (3) deep engagement; and (4) impact on mathematical knowledge for teaching.

VISUALIZATION OF DATA AND RESULTS AS А METHODOLOGICAL BASIS OF APPLIED STATISTICS TEACHING

Traditional methods of teaching in medical high school of informatics as computer sciences and statistics as a section of high mathematics contradict to requirements of modern applied medicine and a medical science. A research objective is revealing of the reasons of the given discrepancy and its elimination ways. Similar discrepancy was revealed earlier by foreign researchers studying efficiency of the statistic school programs. The revealed laws appeared to be extended to a technique of teaching of statistics in a high medical school. Pursuing this aim the tests of educational achievements developed by the author were applied on the students of medical and biologic department of the Siberian State Medical Universirty that trained on specialities of “biophysics" and “biochemistry". The fundamental problem of statistical education is that symbols used by these science concern to the objects, which students still have to design. As a substantiation of this conclusion serves the ontosemiotical approach to working out of the maintenance of a course. In the article there are considered the approaches to the permission of the given contradiction, based on the experience of teaching of statistics in foreign schools and on the wor­kings out of the author. In particular the conclusion about necessity of revision the tradition of using professional statistical packages and introduction of a special educational software. To working out the maintenance of a learning course it is offered to more widely apply the historical approach which concrete definition is represented by a principle of a guided reinvention.