Bronislaw Czarnocha

From Arithmetic to Algebra.

The chapter deals with language in the mathematics classrooms, especially with mathematics remedial classrooms. It presents an unusual example of integrating two independent theories, the Sfard (1991) theory of reification and Shepard (1993)/Shuell (1990) integrated theory of cognitive development and writing categories. In the first cycle it’s the TR Design Type A, from Practice; it uses problem types designed through practice and supports itself by a standard yet simple statistical analysis.

Conceptions of Area: In Students and in History

Bronislaw Czarnocha, Ed Dubinsky (edd@cs.gsu.edu), Sergio Loch (sloch@gvc.edu), Vrunda Prabhu (vprabhu@williamwoods.edu), and Draga Vidakovic (draga@cs.gsu.edu) have origins in five different countries: Poland, the United States, Brazil, India, and Serbia. They are all members of the collaborative research group, RUMEC—Research in Undergraduate Mathematics Education Community. They are currently conducting research in topics in calculus, linear algebra, set theory and cooperative learning. Their training and professional experience is in the field of physics, mathematics, and mathematics education, and they all share a keen interest in the improvement of undergraduate mathematics education.

Creativity Research in Mathematics Education Simplified: Using the Concept of Bisociation as Ockham’s Razor

This chapter proposes that bisociation, the Koestler theory of the creativity of the “Aha!” Moment, is the Ockham Razor for creativity research in mathematics education. It shows the power of bisociation in simplifying unnecessary components and in the synthesis of the fragmented ones. The discussion leads through the relationship of bisociation with Piaget’s reflective abstraction, proposes cognitive/affective duality of the “Aha!” Moment and enriches Mason’s theory of attention by the new structure of simultaneous attention necessary for the Eureka experience.

Creativity, Aha!Moments and Teaching-Research

Koestler definition of creativity uncovers creativity’s cognitive aspect in the creation of new schema of thinking by connecting previously unconnected frames of reference; his realization connects the cognitive and affective aspects through the principle of cognitive/affective duality of the Aha!Moment (Czarnocha, 2014). That act of liberation has the power to significantly increase motivation of students, and consequently, their levels of achievement. Presence of an affective dimension of the Aha!Moment has been empirically observed and discussed by Liljedahl (2013). (Palatnik, & Koichu, 2015) realize that the aha-experience might be found over a consideration of what might students attend to, and how, and why.

Professional Development of Teacherresearchers (Pdtr) in Tamil Nadu, India

We report on our investigation of the applications of the TR/NYCity model of mathematics teaching-research approach to teaching and learning in Tamil Nadu, India. The TR/NYCity methodology and the design experiment were presented during epiSTEMe-1 (Czarnocha & Prabhu, 2004).

Teaching Research Communities

We have spoken of the traditional view of mathematics in the classroom in which the teacher is the authoritarian voice and students – passive recipients of his/her knowledge, and the alternate or reform view exposed by constructivists, as well as Koestler and most prominent mathematical educational institutions in which the focus is on the role of students as active participants in the construction of knowledge.

Tools of Teaching-Research

Vrunda Prabhu remarked at the end of Unit 2 that Teaching-Research, just like mathematics is not a spectator sport. Unit 3 develops that view in an effort to encourage colleagues, teachers of mathematics in schools and colleges to pick up the mantle of this unusually creative bisociative approach to teaching and research. Involvement in teaching-research is not particularly difficult especially taking into account again the comment of William J. Harrington, describing his work of a teacher-as-researcher in Laura R. Van Zoest (2006)

Teacher as the Designer of Instruction

Unit 4 presents the designs of TR investigations and teaching experiments conducted by teacher-researchers in their classrooms. It represents three type of TR activity: daily classroom TR investigations (Chapters 4.2–4.5), construction of learning trajectories through iterated classroom teaching experiments (Chapters 4.6–4.8) and two teaching experiments of opposite types (Chapter 4.9) and (Chapter 4.10).

Creativity Research and Koestler

This section provides an overview of research on creativity in mathematics education: Koestler’s understanding of creativity, the role of creativity with mathematics students, especially those who do not view themselves as gifted and a discussion on the how to support a creative learning environment within the mathematics classroom.

Teaching Research Interviews

This project is based on a study assessing the effectiveness of teaching research interviews in mathematics with urban high school students. The subjects of the study were public high school students enrolled in the Mathematics and Science Partnership in New York City (MSPinNYC), a multi-year program funded by the National Science Foundation. The methodology was geared to a target population consisting of the lowest third performing in Math A Regents exams.