Components of Learning Environment

Anchors of Creative Learning Environment Teaching-Research

Methodology (TR-NYC model)

Mathematical Creativity Integration of craft knowledge, and Koestler in Act of Creation in the form of triptychs, facilitation of bisociation, supported by mathematical writing. Triptychs shade 3 domains of creativity: Humor, Discovery and Art and so also bridge the cognitive affective divide and build in SRLpractices.

Didactic Contract Integration of need in the classroom with G. Brousseau’’s work, and supported by Students as Partners in Learning. Journal writing and triptychs act as thinking aside tools.

Foundations of Mathematics and Remedial Mathematics Design of instructional materials in accordance with development of concepts as suggested by Bruner’s concrete-iconic-symbolic forms and with historic development of concepts, makes the number line the central focus, and leads research in both areas - Foundations & Pedagogy.

Paradigm shift Learning Paradigm approach of Barr and Tagg in accordance with goal of improvement of learning in TR-NYC. Learning becomes central and is self-guided through handshake/didactic contract

Timeline with Outcomes 2006 Conclusion of NSF-ROLE Discovery based TR-NYC Teaching Research Experiments (TRE) in calculus classrooms; beginning of TREs in Remedial Mathematics 2007 CUNY-funded TRE, Investigating Effectiveness of Fractions Grid, Fractions Domino in Community Colleges of the Bronx, Librarian part of the TR Team; Need for Didactic Contract evidenced; Brousseau intervention begins 2008 Application to MSP-START, cognition and affect mutually affecting pathways; need for simultaneous attention 2010 CUNY funded TE, A Jumpstart to Remedial Reform; Creative Problem Solving; USAID funded Bronx Community College (BCC) consulting to FET Colleges in South Africa to replicate the successful community college model; Development of model for South Africa begins in remedial classes at BCC with intervention of Vice President of Student Development; Vice President part of Teaching Research Team 2011 Mathematical Creativity emerges as a route to increased engagement and mastery of concepts 2012 Students as Partners in Learning is a construct with students of Creative Writing Club as leaders; students part of Teaching-Research Team

Publications Barbatis, P., Leyva, A., Prabhu, V., Sidibe, A., & Watson, J. (2012). Mathematics Classrooms, Sites of Creativity. (Submitted) Todos Research Monograph. Barbatis, P., Prabhu, V., & Watson, J. (2012). Making Sense of Number, Creative Learning Environment. Mine and Minds, Experiments in Education. Publication December 2012 Prabhu, V., Barbatis, P., & Watson, J.

(2011). Creativity as the engine of

mathematical discovery : Students as

Partners in Learning. Proceedings of

the 16th International Seminar on

Education and Gifted Students in

Mathematics, 353-369. www.hostos.cuny.edu/mtrj

Presentation at the Concept Mapping Conference CMC-5, University of Malta, September 2012

Story of Number, Syllabus of Arithmetic conceptualized

References Czarnocha, B., & Prabhu, V. (2006). Teaching Research NYCity Model. . Dydaktyka Matematyki, 29. Koestler, A. (1964). The act of creation. New York: Macmillan. Tagg, J. (2003). The Learning Paradigm College. Bolton, MA:

Anker Publishing Company.

Research Direction 1. Learning Trajectories are the mandated means within the CCSS

starting 2014. Concept maps are being re-envisioned to fit the LT model.

2. Development of Inventory assessing Mathematical Creativity.