Using interactive algebra software to support a discourse community

Abstract In this work we studied the impact of using NuCalc, an interactive computer algebra software, on the development of a discourse community in a college level mathematics class. Qualitative and quantitative data were collected over the course of 3 weeks of instruction. We examined the influence of the software on: group interactions; the mathematical investigations of learners; and the teacher’s interactions with students. Data points to four distinct ways in which the presence of NuCalc positively impacted the learning community we studied: (1) it served as a tool for extending students’ mathematical thinking, (2) it motivated students’ engagement in group discourse, (3) it became a tool for mediating discourse, (4) it became a catalyst for refining the culture of classroom, shifting the patterns of interactions between the teacher and learners.

[1]  J. Roschelle.  Learning by Collaborating: Convergent Conceptual Change , 1992 .

[2]  Neil Mercer,et al.  Common Knowledge: The Development of Understanding in the Classroom , 1987 .

[3]  G. Salomon.  Distributed cognitions : psychological and educational considerations , 1997 .

[4]  Ralph E. Reynolds,et al.  Views of knowledge acquisition and representation: A continuum from experience centered to mind.. , 1996 .

[5]  Paul Cobb,et al.  Interaction and learning in mathematics classroom situations , 1992 .

[6]  Michael Stubbs,et al.  Discourse Analysis: The Sociolinguistic Analysis of Natural Language , 1983 .

[7]  Jeremy Roschelle,et al.  Correspondence Section Educational Software Architecture and Systemic Impact: The Promise of Component Software , 1996 .

[8]  M. Cole.  Cultural psychology: a once and future discipline? , 1996, Nebraska Symposium on Motivation. Nebraska Symposium on Motivation.

[9]  B. J. Winer.  Statistical Principles in Experimental Design , 1992 .

[10]  A. Bandura.  The self system in reciprocal determinism. , 1978 .

[11]  R. Lebeau,et al.  Cognitive Tools in a Clinical Encounter in Medicine: Supporting Empathy and Expertise in Distributed Systems , 1998 .

[12]  Ann L. Brown,et al.  Guided, Cooperative Learning and Individual Knowledge Acquisition , 2018, Knowing, Learning, and Instruction.

[13]  P. Mussen,et al.  Carmichael's Manual of Child Psychology , 1972 .

[14]  M. Wittrock.  Handbook of research on teaching , 1986 .

[15]  A. Bandura.  Social Foundations of Thought and Action: A Social Cognitive Theory , 1985 .

[16]  A. King.  Discourse patterns for mediating peer learning. , 1999 .

[17]  Thomas L. Good,et al.  International handbook of teachers and teaching , 1997 .

[18]  C. Goodwin,et al.  Rethinking Context: Language as an Interactive Phenomenon , 1992 .

[19]  J. Piaget.  Judgement and Reasoning in the Child , 1962 .

[20]  Magdalene Lampert,et al.  When the Problem Is Not the Question and the Solution Is Not the Answer: Mathematical Knowing and Teaching , 1990 .

[21]  Courtney B. Cazden,et al.  Classroom Discourse: The Language of Teaching and Learning. Second Edition. , 2001 .

[22]  Jean Piaget.  Piaget’s Theory , 1976 .

[23]  Judith L. Green,et al.  Discourse Analysis, Learning, and Social Practice: A Methodological Study , 1998 .

[24]  A. King.  Facilitating Elaborative Learning Through Guided Student-Generated Questioning , 1992 .

[25]  Paul Cobb,et al.  Constructivist, emergent, and sociocultural perspectives in the context of developmental research , 1996 .

[26]  M. Chi.  Quantifying Qualitative Analyses of Verbal Data: A Practical Guide , 1997 .

[27]  Jeremy Roschelle,et al.  Educational Software Architecture and Systematic Impact: The Promise of Component Software. , 1996 .

[28]  L. Resnick,et al.  Knowing, Learning, and Instruction , 2018 .

[29]  J. Sinclair,et al.  Towards an Analysis of Discourse: The English Used by Teachers and Pupils , 1975 .

[30]  William Damon,et al.  Problem solving with equals: Peer collaboration as a context for learning mathematics and spatial concepts. , 1989 .

[31]  J. Booth,et al.  Resampling-Based Multiple Testing. , 1994 .

[32]  G. Roland,et al.  Council of Teachers of Mathematics , 1999 .

[33]  Geoffrey B. Saxe,et al.  Culture and cognitive development , 1990 .

[34]  J. Holt.  How Children Fail , 1964 .

[35]  L. Vygotsky.  Mind in Society: The Development of Higher Psychological Processes: Harvard University Press , 1978 .

[36]  R. Pea.  Practices of distributed intelligence and designs for education , 1993 .

[37]  Paul Cobb,et al.  An Analysis of Development of Sociomathematical Norms in One First-Grade Classroom , 2001 .

[38]  Judith L. Green,et al.  Chapter 4: Discourse Analysis, Learning, and Social Practice: A Methodological Study , 1998 .

[39]  P. Willis.  Learning to Labor: How Working-Class Kids Get Working-Class Jobs , 1976 .

[40]  Timothy Koschmann,et al.  Cscl : Theory and Practice of An Emerging Paradigm , 1996 .

[41]  James Paul Gee,et al.  Units in the production of narrative discourse , 1986 .

[42]  Richard C. Anderson,et al.  The Structure of Discussions that Promote Reasoning , 1998, Teachers College Record: The Voice of Scholarship in Education.

[43]  Angela M. O'Donnell,et al.  Cognitive Perspectives on Peer Learning , 1999 .

[44]  A. Su,et al.  The National Council of Teachers of Mathematics , 1932, The Mathematical Gazette.

[45]  Kenneth Tobin,et al.  The Practice of constructivism in science education , 1993 .

[46]  D. Ball.  What Do Students Know? Facing Challenges of Distance, Context, and Desire in Trying to Hear Children , 1997 .

[47]  Janice F. Almasi.  The Nature of Fourth Graders' Sociocognitive Conflicts in Peer-Led and Teacher-Led Discussions of Literature. IRA Outstanding Dissertation Award for 1993-94. , 1994 .