Learning and Participation in High School Classrooms

In this chapter, we report quantitative and qualitative findings of a curricular approach to investigating quadratic and exponential functions in conjunction with the representationally rich software. The quantitative findings we report demonstrate the positive effects SimCalc has on student learning in comparison to similar algebra classrooms, as measured by pre and posttests. The qualitative findings show us the positive effects SimCalc has on students’ participation in the SimCalc environment through participatory discourse where students partake in mathematical communication to add ideas, justify their ideas, and challenge one another’s ideas about varying rate using the various representations available in the SimCalc technology. We present our qualitative findings through two classroom case studies in which we analyze the classroom discourse.

[1]  Barbara J. Dougherty,et al.  Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education , 2020 .

[2]  L. Quéré Cognition in Practice , 1996 .

[3]  Luis Moreno-Armella,et al.  Co-action with digital technologies , 2009 .

[4]  Etienne Wenger,et al.  Situated Learning: Legitimate Peripheral Participation , 1991 .

[5]  James Paul Gee,et al.  Assessment, Equity, and Opportunity to Learn: Frontmatter , 2008 .

[6]  Roy D. Pea,et al.  A walk on the WILD side How wireless handhelds may change computer-supported collaborative learning , 2002 .

[7]  Ricardo Nemirovsky,et al.  Body Motion and Graphing , 1998 .

[8]  M. Resnick,et al.  Beyond Black Boxes: Bringing Transparency and Aesthetics Back to Scientific Investigation , 2000 .

[9]  Ricardo Nemirovsky,et al.  On Mathematical Visualization and the Place Where We Live , 1997 .

[10]  M. Resnick,et al.  Thinking in Levels: A Dynamic Systems Approach to Making Sense of the World , 1999 .

[11]  Walter M. Stroup,et al.  A Dialectic Analysis of Generativity: Issues of Network-Supported Design in Mathematics and Science , 2005 .

[12]  David Kirshner,et al.  Situated cognition : social, semiotic, and psychological perspectives , 2009 .

[13]  Walter M. Stroup,et al.  Understanding Qualitative Calculus: A Structural Synthesis of Learning Research , 2002, Int. J. Comput. Math. Learn..

[14]  A. Sfard Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing , 2008 .

[15]  Luis Moreno-Armella,et al.  Intersecting representation and communication infrastructures , 2009 .

[16]  Uri Wilensky,et al.  Learning through participatory simulations: network-based design for systems learning in classrooms , 1999, CSCL.

[17]  James Paul Gee,et al.  A sociocultural perspective on opportunity to learn. , 2008 .

[18]  William R. Penuel,et al.  Studying new forms of participation and identity in mathematics classrooms with integrated communication and representational infrastructures , 2008 .

[19]  Richard Lesh,et al.  Foundations for the Future in Mathematics Education , 2007 .

[20]  James J. Kaput,et al.  From static to dynamic mathematics: historical and representational perspectives , 2008 .

[21]  Uri Wilensky,et al.  Networked Gridlock: Students Enacting Complex Dynamic Phenomena with the HubNet Architecture , 2000 .