Questions to Ponder… Why do you invert and multiply when dividing fractions? Why does anything raised to the zero power equal 1? Why does a negative times a negative equal a positive?

“In American schools today, parents and school boards would fire any teacher who was found to be illiterate but are quite happy to have their children taught by teachers who don't understand even one important idea of mathematics and science.” Alan Kay, designer of eToys.

“T eachers are mostly a product of this poor education process, so most of them have no idea of what is being missed.” Alan Kay, designer of eToys. It is not the teachers fault….

A Nation at Risk "If an unfriendly foreign power had attempted to impose on America the mediocre educational performance that exists today,we might well have viewed it as an act of war."

National Math Panel Foundations for Success Curricular Content Learning Processes Teachers and Teacher Education Instructional Practices Instructional Materials Assessment Research Policies and Mechanisms

Constructivism vs. Didactic

ConstructivistDidactic Student centered instead of teacher directed. Learner controls their environment. Learning goals and problems are authentic. Teacher directs the lesson. Clearly stated, predetermined objectives, activities, and assessments. Computer programming, simulations and models such as LOGO, Squeak, Scratch, and Alice Computer Assisted Instruction (CAI) such as PLATO, ALEKS, and Study Island.

What the research says… There is LOTS of research that supports using computers in a constructivist fashion. (Research found in Wenglinsky’s book and The Milken Exchange as well as on Massachusetts Institute of Technology’s (MIT) Squeak and StarLogo, Northwestern's Center for Connected Learning (CCL) NetLogo, and Carnegie Mellon’s Alice environment,) AND…… There is LOTS of research that supports using computers in a didactic fashion. (National Math Panel’s Report of the Task Group on Instructional practices)

Can both approaches be right? Reiser and Dempsey (2007) allude to the notion of whether both approaches can be valid. The authors suggest that both perspectives can be valid provided that the pedagogy is consistent with the theory.

Contrasting results in research can be attributed to: software design types of studies student demographics professional development student access educators’ role mathematical content plus many other factors… (National Mathematics Advisory Panel, 2008; Schacter, 1999; Wenglinsky, 2007).

It’s a balancing act… skills conceptual understanding problem solving

Remember what Alan Kay said about teachers… Squeak EToys Scratch Alice StarLogo NetLogo