SimCalc

Draft

This article is in a large part a synthesis of Rieber 1996

Definition

SimCalc is a type of microworld

“The SimCalc MathWorlds Curriculum: Bring your Algebra class to life-allow students an opportunity to explore and personalize core algebraic concepts through analyzing the mathematics of motion. Activities range from Pre-Algebra through Pre-Calculus topics.” (The SimCalc MathWorlds Curriculum, retrieved 22:54, 4 October 2006 (MEST).)

The SimCalc Projects

The SimCalc "curriculum" is concerned with the mathematics of change and variation (MCV) and aims to give ordinary children the opportunities, experiences,and resources they need to develop an extraordinary understanding of and skill with MCV (Roschelle et al., 2000).

It is based on 3 lines of innovation.

1. a deep reconstruction of the calculus curriculum, both its subject matter and the way in which it is taught. The goal is to allow all children, even those in elementary school, to access the mathematical principles of change and variation. The developers assert that this is possible through the design of visualizations and simulations for collaborative inquiry. The most notable innovation in the SimCalc curriculum is the use of piecewise linear functions as the basis of student exploration. In a velocity graph, for example, a student can build a function by putting together line segments, each of the same time duration A series of joined horizontal segments denotes constant velocity and a set of rising or falling segments denotes increasing or decreasing speed.
2. to root the learning of these mathematics principles in meaningful experiences of students. Students bring with them a wealth of mathematical understanding that is largely untapped in traditional methods of learning calculus. The SimCalc project does not require students to understand algebra before exploring calculus principles.
3. creative use of technology, namely, special software called MathWorlds.

• 1. makes extensive use of concrete visual representations, coupled with graphs that students can directly manipulate and control.
  2. graphs can be based on data sets generated by computer-based simulations (animated clowns, ducks, and elevators), laboratory experiments, and even the students’ own body movements by capturing their movements with microcomputer-based (or calculatorbased) motion sensors, then importing these data into the computer.

Expressive constructions

The SimCalc project has reconceptualized the teaching of mathematics at all grade levels, starting with elementary school and has put its focus on meaningful student experience based on graphs of interesting visual phenomena that students can manipulate directly. E.g. as an example the project site mentions "creating dances between characters, or choreographing a whole marching band using graphical descriptions of the marchers-either velocity or position graphs."

The SimCalc project places much value on students experiencing phenomena as the basis for their mathematical explorations. The SimCalc curriculum is based on 4 strategies that counter traditional teaching of calculus;

1. Phenomena before formalisms: phenomena are studied and understood before delving into mathematical formalisms.
2. Discrete variation before continuous variation: the mathematics are based on discrete variation before turning to continuous variation.
3. Accumulation and integrals before rates and derivatives: the mathematics of accumulation and integrals are taught before rates of change and derivatives.
4. Graphs before algebraic symbolism: students learn to master graphs before algebraic symbolism. So, instead of requiring algebra as a prerequisite skill for studying calculus, the SimCalc project using students’ grasp of visual problem solving with graphs to enter the mathematical world of change and varying quantities.

Technology

SimCalc is available in several variants at SimCalc MathWorlds Software

• Java-based MathWorlds for computers (available for download)
• TI Calculator version (available for download)
• TI Calculator connected to the teachers computer (available for download)
• Some PDA version (?)

Links

• Simcalc Home Page

References

• Rieber, L. P. (1996) Microworlds, in Jonassen, David, H. (ed.) Handbook of research on educational communications and technology. Handbook of Research for Educational Communications and Technology. Second edition. Simon and Schuster, 583-603 ISBN 0-02-864663-0

• Roschelle, J., Kaput, J., & Stroup, W. (2000). SimCalc: Accelerating student engagement with the mathematics of change. In M. J. Jacobson & R. B. Kozma (Eds.), Learning the sciences of the 21st century: Research, design, and implementing advanced technology learning environments (pp. 47–75). Mahwah, NJ: Lawrence Erlbaum Associates.

• Roschelle, J., & Kaput, J. (1996). SimCalc MathWorlds for the mathematics of change: Composable components for calculus learning. Communications of the ACM, 39 (8), 97-99. PDF Reprint

• Tatar, D., Roschelle, J., Vahey, P., & Penuel, W. R. (2003). Handhelds go to school: lessons learned. IEEE Computer, 36(9), 30-37. PDF Reprint