SimCalc

Draft

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

(http://www.simcalc.umassd.edu/)

SimCalc is a type of microworld.

• is concerned with the mathematics of change and variation (MCV).
• 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).
• 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.
     • makes extensive use of concrete visual representations, coupled with graphs that students can directly manipulate and control.
     • 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.

The SimCalc project

1. has reconceptualized the teaching of mathematics at all grade levels, starting with elementary school.
2. has put its focus on meaningful student experience based on graphs of interesting visual phenomena that students can manipulate directly.

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 are studied and understood before delving into mathematical formalisms.
2. the mathematics are based on discrete variation before turning to continuous variation.
3. the mathematics of accumulation and integrals are taught before rates of change and derivatives.
4. 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.

Back to Microworld

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.