Week 8 Readings...

SimCalc: Accelerating Students' Engagement with the Mathematics of Change

I made the mistake of trying to tackle this Roschelle et al. paper first. This paper was entirely too versed in the mathematical language of calculus for me to understand the details. (Terms such as "piecewise linear functions" are simply beyond me.) Instead, what I got from the reading was more of a broad overview of what SimCalc is all about.

From what I understand, Roschelle et al. believe that a type of mathematics, called "the mathematics of change and variation" (p. 1) or MCV, is important and necessary in our 21st century world of technological change and innovation. Yet, students must wait until calculus (if they last that long - I cut out after trig) before being exposed to MCV concepts.

Roschelle et al. wanted to find a way to introduce these calculus MCV concepts to middle school students through the use of technology since (among other things) "In education, simulations and animations that display conceptual objects have proven particularly valuable in advancing children's thinking." (p. 10) They hoped to use today's computer technology to help further the math skills that the students have already learned by providing them with a visual display of graphs connected to the idea of motion and velocity, such as what the graph looks like over time of a descending elevator as it decreases in speed. (Or something like that.)

Rather than slow learning speed down to insure that "no child is left behind," Roschelle et al. believe the better approach is to take the higher level MCV calculus concepts and (through the use of educational technology) make them accessible to younger students. They point out that a hundred years ago, most high school students never took algebra, whereas now it is a basic high school requirement. With SimCalc's help, perhaps this century will see a new high school revolution - one where calculus is taught to the majority, rather than a minority, of students.

Getting to Scale With Innovations That Deeply Restructure How Students Come to Know Mathematics

This paper is about the history and current status of SimCalc. I should have read it first, and I would have better understood what SimCalc is all about. The idea for SimCalc apparently originated in the early nineties with the idea that calculus should be democratized so that instead of only a small handful of students taking it, it could be available to all students, especially minorities, who usually never make it that far.

I am oversimplifying the situation, but from what I understand the way SimCalc approaches this task is by through use of a software program that links "motion phenomena to mathematical formalisms." (p.7) This paper goes on to enumerate six phases consisting of design, testing, implementation, and so forth of SimCalc on an increasingly larger scale. (What Roschelle et al. call "scaling up.") The current phase is now being implemented in the state of Texas to seventh and eighth graders. Roschelle et al. caution us to remember that changing curriculum takes years to implement and "some educational reforms take multiple decades to implement." (p.21)

Based on their previous limited research, it is clear that Roschelle et al. are confident in SimCalc's ability to make an improvement in the way middle schoolers learn math. Once more we see the important role that computers can play in the classroom to help ease the acquisition of knowledge. I would be interested in knowing the outcome of the Texas results. I was always told that calculus was too hard to be taught to anyone lower than high school. The fact that certain calculus principles can be taught to middle school students is interesting to me.

Technology Meets Math Education: Envisioning a Practical Future Forum on the Future of Technology in Education

This reading was to the field of mathematics, what the readings of week six were to the field of history. In it Rubin describes "five powerful uses of technology in math education." (p. 2) One use is "Dynamic Connections" (p. 3) in which technology can help students draw connections between mathematical principles. He mentions the example of Geometer's Sketchpad that graphically shows that a parabola with a coefficient of zero is basically a straight line.

Another use of technology in math education has to do with using "sophisticated tools" (p.6) such as graphing calculators to help make math more understandable and accessible to students.

A third use of technology in math education are "resource-rich mathematical communities" (p.8) that help to connect students and teachers via the web. He mentions a web site called "The Math Forum" that reminds me a lot of a community of practice for mathematically inclined people and also sort of resembles "Tapped In" with its ability to connect math teachers together online.

Another use of technology in math education is through "construction and design" tools. (p.10) He gives the example of LOGO here.

The final use of technology in math education that Rubin gives is "tools for exploring complexity." (p.12) Here he mentions SimCalc as an example.

Rubin goes on to state certain conditions that must be met for technology to have a significant effect on math education, such as more support for development, curriculum integration, professional development, and public education. He also lists his concerns about technology in math education that include equity concerns (i.e., girls and minorities being left behind), risks of inappropriate use (causing students to rely too much on their calculators without understanding the theory behind the math), trying to replace teachers (which no software can do) and succumbing to "web ecstasy." (p.17)