SimCalc: The Mission
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Democratize Access to Big Mathematical Ideas
Students Need Early Access To Powerful Mathematics
The central ideas of calculus — change and accumulation of quantity — are
critically important tools for understanding science, engineering and business.
Related ideas include the different kinds of variation, mean values,
approximation, sampling and limits. The mathematics of change is essential for
informed citizenship in a rapidly evolving democratic society. These ideas
should be learnable by ALL children, without a long series of prerequisites.
We must introduce these powerful ideas early, using techniques that tap into
kids' natural abilities. We must avoid well-known difficulties with mathematical
symbols. Activities should draw upon diverse worlds, real and imagined, and build
upon students' strengths. Students need to develop these ideas gradually, over
many years, rather than waiting until a single senior year elective. Moreover,
many students are systematically prevented from ever reaching a senior year
calculus course by the long series of prerequisites. These prerequisites unfairly
eliminate many women and minorities from the mathematics pipeline. We seek deep
changes in the mainstream curriculum which controls what virtually all students
and teachers do every day.
Using Technology To Transform The Core Curriculum
The SimCalc Project believes that technology provides essential means to
restructure this curriculum in order to:
- Democratize access to important and powerful ideas.
- Build much more longitudinal coherence between early and later years.
- Focusing on the growth of big ideas, and their roots in everyday human
experience.
- Crack the formalism barrier by providing multiple ways of
working with mathematical ideas, using the full range of
human linguistic, visualization and cognitive capacities.
- Increase efficiency by teaching several important ideas simultaneously.
- Make room for more modern mathematics, moving out of the 19th century and
into the 21st.
To this end we are building and testing software simulations and curricular
activities for a wide range of students beginning in third grade and continuing
through college calculus — with a special focus on students who would not
otherwise have access to these important ideas and skills.
To achieve the needed flexibility of design, we are exploiting a combination of
interoperable component architecture, plug/play animation worlds, and deep
scriptability. Our teaching strategies include everything from computer-based
games, to guided exploration, to open-ended free exploration — in student
centered labs as well as teacher-centered classrooms. And we mix computer-based
technology with graphing calculators, and mix physical experiences with computer
simulations.
Collaborating On A New Mathematics Curriculum
We cannot achieve our mission alone. The SimCalc team is active in the reforms of
the National Council of Teachers of Mathematics, and leads the Algebra Working
Group of the National Center for Research in Mathematical Sciences Education.
Likewise, we have been leading a
discussion on the future of educational components. Together with others, we are
working towards a future in which every child becomes a fluent user of powerful
mathematical ideas.
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