Learning Objectives of the Calculus throughout the Curriculum linking course:
In addition to and in coordination with the general goals of the M302 courses, students in M302: Calculus will...
- Learn how to pose conceptually focused problems in high school calculus.
- Explore calculus concepts present in the secondary math curriculum (grades 7 – 12) such as rate of change, area, volume, integral as accumulator, optimization (maxima and minima), average value, linear approximation, higher degree approximations, series, and limits, etc.
- Learn how to support future calculus learning with 7 – 12 conceptual development and task design.
- Develop insights about teaching the concepts of calculus graphically, numerically, analytically, and verbally in the calculus course proper and in the earlier 7 – 12 courses.
- Learn how to maintain and enhance student proficiency in deductive proof which begins in high school geometry through the subsequent math courses of algebra 2, trig / precalculus, calculus.
- Understand the Fundamental Theorem of Calculus and its proof.
- Understand the epsilon – delta definition of limit and connect an epsilon – delta proof to the ideas of deductive proof learned in high school geometry.
- Learn how to use various technologies effectively to represent the mathematical ideas of calculus. This would include graphing calculators, Geometer’s Sketchpad using support scripts such as Calculus-In-Motion from Audrey Weeks, and graphing packages such as Nu-Calc or Maple or Mathematica.
- Appreciate the development of calculus as one of the great human achievements.
Summary of Objectives:
The learning objectives listed above revolve around the idea that we can help many more students get to calculus and successfully learn calculus by one: being aware, as teachers, of the presence and articulation of these concepts in the lower courses and two: how we can, with proper task design, have our students learning their mathematics in a way that will effectively support their subsequent official calculus course.