Calculus at RIT

• Placement
• Workshops
• Common Core Exam
• "C"-or-Better policy
• The Net Effect

One of the most important factors in student success in mathematics is correct placement, so calculus at RIT begins with the Math Placement Test. Based on the results of the Placement Test, students in Science, Engineering, Mathematics and Computer Science are directed to one of three sequences, shown in the flow chart below (students in other majors are directed to other courses, pursuant to the requirements of their degree program).

The following data, which tracks students who followed recommendations based on the Math Placement Test versus those who did not, was taken during a single academic year.

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• Principal Organization

  Each of the courses in the flow chart (above) has at least one hour of workshop each week, and sometimes two. The academic content of a workshop depends on the particular educational objectives of the course to which it's attached; but all workshops, regardless of the course they support, are organized around cooperative study, interaction, and participation in the problem-solving process. They are not traditional recitations. Nor are they a time for students to do or discuss homework from the lecture series. Then what are they? Click on the picture below to watch a streaming video about workshops at RIT. (Click here to download a free version of Real Player.)

  Click on the image above to watch a streaming video about workshops

• Worksheets

  As mentiond above, the particular content of a workshop is designed by the primary instructor to support the educational objectives of the course to which the workshop is attached. In the case of 1016-261 and 1016-262 (Calculus with Foundations I and II), worksheets help students master the mechanics of algebra while introducing the fundamental ideas of calculus. This is in stark contrast to the worksheets that instructors design for the Project Based Calculus sequence, which are intended to stretch students abilities and deepen their understanding by tapping into their imagination and sparking their creativity. Such exercises are very different than the standard "kill-and-drill" exercises that many students see in high school. Here are some examples of topics from worksheets in the Project Based Calculus sequence.

  (Using calculus to demonstrate that the "focus" of a parabolic dish is really where the incoming rays are focused)	(Designing ellipitcal couplers for optical fiber)	(Mathematically modeling wave fronts)
  (Galileo's argument with gunners over range and angle)	(Heat dissipation in microactuators)	(The Golden Ratio and DaVinci's Vitruvian Man)
  (Pike dives and parametric curves)	(Apportionment of valuable resources)	(Hydrostatic force and Hoover Dam)
  (Using data from Road and Track)	(Solids of revolution and Hershey's kisses)	(Predator-prey models)
  (Sometimes students use Maple)	(Sometimes students use on-line applets)	(Sometimes students use spreadsheet programs, like Excel)

  Worksheets are written to be relevant to students' lives (either personally or professionally) and often introduce students to "real" problems. Of course, "real" problems are "real" hard. To help them make the transition to collegiate level thinking and ability, each workshop is supported by both a facutly member and a Teaching Assistant (TA). The TAs not only attend workshops but also supplement the professor's office hours by making themselves available in the Bates Study Center (on the first level of the Gosnell Building, facing the quad) several hours each week.

  Students work in teams of 3 or 4	Visualizing satellites (the calculators) moving around the earth (the hats)
  Workshop is often noisy with the work of problem solving

• Projects

  Each course in the Project Based Calculus sequence has, as you might expect, a term project. These projects vary from quarter-to-quarter, and from instructor-to-instructor. Students are expected to solve the given problem, and to write a clear, concise, technical report in which they delineate the process by which they found the solution. Some recent topics for projects are given below.

  (Bezier curves, such as those used by Adobe® Illustrator® and other vector graphics programs)
  (Mathematical models of toxins in the body)	(Satellite positions and orbital transfer)	(Kepler's Laws of planetary motion)

• Why a Workshop?

  Frankly, because more students succeed with them that without them. For example, the following table comprises data regarding students in Calculus II and III.

  Calculus II Description % of students who earned an A, B, or C Without Placement Test Without Workshops (AY 2000) 70.0 WITH Placement Test Without Workshops (Fall/Win qtrs 2001) 69.0 WITH Placement Test WITH Workshops (Spring qtr 2001) 77

  Calculus III Description % of students who earned an A, B, or C Without Placement Test Without Workshops (AY 2000) 66.6 WITH Placement Test Without Workshops (Fall/Win qtrs 2001) 70.0 WITH Placement Test WITH Workshops (Spring qtr 2001) 79.0

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The final exam for each section of each calculus course is given in two parts, a free-response part that's writen by the individual instructor in which students demonstrate skills and knowledge particular to that section and instructor, and a multiple-choice "common core" in which students are asked to demonstrate skills and knowledge that are fundamental to the subject. This helps to ensure that students can "leap-frog" between professors if they need to, and also helps maintain a nominal degree of uniformity in grading criteria across all sections of a course.

The School of Mathematical Sciences prohibits calculators on the final exam of calculus (and other first-year) courses. Many professors prepare students for this by prohibiting calculators on exams during the term, or by giving exams in two parts (one with, and one without calculators).

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Common sense points to adequate preparation as an important element in student success. Particularly when courses are in sequence, demonstrated competence in one course provides the best foundation for success in the next. For this reason, students in calculus must earn a letter grade of at least "C" before continuing on to subsequent courses. A brief statistical analysis (gathered before the "C"-or-Better policy was implemented) bears this out.

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In short, the net effect of the Placement Test, workshops, common core, and "C"-or-Better policy has been tremendous! Success rates in Calculus I, alone, have risen by more that 16 percent! (The chart below depicts the increase student success in the first two years after these facets were introduced.)

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