SCI-400 Spring 2008

1. SCI-400Spring 2008 • TOPIC: Ways to efficiently run a tutoring center in the midst of the current budget crisis. • Tutor will teach tutees to grasp the overall concept of the problem in order to solve similar problems. • Presented by Roman Selezinka 1

2. Presented by Roman Selezinka.

3. One of the ways to increase efficiency of MASH is to teach the tutees to develop the ability to categorize mathematical problems. Then similar problems will not have to be solved starting from scratch but, rather, a new problem will be assigned to a corresponding category and solved in a way similar to other problems that belong to the same category.

4. The next couple of examples illustrate the above approach and are taken from the real life situation experienced during the Spring quarter 2008 tutoring sessions at MASH.

5. Here is a problem on p.40 of the Calculus book by John Rogawski currently used by Cal Poly students. It asks a student to sketch the region enclosed by the curves of the two equations and compute its area.

6. The two equations are x = y3 – 18y and y + 2x = 0. The student put together the table of values of x and y and sketched the graphs of both equations in one and the same coordinate system.

7. The most interesting was, of course, the first equation. The question that perplexed the tutee was: “How do we know that the graph of x = y3 – 18y is symmetric?” That’s precisely where our idea of teaching the tutee to grasp the overall concept comes in. We tried graphing a couple of similar equations, likex = y3 – 58y, x = y3 + 15y, etc., using the graphing utility and re-discovered a very important property of the end behavior of the graph of a function.

8. From there, the student could clearly see that, since the basic equation of the cubic function, that is, y = x3, is symmetric about the origin, which is the first thing we learn about the cubic function, any modification of this function only changes the curvature of the graph but the function stays the same, that is, the symmetry is preserved.

9. To realize this means to grasp an overall concept of the cubic function and its behavior. The symmetry of the graph of a cubic function is no longer in question, and the other graph is just a graph of a linear equation and we can now confidently calculate the area enclosed by these two curves using the techniques of integration.

10. Another example is that of a distance formula. The problem that another tutee had was to find some distance in a three dimensional coordinate system. The source here is omitted since the student had the problem hand-written on a piece of paper with no reference to the source.

11. We started applying our method by recalling a well-known Pythagorean equation which works in a two dimensional coordinate system. We showed the student that the hypotenuse of a right triangle can be thought of as a linear segment connecting two points, that is, the hypotenuse IS distance.

12. Let us denote it by letter D. Then, the Pythagorean equation D2 = a2 + b2 becomes . Generalizing even further, we find that the distance concept can work in three dimensions as well and our good old Pythagorean formula becomes

13. To conclude our presentation, we would like to stress the importance of teaching the tutee to classify problems by categories. This will enable the tutee to develop analytical thinking of their own by identifying the features that many problems have in common which, in turn, will lead to successful solutions of those by the tutee. This way, the need to hire more tutors will be diminished and we will get out of the current budget crisis sooner.

14. THANK YOU FOR YOUR ATTENTION.