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SCI-400SCI-400Spring 2008Spring 2008TOPIC: Ways to efficiently TOPIC: Ways to efficiently run a tutoring center in the run a tutoring center in the midst of the current budget midst of the current budget

crisis.crisis.

““Cloning Tutors”Cloning Tutors”

To efficiently and effectively tutor To efficiently and effectively tutor when there are many tutees seeking when there are many tutees seeking help, tutors can use the “cloning” help, tutors can use the “cloning” method.method.

Tutors teach tutees and have tutees Tutors teach tutees and have tutees teach other tutees that come in with teach other tutees that come in with similar problems. similar problems.

The Pros and ConsThe Pros and Cons

This method This method ultimately helps ultimately helps the tutor because the tutor because now the tutor can now the tutor can help another tutee help another tutee with a different with a different subject.subject.

This method helps This method helps the tutee reinforce the tutee reinforce what he/she just what he/she just learned.learned.

The tutee that you The tutee that you helped may have helped may have not understood the not understood the concept fully when concept fully when helping the other helping the other tutee.tutee.

Now you have two Now you have two tutees that are tutees that are misguided and misguided and need your help.need your help.

Encouraging New Encouraging New VolunteersVolunteers

Review knowledge for pre-Review knowledge for pre-professional tests (MCAT, GRE…)professional tests (MCAT, GRE…)

Meet new people form new Meet new people form new friendshipsfriendships

Improve communication skillsImprove communication skills Gain self-confidenceGain self-confidence Gain volunteer hours for a program Gain volunteer hours for a program

or clubor club

Finding volunteersFinding volunteers

Talk to organizations that encourage Talk to organizations that encourage or require volunteer work:or require volunteer work: Sororities or FraternitiesSororities or Fraternities Golden KeyGolden Key Honor’s ClubHonor’s Club SACCS (chemistry club)SACCS (chemistry club) Tri-beta (biology honors club)Tri-beta (biology honors club) Pre-professional clubsPre-professional clubs

Help Students Utilize Other Help Students Utilize Other

Resources Besides the TutorResources Besides the Tutor

Resources include things like:Resources include things like: Class notes Class notes

Textbooks – especially examples in the Textbooks – especially examples in the

textbooktextbook

The internet - Google.comThe internet - Google.com

Professor office hoursProfessor office hours

Class NotesClass Notes Class note are a great Class note are a great

resource resource

As tutors we need to teach As tutors we need to teach

students how to use their students how to use their

notes to find answers to notes to find answers to

their questionstheir questions

This way when the students This way when the students

are on their own, they will are on their own, they will

be able to find the answers be able to find the answers

TextbooksTextbooks Textbooks provide examples Textbooks provide examples

that help solve problemsthat help solve problems

Reading the textbook helps Reading the textbook helps

find the answers to find the answers to

questions!questions!

You have to spend the time to You have to spend the time to

understand textbooksunderstand textbooks

As tutors we need to help As tutors we need to help

students learn how to use students learn how to use

their textbooks as welltheir textbooks as well

The InternetThe Internet When class notes and textbooks do When class notes and textbooks do

not help, the internet can be a great not help, the internet can be a great

resourceresource

Google.com can help you find Google.com can help you find

information regarding many topics – information regarding many topics –

you need to know how to searchyou need to know how to search

Tutors can show students how to use Tutors can show students how to use

the internet to get proper the internet to get proper

informationinformation

Professor Office HoursProfessor Office Hours A lot of students don't realize how A lot of students don't realize how

helpful going to office hours can behelpful going to office hours can be

Professors are able to explain things in Professors are able to explain things in

more detailmore detail

Going to office hours helps students Going to office hours helps students

become familiar with their professorbecome familiar with their professor We as tutors can tell students

to make use of this resource

when we are unable to help

Sub-topic: Sub-topic: Tutor will teach tutees to grasp the Tutor will teach tutees to grasp the overall concept of the problem in overall concept of the problem in order to solve similar problems.order to solve similar problems.

Presented by Roman Selezinka. Presented by Roman Selezinka.

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.

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.

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.

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.

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.

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.

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.

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.

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.

D

a

b

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

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.

THANK YOU FOR YOUR ATTENTION.