My first experience tutoring high school math was during the 60s, when I was an undergraduate. I really liked it and during my first career as an economist I availed myself of any chances that came my way to help neighbors and children of friends and coworkers. I have returned to graduate school and I am pursuing advanced studies in probability theory hoping to make a practical contribution in the area of personal and small firm decision theory. Participation in study groups and the on campus tutoring program reminded me how much I enjoyed working one-on-one with students.
This led me to sign up with online math sites, which do provide valuable services to math students. But they are not as fulfilling as tutoring one-on-one because of their one problem at a time nature. One does not get to see and share in the progress of an individual student.
When I started, paper and pencils or chalkboards were the only aids. Today we have much better tools, but the fundamentals of mathematical learning have not changed. Since retiring from my first career, I have started graduate school
Mastering any element of mathematics requires a certain amount of practice, but drill and repetition before the student has grasped the fundamental concepts is worse than wasted effort. It can eat away at the student’s confidence and turn what should be an enjoyable and fulfilling experience into drudgery. I believe that anyone can learn math with the right combination of motivation and guidance. I have seen many students who “hated” math become good and enthusiastic mathematicians.
The three stages of learning any area of mathematics are assessment, explanation and practice. It is crucial to distinguish between what the student knows and where he/she is challenged.
Once the problem areas have been identified, it is time to convey the concepts. Patience and creativity are vitally important here. Often the same concept can be presented analytically, graphically, or through examples drawn from the real world. One can teach anything by breaking it down into an array of simpler concepts and then reassembling the elements into a larger whole. This requires sensitivity. Present the concepts in ‘chunks’ that are too big and they will be incomprehensible. Present them broken down into too much detail and the student will become board and his/her mind will wander. This is where a tutor can be better than even the best books and on-line courses. A tutor can tell when the student ‘gets it’ and it is time to move on. It is very important at this stage to sometimes just let the student ask questions. Students know what they understand and where they need help.
Finally, a certain amount of practice is required to make concepts and techniques sink in. Again the practice should be calibrated to be challenging and fun. Spaced repetition is used to assure the lessons stick. The ideal is to assign problems that enhance the student’s confidence while cementing his/her skills. Some problems should be worked out completely by hand but many can be solved with modern tools such as Wolfram|Alpha and its associated apps or Microsoft Mathematics. Tools that help the student master concepts and techniques without getting bogged down in the details of calculation make learning go faster.
Through high school, I believe in working with parents and providing them with the tools they can use to improve their child’s knowledge and grades. For college students I will recommend an array of tools and techniques.
I love to tutor and look forward to helping you catch my enthusiasm.
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