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Mathematics uses building blocks, meaning it requires mastery of the fundamentals before moving on to advanced concepts thus requiring a certain approach different from History or English. My approach is designed to accommodate different types of learners. I call it the 'concept-details-confirm' approach.
Here are two examples of how I used 'concept-details-confirm' approach when tutoring Mathematics in Elementary Math and Calculus I, respectively:
Tutoring Elementary Math:
One of the most challenging concepts in Elementary math is multiplication. To do multiplication, the student should have mastered addition first. The approach I am going to take when a student is having trouble with multiplication is make them understand the concept first, then show them step-by-step how to multiply.
1.) CONCEPT
Understanding the concept is important, a student can learn how to multiply using certain techniques, but if they do not know why they are doing it then they will eventually forget after the test.
To make students understand the concept, I will use objects like marbles as visual representation. For example, to represent 3x5 with marbles, I would have 3 SETS OF 5 MARBLES, and I would make the student count it. The total number of marbles from all sets is the answer, which is 15. Then I would have the student represent 4x6 in marbles to get the total number. Once the student understand this concept, he/she can move on to memorizing the multiplication table.
2.) DETAILS
After memorizing the multiplication table, I would now show the student step-by-step how to do one-step multiplication and two-steps or more multiplication. Two-steps multiplication requires mastery of addition.
3.) CONFIRM
As I give the student math problems, I would oversee how they do the problems step-by-step, if the student is prone to making mistake in the addition part of two-steps multiplication, then that means the student has not mastered addition, and I would go back and make sure the student masters addition using the 'concept-details-confirm' approach. Once the student mastered addition, I would have them correct the mistake they made in two-steps equation. With practice, the student will master two-steps multiplication.
Tutoring Calculus I:
One of the most challenging concepts in Calculus I is Derivatives. There are many different derivative techniques such as Limit Definition, Product Rule, Quotient Rule, Chain Rule, Impartial differentiation. etc. Before a student can learn these derivative techniques, it is imperative that they have mastered Algebra I, Algebra II, Geometry, and Pre-Calculus, and understand the derivative concept first. Otherwise, if they do not have the prerequisites math mastered, they will be prone to making small mistakes even if they understand the concept really well. If they do not understand the concept, even if they execute the derivative techniques well, they will most likely forget the material after the exam, which will be detrimental when they take Calculus II and higher level math.
1.) CONCEPT
To make students understand the derivative concept, I will use concrete world examples. I would use a story and a visual, these would ensure to accommodate all types of learners.
To represent the concept of derivative in a story, I would use a car going from home to school. As the driver steps on the gas to go to school, the vehicle accelerates, the rate of which the car velocity is increasing is the derivative. When the driver is reaching a red light, the driver will step on the break decelerating the car, the rate of which the car velocity decreases to stop is also the derivative.
To represent the concept of derivative in a visual, I would use two graphs of of the car acceleration, and the car speed. In the acceleration graph, I would have x-coordinate as time and y-coordinate as acceleration. In the velocity graph, I would have x-coordinate as time and y-coordinate as speed. The two graphs is a representation of one car. If the car is accelerating in a constant acceleration say 3 m/s^2, then the velocity of the car is increasing by 3 EACH SECOND.
So in this case, the layman's definition of derivative is the rate of how fast and slow is something changing.
2.) DETAILS
Once the concept is understood, I would teach the mathematical definition of derivative and theorem of the particular derivative technique they need help, and show step-by-step how to do problems using the particular derivative technique.
3.) CONFIRM
Calculus problems are not easy to make up, so I would assign 3 total problems from their book (if they have one) and my Calculus I book which I still have, and oversee how they are solving the problems step-by-step. If they got the incorrect answer, I would oversee and analyze their steps. There are two possible causes of wrong answer in Calculus I: Not following the calculus steps properly and/or algebra mistake. If it calculus steps, I would have them correct the steps they got wrong. If it's algebra mistake, I would analyze what part of algebra they are prone to making mistakes and review that concept of algebra with them using 'concept-details-confirm' approach. Once the student mastered that algebra concept, I would have them correct that algebra mistake they made for their assigned Calculus I problems.
Conclusion:
Whether it's Elementary Math or Calculus I, Ultimately, I would make sure my clients are one-step ahead of their math class by teaching the future materials in their classes using this approach before my clients learns the material in their classes.
