Examples on Tutoring Math

Word Problem

Concept: Word (Story) problems with 1 variable

Tutoring methods:

  • Recording the information in English and Math

  • Appropriate sequencing

  • Appropriate usage of old resources to solve new problems

  • Summarization of the though process
 

Example: The sum of two consecutive numbers is 11. Find the numbers.

Experienced tutors use different sequencing  to provide opportunities for a fluent and creative  thought process. A summary of the steps that I use most often for my tutorials is given in Table 1.

Steps

Tutoring Tips

1.    Ask the student to read or explain the problem with understanding.

Slow the process; ask for the original problem. Ask the student to open all notes and the textbook. This is something that everybody can do. Use it as an ice-breaker.

2.    Help the student to record the information given in the problem.

Lead the student with appropriate questions to record the information in the problem in English and Math (Table 2).

3.    Help the student to select appropriate strategy for solving the problem.

Make sure that the student understands the meaning of the word strategy. Help with a list of strategies. Suggest appropriate visual or tabular organization to see the relation between data.

4. Summarize and reflect on the process.

Your goal in this step is to help with internalization of the new knowledge Help the student to identify what is the new knowledge and to find appropriate category for the data in the larger scope of his understanding of math.

5. Solve the problem and present solution for instructor.

Let the student do the solution. Your goal is to celebrate the manifestation of learning. Be enthusiastic and positive. In this moment the presentation of solution is a critical repetition of the entire thought process.

 

 

Record and reflect on your work with this student.

Tutoring is an art; you need constant feedback and improvement.  By recording your work, later on you will be able to discuss with other tutors your concerns and accomplishments.

In Step 1, you should guide the student to understand the problem. Encourage the student to read the problem for you, do not read the problem for the student. Brainstorm with the student.

In Step 2, you ask the student to record the information given in the problem. If the student has never done this step before, guide the student to fill a table (Table 4 is one example) to make a list, or draw a picture or chart to organize the information.

Table 2

Lead the student to record the information in English

Lead the student to record the information in Math

As a result:

The student's table will look like this

First number

How to present the number? Which letter symbolizes the unknown quantity?

 First Number x

Second number

What is the difference between two consecutive numbers?

Second Number x + 1

The sum of the two numbers is …

What mathematical operation do we use in case like this? What is the key word? (sum)

 Total x + x + 1 = 11

If the student has no trouble with step 2, skip step 3 and move to step 4. If the student has trouble filling table 2, continue with step 3. Step 3 If step 2 was too difficult for the student, use some visual tools.  For example, the number line.

 

 

Ask: If the first number is x = 5, what will be the second number? Use the same variable x. The sequencing of your work with the student will depend on his or her prior knowledge.

Text Box: -9  -8  -7  -6  -5  -4  -3 -2 -1 0  1  2  3  4  5  6  7  8  9  

 

Fig. 1

Figure 1 shows the idea of sequencing and working on different pieces of the sequence to prompt a thought process.  It is important to find the exact sequencing for the student. Just braking the problem in pieces is not enough; the art of tutoring is to decide in each case in how many pieces to brake the problem. This art of finding the right frequency is something that you will learn by practicing.

Step 4: After the student has all information decoded in English (with words) and Math (with symbols, numbers, expressions, variables, units, and such.), ask for the key words to construct the equation. The list with the key words are in the textbook of Arithmetic. Bringing one of the arithmetic textbook will help to Bridge old and new knowledge.  Also, this is disciplining the thought process to memorize important mathematical facts.

Step 5 Summarizing the information: Simple questions will lead the student to memorization and deep understanding.

What did you learn? What if the two numbers were even or odd consecutive. What was the most difficult step? Let us try a similar problem.

Record your work. All these tutoring takes no longer than 2 to 5 minutes. Some parts are routine, some are new to you. Please, record the new methods that work.

Table 3 is one way to fast record your information.

Problem, class, Instructor Student Level of Independence Resources Sequencing Tutoring Methods
math 086

Prof. Adams

 Dependent Course Compass - online tutorial Very Fine - about 6 steps.

Total time 10 minutes.

 Number Line (a meta-cognitive tool), Table with given information