Substitution with Decomposition Strategy
A second example of a tutorial strategy that Ms. Lindquist uses is what we call the substitution with decomposition strategy. The key tutor step below is at T4.
This strategy is motivated by previous cognitive analysis and experimentation. The following example is Ms. Lindquist working with a real student.
T1: Hello. Jane is "j" years old. Peg is "p" years old. Mary is Peg's age minus Tom's age. Tom is 3 years younger than Jane. Peg is "x" years older that Mark. Write an expression for Mary's age.[correct answer is "p-(j-3)"]
S1: (p-3)-(3-j)+(p+x)
T2: Hmm. ["Hmm" indicates students response was not diagnosed so Ms. Lindquist will tutor the student on the two sub-goals for this problem.] No. Let me ask you and easier question. Use j and 3 to calculate Tom's age. [ask for one subgoal first]
S2: 3-j [This is a common error type that the tutor should be tactical enough to recognize. The tutor has since been modified to be able to respond with the strategy of asking the student "Which is larger, the ‘3’ or ‘j’?]
T3: Hmm. No. Try again please. What is Tom's age? Hint: pick one of these: j-3, 3-j, j+3, j*3, j/3, or 3/j. [Since the student got this question wrong the tutor is helping the student by limiting the number of possibilities. ]
S3: j-3
T4: Correct. Calculate Mary's age. Use A instead of j-3 for Tom's age. [Here a new variable is introduced. Our research shows that it is much easier for students to answer this question because they only have to worry about one operator at a time. They also don't need to worry about parentheses at this point.]
S4: p-a
T5: Correct. You are correct that p-A is Mary's age. Now, can you state this in terms of the numbers given in the problem. [Ask the student to algebraically substitute. ]
S5: p-(j-3)
T6: Correct.
Tutors should break problems down when students are having difficulty. So Ms. Lindquist broke down the above problem into three separate steps that asked the student to answer questions are easier for a struggling student. This allows the student to gain confidence and build his own knowledge rather then being told the answer.