urban teaching

I was proctoring a session of the MCAS English Language Arts test. The students had just opened up their test booklets to page one, which was all white, except for a black box in the center with the following sentence written inside: “In the space provided in your answer booklet, write a one-page essay about a person who has been a hero to you.”

A hand went up. I walked over to the student and she asked, with near desperation in her voice: “What am I supposed to do?”

***

This piece fit well into the already-existing puzzle whose name is: Many students at this school don’t know how to read a simple instruction and turn it into action. Later that year I designed a little assessment to examine the hypothesis. This essay is about what I learned from that assessment.

It was a five-question test on one side of a sheet of paper; the students were to return the paper with their answers. The students knew that it was important to me that they did their best but that the result would have no effect on their grades. I’ll describe only the first three questions and their results.

I gave it to students in my Math MCAS Prep classes. These were students who were considered to be at risk of failing the test, either because they had already taken the Math MCAS and not yet passed it or because their math records suggested that they might fail the test when they were to take it as tenth-graders. Here are the first three questions (slightly modified for the purpose of this essay only to eliminate one reference to question 4).

Read carefully and follow the instructions for each question.

Questions 1 and 2 refer to the following description.

Alfred, who had no children of his own, married and moved in with Barbara, who was caring for and living with her only three children, who had resulted from her previous marriage. Alfred did not legally adopt any of these children.

Alfred and Barbara then had two children of their own. Shortly after the younger of these was born, Clara, the oldest of all Barbara’s children, went away to college.

1. Immediately after Clara’s departure how many children were living with Alfred and Barbara? Place a check mark to the right of the correct number.

A.None

B.1

C.2

D.3

E.4

F.5

G.6

H.More than 6.

2. Immediately after Clara’s departure how many of the children whose legal father was Alfred were living with Alfred and Barbara? Circle the letter of the correct answer.

A.None

B.1

C.2

D.3

E.4

F.5

G.6

H.More than 6.

In question 3 assume that the description above is changed in only one detail: When Alfred married Barbara, he legally adopted all of the children of Barbara’s previous marriage.

3. Immediately after Clara’s departure how many of the children whose legal father was Alfred were living with Alfred and Barbara? Circle the correct number of children.

A.None

B.1

C.2

D.3

E.4

F.5

G.6

H.More than 6.

What I was looking for in particular was the accuracy with which the students would respond to the second sentence of each question; this sentence instructed the student how to mark his or her answer to that question.

The entire rest of this essay is taken from a paper I wrote analyzing the results of this assessment.

The sample size (the number of graded quizzes) is 47.

Questions 1, 2, and 3 are graded two independent ways: on the correctness of the numerical answer chosen, and on the correctness of the mark made to indicate the choice. Each of the three questions requires the student to make a different mark (circle the letter, circle the number, and place a check mark to the right of the number).

Questions 1-3 are evaluated in the aggregate as a sample of 141 (3x47) questions. 55% of these 141 questions were answered with the correct numeric value.

Questions 1-3 are also evaluated by the correctness of the mark the student made, independently of the student’s choice of answer. Of the 47 quizzes, 31 of them (66%) had the same mark on all three questions. No mark on these 31 quizzes was considered correct, because the presence of three identical marks indicates no effort to make a distinction, and the appearance of a correct mark due to sheer chance (just as a broken clock is accurate twice a day) must not be considered correct. Among the remaining 16 quizzes containing at least two distinct marks (48 marking opportunities), there were 14 correct marks. That is, 10% of the total possible number of marks were correct.

One cannot explain this very low rate of correct marks on the basis of reading comprehension alone. The numeric questions were answered correctly at a 55% level, whereas only 10% of the selection marks were correct, and 55% is significantly better than 10%. For some reason the marking instruction in the second sentence of each question was effectively invisible, did not register, or did not move the student to action, 90% of the time.

This 10% statistic begs for an explanation. Whatever the explanation might be, the performance of the students in following detailed, multiple-part instructions was very poor, which does not bode well for performance on the MCAS test. (The MCAS questions CHS students invariably do the worst on–compared to state averages–are the six open-response questions in each test. The attention deficit the students exhibited on quiz questions 1-3 might in part explain our uniformly poor performance on the sequential open-response questions.)

Conclusion

I regard what I have observed as a behavior disorder. One might be tempted to diagnose the cause of this disorder as a missing skill that needs to be taught. My view is that the disorder is a syndrome of underdeveloped habits of mind, a consequence of absent training needed earlier for the development of conscious habits of mind. The therapy for such a syndrome in high-school students requires intense training, not solely conventional teaching of mathematical concepts. I believe it will be futile to attempt to teach many of our at-risk students mathematical skills until we enable them to think, focus, and sustain concentration.

What Am I Supposed to Do?

Monday, July 17, 2006