Basic Skills Forum

Learning and Problem Solving Strategies of ESL Students

By Anna Uhl Chamot, Marsha Dale , J. Michael O’Malley, George Spanos (1992).

By Soledad Knipp

I will start my summary of this research by stating the word math problem given to a group of ESL students in a small urban school district in Arlington, VA. The students (32 in all) were beginning and intermediate level ESL students in elementary, middle school and high school. Additionally, the students were enrolled in mathematics classes implementing the Cognitive Academic Learning Approach (CALLA). A discussion of this approach is included below.

Word problem 1

Carlos and Gloria work at McDonald’s at 4238 Wilson Boulevard.
Carlos works 8 hours per week and gets $4.50 per hour. Gloria works
6 hours per week and gets $6.15 per hour. Who works more? Who
gets more money per week? How much more?

Word Problem 2 (Alternate)

In 1989, there were 36 students in the HILT math class. In 1990,
there were 27 students. Which year had more students? How
many more students were there in that class?

The teachers chosen to participate in the study were classified as either high implementation teachers (translation: they were involved extensively in staff development and other project activities) or low implementation teachers (limited involvement in project activities).

The CALLA is based on a cognitive model of instruction and integrated high priority content from the grade level curriculum, a focus on academic language development through content and overt instruction in learning strategies (Chamot & O’Malley). It incorporates cognitive theory in which students learn both language and content.

Purpose of the Study

The research focused on the effects of cognitive instruction in math on ESL students specifically on their problem-solving approach. What problem-solving strategies do ESL students use in dealing with word problems? Compare these strategies at different levels of English proficiency. Also, find out if the problem-solving techniques of those students receiving instruction from high implementation teachers differ from those under low implementation teachers.

Experienced ESL teachers will agree with me (just looking at the above problems) that the intermediate level students will have a better chance of solving the problems than the beginning students. We can also make the prediction that it will take more time for the beginning students to solve them if they could at all. We can also say with certainty that the techniques that would be used by the intermediate students would be different from those of the lower level students.

Learning and Problem Solving Strategies Implemented

The CALLA method mentioned in the beginning of this paper was used in the research. CALLA emphasizes the importance of giving direct instruction in learning strategies and teaching problem solving procedures.

● Learning strategies used:

1. Metacognitive strategies:

a. planning - explicitly identifying the central question that needs to be
answered; identifying information needed to solve the
problem and eliminating unnecessary information;
b. self-evaluation – checking on the progress of solving the problem, catching
mistakes as they happen.

2. Cognitive strategies:

a. grouping – classifying concepts according to their attributes (like making
a table or a list of information in a problem;
b. elaboration – relating new information to prior knowledge/experiences;
c. note-taking – writing needed information and using it to solve problem;
d. deduction – applying rules to solve problem;
e. imagery – using mental or real pictures to understand or solve problem.

3. Social Affective Strategies:

a. questioning for clarification – getting additional information from teacher or
other experts or posing questions to one’s self;
b. cooperation - working with peers to understand and solve the problem;
c. self-talk – reducing anxiety through positive self-direction.

● Problem-solving techniques taught:

The following five-step problem solving sequence was featured in the study. Teachers were encouraged to make posters of this 5-step problem solving techniques to use as a visual aid to assist students in approaching the word problem in a systematic way.

1. Understand the question by reading the problem aloud, discussing prior
knowledge about the problem type, drawing a picture of the problem, rewriting
the question as a statement with a blank for the answer, paraphrasing the
question;

2. Find the needed data which included underlining or circling data needed,
crossing out extraneous information, and comparing circled numbers to the
pictorial representation developed in 1.

3. Make a plan by deciding if one step or multiple steps are called for, choosing the
operation(s), making a table or other graphic representation, guessing and
checking, writing a number sentence, or otherwise setting up the problem.
4. Solve the problem included activities such as working with pencil and/or
calculator or compute the answer to the problem.

5. Check back by comparing the answer to the representation made in 1 to see
if it makes sense, reviewing the problem solving steps, looking for more
information in the problem, estimating the answer, checking calculations.

Results

As personally predicted in the beginning of this summary, more students in the high implementation classroom and high in their language and math abilities scored correctly on the problem. None of the students rated average of low solved the problem correctly. Length of residence in the United States did not reveal any meaningful effect on the students’ capability to solve the problem.

Students in high implementation classrooms used significantly more metacognitive strategies than students in low implementation classrooms. No differences were found in the number of cognitive strategies mentioned among students in the high vs. low implementation classrooms.

The students in the high implementation classes used the problem solving steps in their correct sequence more than low implementation students. The latter suggested that the avenue to correct answers on word problems is through using the problem solving steps in their correct sequence.

Conclusion

From the findings, it was concluded that teachers who participated in staff development activities to introduce problem solving steps and learning strategies to their students appear to have an impact on the strategies students actually used in problem solving and in correctly solving the word problem. The opposite was also true: teachers who did not participate had students not only failing to use the strategies but also not obtaining the correct answers on the word problem.

One significant item identified in this study, however, was that lower ability students, even when they were in high implementation classrooms, did not tend to use the correct sequence or problem solving steps more than the students in low implementation classrooms. One reason could be that lower ability students were operating on lower linguistic competence and were not ready to deal with math texts in a systematic fashion.