Middle school students' understanding of number sense related to percent

School Science and Mathematics, Jan 1997 by Gay, A Susan, Aichele, Douglas B

Procedures

In September, 1990, the written test was administered by the district's mathematics coordinator during the regularly scheduled mathematics class. On the second day following the written test, student interviews took place with the mathematics coordinator taking notes during each interview; questions, answers and comments were recorded.

Individual student interviews were conducted with 28 students to gather information on the thinking strategies students used to answer questions from the written test. For this study, maximum variation sampling (Patton, 1987) was applied to select students to be interviewed who represented a wide range of ability on the written test as a whole, as well as on the open-ended test question.

During the interview, a student was presented with a test item on a card and asked to select an answer to the question. After the student selected one of the multiplechoice responses, the interviewer asked the student to explain what he or she thought about to determine the answer. Probing follow-up questions were used with students, when needed, for clarification of their responses. An outline of the interview structure with some examples of prompts and probing questions is located in the Appendix.

Analysis

For each grade level, the arithmetic mean and standard deviation for each part of the test, as well as the overall mean and standard deviation, were calculated. The range of individual student scores was determined for each part of the test and for the entire test.

Analysis of the responses to the open-ended question in Part 3 began with classifying student answers to the multiple-choice question comparing 87% of 10 to 10 (see Figure 2) as given by successful or unsuccessful performers. Thus, students who chose the multiple-choice response that 87% of 10 is less than 10 were classified as successful. The written explanations of each type of performer were classified using a category system which resulted from content analysis involving organizing data by identifying important examples and patterns. Through this process of content analysis, the data was organized into manageable categories which form a classification scheme (Patton, 1987). In developing the scheme, continual adjustments were made to verify the accuracy of the categories and the placement of data into categories.

The process of inductive analysis is one of analyzing data to identify patterns and themes (Patton, 1987). These patterns and themes are then used to organize the description of the data in a way that makes it manageable and meaningful (Patton, 1987). An inductive analysis was conducted on the interview data. Results

Multiple-Choice Test

The range, mean score and standard deviation shown in Tables 1 and 2 were determined for each of the three parts of the test and the entire test for grades seven and eight. For both grades, the mean scores were highest for Part 2 and lowest for Part 3. For each part of the test, as well as for the overall test, the mean scores of eighth-grade students were higher than the mean scores of seventh-grade students.