Interpreting Test Results

This page gives a detailed explanation of the test results. At the end are links that you can use to download PDF files (click here to get Acrobat Reader):

• The sample Test Results file is a set of test results for a class.
• The sample Student Letter is the letter that is printed for each student.
• The Test Analysis Worksheet document is a worksheet (3 pages) that you might find very useful in analyzing your class test results.

The Test Results Report begins with several pages of summary information intended to be used primarily by the class instructor. These pages are followed by a set of individual student letters. Each student should be given his or her own letter and encouraged to discuss the results with the instructor and parents.  Students should keep the letter for possible later use in tutorials or specially designed summer courses that may allow them to concentrate on those topics needing review.

Each summary information page contains the name of the school, the instructor, the course, test date, and test type. This information is provided by the instructor when the answer sheets are sent to the scoring center. The instructor should have a copy of the test available when reviewing the Test Result Report.

·  Class Results - The class averages on each topic and on the entire test are reported on the Class Results page. These averages are expressed both as raw scores and as percentages. The mastery level is reported for each topic, and for the number and the percentage of students scoring at or above the mastery level for each topic.

The information reported on the Class Results page provides some indication of the class's overall level of preparedness for the next mathematics course and in each of the topics of the test. The topic results may be helpful in identifying topics where further review is needed or where ways to strengthen the curriculum might be sought. They also provide an indication of which topics to examine first on the following page in the report. The total score may be useful to indicate the level at which the next course should begin.

·  Graphic Display of Class Results - The Graphic Display of Class Results page contains bar graphs indicating the percentage of students in the class answering each item correctly. These graphs are grouped by the topics of the test. Within each topic, the graphs are ordered by the percentage of students correctly answering each item. The graphs show the relative difficulty for the class of each item. The bar graphs provide a quick way of identifying those items that were most difficult for a class. These more difficult items might be examined first on the following page in the report. Similarly, the bar graphs provide a quick way of identifying the items and topics where the students did best, and thus, where the curriculum and instruction is working most successfully.

·  Item Analysis - The Item Analysis page reports the performance of the class on each item in the test. The results are presented in terms of both the number of students and the percentages of students choosing each response. We recommend that each reader of these reports concentrate on whichever form (number or percentage) seems more appropriate. We will discuss only the percentage report since the discussion for number would be virtually the same.

The following information is listed for each item: the item number; the key (i.e., the correct response for the item); the topic of the item (or a code for the topic, the codes are listed on the cover letter of the report); the percentage of students who did not select any of the possible answers for the item (or "omits"); and, for each possible response (A) through (E), the percentage of students who selected that response. An asterisk appears with the percentage of students who selected the correct answer. The Item Analysis page can provide very detailed information about the students' ways of working problems. We suggest that the previous pages be used to identify items of special interest to be examined first. Often, analysis of common wrong responses will indicate types of errors students have made.

An example of the kind of analysis that can be made is as follows:

Suppose that the following appeared for item #43:

The popularity of response (C) suggests that most of the students converted the denominator to before inverting and multiplying. It appears that they are still adding fractions by adding denominators instead of first finding a common denominator. Another explanation may be that each term in the denominator was first inverted, giving a - b and then the result inverted and multiplied to yield (C). In any case, an analysis of the students' responses to this item would show that a large percentage of students are having difficulty with literal fractions.

Individual Student Results - The Individual Student Results page gives summary information about each student's performance on the test. This information includes the total number of items that the student answered correctly, and the number of items to which the student responded. An asterisk appears with each score that is below mastery level. The number of items attempted and the last item attempted may provide some indication of the extent to which a student has difficulty in finishing the test rather than in solving certain problems on it.

Individual Student Letters - Following the summary information reporting the class results as a whole, are individual, one-page letters addressed to each student in the class. These letters give the student his or her total score on the test along with scores in each topics. Further, the topics are separated into those in which the student scored at or above mastery level, those in which the student needs some review, and those in which the student needs substantial review.

Click here to download:

The sample Test Results: TestResults.pdf

The sample Student Letter: StudentLetter.pdf

The Test Analysis Worksheet: TestAnalysis.pdf