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Major Field Achievement Test (MFAT) in Mathematics

The Major Field Test in Mathematics consists of about 50 questions, some of which may be grouped in sets and based on such materials as diagrams and graphs. The questions are drawn from the courses of study most commonly offered as part of an undergraduate mathematics curriculum.

ETS website

Test Description from the ETS website

Sample test questions from the ETS website

Spring 2015: Friday, May 1st, 2:00pm - 4:30, Kayser Hall Computer Lab, room 541

Major Field Tests Description
(from the Program Manual, ETS Higher Education Assessment, Educational Testing Service, Princeton, NJ, 1994, pp.5-7)

Assessing student outcomes in higher education has received increasing emphasis and attention in recent years. Outcomes assessment has been defined in variety of ways, from measuring student progress in general education programs to assessing learning at graduation to evaluating postgraduate activities and trying to relate success in career goals and objectives of a college or university. No matter how broad the definition of outcomes assessment, a key element for most institutions is that it is a way to evaluate student academic achievement and growth. It was in response to these concerns--specifically, the need voiced by undergraduate institutions for valid, reliable measures of the outcomes of instruction in the disciplines--that Educational Testing Service (ETS) and the Graduate Record Examinations (GRE) Board developed the Major Field Tests.

Background and Development:
The Major Field Tests are objective, end-of-program tests in 14 disciplines. Based on the Graduate Record Examinations Subject Tests, they have been shortened to two hours each, made less difficult than the GRE tests, and revised to reflect undergraduate programs and to be appropriate for all seniors majoring in a field, not just those planning graduate study. (Since there is no GRE Subject Test in Business, the Major field Test in Business is based on a complete revision of the Undergraduate Assessment Program Business Test.) Scores on these tests provide useful information for institutions seeking outcomes measures, for departments in evaluating their curriculum, and for faculty in measuring the progress of their students and considering curriculum changes. The major Field Tests provide reliable data for individual and group measurement at the undergraduate level by assessing student learning in major fields of study. Major Field Tests are available for the following disciplines: biology, business, chemistry, computer science, economics, education, history, literature in English, mathematics, music theory and history, physics, political science, psychology and sociology.

Test Content:
The content specifications for the Major Field Tests reflect the basic knowledge and understanding gained in the undergraduate curriculum. They have been designed to assess the mastery of concepts, principles, and knowledge expected of students at the conclusion of a major in specific subject areas. In addition to factual knowledge, the tests evaluate students' ability to analyze and solve problems, understand relationships, and interpret material. They contain questions that call for information as well as questions that require interpretation of graphs, diagrams, and charts based on material related to the field.

Test Construction:
The Major Field Tests were constructed according to specifications similar to the specifications for the current GRE Subject Tests, which are developed and reviewed by committees of experts in each subject area. ETS test development specialists assembles the Major Field Tests using questions that had been used in GRE Subject Tests and other questions written by subject matter experts. The complete tests and the specifications were then reviewed by selected experts in appropriate subject matter areas both during the development process and before the pilot testing. The test development process included an extensive review of each test to eliminate language, symbols, or content considered to be potentially offensive, inappropriate for any subgroups of the test-taking population or serving to perpetuate any negative attitudes that may be conveyed to these subgroups. After the tests were administered during pilot administrations, each test underwent a rigorous statistical analysis to see whether each question yielded the expected result. Such an appraisal sometimes reveals that a question is not satisfactory. A question that proves to be ambiguous or otherwise unsuitable is not used in computing scores. The tests will be reviewed periodically for currency, and they will be revised and updated with the aid of expert consultants, as required. Statistical properties of each question, such as difficulty level and degree of correlation with the total score, are on record or are computed when new or revised test forms are first administered to help ensure that each question contributed meaningfully to the test results. For each test, the aim is to provide an instrument that measures the subject matter and skills a student is expected to have mastered in the undergraduate program.

Three types of scores are provided for the Major Field Tests:

  • Individually Reliable Total Scores - Each test yields an individually reliable total score for each student. An individually reliable score is one with statistical properties such that decisions about individual students can be made based on the scores. The length of the test and content coverage are factors in determining score reliability. Total scores are reported on a scale of 120-200.
  • Individually Reliable Subscores - Five of the tests, Biology, Economics, History, Music, and Psychology yield individually reliable subscores for each student (in addition to the total score). Subscores represent achievement in broad areas within the field reflecting students' strengths or weaknesses by area within their major. Subscores are reported on a scale of 20-100.
  • Group-Reliable Scores - Known as Assessment Indicators in the Major Field Tests, these scores relate to a subfield within a major field of study (e.g., Methodology and Statistics as a subfield of Sociology). Since only group data are involved, assessment indicators need not meet the more stringent statistical requirements for individually reliable scores. Assessment indicator scores are reported as mean percent correct for the department. By obtaining data on the performance of total groups of students (all Sociology majors at an institution, for example), it is possible to report group scores on the reduced number of test questions that constitute the assessment indicators. A minimum of five students is required for any test in order for assessment indicators to be reported. Assessment indicators are not reported for individual students. The assessment indicator approach to academic outcomes measurement increase an institution's ability to examine the performance of groups of students on various elements of the curriculum and enables a department to disregard results from an area covered by the test but not by the curriculum.