This research was concerned with the clarification of the role that the external representation process (e.g. drawing) plays in children's solving of complex arithmetic problems. Fourteen children in the 10- to 12-year-old age range were asked to represent and solve five complex arithmetic problems (three with temporal organization of data, two…

This paper discusses new psychometric analyses that improve capabilities for relating performance on achievement test items to instruction received by examinees. The modeling discussion is closely tied to data for eighth graders in the United States provided by the Second International Mathematics Study (SIMS), comprising not only responses to a…

This book provides elementary and middle school teachers with practical ideas on the use and teaching of graphs. Five sections consist of: (1) "Graphs--What Are They and How Are They Used?"; (2) "Levels of Graph Comprehension"; (3) "Collecting, Organizing, and Analyzing Data"; (4) "Constructing, Interpreting, and Writing about Graphs"; and (5)…

Mathematics competitions are a popular extracurricular activity for students at all grade levels. This booklet outlines some of the logistical and structural issues that competition organizers, administrators, coaches, and question writers face when they incorporate calculators into their competitions. Main topics included are: (1) "Decisions…

The issue of parallel forms is of paramount importance for producers of standardized tests. With increasing emphasis being placed on standardized test results it is necessary that each student achieve the same standard score regardless of the form he or she was administered. In the case of the American College Testing (ACT) Assessment Program,…

In item response theory (IRT), preequating depends upon item parameter estimate invariance. Three separate simulations, all using the unidimensional three-parameter logistic item response model, were conducted to study the impact of the following variables on preequating: (1) mean differences in ability; (2) multidimensionality in the data; and…

Open-ended individually administered questions can ascertain whether students can reason about arithmetic problems. Free response test items are useful in assessing students' thought processes as they solve mathematics story problems. Since story problems do not state explicitly which arithmetic operations are required for solution, students must…

This test for third grade students in Alberta, Canada, consists of two sections. Section I is divided into two parts: Part A has 25 questions covering numeration, geometry, and graphing, and part B has 25 questions covering operations and properties, measurement, and problem-solving strategies. Section II consists of four basic-fact tests in…

The purpose of this paper is to present two new alternative methods to the current goodness of fit methodology. With the increase use of computerized adaptive test (CAT), the ability to determine the accuracy of calibrated item parameter estimates is paramount. The first method applies a normalizing transformation to the logistic residuals to make…

The practical use of such concepts as sets, probability and statistics are considered by many to be vital and necessary to our everyday life. This student manual is intended to familiarize students with these concepts and to provide practice using real life examples. It also attempts to illustrate how the insurance industry uses such mathematic…

A method for obtaining curriculum-based estimates of student achievement is described. These estimates can be obtained through the use of a set of curriculum weights designed to reflect student opportunity to learn. If the match between the presented curriculum and test content is low, then the curriculum weights can be used to minimize potential…

This is the final test for students in the twelfth grade course Mathematics 30, offered in schools in Alberta, Canada. Intended for administration in 1988, it is available in both English and French. It contains 52 multiple-choice questions and 3 written-response problems, with 2.5 hours allowed for completion. Approved calculators may be used.…

This pilot test for ninth grade mathematics is written in both French and English. The test consists of 75 multiple-choice items. Students are given 90 minutes to complete the examination and the use of a calculator is highly recommended. The test content covers a wide range of mathematical topics including: decimals; exponents; arithmetic word…

This achievement test for ninth grade mathematics is written in both French and English. The test consists of 75 multiple-choice items. Students are given 90 minutes to complete the examination, with the use of calculators permitted. The test content covers a wide range of mathematical content including: positive and negative exponents; word…

The Provincial Assessment of Mathematics was conducted at grades 3, 6, 9 and 12. There are three major components to the assessment: (1) a written test of the curriculum objectives carried out in May, 1987 for grades 3, 6, and 9, and in June, 1987 for grade 12 (Mathematics 300 and Mathematics 301); (2) a survey of teachers at these grade levels;…