skip to main content skip to footer

Mathematics Items With Hints

Trismen, Donald A
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Guessing Tests, High School Students, Mathematics Tests, Multiple Choice Tests, Problem Solving, Test Construction


A set of 40 mathematics items was developed, intended for high school students who had completed at least one high school course in each of algebra and plane geometry. The items represented relatively unstructured problem situations, and each was supplemented by a sequence of hints which would progressively structure the problem for the examinee. A subset of nine of the items was rewritten, replacing the original hints with multiple-choice question hints. The rewritten items were administered to a group of 107 examinees, using latent image materials. This report describes the characteristics of hints, their relationships to the items they accompany, and their effectiveness in helping examinees to answer the item correctly. Its primary aim is to examine the function of hints in the problem-solving process. Three major findings were suggested: 1. The use of hints increases the percentage of correct answers to an item, regardless of whether the hints themselves are answered correctly. 2. The presentation of an open-ended item, recast in multiple-choice format, can, in some instances, act as a hint. 3. Answering hints correctly is related to answer- ing the item correctly when a specific examinee misconception of the problem is involved. (83pp.)

Read More