Describes the application of basic factor analytical and classical scaling techniques to mathematics placement test data that indicates that the sequence of mathematical skill areas traditionally taught in schools should be somewhat altered in order for students to reach optimal achievement levels. (FL)

This article presents a graduated word problem sequence in mathematics, beginning with simple words; progressing to phrases, sentences, and paragraphs; advancing to paragraph word problems with extraneous information; and finally having students create their own word problems. Results from 67 elementary students with learning disabilities support…

This study compared the effectiveness of 3 procedures for teaching 62 elementary students with learning disabilities to identify the correct algorithm in solving addition and subtraction word problems. The group receiving strategy teaching and sequencing practice problems and the group receiving strategy teaching only scored higher than…

Nine students (ages 7 to 11) with math disabilities were effectively taught using an instructional sequence that moved from the concrete to the semiconcrete to the abstract. Subjects needed between three and seven lessons using manipulative devices and pictures before being able to do abstract-level problems. (Author/DB)

A study was made of the effect of various learner and task characteristics on learning from scrambled frames in an instructional program. The independent variables were: sequence (scrambled vs. logical), grade, sequence length, criterion test complexity, sex, IQ, mathematics achievement, and reading comprehension. The dependent variables were:…

Discussed is a report of a British government advisory group concerning programs of study in mathematics education, as related to students with special education needs. Described are the progression of levels, the spread of levels normal for particular age groups, and the notion of age determining the work of students. (JDD)

The purpose of this study was to develop and evaluate procedures for validating a learning hierarchy from test data. An initial hierarchy for the computational skills of adding rational numbers with like denominators was constructed using Gagne's task analysis. A test designed to assess mastery at each of the 11 levels in this hierarchy was…

This study compared effectiveness of either a concrete-representational-abstract (CRA) or a representational-abstract (RA) instructional sequence in teaching fraction concepts to 50 middle school students with mathematics disabilities. On all achievement measures, students in the CRA group had overall higher mean scores than did students in the RA…

The effects of three variables on the difficulty of verbal arithmetic problems were examined. Variables included problem form, sequence of information, and problem verb. A total of 32 problems was generated, four in each of four problem forms and two sequences of information. Vocabulary words were not above second-grade level, and numbers used…

Engineering students use spatial thinking when examining diagrams or models to study structure design. It is expected that most engineering students have solidified spatial thinking skills during K-12 schooling. However, according to what we know about geometry learning and teaching, spatial thinking probably needs to be explicitly taught within…

Argues that reasons for teaching geometry before second-year algebra include higher student achievement and attitude and better abstract thinking. (PK)

At a middle school in suburban Pittsburgh, Pennsylvania, administrators and teachers used the cognitive domain of the National Association of Secondary School Principals' Learning Style Profile to design "products" that helped compensate for underachieving sixth and seventh graders' skill deficits in mathematics and science. Success…

This article presents the "concrete semiconcrete abstract" (CSA) teaching sequence for teaching basic math skills to students with and without learning disabilities. Guidelines include providing a minimum of nine instructional lessons (three at each level), each with four lesson steps. Validation of the CSA sequence and lesson format with 15…