The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…

The effects of negative instances on the acquisition of the mathematical concepts of commutativity and associativity were examined. Also investigated were possible transfer effects that might result from the use of negative instances. For 64 ninth-grade subjects, results favored the treatments containing mixed instances and supported the transfer…

This study identified significant predictors of whether or not students completed a self-paced, mastery-oriented arithmetic course. Under varying conditions, a stepwise discrimination procedure identified 11 significant predictors. Precourse arithmetic computation achievement was the best while 7 others related to students' reasons for enrolling…

This study investigated whether reasoning ability improves with age and whether reasoning from negatively worded hypotheses is more difficult than from positively worded hypotheses. A 30-item logic test was constructed and given to elementary-school children and prospective elementary-school teachers. Only on certain forms was maturation a factor.…

Research reported during the 1973 calender year is listed, accompanied by brief annotations of findings. The listing is alphabetical by author within each of three categories: research summaries, journal-published reports, and dissertation abstracts. (Author/LS)

Twelve fourth-grade classes in two schools were taught division using either the subtractive approach to the Greenwood algorithm or a partitioning approach to the standard algorithm. Analysis of class means on immediate, retention, and delayed retention tests indicated that use of the standard algorithm was more effective. (JP)

This annual annotated listing of research pertaining to elementary and secondary school mathematics includes 13 research summaries, 71 journal-published reports, and 335 dissertations. (JP)

To help the reader understand the scope and diversity of the Wisconsin R & D Center's research effort in mathematics, four perspectives are presented: (1) the Center's approach to research, development, and practice; (2) the origins of the current research effort; (3) a description of current research; and (4) a projection for future research. (JP)

Second-grade students were randomly assigned to either an instructional unit within which addition and subtraction of two digit numbers were treated as a single integrated process of regrouping or one which developed the addition and subtractive algorithms sequentially. Periodic assessments favored the sequential approach, but differences were not…

Described is a method to assist developers of mathematics programs to make formative evaluations. The method involves periodic achievement testing via item sampling. Details of item construction, periodic testing, and profile construction are given in a discussion of how this method was applied to modify a sixth-grade mathematics program. (JP)

The ability of second- and third-grade students to learn unit-of-length concepts based on area and unit-of-area concepts was assessed. No significant aptitude treatment interactions were found on tests of achievement and retention. Significant results were found favoring the higher aptitude level and the treatment emphasizing the unit. (Author/JP)

A developmental sequence of stages in the representation of regular space figures, first obtained in Jamaica, was cross-validated on a U.S. sample. Discussion centers on the relation between representational ability and perceptual development and on the variation in the difficulty of drawing different figures. (Author/MK)

The interaction of two aptitude variables, field independence and general reasoning, with treatments that differed in sequence of instruction, was investigated using either an inductive or deductive appraoch to the learning of properties of equivalence relations. Significant interactions were found. (Author/MK)

Results of a survey concerned with basic skills on mathematics, conducted by the Instructional Affairs Committee of the National Council of Teachers of Mathematics, are given. A wide acceptance of a broad interpretation of "basic skills" was indicated. (MK)

This 12-week study examined attitudes and performance of 187 preservice elementary teachers on computational estimation and evaluated practice with and without instruction on specific mental estimation strategies. Analysis showed significant differences in estimation performance in favor of the groups receiving regular practice. (MK)