The author clarifies his position regarding what features of the examples used by Kaminski, Sloutsky, and Heckler (2008a) constitute substantive differences affecting performance. I also reiterate my hesitancy to extrapolate their findings to the broader realm of mathematics.

Investigated were the effects of five verbalizing methods (subject speaks, reads, writes, listens, or does not verbalize) on short-term retention of the ability to use discovered generalizations. No significant differences were found among the effects of the verbalizing methods for a retention test. (JP)

A concrete and a symbolic approach to learning multiplication in the second grade are studied. The results, indicating that children using the symbolic model performed at a higher level than those using a concrete model, are discussed. (DT)

Self-instructional booklets containing the advance organizer, cognitive set, and post organizer varying according to experimental treatment were randomly assigned within nine Algebra 2 classes. Results showed a significant interaction between advance and post organizers: either one used separately facilitated learning and retention, but when used…

The performance of students from three intelligence levels at grades 4, 5, 6, and 7 on certain discovery tasks in arithmetics are examined. Results indicate that students should be given from 3 to 6 instances to make discoveries of the type tested and that students of lower intelligence levels can form generalizations. (FL)

Reported is a study which compared two instructional methods involving discovery learning and a verbal didactic instructional method. The verbal didactic method was significantly better for immediate learning; the verbal didactic method and a guided discovery method were better for retention. No differences were noted regarding transfer. (CT)

The effects of numerical and visual cues, equality or inequality of initial volumes, size of measurement unit, and order of cue presentation on conservation of liquid volumes by first- and second-graders were investigated. Some findings extend, and others contradict, those of Piaget. (SD)

The influence of artistic style and number of pictures was investigated relative to the ability to associate these pictures with the addition and subtraction of whole numbers. (MP)

The authors concede that thinking strategies are important, but argue that instruction in these strategies may not be warranted. (MK)

The author defends the teaching of thinking strategies. (MK)

A general discussion of thinking strategies is given and researchable questions related to thinking strategies are presented. (MK)

Self-instructional booklets varying advance organizers, post organizers, and knowledge of behavioral objectives according to experimental treatment were used with 348 eighth graders and 259 preservice elementary education students. A significant interaction between the advance and the post organizers was found on one learning test. Students scored…

Performance of first and second graders on measurement problems indicated that they are unable to relate the measurements of objects using different units to visual comparisons of quantities. (SD)

The fraction concept was analyzed to yield 16 subconcepts which are hypothesized to be hierarchically ordered. This ordering was tested using subjects in grades 4 through 6, and 18 of 23 dependencies hypothesized were confirmed. (SD)

Research designed to determine whether the phenomena observed by Piaget were task specific was performed. The results did not confirm Piaget's notion that topological concepts develop prior to the concepts of Euclidean geometry. (SD)