Describes the success, the methods (mental, informal written, standard algorithm) and the strategies of informal written arithmetic to be observed when 300 elementary students worked on six addition and six subtraction problems with three-digit numbers. (Author/MM)

Assesses two aspects of the validity of verbal reports in children's subtraction: reactivity and veridicality. Results reveal that students were able to able to provide veridical strategy reports, and that the instruction to verbally report had few effects on task performance. Informal findings indicate that students had less difficulty reporting…

Most of the research on mathematical and scientific thinking has been concerned with uncovering knowledge structures and reasoning processes in people of different levels of competence. How these structures and processes are acquired has only recently become a major concern. Thus, some of the major research on mathematical and scientific thinking…

A study asked 24 first grade children from 3 different classes to write number sentences and select appropriate alternative number sentences for addition and subtraction word problems. Results indicated that children could be characterized into five clusters according to their flexibility in accepting alternative number sentences and that…

Investigates issues of conceptual understanding in teaching and learning mathematics provided conceptually based instruction on place value and two-digit addition and subtraction without regrouping in four first grade classrooms. Conventional textbook-based instruction was provided in two first grade classrooms. Experimental-group students scored…

Describes research which compared the processing loads of mathematical representations and strategies used by (n=3) teachers and (n=29) children aged 5-8 for interpreting subtraction operations represented in numerical form. Some representations and strategies appeared to impose an extra processing load which can interfere with conceptual…

After a year of instruction, 70 kindergarten children were individually interviewed as they solved basic, multistep, and nonroutine word problems. Thirty-two used a valid strategy for all 9 problems, and 44 correctly answered 7 or more problems. Modeling provided a unifying framework for thinking about problem solving. (Author/MDH)

Prior research on learning has been linked to instruction by the derivation of general principles of instructional design from learning theories. However, such design principles are often difficult to apply to particular instructional issues. A new method for relating research on learning to instructional design is proposed: Different ways of…

Suggests that children enter school with a great deal of informal intuitive knowledge of mathematics that can serve as the basis for developing much of the formal mathematics of the primary school curriculum. Describes a research-based model of children's thinking that teachers can use to interpret, transform, and reframe their informal or…