The nature of the development of arithmetic performance has long been intensively studied, and available scientific evidence can be evaluated and synthesized in light of Nelson and Narens' model of metacognition. According to the Nelson-Narens model, human cognition can be split into two or more interrelated levels. Obviously, in the case of more…

Proficiency in mathematics across the United States has become an area of concern as performance on state accountability tests continues to demonstrate that less than 50% of students in 4th and 8th grade are proficient in mathematics (NCES, 2013). With such large numbers of students lacking proficiency in mathematics, systematic interventions that…

This study investigated the role of cognitive interventions on word problem solving (WPS) accuracy in children who are English learners (ELs) and at risk for math difficulties (MD). Grade 3 children (n = 158) within classrooms were randomly assigned to either an untreated control group or one of three treatment conditions: paraphrase question…

This study compared the performances of college mathematics students on mathematics problems stated in three different contexts: in arithmetical form, in the form of algebraic expressions to be simplified, and in the form of practical situations stated in words. Both single-step and multi-step problems were used. For all three contexts, there were…

Measure Up is a research and development project that uses findings from Davydov (1975) and others to introduce mathematics through measurement and algebra in grades 1-3. This paper illustrates the use of generalized diagrams and symbols in solving word problems for a group of 10 children selected from a grade 3 Measure Up classroom. Students use…

Investigated is whether children would spontaneously model problems with superfluous information and whether their modeling would facilitate problem solving. Included are the addition/subtraction story problems used in this study, introduction, method, results, discussion, and conclusions. (KR)

This study investigated children's ability to interpret a natural social situation, depicted in a narrative story, and to use their understanding of that situation to generate and apply a mental model of debts and assets in solving problems including negative quantities. Fifty-one American students from a parochial school in a predominantly middle…

Applications of generalizations of both arithmetic and geometric progressions are presented. The first-order difference equation is used in solving seven examples from finance, business, and medicine. Detailed directions are included for each example. (KR)

Discusses the role of teacher questioning in the development of a child's concepts of and about mathematics. Proposes the development of mathematical concepts and procedures in problem-solving situations through questioning that engages student thinking and decision making. (MDH)

Describes seven number-sense skills for elementary and middle school grades. Provides eight short stories for grades three through eight designed to develop students' number-sense skills in which students replace missing data so that the story makes sense. (MDH)

Children's (n=70) solution strategies to a variety of multiplication and division word problems were analyzed to determine performance levels and strategies used. Solution strategies were classified at three levels: direct modeling with counting; no direct modeling with counting, additive, or subtractive strategies; and use of known derived facts.…

Although many common problem-solving errors within the realm of school mathematics have been previously identified, a compilation of such errors is not readily available within learning disabilities textbooks, mathematics education texts, or teacher's manuals for school mathematics texts. Using data on error frequencies drawn from both the Fourth…

Presents a study of 87 second graders to demonstrate that achievement tests in primary mathematics emphasize pupil's lower-order thinking by comparing answers to interview questions from constructivist and traditionally instructed groups. Results indicated that constructivist instructed students demonstrated superior higher-order thinking on tasks…

Does conceptually oriented instruction jeopardize students' computational competence? If it does, then why are so many reform efforts continuing to emphasize the importance of teaching for conceptual understanding? If it does not, then why are the majority of teachers at all grade levels continuing to teach for computational competence without…