Even though there is a great temptation as teachers to share what is known, many are aware of an idea called "rules that expire" (RTE) and have realized the importance of avoiding them. There is evidence that students need to understand mathematical concepts and that merely presenting rules to carry out in a procedural and disconnected…

This paper uses a post-qualitative philosophical perspective to find new ways of understanding teaching and learning. The paper presents a series of examples that were used in a longitudinal study, with the aim of creating variation patterns that would make it possible for students to discern the use of the four basic arithmetic operations in…

Math fluency, which refers to the ability to solve single digit arithmetic problems quickly and accurately, is a foundational mathematical skill. Recent research has examined the role of phonological processing, executive control, and number sense in explaining differences in math fluency performance in school-aged children. Identifying the links…

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

Over the last two decades, students in Singapore consistently scored above students from other nations on the Trends in International Mathematics and Science Study (TIMSS; Provasnik et al., 2012). In contrast, students in the United States have not performed as well on international and national mathematics assessments and students with…

Describes two experiments that investigate how "buggy algorithms" in multi-digit subtraction are used. The first experiment tested third grade students (N=110) and repeated the test two years later. The second experiment tested students in grades 3-6 (N=301). Contains 21 references. (DDR)

Reports research designed to explore the possibility that conceptually different forms of common-fraction understanding can be identified. Such forms may be associated with differences in fraction problem solving-performance. Contains 50 references. (DDR)

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in pre-algebra from the Moebius strip to the googol. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally on concerns for…

Hypothesizes that the incidence of process-oriented thinking increases with the syntactic complexity of the problem presentation. Presents data confirming students' arithmetic preferences in the form of left-to-right translation along with evidence to show the effects of the ordering of data presentation in the problem statements on the…

Presents activities related to some obscure tests for divisibility, which teachers may wish to develop as illustrative examples in the classroom, or as extension activities for groups of students. Begins with an exploration of divisibility by three, then discusses application of the technique to other numbers, and for numbers written in other…

The relation of knowledge for solving problems to understanding of general principles in a subject-matter domain is discussed. Theoretical representations, called "conceptual competence," are presented to represent principles that are believed to be understood implicitly by individuals. Implications for problem-solving procedures can be…

The study with 989 learning-disabled students supported the cognitive-based arithmetic problem-solving model of Dinnel et al. under continuous visual stimulus conditions but suggested a more complex neuropsychological underpinning to arithmetic performance in both visual and aural stimulus conditions. (Author/DB)

This book is one in a series of teacher resource books developed to: (1) rescue students from the clutches of computers that drill and control; and (2) supply teachers with computer activities compatible with a mathematics program that emphasizes investigation, problem solving, creativity, and hypothesis making and testing. This is not a book…

Children between the ages of 10 and 13 were asked to write stories to accompany five computational problems. Stories were scored for suitability and it was found that students were most successful on subtraction and least successful on multiplication stories. Scores on this test correlated with mathematics achievement scores. (SD)