In current teaching materials, when using Dedekind cuts to construct real numbers, the definition of a Dedekind cut is always involved in defining addition and multiplication. In this paper, as it is done in many current textbooks, Dedekind cuts are used to construct the set of real numbers. Then the order in it is defined, and the…

Students encounter mathematics word problems as early as kindergarten and continue to see them throughout their schooling experience. Schema instruction with an attack strategy can support students to successfully navigate word-problem solving. Schemas help students categorize word problems by similar characteristics. To better support students…

As students develop understanding and fluency in single-digit operations such as addition, they develop sophisticated strategies and number sense (magnitude, number order, and composition). Deficits in number sense and reliance on inefficient approaches can lead to struggle in mathematics. Intervention research in this area reported effects on…

Strategic incremental rehearsal (SIR) is an efficacious flashcard intervention shown to improve foundational skill acquisition. However, there is limited research examining the feasibility and effectiveness of SIR when used by school-based implementers. We present two studies to address this limitation. Study 1 examined the effects of SIR…

In this writing, I report on how two 12-year old children used fraction strips to add 1/2 and 2/5. In their interaction with the tool, I look for the emergence of the tool-mediated Zone of Proximal Development to analyse the knowing that become available to the children. In thinking about this interaction, I ask what is the role of the more…

The aim of this study is to determine the effect of the emotion "happy" as induced by colors on the addition performance of grade 1 pupils. The experiment involved the pupils in the experimental group (n=80) were taught addition, using modules developed by the researcher which utilized seductive augmentation of learning materials through…

The present mixed-methods quasi-experimental study (embedding a case study and a mixed factorial within-between ANOVA test), conducted in a private English school in Limassol, Cyprus, investigated how the use of the schematic learning aids (researcher-made color-coded flash-cards and grids) influence year-2 children's ability to read, write and…

The author explains how "structured material such as the Colour-Factor Set can show all the properties, patterns and characters of numbers. Given the mastery over numbers with which these materials provide children, he condemns teachers who require children "to learn multiplication tables by rote and the so-called four rules by…

This booklet, one of a series, has been developed for the project, A Program for Mathematically Underdeveloped Pupils. A project team, including inservice teachers, is being used to write and develop the materials for this program. The materials developed in this booklet include (1) the addition and subtraction of whole numbers on the number line,…

In the winter of 1965, an experimental course in Elementary Number Theory was presented to a 6th grade class in the Hosmer School, Watertown, Massachusetts. Prior to the introduction of the present material, students had been exposed in class to such topics from the University of Illinois Arithmetic Project as lattices, number lines, frame…

The second in a series of three workbook texts on beginning algebra. Designed primarily for use by lower ability mathematics students, the texts have been used by average ability students as supplementary materials. Volume 2 contains material on operations, variables and phrases, equations, exponents equivalent phrases, terms, and adding like…

A problem about minimum distance travelled on a route through ten cities is used as a means for giving students practice in addition and with problem-solving skills. (DT)

Presented are two self-contained worksheets and teacher guides for open-ended experiences in recording and reading data which require the use of basic addition facts. One is for grades 1-3; the other for grades 4-8. (CT)

Discusses a tally device using discs on a paper diagram. Instructions given for number representation, negative values, games, addition and subtraction. (RS)