Learning the concept of perimeter and area is not easy for students in grade 3 of primary school. A common mistake is that students think that if the area is the same, the perimeter also has to be the same. It is difficult for them to understand that for a given area, there are many possibilities of perimeter and vice versa. When student are not…

The meaning of fractions with integer multiplication is something that is difficult to understand by students. They tend to think that the product it produces a larger number, while the multiplication of fractions with integers, the result can be any number larger or smaller. This study is a research design that aims to develop a local…

Research documents an income-based achievement gap in mathematics, yet children from lower-income backgrounds do not lag behind their more advantaged peers in high-level social reasoning tasks. The purpose here was to investigate whether modifying mathematics word problems to make them more socially based would impact the mathematics performance…

This study examined whether a story/language based method of teaching the multiplication facts would be helpful to students who previously had difficulty with the memorization of those facts. Using the curriculum "Memorize in Minutes" by Alan Walker (Walker, 2000), the researcher taught six fourth-grade students the multiplication facts (3s…

This paper discusses the impact of action research methodology used in the teaching and learning process and professional teacher development. In this study are including 58 students of three second grade classes, 3 teachers of those classes and a university professor. Aiming at using a different approach in their teaching of multiplication and…

Teaching students how to multiply fractions is challenging, not so much from a computational point of view but from a conceptual one. The algorithm for multiplying fractions is much easier to learn than many other algorithms, such as subtraction with regrouping, long division, and certainly addition of fractions with unlike denominators. However,…

The main purpose of the present study was to examine the long-term effects of a previous quasi-experiment that used inner speech as a tool to promote appropriate strategies in multiplication. Results one year after the intervention were published by Ostad and Askeland. This is a follow-up study. The 50-week intervention program was conducted in…

The author has been prompted to write this article about finger multiplication for a number of reasons. Firstly there are a number of related articles in past issues of "Mathematics Teaching" ("MT") which have connections to this algorithm. Secondly, very few of his primary teaching students and professional colleagues appear to be aware of the…

A multiple-probe-across-problem-sets (tasks) design was used to evaluate the effects of the Detect, Practice, and Repair (DPR) on multiplication-fact fluency development in seven third-grade students nominated by their teacher as needing remediation. DPR is a multicomponent intervention and begins with a group-administered, metronome-paced…

Educational systems throughout the world serve students from diverse populations. Often students from minority populations (i.e. racial, ethnic, linguistic, cultural, economic) face unique challenges when learning in contexts based on the cultural traditions and learning theories of the majority population. These challenges often leave minority…

We give an irredundant axiomatization of the complete ordered field of real numbers. In particular, we show that all the field axioms for multiplication with the exception of the distributive property may be deduced as "theorems" in our system. We also provide a complete proof that the axioms we have chosen are independent.

A multiple baseline design was used to evaluate the effects of a modified Detect, Practice, and Repair (DPR) procedure on multiplication-fact fluency with 10 low-achieving 5th-grade students. Experimenters modified the DPR procedure using Microsoft[C] PowerPoint[C] slide shows to conduct the assessments and allow for more rapid self-evaluation in…

This note presents demonstrations of mathematics that emerges when problems are posed with respect to a combined 12 x 12 multiplication table showing multiplier and multiplicand. Through processes such as recognizing and extending patterns, specializing and generalizing particular functional relationships between the diagonal and row sequences are…

In two experiments, we studied how people's strategy choices emerge through an initial and then a more considered evaluation of available strategies. The experiments employed a computer-based paradigm where participants solved multiplication problems using mental and calculator solutions. In addition to recording responses and solution times, we…

The study explored the effects of a computer-assisted COnceptual Model-based Problem-Solving (COMPS) program on multiplicative word-problem-solving performance of students with learning disabilities or difficulties. The COMPS program emphasizes mathematical modeling with algebraic expressions of relations. Participants were eight fourth and fifth…