In this technological age, digital devices are conspicuous examples of extraordinary complexity. When a user clicks on computer icons or presses calculator buttons, these devices channel electricity through a complex system of decision-making circuits. Yet, in spite of this remarkable complexity, the hearts of these devices are components that…

Using the concept of exploded and compressed numbers the author constructs the supercone which is able to turn upon the border of three dimensional space and breaks through it. The introduction of super-cone gives a possibility for students to see the properties of traditional cone while the super-cone is not a traditional cone. Moreover we show…

Recent studies on nonsymbolic arithmetic have illustrated that under conditions that prevent exact calculation, adults display a systematic tendency to overestimate the answers to addition problems and underestimate the answers to subtraction problems. It has been suggested that this "operational momentum" results from exposure to a…

There is a very natural way to divide a four-digit number into 2 two-digit numbers. Applying an algorithm to this pair of numbers, determine how often the original four-digit number reappears. (Contains 3 tables.)

In the September 2010 issue of "Mathematics Teaching," Tom O'Brien offered practical advice about how to teach addition, subtraction, multiplication, and division and contrasted his point of view with that of H.H. Wu. In this article, the author revisits Tom's examples, drawing on his methodology while, hopefully, simplifying it and giving it…

This paper illustrates that the psychometric properties of scores and scales that are used with mixed-format educational tests can impact the use and interpretation of the scores that are reported to examinees. Psychometric properties that include reliability and conditional standard errors of measurement are considered in this paper. The focus is…

Research literature is reviewed, identifying a need to design instruction to support multi-digit mental computation and critiquing conventional place value instruction. A distinctive instructional domain is proposed, called conceptual place value (CPV)--incrementing and decrementing numbers by units of ones, tens and hundreds. A design research…

Active student responding (ASR) has been shown to be an effective way to improve the mathematical skills of students. One specific method of ASR is the use of response cards. In this study, a system of least prompts combined with response cards was used to increase mathematical knowledge, and number identification, of three elementary students…

Recognizing the role numbers play in people's everyday lives is crucial to students' math understanding now and down the road. That's why Bob Krech, a curriculum specialist in New Jersey's West Windsor-Plainsboro district, likes to teach a lesson he calls "Numbers All Around Us." This lesson uses real-world examples to show that numbers…

This article shows how Yup'ik cosmology, epistemology, and everyday practice have implications for the teaching of school mathematics. Math in a Cultural Context (MCC) has a long-term collaborative relationship with Yup'ik elders and experienced Yup'ik teachers. Because of this long-term ethnographically-oriented relationship, the authors--both…

The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. When absolute value problems become more complex, students often do not have sufficient conceptual understanding to make any sense of what is happening mathematically. The authors suggest that the…

Even when two-digit numbers are irrelevant to the task at hand, adults process them. Do children process numbers automatically, and if so, what kind of information is activated? In a novel dot-number Stroop task, children (Grades 1-5) and adults were shown two different two-digit numbers made up of dots. Participants were asked to select the…

In this article, the authors discuss their approach to column addition and subtraction algorithms. Adapting an original idea of Paul Cobb and Erna Yackel's from "A Contextual Investigation of Three-Digit Addition and Subtraction" related to packing and unpacking candy in a candy factory, the authors provided an analogous context by…

This research investigates similarities and differences in young children's early numeracy skills related to age, nationality and gender. The participants were five- to seven-year-old children from Finland and Iran. Early numeracy was investigated by using tasks measuring number-related relational skills (e.g. comparison, one-to-one…

The purpose of this causal-comparative study was to examine whether differences exist in the mathematics achievement of fifth grade gifted students based on the instructional delivery model used for mathematics instruction, cluster or collaborative, as defined by the Georgia Department of Education. The content area of mathematics, an area…