This note generalizes the formula for the triangular number of the sum and product of two natural numbers to similar results for the triangular number of the sum and product of "r" natural numbers. The formula is applied to derive formula for the sum of an odd and an even number of consecutive triangular numbers.

The SNARC (spatial-numerical association of response codes) effect refers to the finding that small numbers facilitate left responses, whereas larger numbers facilitate right responses. The development of this spatial association was studied in 7-, 8-, and 9-year-olds, as well as in adults, using a task where number magnitude was essential to…

In synesthesia, stimulation of one sensory modality leads to a percept in another nonstimulated modality, for example, graphemes trigger an additional color percept in grapheme-color synesthesia, which encompasses the variants letter-color and digit-color synesthesia. Until recently, it was assumed that synesthesia occurs strictly unidirectional:…

Several new and sharp inequalities involving the constant e and the sequence (1 + 1/n)[superscript n] are proved.

R. Sekuler, P. Tynan, and E. Levinson (1973) found that when 2 characters are presented side-by-side with a short onset asynchrony, subjectively they often appear in a "first-left, then-right" order. The authors of this article conducted 6 experiments in which observers judged the temporal order (TOJs) in which 2 digits were presented. They found…

Previous research has shown that time to name single-digit Arabic numbers is about 15 ms slower when naming trials are interleaved with simple multiplication (e.g., state product of 2 x 3) than when naming digits is interleaved with magnitude comparison (e.g., state larger; 2 [arrow up] 3). To explain this phenomenon, J. I. D. Campbell and A. W.…

While there is convincing evidence that preverbal human infants and non-human primates can spontaneously represent number, considerable debate surrounds the possibility that such capacity is also present in other animals. Fish show a remarkable ability to discriminate between different numbers of social companions. Previous work has demonstrated…

It is known that the ratios of consecutive terms of Fibonacci and Tribonacci sequences converge to the fixed ratio. In this article, we consider the generalized form of Tribonacci numbers and derive the "golden proportion" for the whole family of this generalized sequence. (Contains 2 tables.)

The purpose of this study was to examine the effects of a Tier 2 supplemental intervention focused on rational number equivalency concepts and applications on the mathematics performance of third-grade students with and without mathematics difficulties. The researcher used a pretest-posttest control group design and random assignment of 19…

One tool for enhancing students' work with data in the science classroom is the measure line. As a coteacher and curriculum developer for The Inquiry Project, the author has seen how measure lines--a number line in which the numbers refer to units of measure--help students not only represent data but also analyze it in ways that generate…

This article highlights investigating intriguing number patterns utilising an emerging technology called the Square Tool. Mathematics teachers of grades K-12 will find the Square Tool useful in making connections and bridging the gap from the concrete to the abstract. Pattern recognition helps students discover various mathematical concepts. With…

Elementary school teachers are responsible for constructing the foundation of number sense in youngsters, and so it is recommended that teacher-training programs include an emphasis on number sense to ensure the development of dynamic, productive computation and estimation skills in students. To better prepare preservice elementary school teachers…

As young children make sense of mathematics, they begin to see with new eyes. What once was uncertain may now be determined. Objects become countable; fingers become tools; and numbers become more than just names. Educators revel in such developments--which mark significant progress toward more sophisticated understanding of number--and work…

Neuropsychological and functional imaging studies have associated the conceptual processing of numbers with bilateral parietal regions (including intraparietal sulcus). However, the processes driving these effects remain unclear because both left and right posterior parietal regions are activated by many other conceptual, perceptual, attention,…

As part of an NCETM project, the author is involved with three local schools investigating how engaging in role play might aid children's mathematical development. The project embraces children ranging from part-time Reception to Y4. In this extract, two Reception-age girls, Rachel and Connie, are playing in their classroom spacecraft, and need a…