Mapping skills between different codes to represent numerical information, such as number symbols (i.e., verbal number words and written digits) and non-symbolic quantities, are important in the development of the concept of number. The aim of the current study is to investigate children's mapping skills by incorporating another numerical code…

Knowing what kinds of patterns are easy for children to recognize early in their kindergarten year, and what kinds are difficult, can be a useful guide for patterning instruction. Hence, the ability of children to recognize complex patterns early in their kindergarten year was assessed in two experiments. One experiment showed that the children…

In the transition from secondary to tertiary mathematics, students try to participate in tertiary mathematics by replicating familiar school mathematical discourses. The objective of this case study is to investigate the conditions and affordances under which students proceed from familiar school mathematical discourses to new, tertiary discourses…

The purpose of the current study was to examine dimensionality and concurrent validity evidence of the EARLI numeracy measures (DiPerna, Morgan, & Lei, 2007), which were developed to assess key skills such as number identification, counting, and basic arithmetic. Two methods (NOHARM with approximate chi-square test and DIMTEST with DETECT…

Evidence is presented for the immediate apprehension of exact small quantities. Participants performed a quantification task (are the number of items greater or smaller than?), and carry-over effects were examined between numbers requiring the same response. Carry-over effects between small numbers were strongly affected by repeats of pattern and…

Through the importance of the number three in our culture and the strange preference for a ternary pattern of our nature one can perceive how and why number theory degraded to numerology. The strong preference of our minds for simple patterns can be read as the key to understanding not only the development of numerology, but also why scientists…

Discusses the relationship between the world of mathematics and the real world through a consideration of Mitsumasa Anno's exploration of the two different yet connected worlds in five picture books. (SR)

The use of dice and dominoes in the classroom is discussed as leading from counting activities to pattern recognition and discovery learning. (MP)

Some patterns resulting from certain operations on numbers are discussed, analyzed, and explained. A method for predicting the outcome of these operations for any number is developed.

A student noticed an interesting fact about the base two numerals for perfect numbers. Mathematical explanations for some questions are given. (MNS)

This study of 73 children sought to determine if children's perceptual comprehension of numerals is higher when they are shown symmetrical rather than asymmetrical arrangements of pegs, and if comprehension scores related to age, sex, and/or social class. The main hypothesis was rejected but some age and class differences were found. (SJL)

Learning activities are given for instruction in the skill of associating numbers with sets of dots, a skill intermediate between counting and higher number concepts. (MP)

Describes learning activities in which fifth and sixth graders used spreadsheets to explore the shapes of numbers. Discusses creating spatial patterns with a computer draw program; examining number patterns in a spreadsheet; comparing square and rectangular numbers; and creating the multiplication times table. (AEF)

Seven-year-olds who had difficulty understanding 1st-grade work received one of two forms of small-group instruction. Half of the children were randomly assigned to receive four months of instruction in recognizing, comprehending, and reproducing both logical and arbitrary patterns (sequences) involving numbers, letters, shapes, colors,…