Presents a covariation approach to learning exponential and logarithmic functions based on a primitive multiplicative operation labeled splitting that is not repeated addition. Suggests that students need the opportunity to build a number system from splitting structures and their geometric forms. (30 references) (MKR)

Discusses explorations that students can engage in using the interstate highway system. (MKR)

The objective of this activity is to help beginning students learn numbers and practice vocabulary and verbs in an interesting and meaningful way. In addition, the game is used to improve their listening comprehension and speaking ability. (Author/CK)

Presents an activity using base-10 blocks and the TI Explorer calculator to help fifth and sixth graders represent their ages in different numerical bases to appear older or younger than their real age. (MKR)

An algebra test administered to (n=18) first-year college students found a disregard for negative numbers, ineffective use of counterexamples, misapplication of rules, and a lack of a good grasp of relevant mathematical terminology. (12 references) (MKR)

Many students can calculate the arithmetic mean but do not understand the concept. The article presents four activities designed to help elementary and middle school students develop this concept. The activities presented assume previous exposure to the computational algorithm for the arithmetic mean. (Author/EK)

Describes a school-wide project using popcorn to gain number sense by learning more about a million. Used the books "How Much Is a Million?" and "If You Made a Million" to introduce the project. (MKR)

Discusses children's place-value understanding, including initial learning interference, vertical number lines, and planned discourse. Describes a learning activity that can guide children from a concrete to a symbolic understanding of place value. (11 references) (MKR)

This case study of a 30-year-old woman with a developmental learning disability (including anomia, auditory processing problems, difficulty in learning reading and spelling skills, and a poor sense of number) suggests that all these impairments may be explained in terms of a sequential processing deficit. (Author/DB)

Presented are the results of two pilot studies about multidigit addition and subtraction. The results are discussed in relation to possible alternative sequences in the teaching of addition and subtraction and the relationship between basic fact mastery and numeration concept attainment. (CW)

This paper theoretically characterizes number sense as a set of cognitive capabilities for constructing and reasoning within mental models. This perspective provides support for viewing various aspects of number sense as features of students' general condition of knowing about numbers and magnitude, rather than as skills needing specific…

The relationship between elementary operations underlying processing of numerical information and performance on psychometrically derived ability measures requiring processing of numbers but defining separate ability factors was studied for 102 Air Force recruits (54 males and 48 females). Patterns of convergent and discriminate relationships for…

Provided are examples from many domains of mathematics that illustrate the Fubini Principle in its discrete version: the value of a summation over a rectangular array is independent of the order of summation. Included are: counting using partitions as in proof by pictures, combinatorial arguments, indirect counting as in the inclusion-exclusion…

Children in grades three through five and adults performed a number-matching task. Found that changes in the strength of arithmetic connections occurred with development and accounted for individual differences among adults. Individual differences among children were related to changes in the strength of number-line connections. (Author/GLR)

Described is a classroom activity incorporating a computer spreadsheet to study number patterns generated by the Fibonacci sequence. Included are examples and suggestions for the use of the spreadsheet in other recursive relationships. (JJK)