Introduces basic principles of coding and decoding including the use of letter frequencies to decode secret messages by using the radio premium codes of Little Orphan Annie and Dick Tracy. (KHR)

Proposes a word problem concerning placing students around triangular tables. Students must determine how to place the touching tables so that everyone can be seated. (KHR)

Describes the successful use of a computer algebra system (CAS) with a student as he worked on a problem involving functions far more difficult than he had previously encountered. (Author/NB)

Investigated whether children who reflected the structure of word problems with their concrete models were successful in learning to symbolically represent problems with structure-based open number sentences. Forty-five first graders were taught to write canonical and noncanonical open number sentences. (Author/YP)

Discusses the geometrical array of the keys on a calculator that can be turned into a problem-solving, problem-posing situation for the upper elementary or middle school classroom. Provides figures showing the arrays, including rows, diagonals, crosses, rhombi, angles, and squares. Lists seven references. (YP)

Suggested that strategy choices for solving addition problems were related to numerical and spatial ability domains, while the speed of executing the component process of fact retrieval was related to arithmetic ability only. Findings supported the convergent validity of the strategy choice model and its discriminant validity. (RH)

The described activities give children an opportunity to use geometric ideas to reinforce arithmetic concepts and to use arithmetic ideas to generate geometric figures (both circles and polygons). (MNS)

Assessing Markman's hypothesis that the organizational principles underlying collection concepts facilitate children's performance on cognitive tasks requiring part-whole comparisons, three experiments indicated that the facilitative effect of collection labels appears to be specific to the class-inclusion task. Results suggest that Markman's…

Compares the cognitive representation of number of 24 American, 25 Chinese, 24 Japanese, and 40 Korean first-graders, and 20 Korean kindergartners. Chinese, Japanese, and Korean children preferred to use a construction of tens and ones to show numbers, whereas English-speaking children preferred to use a collection of units. (RJC)

This research was designed to document the ability of Down's Syndrome children aged 5-10 to perform equivalence tasks, and to investigate possible relationships between such performance and the presence of certain potentially confounding task variables. (MNS)

Use of a microcomputer spreadsheet program to help students understand long division is described. An example of a problem with powers of 10 used with seventh graders is presented, with note of another lesson on decimals for grade 6. (MNS)

Why students have difficulty with a proof (such as Cantor's) is discussed, with the focus on proof by contradiction. Methods may fail due to the difficulty of the concept and lack of understanding of how students are thinking. (MNS)

Analyzes (n=346) grades 4-8 children's partitioning strategies in terms of a framework that translates economy in number or size of pieces and use of perceptual cues into sophistication in unitizing. Proportionately more students used economical partitioning strategies than used less economical cut-and-distribute strategies. (Author/MKR)

Presents a mathematics investigation in which students discover number patterns in physical structures and express their generalizations algebraically. (MKR)

Analysis of the role that (n=4) second graders' use of the hundred board played in supporting their conceptual development found that the board did not support the construction of increasingly sophisticated concepts of 10, but did support their ability to reflect on their mathematical activity. (54 references) (Author/MKR)