In the disciplines of dance and mathematics, binary identities commonly split individuals into either (non)dance and/or (non)math people. However, these shorthand assessments become dangerous because they constrain disciplinary knowledge, and limiting one's identity and capabilities remains antithetical to broad education goals. Capitalizing on…

Map reading is unique to humans but is present in people of diverse cultures, at ages as young as 4 years old. Here, we explore the nature and sources of this ability and ask both what geometric information young children use in maps and what nonsymbolic systems are associated with their map-reading performance. Four-year-old children were given…

On February 18, 2015, the New York State Education Department (NYSED) conducted a Performance Level Description Development meeting in Albany, New York. The meeting was convened to articulate the knowledge and skills expected of students at each level of performance, consistent with the policy vision set forth by the NYSED. The Performance Level…

This quantitative, quasi-experimental, nonequivalent group study examined the impact on levels of measure that determine a return on investment of differing forms of interactive whiteboard (IWB) technology used at a high school in a suburban school district in southeastern Virginia. Three forms of IWB were compared: a full-screen IWB, a mobile…

An experiment is reported comparing human performance on two kinds of visually presented traveling salesperson problems (TSPs), those reliant on Euclidean geometry and those reliant on city block geometry. Across multiple array sizes, human performance was near-optimal in both geometries, but was slightly better in the Euclidean format. Even so,…

A selection of 14 tests of five cognitive factors was administered to 95 senior high school geometry students. These cognitive factors were then related to six measures of performance in mathematics and subjected to correlation analysis and stepwise regression. The findings indicated that the selected cognitive factors correlated with all measures…

The relationship of performance in mathematics to syntactical language factors obtained from speech samples was investigated with 95 senior high school geometry students. Statistical procedures included correlation analysis and stepwise regression. The findings indicated that certain syntactical measures indicating logical thought processes…

THE EXPERIMENT PROPOSED IN THIS STUDY WAS TO SUPPLY EVIDENCE RELEVANT TO THE QUESTION OF HOW MUCH INFLUENCE, IF ANY, A POSTULATED NOVELTY EFFECT WOULD HAVE UPON THE EFFECTIVENESS OF LEARNING IN A SELF-INSTRUCTIONAL SITUATION. THE HYPOTHESIS WAS--THERE WILL BE NO SIGNIFICANT DIFFERENCES IN ACHIEVEMENT OF TWO COMPARABLE GROUPS OF ELEMENTARY PUPILS…

In 1981 a nationwide assessment of achievement in writing geometry proofs was conducted by the Cognitive Development and Achievement in Secondary School Geometry project. Over 1,500 students in 11 schools in 5 states participated. This paper describes the sample, instruments, grading procedures, and selected results. Results include: (1) at the…

TWO METHODS OF RESPONSE DESCRIBED BY PIAGET AND INHELDER FOR DRAWING APPROPRIATE BOUNDARIES AND SELECTING APPROPRIATE PREDRAWN BOUNDARIES FOR HYPOTHETICALLY CUT, SOLID GEOMETRIC FIGURES WERE INVESTIGATED TO SEE WHETHER SECONDARY SCHOOL STUDENTS COULD RESPOND IN APPROPRIATELY TO THE MATHEMATICAL TASKS. THE RESPONSES OF 8TH-, 10TH-, AND 12TH-GRADE…

This study investigated the effect of diagram formats on performance on geometry items in order to determine whether certain examinees are affected by different item formats and whether such differences arise from the different intellectual demands made by these formats. Thirty-two experimental, multiple-choice geometry items were administered in…

High school geometry students were presented lessons with either a high degree of structure or a low degree of structure. Structure was defined in terms of the frequency with which concepts were repeated from one sentence to the next. After the lessons, students were tested for comprehension of the material covered and then they rated the lessons…

During the Spring of 1989, the North Carolina Department of Public Instruction field-tested a geometry proof performance assessment as a component of the High School End-of-Course Testing Program (EoC). The existing geometry EoC test consisted only of multiple-choice items. The performance assessment was added to the multiple-choice component to…

The effects of an experimental geometry course on gender differences in standardized test performance were studied. The experimental approach involved: (1) reading new concepts and materials followed by class discussion; (2) relating applications to real-life situations; and (3) conducting a spiraling review of concepts throughout the year.…

The effects of a mathematics lesson's complexity were studied, using 128 female and 122 male first-year algebra students in Georgia high schools. Achievement scores were slightly, but not significantly, higher with low complexity lessons, and students preferred the low-complexity lessons. Implications for teaching secondary mathematics are…