We examine the behavior of the curvature function associated with most common families of functions and curves, with the focus on establishing where maximum curvature occurs. Many examples are included for student illustrations. (Contains 18 figures.)

Certainly, the process of decision-making and problem-solving in a shifting playing environment lies at the core of the Teaching Games for Understanding (TGfU) model. What is not clear is how, at the time of decision-making, players' feelings or affective factors and their subsequent influence on thinking, influence these processes. Affect has a…

During the early 20th century, practicing San Antonio teachers took part in several different types of in-service education. This paper investigates the types of in-service education present during the superintendency of Lloyd Wolfe (1902-1908), a progressive San Antonio educator who employed innovative approaches to in-service education.…

In this paper, results of a questionnaire about continuity of functions are analysed. The tested students attend Novi Sad grammar school. The aim of this test was to check the student's theoretical and visual knowledge of continuous functions at the end of their high school education. The questions were given with and without the graphs of…

The authors discuss proportional reasoning as a challenging yet central concept for students in the middle grades that lays a foundation for mathematics studied later in high school. Four types of proportional reasoning problems are discussed: (1) Part-part-whole (comparing a subset (part) of a whole with its complement (other part) or the whole…

Recently, the author has been fortunate to be a visitor in a number of classrooms in the United States, England and Europe. On one such visit to an Elementary School in Columbia, Missouri, the teachers accepted him into their normal classrooms for their normal lessons. He moved between three classes: Grade 1, Grade 2 and Grade 4. A snapshot…

According to Piaget's theory, maturation of the nervous system is sufficient for the development of formal thought. If this were the case, the job of the educational system would be small indeed. Rather, maturation determines only the totality of possibilities and impossibilities at a given stage. This study investigates whether instructional…

Problem-solving discussions were observed within families of children with mental retardation and multiple comparison groups (total N = 162 families). As expected, parents were more persistent and directive with their children who had mental retardation, but they also avoided negative exchanges with these children. These patterns did not spillover…

In 1997, the Ontario government, like many other jurisdictions, undertook systemic reform of their elementary school mathematics programme, developing a new mathematics curriculum, report card, and province-wide assessment. The curricular reform embodied a new vision of mathematics learning and instruction that emphasized instruction using…

This paper explores the wide range of mathematics content and processes that arise in the secondary classroom via the use of unusual counting problems. A universal pedagogical goal of mathematics teachers is to convey a sense of unity among seemingly diverse topics within mathematics. Such a goal can be accomplished if we could conduct classroom…

This study investigated the effects of the Self-Determined Learning Model of Instruction (SDLMI) on the academic skill performance of three junior high school students with moderate to severe intellectual disabilities. The academic skills taught were aligned to the district general curriculum, and extended benchmarks were individually determined.…

I altered the format of an exercise physiology course from traditional lecture to emphasizing daily reading quizzes and group problem-solving activities. I used the SALGains evaluation to compare the two approaches and saw significant improvements in the evaluation ratings of students who were taught using the new format. Narrative responses…

Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

In 2 experiments with 74 high school students, subjects studied worked examples while learning how to translate English expressions into algebraic equations. Those using worked examples outperformed the control group on posttests, made fewer errors, completed work more rapidly, and required less assistance from the teacher. (SLD)

The "I CAN Learn[R] Mathematics Curriculum" is designed to help ethnically diverse, inner-city students in grades 7 through 10 achieve parity in mathematics and problem-solving skills. It uses an interactive software program to teach pre-algebra and algebra. The "I CAN Learn[R] Algebra 1" course, which was used in all of the…