This qualitative study developed a preparation series to prepare principals in the approach of Cognitively Guided Instruction (CGI) to support teachers in implementation. The series included six virtual sessions that prepared principals in understanding the "Why" behind CGI, the connection to the state standards, number sense routines,…

The article introduces a software application (MATH) supporting an education of Applied Mathematics, with focus on Numerical Mathematics. The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt…

Student access to technology is no longer a privilege: it is a prerequisite for full participation in high-quality education opportunities. While this fundamental right to technology access for learning is nonnegotiable, it is also just the first step to equitable learning opportunities. Society must continue to ask questions about the…

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

Reports on an intensive study of problem-solving activity of female students at the senior secondary level. Focuses on both the mathematical processing and the underlying cognitive and metacognitive activities that led to that processing. Concludes that all successful groups displayed a high number of key points where metacognitive decisions could…

Several studies have shown the difficulties students encounter in making sense of situations involving rate of change. This study concerns how students discover errors and refine their knowledge when working with rate of change. The part of the study reported here concerns the responses of four precalculus students to a task which asked them to…

This paper proposes a theory that can account for differences between everyday and formal mathematics knowledge and a set of processes by which informal knowledge is transformed into formal mathematics. After an introduction, the paper is developed in five sections. The first section lays out the nature of informal, everyday mathematics knowledge.…

This paper reports the latest in a series of studies investigating children's performance in solving division story problems involving remainders. One aspect of the work involved examining the way in which "sense-making" is involved in the interpretation of the numerical solution obtained. Subjects were 195 sixth, seventh, and eighth…

THE OBJECTIVE OF THIS RESEARCH WAS TO EXTEND, ELABORATE, AND IMPROVE THE SET-FUNCTION LANGUAGE (SFL). THE SFL IS A NEW SCIENTIFIC LANGUAGE FOR FORMULATING RESEARCH QUESTIONS ON MEANINGFUL LEARNING, FRAMED IN TERMS OF THE MATHEMATICAL NOTIONS OF SETS AND FUNCTIONS. IN THE FIRST PAPER, THE SFL IS DESCRIBED. ITS RELATION TO THE STIMULUS RESPONSE…

This volume is largely based upon the preparation for and proceedings of the Third International Congress on Mathematical Education (ICME) held in Karlsruhe, Federal Republic of Germany, in August 1976. The volume deals with 13 broad themes of general educational interest for mathematics teachers and educators. Six of these themes divided the…

A longitudinal study followed Brian from grade five through grade seven to examine his representation and development of mathematical knowledge. Some observations over the four years were that Brian liked to figure things out, responded poorly to suggestions not fitting the representation he constructed, and changed attitudes from purposeful and…