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,…

In this note, I argue for and discuss my experiences with explicitly incorporating principles of critical and creative thinking in a transitions course which serves mathematics, mathematics education, and statistics majors. I describe several specific assignments and classroom tasks designed to enhance critical and creative thinking. I also…

This study gives insights into how Logo-like microworlds can affect cognitive development related to mathematics education of students with math learning difficulties. In particular, we analyse the case of a 15-year-old student with dyslexia and severe dyscalculia. Among the various cognitive aspects involved, here we delve into the development of…

The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding…

Developing critical numeracy is important in a society where mathematics plays a particular and significant role. One way of helping learners to develop the level of numeracy required to participate in society is by exploring ideas embedded in rich, accessible tasks. These can be linked to contexts that have relevance in their lives. One…

SProblem solving has a long and successful history in mathematics education and is valued by many teachers as a way to engage and facilitate learning within their classrooms. The potential benefit for using problem solving in the development of algebraic thinking is that "it may broaden and develop students' mathematical thinking beyond the…

No Child Left Behind legislation developed goals for every student to be proficient in each academic subject by 2014. California's students are far from meeting this goal, especially in mathematics. One Southern Californian school district, renamed Green Valley Unified School District for anonymity, began using Cognitively Guided Instruction…

Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively…

This study investigated the comprehension and effectiveness of teaching formal, probabilistic decision-making skills to middle school students. Two specific objectives were to determine (1) if middle school students can comprehend a probabilistic decision-making approach, and (2) if exposure to the modeling approaches improves middle school…

The focus of this discussion is on the providing of educational experiences which will help students develop skills at various levels of learning awareness. Examples of different levels and the skills associated with them are presented. (JP)

A review of 25 years of Piagetian research in intellectual growth as it pertains to the learning and understanding of mathematics and implications for teaching. (MM)

Discussed are difficulties which occur while the student is using mathematical induction as a tool to prove theorems. An appropriate approach is suggested. (MP)

Synthesized are a number of learning theories (those of Piaget, Bruner, Gagne, Dienes and Skemp) to form one composite teaching-learning model. This model is then applied to mathematics teaching. An example is provided to illustrate how the model may be used to elaborate a teaching-learning scheme for solving quadratic equations. (Author/DS)

Many high school and college students seem to dislike mathematics, do poorly in the subject (as evidenced by declining test scores), and avoid scheduling courses in mathematics. Answers to why test scores are declining and why mathematics achievement is low among adults are speculative and as varied as the educators who offer them. However, one…

This essay discusses the sketching and transformation of parabolas and other curves as areas where learners can exercise and develop control of their mental imagery. (MN)