Algebraic Thinking (AT) and Computational Thinking (CT) are pivotal competencies in modern education, fostering problem-solving skills and logical reasoning among students. This study presents the initial hypotheses, theoretical framework, and key steps undertaken to explore characterized learning paths and assign practice-relevant tasks. This…

For Freudenthal, the practice of mathematics in the curriculum is not a set of predetermined theories, goals and means. On the contrary, it is always associated with positively understood phenomenological processes in mathematics, as the curriculum is often used in conjunction with the transformation or development of practice. For Freudenthal…

Although lesson study has been shown to improve the teaching and learning of mathematics, little research has focused on reasons for engaging in it from a teacher's perspective, particularly after sustained engagement with lesson study. This qualitative study reports on thirty-three teachers from the United States who were involved in twelve…

The Algebra Project DR K-12, funded by the National Science Foundation as a Research and Development Project, addressed the challenge of offering significant STEM content for students to ensure public literacy and workforce readiness. The project's primary purpose was to test the feasibility and effectiveness of a model for establishing four-year…

This issue of Changing Schools explores what algebraic thinking is and why students need algebraic thinking. The efforts of Kansas and North Dakota to incorporate algebraic thinking into their state mathematics standards are described. Contents include: (1) "Algebraic Thinking: Preparing Students for Mastering Algebraic Concepts" (Vicki…

This report is the second in a series of RAND reports on the topic of education research and development proposing a long-term, strategic program of research and development in mathematics education. The RAND Mathematics Study Panel's recommendations for the substance and conduct of the program are presented in this report. The program is designed…

This paper posits that, as educators' attention turns to elementary mathematics as preparation for algebra, it is important to begin by examining the kind of elementary mathematics content teaching that is aligned with reform. The paper calls for a close examination of students' development of operation sense. The role of children's engagement…

The 13 leading mathematics educators who made up the task force that prepared this report were thoroughly acquainted with every major report on math education produced within the last decade. They were also thoroughly acquainted with the realities of instruction in the K-12 classrooms. Their aim, therefore, was to make appropriate compromises…

This document is designed to assist administrators and teachers in planning, developing, and implementing grades K-9 mathematics programs and to provide some guidelines for grades 10-12 instruction. It is intended to provide a philosophical foundation and curricular framework from which educators may construct a comprehensive local program to meet…

After noting that research and development reports indicate that there are strong psychological arguments for approaching algebraic concepts through the use of computer programming, the work of the Nottingham Programming in Mathematics Project with pupils aged 11-13 is briefly described. What is meant by understanding of a concept and how pupils…

Replication of the Second International Mathematics Study (SIMS) in Ontario, Canada, is described and assessed. The curriculum and testing program covers numerical methods, geometry, and algebra. Whereas classical studies focused on mean scores of a system's students and on percentages of teachers for opportunity to learn (OTL), SIMS aggregates…

This document ties the essential skills needed in mathematics to the National Council of Teachers of Mathematics' (NCTM) Curriculum and Evaluation Standards to help facilitate future curriculum development. The overall goal for the 21st century is to make mathematical power a reality for all students. The rationale for this document can be found…

This guide was written under the basic assumptions that the mathematics curriculum must continuously change and that mathematics is most effectively learned through a spiral approach. Further, it is assumed that the audience will be members of district mathematics curriculum committees. Instructional objectives have been organized to reveal the…

The teaching of mathematics from a multicultural perspective is discussed. The first two chapters present a rationale for a multicultural approach to teaching mathematics. The third chapter aims to show, through brief examples, how such an approach can be applied to any school curriculum. The remaining four chapters discuss, in greater detail,…

In 1983, the Ohio State Board of Education responded to the public's expectations for schools by adopting minimum standards requiring competency-based education in mathematics on a 5-year cycle, of each school district's competency-based education program; and to publish an annual report on competency-based education in Ohio. This document is the…