This is a study of student engagement with computational labs in Calculus 2. The labs task students with using MATLAB to investigate contexts such as rocket science, disease modeling, and market economics forecasting by modifying and executing provided code, guided by questions that have students report the results of their simulations or…

Background: The study on which this article is based investigated the Mathematics Knowledge for Teaching (MKfT) that a well experienced Grade 2 teacher utilized when teaching counting. Aim: In this paper we share excerpts from one of the lessons of this Grade 2 teacher, which we analyzed to illuminate the various domains of MKfT and their…

This paper describes the development and intended uses of the Early Grades Mathematics Assessment (EGMA), which measures essential early mathematical knowledge and skills that are foundational to more sophisticated mathematical abilities, predictive of later achievement, and teachable. Administering the EGMA can provide policy makers,…

This fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasizing computational fluency and the…

How this teacher develops composition of ten with second graders was dramatically reshaped by the 2006 release of NCTM's "Curriculum Focal Points." The release of "Curriculum Focal Points"--particularly the suggestion that number sense and computation be focal areas in the second-grade mathematics curriculum--resulted in positive changes in this…

The results of the cognitive research on numbers' representations can provide a sound theoretical framework to develop educational activities on representing numbers. A program of such activities for a nursery school was designed in order to enable the children to externalize and strengthen their internal representations about numerosity and link…

These proceedings contain the papers of the 18th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2021), held virtually, due to an exceptional situation caused by the COVID-19 pandemic, from October 13-15, 2021, and organized by the International Association for Development of the Information Society…

What students need to know in a world where most computations are done by machine is discussed. Needed changes in the mathematics curriculum are then detailed in relation to mental arithmetic, numeration, decimals and fractions, paper-and-pencil computation, order of operations, problem solving, and instruction on calculator use. (MNS)

This paper focuses on using technology to support mathematics instruction. Technologies such as computers and calculators are widely used in the teaching of mathematics. The educators advocate the use of these tools to reduce tiresome computations and tasks so that class time can be more effectively used for learning mathematics. The purpose of…

This report summarizes a project to develop computational estimation materials for students in grades 6, 7, and 8. In chapter 1, the need for estimation skills is discussed and the goals of the project are stated: to develop a carefully sequenced set of lessons, activities, and maintenance work on estimation with whole numbers, fractions,…

Discusses the importance of mental mathematics beyond the middle school. Presents sample objectives for different courses or strands, and teaching ideas to make mental mathematics an important, ongoing goal in secondary mathematics instruction and beyond. (KHR)

An experimental program using the calculator in third, fourth, and fifth grades is described. Three example lessons are included, on (1) subtraction with regrouping, (2) estimation, and (3) number theory: Quadratics. (MK)

This paper presents an overview of the Comprehensive School Mathematics Program (CSMP) elementary school mathematics curriculum. The philosophy behind the program, content goals, and teaching strategies are briefly discussed. Then ways in which the program develops facility in mathematics are described in discussions of the language of arrows, in…

This study assessed the effectiveness of the remedial/developmental mathematics program developed at Ramapo College of New Jersey. Data was gathered from a random sample of 604 students who participated in the program for at least part of the three-year period 1981-84 and for whom both pretest and posttest scores were available in at least one…

A proposal to shift to a conceptually oriented curriculum using the calculator as an instructional tool and to eliminate the teaching of complex computations in elementary school is presented. (MP)