This article describes how sixth-grade students developed concrete models to solve division of fractions story problems. Students developed separate two-step procedures to solve measurement and partitive problems, drawing on invented procedures for division of whole numbers. Errors also tended to be specific to the type of division problem…

During the last decade, global optimization has attracted a lot of attention due to the increased practical need for obtaining global solutions and the success in solving many global optimization problems that were previously considered intractable. In general, the central question of global optimization is to find an optimal solution to a given…

In the late seventies, Guy Brousseau set himself the goal of verifying experimentally a theory he had been building up for a number of years. The theory, consistent with what was later named (nonradical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment,…

This little problem arose because I was frustrated with the standard electromagnetism texts, which show the magnetic field due to a current-bearing wire outside the wire [proportional to] 1/r and inside [proportional to] r. However, they never point out that the moving electrons must be influenced by the magnetic field created by the other moving…

Executive functioning (EF) refers to higher order thought processes considered foundational for problem-solving. EF has both "cool" cognitive and "hot" emotional components. This study asks: (a) what are the relative contributions of "hot" and "cool" EF to children's academic achievement? (b) What are the relative contributions of "hot" and "cool"…

Previous research has shown that when confronted with missing-value word problems, primary school students strongly tend to use proportional solution approaches, even if these approaches are inappropriate. The authors investigated whether (besides the missing-value formulation of word problems) the numbers appearing in word problems are part of…

A 3-week problem-solving practice phase was used to investigate concept-procedure interactions in children's addition and subtraction. A total of 72 7- and 8-year-olds completed a pretest and posttest in which their accuracy and procedures on randomly ordered problems were recorded along with their reports of using concept-based relations in…

The National Council of Teachers of Mathematics' (NCTM's) Process Standards support teaching that helps students develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every middle grades math teacher the opportunity to explore each standard in depth. The series offers friendly,…

PreCalculus students can use the Completing the Square Method to solve quadratic equations without the need to memorize the quadratic formula since this method naturally leads them to that formula. Calculus students, when studying integration, use various standard methods to compute integrals depending on the type of function to be integrated.…

"Dimensions of possible variation" is a phrase that now occupies a safe place in the literature describing the application of education theory to education practice: "asking yourself what could be changed [in the task], while using the same approach or technique, opens up dimensions of possible variation. A set of exercises forming a sequence of…

Data literacy is recognized as a critically important skill in today's society, but thinking with and about data is often ignored in K-12 curricula. The Thinking With Data (TWD) project advocates that data literacy is a skill that should be addressed in an interdisciplinary manner. This article provides an overview of the TWD curriculum for middle…

The Institute of Education Sciences (IES) publishes practice guides in education to bring the best available evidence and expertise to bear on current challenges in education. Authors of practice guides combine their expertise with the findings of rigorous research, when available, to develop specific recommendations for addressing these…

The Department of Education has been under attack by people motivated by the perceived failure of the system to improve educational achievement on the elementary and high school levels or the desire to dramatically reduce spending and waste during troubled economic times. A new program introduced in four states seems to address competency and…

Active Learning in Maths and Science (ALMS) was a six-month face-to-face professional development program for middle school maths and science teachers carried out between June and November, 2010 in two Indian states. ALMS's theory of action is grounded in the belief that collaborative learning serves as a "gateway" to learner-centered…

This article will share results from research that investigated how sixth-, seventh-, and eighth-grade students who had not been exposed to formal algebraic methods approached word problems of an algebraic nature. Student use of systematic guess and check, the predominate approach taken by these students, is the focus. The goal is to consider the…