In the international literature, increasing numbers of articles and books are published about teaching and learning, with the brain in mind. For a long time, I have been sceptical about this question. However, seeing many unresolved issues in the teaching and learning of mathematics, I slowly started to study the relevant literature and have…

The purpose of this study is to determine how Finnish pupils' problem-solving skills develop from the 3rd to 5th grade. As research data, we use one non-standard problem from pre- and post-test material from a three-year follow-up study, in the area of Helsinki, Finland. The problems in both tests consisted of four questions related to each other.…

Many learners hold traditional beliefs about mathematics that can hamper their learning in the discipline. To address this issue, a "history-based" intervention program entailing problem-solving and writing activities that instigate cognitive conflict was implemented. Data sources were pretest and posttest scores of a 12-theme…

The purpose of this article is to offer teacher training and professional development recommendations in mathematics based on the findings of a federally funded 3-year intervention study that improved the problem solving of middle school students with a focus on students with learning disabilities. Over the 3-year project, 29 seventh and eighth…

Teachers are challenged to create flexible learning environments that prepare students with diverse learning needs for adaptable thinking in a fast-paced and changing society. To address this need, we used a design-based research approach to develop a technology-based solution to individualize mathematical problem solving instruction to students…

This study reports on the use of formative, diagnostic online assessments for the topic percentages. Two new item formats (drag-drop and slider) are described. About one-third of the school students (Years 7 to 9) could, using a slider, estimate "80% more than" a given length, in contrast with over two-thirds who could estimate "90%…

Research investigating the cognitive effect of bilingualism on mathematical learning began just over 25 years ago and has progressed from there, although research focusing on the Asia-Pacific region is still quite limited. This paper presents details about a current project in this area. CARE's Riel Maths research project investigates ethnic…

Research has shown that affordances of computers may be exploited in the design of mathematical tasks so as to provide interesting and challenging activities. At the same time, opportunities for learning mathematics may be constrained if the design of the task is not appropriate. A tool which allows teachers, researchers and task designers to…

This study determined the effects of the Explicit Inquiry Routine (EIR), a teaching routine, on the math performance of 14 middle-school students with math learning disabilities. The routine integrates validated mathematical teaching practices from general education (inquiry, dialogue) and special education (intensive, explicit instruction) to…

The Stoltz-Cesaro Theorem, a discrete version of l'Hopital's rule, is applied to the summation of integer powers.

Several jeeps are poised at base camp on the edge of a desert aiming to escort one of them as far as possible into the desert, while the others return to camp. They all have full tanks of gas and share their fuel to maximize penetration. In a friendly desert it is best to leave caches of fuel along the way to help returning jeeps. We solve the…

A secretary has "n" letters and "n" addressed envelopes. Instead of matching each letter with the corresponding envelope, she inserts the letters in a random manner. What are the chances that every letter will be in the wrong envelope? In this article, the author presents a solution to this problem and discusses possible ways of placing the…

What if you could challenge your 12th graders to understand car crashes in the context of physical forces, manufacturing challenges, government safety standards, and individual rights? With this volume in the "STEM Road Map Curriculum Series," you can! "Car Crashes" outlines a journey that will steer your students toward…

This study used HIMATT (Highly Interactive Model-based Assessment Tools and Technologies) to evaluate the cognitive models of individuals who are solving complex mathematical problems. The goal was to determine the ability of HIMATT to assess learning in mathematics. Research on cognitive and mental models proposes that internal conceptual systems…

The problem of optimizing the number of circular sprinklers watering large fields is used to introduce, from a purely elementary geometrical perspective, some basic concepts in crystallography and comment on a few size effects in condensed matter physics. We examine square and hexagonal lattices to build a function describing the, so-called, dry…