Blocks are not just for play! In this article, Nicole Andrews describes observing the interactions of three young boys enthusiastically engaged in the kindergarten block center of their classroom, using blocks in a building project that displayed their ability to use critical thinking skills, physics exploration, and the development of language…

This study aimed to examine the relations among property strategies, working memory, and multiplication tasks with 101 Chinese fourth-grade students. Two multiplication property strategies (associative and distributive) were compared with no strategy and demonstrated differentiated effects on students' accuracy and reaction time. Associative…

Researchers have extensively documented, and math teachers know from experience, that algebra is a "gatekeeper" to more advanced mathematical topics. Students must have a strong understanding of fundamental algebraic concepts to be successful in later mathematics courses. Unfortunately, algebraic misconceptions that students may form or…

In the current educational climate, teachers are required to find methods to give all students, including students with mild intellectual disability, access to the general education curriculum. The purpose of this study was to investigate the combined effects of the concrete-semiconcrete-abstract instructional sequence and model-based problem…

In this article we intend to analyze the effectiveness of an educational program of mathematical creativity, designed for learners aged 10 to 12 years, which has been implemented in an urban school of Iasi, Romania. This analysis has both a psycho-educational dimension and a statistical analysis one. The psycho-educational dimension refers to the…

This paper reports on a component of a large yearlong study in three Year 7 classes in three different schools. The aim of this research component was to determine the relationship between students' number sense and their problem-solving ability by means of paper-and-pencil tests, classroom observations, and interviews of students and teachers.…

In "MT218" the author looked at the possibility of basing a classroom activity on a simple, though not totally transparent, number-theoretic result. In this article he considers another relatively straightforward idea from number theory that could be used either as a lesson starter or as the basis of a more substantial task, requiring students to…

It seems rather surprising that any given polynomial p(x) with nonnegative integer coefficients can be determined by just the two values p(1) and p(a), where a is any integer greater than p(1). This result has become known as the "perplexing polynomial puzzle." Here, we address the natural question of what might be required to determine a…

Using different representations and having flexibility of transition between representations throughout the definite integral problem-solving process are thought to be effective on the development of conceptual understanding and students' performance. The study aims at considering the effects of representations used in the definite integral on…

A perennial problem in computer-aided assessment is that "a right answer", pedagogically speaking, is not the same thing as "a mathematically correct expression", as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was "the right…

Mathematics teachers are often asked, "What is the most difficult topic for you to teach?" Their answer is teaching students to count. The concepts can be challenging and slippery to apply in problems. Many times, no rigid procedures or formulas can be used to solve the problems directly, and students simply do not know where or how to approach…

How can statistics clearly be mathematical and yet distinct from mathematics? The answer lies in the reality that statistics is both an art and a science, and both aspects are important for teaching and learning statistics. Statistics is a mathematical science in that it applies mathematical theories and techniques. Mathematics provides the…

In this study, it was hypothesized that problem solving success is dependent upon two related but district types of mathematical knowledge, content indicators and connectedness indicators. Results did indeed display that the problem solving success of 188 undergraduate students was related to these two indicators. The correlations of content…

When faced with mathematical methods, undergraduate students have difficulty in grasping the reality of various approaches and special functions. It is only when they take a more specialized course such as classical electromagnetism that they finally see the connection. A problem that we believe illustrates very well the depth and variety of…

Visualizing complex roots of a quadratic equation has been a quest since the inception of the Argand plane in the 1800s. Many algebraic and numerical methods exist for calculating complex roots of an equation, but few visual methods exist. Following on from papers by Harding and Engelbrecht (A. Harding and J. Engelbrecht, "Sibling curves and…