The purpose of this study was to determine how the study of number theory might affect high school students' metacognitive functioning, mathematical curiosity, and/or attitudes towards mathematics. The study utilized questionnaire and/or interview responses of seven high school students from New York City and 33 high school students from Dalian,…

Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of…

The purpose of this study was to examine the differences between Finnish and Taiwanese textbooks for grades 7 to 9 on the topic of solving systems of linear equations (simultaneous equations). The specific textbooks examined were TK in Taiwan and FL in Finland. The content analysis method was used to examine (a) the teaching sequence, (b)…

Twenty-four mathematics teachers were asked to think aloud when posing a word problem whose solution could be found by computing 4/5 divided by 2/3. The data consisted of verbal protocols along with the written notes made by the subjects. The qualitative analysis of the data was focused on identifying the structures of the problems produced and…

This article describes how a sixth-grade teacher's "missing word" task uncovered higher-level thinking and engaged her students in the Standards for Mathematical Practice. The role and selection of the task promotes higher-level thinking and connects to the Common Core State Standards for Mathematics. The task required students to apply…

Most mathematics assignments consist of a group of problems requiring the same strategy. For example, a lesson on the quadratic formula is typically followed by a block of problems requiring students to use the quadratic formula, which means that students know the appropriate strategy before they read each problem. In an alternative approach,…

This article presents engaging interactive hypothesis tests which can be conducted with students very efficiently.

Classification problems ("find the odd-one-out") are frequently used as tests of inductive reasoning to evaluate human or animal intelligence. This paper introduces a systematic method for building the set of all possible classification problems, followed by a simple algorithm for solving the problems of the R-ASCM, a psychometric test derived…

This study investigated the promotion of children's understanding and acquisition of arithmetic concepts and the effects of inhibitory skills. Children in Grades 3, 4, and 5 solved two sets of three-term addition and subtraction problems (e.g., 3 + 24 - 24, 3 + 24 - 22) and completed an inhibition task. Half of the participants received a…

In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

A seminal study by Chi "et al." firmly established the paradigm that novices categorize physics problems by "surface features" (e.g., "incline," "pendulum," "projectile motion," etc.), while experts use "deep structure" (e.g., "energy conservation," "Newton 2," etc.). Yet, efforts to replicate the study frequently fail, since the ability to…

This article advocates biased spinners as an engaging context for statistics students. Calculating the probability of a biased spinner landing on a particular side makes valuable connections between probability and other areas of mathematics. (Contains 2 figures and 1 table.)

E-Learning brings access to a powerful but often overlooked teaching tool: random number generation. Using random number generation, a practically infinite number of quantitative problem-solution sets can be created. In addition, within the e-learning context, in the spirit of the mastery of learning, it is possible to assign online quantitative…

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%…

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…