This article reviews the famous "matching problem," with a particular focus on the expected number of objects that are correctly placed. The author discusses the following topics: three versions suitable for teaching the matching problem in the classroom; the solution to the matching problem; the use of the strong form of mathematical…

Students with learning disabilities (LD) consistently struggle with word problem solving in mathematics classes. This difficulty has made curricular, state, and national tests particularly stressful, as word problem solving has become a predominant feature of such student performance assessments. Research suggests that students with LD perform…

Constructing viable arguments and reasoning abstractly is an essential part of the Common Core State Standards for Mathematics (CCSSI 2010). This article discusses the scenarios in which a mathematical task is impossible to accomplish, as well as how to approach impossible scenarios in the classroom. The concept of proof is introduced as the…

How do students think about an angle measure of ninety degrees? How do they think about ratios and values on the unit circle? How might angle measure be used to connect right-triangle trigonometry and circular functions? And why might asking these questions be important when introducing trigonometric functions to students? When teaching…

Error analysis is the study of errors in learners' work with a view to looking for possible explanations for these errors. It is a multifaceted activity involving analysis of correct, partially correct and incorrect processes and thinking about possible remediating strategies. This paper reports on such an analysis of learner tests. The tests were…

We describe an attempt by a former mathematics teacher to read an undergraduate mathematics proof aided by discussions with a mathematician using the language of mathematical problem solving. The literature on successful approaches to reading mathematics is scarce at the secondary and undergraduate levels. Shepherd, Selden and Selden (2012)…

We encounter ratios on a daily basis. They also play an important role as a basic construct of thinking in many areas of school mathematics. For example, a fraction can be interpreted as the ratio of a part to the respective whole. Many children appear to have difficulties with fractions and although the concept of ratios is crucial for this…

"Ensuring Mathematical Success for All" (NCTM 2010) outlines eight teaching practices for effective teaching and learning of mathematics. One of the teaching practices, building procedural fluency from conceptual understanding, states the following: Effective teaching of mathematics builds fluency with procedures on a foundation of…

Using Cuisenaire Rods, metric measurement, and mapping, students worked collaboratively to calculate, keep records, build, and problem solve with use of decimal fractions as a key element.

This research was conducted to investigate 7th grade students' problem solving success rates on proportional reasoning problems and whether these success rates change with different problem types. 331 randomly selected students of grade seven participated in this study. A problem test which contains three different types of missing value (direct…

The theoretical and methodological model of Mathematical Working Space (MWS) is introduced in this paper. For over 10 years, the model has been the object of collaborative research among various researchers, generally coming from French and Spanish speaking countries. Articulating epistemological and cognitive aspects, the MWS model is aimed at…

Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over…

Differences exist between engineering and liberal arts students because of their educational backgrounds. Therefore, they solve problems differently. This study examined the brain activation of these two groups of students when they responded to 12 questions of verbal, numerical, or spatial intelligence. A total of 25 engineering and 25 liberal…

Intelligence is not fixed. While many of us may not be innately talented in all areas of learning, all of us are capable of learning anything. It is important that teachers help communicate this concept to students and help students to develop this growth mindset. This article first compares growth and fixed mindsets, discussing some of the…

Sorting is a fundamental computing concept. As for today, it is taught at the secondary school level. However, this kind of algorithm is an obstacle for some students due to its high level of abstraction. To prevent discouragement as well as to incorporate a fun and challenging algorithmic task, a novel tablet-based digital game,…