Several studies related to mathematics understanding found that many undergraduate students lack some basic knowledge of algebra. They memorized only a few topics, formulas, and algorithms without understanding them conceptually, even though they could manipulate those limited number of points correctly or incorrectly. In comparison, most…

Previous studies have repeatedly shown that children often incorrectly use an additive model for multiplicative word problems, and a multiplicative model for additive word problems. The present study aimed to investigate which model upper primary school children tend to choose in word problems that are open to "both" ways of reasoning.…

Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

Researchers have proposed a variety of methods to make a connection between real life and mathematics so that it can be learned in a practical way and enable people to utilise mathematics in their daily lives. Model-eliciting activities (MEAs) were developed to fulfil this need and are very capable of serving this purpose. The reason MEAs are so…

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

This paper explores sixty-six students' personal meaning and interpretation of the vertex of a quadratic function in relation to their understanding of quadratic functions in two different representations, algebraic and word problem. Several categories emerged from students' personal meaning of the vertex including vertex as maximum or minimum…

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

General problem-solving skills are of central importance in school mathematics achievement. Word problems play an important role not just in mathematical education, but in general education as well. Meaningful learning and understanding are basic aspects of all kinds of learning and it is even more important in the case of learning mathematics. In…

The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…

This study investigates the extent to which pre-service elementary teachers (PETs) use their realworld knowledge to solve problems for which the result of the arithmetic operation is problematic, if one takes into consideration the reality of the context. A paper-and-pencil test was administered to 566 PETs enrolled in mathematics content courses.…

What is the relationship between addition and subtraction? How do individuals know whether an algorithm will always work? Can they explain why order matters in subtraction but not in addition, or why it is false to assert that the sum of any two whole numbers is greater than either number? It is organized around two big ideas and supported by…

Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

Proposes a word problem concerning placing students around triangular tables. Students must determine how to place the touching tables so that everyone can be seated. (KHR)

In this study, we examined 139 prospective elementary teachers' solution processes to additive word problems for which the solution is 1 more or 1 less than the answer produced by the straightforward application of the addition or subtraction of the two given numbers. For each problem, five aspects of their solution processes were examined: (a)…