Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The…

Drawing on research around the utility of worked examples, we examine how 29 first- and 27 third-grade students made sense of integer subtraction worked examples and used those examples to solve similar problems. Students first chose which of three worked examples correctly represented an integer subtraction problem and used the example to solve a…

Successful math word-problem solving is difficult for some students. Getting the right answer involves students engaging correctly in an amalgamation of actions. Schema instruction is an instructional approach aimed at supporting students in identifying the underlying math problem structure to yield an appropriate solution plan. The focus of this…

In mathematics, the expectation to set up and solve word problems emerges as early as kindergarten; however, many students who experience mathematics difficulty (MD) and dual-language learners often present with specific challenges in this area. To investigate why these populations experience word-problem difficulty, we examined the word, problem…

In mathematics, the expectation to set up and solve word problems emerges as early as kindergarten; however, many students who experience mathematics difficulty (MD) and dual-language learners often present with specific challenges in this area. To investigate why these populations experience word-problem difficulty, we examined the word, problem…

The question of teaching a standard written algorithm for the four arithmetical operations in the first years of elementary school is increasingly raised as a consequence of the possibility of using calculators, tablets, and computers. This article first presents arguments both against and for maintaining this teaching in the first school years.…

Developing textbooks of optimal quality is crucial for enriching the students' learning and understanding. This study examined fraction addition and subtraction problems in the U.S. and South Korean mathematics textbooks according to the types of denominators. In particular, we investigated Everyday Mathematics (EM) and South Korean mathematics…

Within the broad area of whole number operations, understanding and solving word problems continues to be an important area of inquiry. In the present study we draw on the framework of representational fluency to examine conceptual and procedural understandings that are exhibited by a group of Malaysian seven-year-olds as they attempted to solve…

In this study, it was aimed to teach the addition and subtraction to a student with dyscalculia who is in third grade at elementary school. Before preparing individualized program, the student was given a pretest to measure about his level of the subject. The instruction was carried out in a room in the school, with a time of 40 minutes per day in…

The aim of this study is to determine the effect of mathematics teaching with cartoons on the problem solving skills of primary school 2nd grade students based on addition and subtraction. In the research, pretest-posttest control group design of the experimental model was used. In the classroom where the experimental group students were present,…

This study established an online game-based assessment to explore third and fourth graders' performance of computational estimation in addition and subtraction. Students' computational estimation strategies could be automatically recorded and classified in this assessment, and the Higher-Order DINA model was used as a measurement model in order to…

Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth…

Learning to solve subtraction problems that require borrowing (e.g., 83-57=) is challenging, and these problems often cause 'bridging' errors, such as the smaller-from-larger error. This study explores how bridging errors in subtraction are related to students' mathematical ability. The study involved 694 third-grade students and 35 teachers from…

Many general and special education teachers teach mathematics word problems by defining problems as a single operation and linking key words to specific operations. Unfortunately, teaching students to approach word problems in these ways discourages mathematical reasoning and frequently produces incorrect answers. This article lists eight common…

Many general and special education teachers across the U.S. teach word problems by defining problems as a single operation (e.g., "Today, we're working on subtraction word problems") and linking key words (e.g., more, altogether, share, twice) to specific operations (e.g., share means to divide). Unfortunately, teaching students to…