Over the past few decades there has been increased interest in how students and teachers think and learn about negative numbers from a variety of perspectives. In particular, there has been debate about when integers should be taught and how to teach them to best support students' learning. This book brings together recent work from researchers to…

Six widely used US Grade 1 curricula do not adequately address the following three developmental prerequisites identified by a proposed learning trajectory for the meaningful learning of the subtraction-as-addition strategy (e.g., for 13-8 think "what + 8 = 13?"): (a) reverse operations (adding 8 is undone by subtracting 8); (b) common…

In the domain of "Operations & Algebraic Thinking," Common Core State Standards indicate that in kindergarten, first grade, and second grade, children should demonstrate and expand their ability to understand, represent, and solve problems using the operations of addition and subtraction, laying the foundation for operations using…

The effects of prior encodings of manipulatives (red and blue plastic chips) on children's ability to use them as representations of quantity were tested. First graders (N = 73) were assigned to four conditions in which the encoding of plastic chips was experimentally manipulated. All children then participated in an addition activity that relied…

Effective use of mathematical representation is key to supporting student learning. In "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), "use and connect mathematical representations" is one of the effective Mathematics Teaching Practices. By using different representations, students examine concepts…

Fact fluency is an important prerequisite to mastering more complex and abstract mathematics principles. Delivering math interventions in the home setting may be a feasible way to expose students to necessary supports and improve math outcomes. The present study utilized a multiple baseline design across parent-student dyads to examine the impact…

Many elementary students have difficulty solving mathematical word problems. To alleviate trouble with word problems, we designed a word-problem intervention for 3rd-grade students with mathematics difficulty. In this intervention, tutors help students understand the three word-problem schemas for addition and subtraction word problems. Tutors…

Fractions are troublesome for many children, especially students with learning difficulties and disabilities in mathematics. To address this serious educational concern, this article recommends the use of number lines to build fraction sense. Math activities that center on the number line build fraction concepts as early as third grade. A number…

Learn the most effective ways to teach elementary math, no matter how much experience you have with the subject. In this book, Fuchang Liu takes you through many common mistakes in math instruction and explains the misunderstandings behind them. He points out practices that should be avoided, helping you to adjust your lessons so that all students…

The aim of this study is to design learning activities that can support students to develop strategies for the addition of number 1 to 20 in the first grade by involving students' spatial structuring ability. This study was conducted in Indonesia by involving 27 students. In this paper, one of three activities is discussed namely ten-box activity.…

In this study, it was aimed to analyze the structure of prospective middle school mathematics teachers' problems posed with regard to given symbolic representation including addition and subtraction operations with integers. The study conducted with 96 last grade elementary school mathematics teacher candidates studying in Faculty of Education of…

Children who experience difficulties with learning mathematics should be taught by teachers who focus on the child's best way of learning. Analyses of the mathematical difficulties are necessary for fine-tuning mathematics education to the needs of these children. For this reason, an instrument for Observing and Analyzing children's Mathematical…

The result of additive colors is always fascinating to young students. When we teach this topic to 14- to 16-year-old students, they do not usually notice we use maximum light quantities of red (R), green (G), and blue (B) to obtain yellow, magenta, and cyan colors in order to build the well-known additive color diagram of Fig. 1. But how about…

Math education consultant Marilyn Burns finds that teachers ask her the same three questions so often she's named them "The Big Three": What can I do with students who finish their math work more quickly?, How can I free up time to work with kids who need extra help?, and How can I differentiate math learning experiences? Burns, who…

This paper focuses on kindergarten teachers' interactions with young children during mathematical learning activities involving the use of digital tools. We aim to characterise the teachers' roles and actions in these activities and extend considerations of teachers' orchestrations current in the research literature with regard to agency and…