In this article, the authors present a brief description of the different views of the "nature of mathematics" (NOM), share a five-point view of NOM that undergirds the teaching profession's guiding documents, and describe ways of providing opportunities for teachers and students to have conversations in the classroom that build…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) identifies the strategic use of appropriate tools as one of the mathematical practices and emphasizes the use of pictures and diagrams as reasoning tools. Starting with the early elementary grades, CCSSM discusses students' solving of problems "by drawing." In later…

Much attention has been devoted in the literature to students' struggles with fraction division. With regard to the traditional invert and multiply algorithm, researchers and educators have examined such areas as typical errors, how to help students understand why this method works, and what alternatives are available that might be more intuitive.…

An interesting change has been occurring in the author's middle school mathematics classes. Some students have become creative, free-thinking inventors. If they have had little experience with an operation, they invent strategies of their own. Sometimes these strategies have been well informed and supported by strong mental math skills and a good…

While there have been many articles published in the area of self-regulated learning, there is a need to have a research article that solely emphasizes on how to put self-regulated learning theory into practice. In order to help teachers incorporate self-regulated learning theory into their classroom teaching and students to do so into their…

Just as ready-made clothes may not provide a perfect fit for all bodies, math lessons may not be a perfect fit for all students. Published instructional tasks, including problems in mathematics textbooks, often need to be tailored to be meaningful, relevant, or accessible to each student. Ways are possible to take high-level reasoning tasks and…

In the upper elementary grades, content-area text gains increasing importance as a primary source of reading and information. This article focuses on the specialized vocabulary demands of social studies texts and presents a framework of teaching and learning strategies based on vocabulary research. Strategies are introduced before, during, and…

Many teachers fall into the pattern of "assumptive teaching" (Herber 1970), assuming that other instructors will teach students the important strategies they need for learning. In this case, tools and strategies may not be taught outside of reading or language arts because a science teacher can say, "It's not my job." However, a sixth-grade team…

Self-regulated learning (SRL) is a conceptual model that can be used to design and implement individualized learning strategies for students with learning disabilities. Students who self-regulate their learning engage in planning, performance, and self-evaluation during academic tasks. This article highlights one approach for teaching SRL skills…

Learning pathways capture the development of competence in a mathematical domain. They have been developed from empirical studies in the areas of mental computation and emergent numeracy concepts. These pathways afford teachers the opportunity to identify students' current levels of understanding, antecedent understandings and the steps that are…

The history of strategies research during the past quarter century has been a story of significant conceptualizations and reconceptualizations regarding the nature, development, and teaching of cognitive and metacognitive strategies. Theoretical models, empirical research, and discussions contributed by Michael Pressley have been central to…

As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that…

When scaffolding is done correctly, students are encouraged to develop their own creativity, motivation, and resourcefulness. How teachers interact with students and how students interact with one another as they complete a task is important to students' ability to perform the activity. This article shows how scaffolding can be effectively applied…

On the surface, gifted children may appear to be well adjusted, but they are often highly sensitive, perfectionistic, and intense. They usually have an acute awareness of moral issues, with a unique perception of themselves and others and deeper feelings at an earlier age than their peers. Because of these intense qualities, they may suffer from…

The inaugural column in the "Content Literacy" department discusses the importance of teachers' assisting students in grades 4-6 to develop content literacy skills. The discussion centers on levels of literacy and diversity issues facing teachers and then identifies three fundamental elements that should be a part of every teacher's content…