After years of noticing the challenge our students have with fraction operations, we decided to implement a scaffold approach that focuses on using benchmarks to better develop both students' understanding of a fraction as a quantity and their ability to think about fraction operations meaningfully. While we found this approach supported students…

Reading outcomes at a national level have remained stagnant for more than two decades. One reason why is that the field has struggled with how to address poor reading comprehension when reading words is not the problem. Another is that limited insight into the causes of poor comprehension performance is offered by traditional reading comprehension…

Let's say you are a Grades 3-5 teacher in search of an activity sheet on different fraction notations. A search in May 2022 on the popular resources sharing site TeachersPayTeachers (TpT) yielded 2,832 results, 105 of which were free. With so many options, how would you go about choosing a resource for your students? What would factor into your…

We share ideas for preparing for and enacting high-cognitive demand tasks in ways that support students in articulating and justifying their ideas. We offer strategies for developing and posing several types of purposeful questions: (1) eliciting thinking, (2) generating ideas, (3) clarifying explanations, and (4) justifying claims.

Learning how to give effective feedback can be a difficult task for teacher leaders. This is especially true for what is called "hard feedback"--that is, feedback that challenges the teacher's practice and therefore may cause some level of professional discomfort. Educators at the University of Pittsburgh's Institute for Learning have…

The quadrilaterals problem is a particularly rich task, applicable to in-service teachers as well as to the students they teach. The ways in which students engage in this task, the strategies they use, and the mathematics that results align well with this "MT" Focus Issue on flexible mathematical thinking. The authors offer their observations of…

This practice guide presents five recommendations intended to help educators improve students' understanding of, and problem-solving success with, fractions. Recommendations progress from proposals for how to build rudimentary understanding of fractions in young children; to ideas for helping older children understand the meaning of fractions and…

In this article, we highlight the need for a precisely defined construct in score-based validation and discuss the contribution of cognitive theories to accurately and comprehensively defining the construct. We propose a framework for integrating cognitively based theoretical and empirical evidence to specify and evaluate the construct. We apply…

"Science Books & Films," the journal of the American Association for the Advancement of Science (AAAS), reviews books for young readers in the sciences to identify winners of these categories: Children's Science Picture Book, Middle Grades Science Book, and Young Adult Science Book. At each age level five finalists are selected for the annual…

Mathematics concepts are most often taught using auditory, sequential instructional methods. Not only are these methods ineffective when used with visual-spatial learners, they may be detrimental to both academic and emotional progress. Ways in which visual-spatial learners process information are explained. One child's story is presented,…

Teacher educators are constantly searching for ways to better prepare preservice teachers to enter the education field. One way that has gained prominence in the last twenty years is through examining and discussing authentic student work samples. Research suggests that doing so helps preservice teachers to (1) gain insight into their own beliefs…

Approximately 100 years ago, Clark Hetherington articulated the primary aims of physical education by identifying four separate areas: (1) psychomotor, which refers to motor skills; (2) organic, the fitness factor; (3) intellectual, or the cognitive component; and (4) character which refers to the affective domain. These categories can be used to…

This article describes how fifth-grade students created collaborative online learning communities while discussing and responding to literature on an asynchronous message board. At their own initiative, students constructed and posted various types of literature response prompts, which elicited rich responses from their peers. Types of identified…

This article discusses a new design for the classic Bloom's Taxonomy developed by Anderson, L. W. & Krathwohl, D. (2001), which can be used to evaluate learners' technology-enhanced experience in more powerful and critical ways. The New Bloom's Taxonomy incorporates contemporary research on learning and human cognition into its model. The…

The purpose of this paper is to focus on the nature of the thinking processes supporting pupils' construction and understanding of mathematical concepts. We assume that interaction with reality plays a crucial role in learning. In particular, human perception and action and, more generally, interaction with artefacts, are very important for…