Circle Geometry, a senior mathematics topic, is often regarded as time-consuming and associated relational concepts difficult for students to grasp. Units of work that introduce students to circle geometry theorems are frequently described as a string of tedious constructions. This article explores teacher-designed dynamic geometry software…

To improve student success in mathematics, the use of research-based interventions is necessary to help secondary students with learning disabilities (LD) access the algebra curriculum. The authors provide an overview of the following research-based approaches: explicit instruction, graduated instructional sequence, technology, and graphic…

Reading aloud to children is a recommended practice in early childhood and primary-grade classrooms that is purported to enhance vocabulary growth. General guidelines can be found in the literature, but practitioners often rely on conventional wisdom and their own instincts to embed vocabulary instruction into their read-alouds. This paper…

Efforts to meet the needs of children's learning in arithmetic has led to an increased emphasis on the teaching of mental calculation strategies in England. This has included the adoption of didactical tools such as the empty number line (ENL) that was developed as part of the realistic mathematics movement in the Netherlands. It has been claimed…

The "What's the "matter" With XOD" activity addresses students' misconceptions and refines their ideas about phases of matter. This activity introduces the characteristics for solids, liquids, and gases, and begins a discussion about physical and chemical changes and how matter can cycle through different phases. Depending on class size and…

This paper reports on a study that explored the use of cognitively challenging tasks with low-attaining mathematics students and in particular, their teachers' attempts at scaffolding. A major finding was that responding appropriately to scaffolding opportunities was challenging for the teachers. In this paper two main factors are discussed which…

The present study describes a case of a 9-year-old girl diagnosed on the autism spectrum who averaged nearly 1200 hand-to-head self-injuries (+attempts) per school day. Given the resources of the school and the significance of the self-injurious behavior (SIB), analog functional analysis is not possible. Moreover, functional assessment results…

Response to intervention is meant to be broad-based and preventative. However, as formulated and practiced the approach often is too limited in how it frames what needs to go on to enable learning, engage students, and keep them engaged. In particular, it pays too little attention to the need to strengthen the classroom and schoolwide context in…

Using investigations in teaching mathematics has for many years become an established feature of most curricula around the world. Investigations can be a vehicle for enabling children to experience the genuine excitement that comes from mathematical discovery. The true spirit of inquiry and investigation lies in the mind-set that continually asks…

The design of problems is crucial for the effectiveness of problem-based learning (PBL). Research has shown that PBL problems have not always been effective. Ineffective PBL problems could affect whether students acquire sufficient domain knowledge, activate appropriate prior knowledge, and properly direct their own learning. This paper builds on…

This article gives a general overview of an alternative instructional sequence that can be used to teach integer concepts and operations. The sequence follows three heuristics from Realistic Mathematics Education (RME) that encourage curricula to be reinforced with real-world applications (financial net worth): move students gradually, yet…

Designing educational sequences that enhance the cognitive, behavioral, and critical skills of a diverse learning community seeking global competencies, requires mindfulness of different international educational models, a tailored curriculum designed to build different types of awareness learning, and clarity in targeted outputs keeping in mind a…

Adaptive learning techniques have typically scheduled practice using learners' accuracy and item presentation history. We describe an adaptive learning system (Adaptive Response Time Based Sequencing--ARTS) that uses both accuracy and response time (RT) as direct inputs into sequencing. Response times are used to assess learning strength and to…

Differentiated instruction denotes varying instruction in terms of content, product, and process to meet the needs of all learners. One way to differentiate the instructional process is to provide multi-tiered instruction. Examples of systematic approaches to multi-tiered instruction are response to intervention (RTI) and school-wide positive…

This contribution reflects empirical data arising from a study based on the testimony of 1523 students referring to the time when they studied history in secondary school. It forms part of an on-going inter-disciplinary research project. By means of open activities, information was compiled on the History classes received by students studying…