Research has shown assistance can provide many benefits to novices lacking the mental models needed for problem solving in a new domain. However, varying approaches to assistance, such as subgoals and next-step hints, have been implemented with mixed results. Next-Step hints are common in data-driven tutors due to their straightforward generation…

Faded worked examples have been used to promote problem solving performance, such as mathematics performance in many laboratory studies and short-term classroom studies. However, few studies have examined the ways educators may use fading in their own classroom on more accessible platforms that do not require programming experience. Further, few…

This article begins by describing a class scenario in which a teacher gives her students the L problem (Watanabe 2008), which involves finding the area of a composite figure. Her students inappropriately extend the area formula for rectangles (A = L x W) to composite figures by multiplying all given dimensions. After class, the teacher concluded…

Although visual representations are generally beneficial for learners, past research also suggests that often only a subset of learners benefits from visual representations. In this work, we designed and evaluated anticipatory diagrammatic self- explanation, a novel form of instructional scaffolding in which visual representations are used to…

This paper presents a case study of an experienced and competent mathematics teacher's classroom instructional practice in a Normal Technical Mathematics course. The topic that was observed was Volume and Surface Area of a Pyramid, a subtopic within the mensuration topic in Secondary Two syllabus. The teacher used a video clip on the Egyptian…

We report on mixed methods research that explored pre-service teachers' pedagogical content knowledge in basic musical methods for teaching and learning of basic fractions within the framework of Vygotsky's Theory of Scaffolding. Vygotsky's use of scaffolding opines that knowledge, skills and prior experiences, create the foundation for potential…

We report on mixed methods research that explored pre-service teachers' pedagogical content knowledge in basic musical methods for teaching and learning of basic fractions within the framework of Vygotsky's Theory of Scaffolding. Vygotsky's use of scaffolding opines that knowledge, skills and prior experiences, create the foundation for potential…

Prior research shows that self-explanation promotes understanding by helping learners connect new knowledge with prior knowledge. However, despite ample evidence supporting the effectiveness of self-explanation, an instructional design challenge emerges in how best to scaffold self-explanation. In particular, it is an open challenge to design…

Many studies have shown that visual representations can enhance student understanding of STEM concepts. However, prior research suggests that visual representations alone are not necessarily effective across a broad range of students. To address this problem, we created a novel, scaffolded form of diagrammatic self-explanation in which students…

This article contributes to the research literature concerning prospective elementary teachers' mathematical thinking and learning with a focus on flexibility. We present a case study of a prospective elementary teachers' development of flexibility in mental addition and subtraction during a Number and Operations course. Building upon the…

Latitude and longitude are foundational concepts for geography education, yet they are typically poorly understood by students and receive indifferent attention from instructors and publishers' materials. Social studies teachers can take advantage of increasingly ubiquitous geolocating devices such as Global Positions Systems (GPS) to provide…

If we want to make something concrete in mathematics education, we are inclined introduce, what we call, "manipulatives", in the form of tactile objects or visual representations. If we want to make something concrete in a everyday-life conversation, we look for an example. In the former, we try to make a concrete model of our own,…

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…

We present a methodology for designing better learning environments. In Phase 1, 6th-grade students' (n = 223) prior knowledge was assessed using a difficulty factors assessment (DFA). The assessment revealed that scaffolds designed to elicit contextual, conceptual, or procedural knowledge each improved students' ability to add and subtract…

What is meant when people say that "learning environments are increasingly complex"? What is known about the cognitive processing that occurs during complex learning? How can educators provide effective instructional support for students who must learn and apply complex knowledge? These questions, and related issues, have fascinated educators and…