Teachers report that engaging students in solving contextual problems is an important part of supporting student understanding of algorithms for fraction division. Meaning for whole-number operations is a crucial part of making sense of contextual problems involving rational numbers. The authors present a developed instructional sequence to…

Developing technology to help people teach and learn is an important topic in Human Computer Interaction (HCI). In this thesis we present three studies on this topic. In the first study, we demonstrate new games for learning mathematics and discuss the evidence for key design decisions from user studies. In the second study, we develop a real-time…

Earth's topographic surface forms an interface across which the geodynamic and geomorphic engines interact. This interaction is best observed along crustal margins where topography is created by active faulting and sculpted by geomorphic processes. Crustal deformation manifests as earthquakes at centennial to millennial timescales. Given that…

The Common Core standards distinguish between domain-specific vocabulary (topic, point on a graph) and general academic vocabulary (consist of, analyze), but is this a false dichotomy, the authors ask? Analyzing character development, they point out, is not the same as analyzing data. This has implications for vocabulary instruction in the areas…

I present an active learning classroom exercise illustrating essential principles of one-way analysis of variance (ANOVA) methods. The exercise is easily conducted by the instructor and is instructive (as well as enjoyable) for the students. This is conducive for demonstrating many theoretical and practical issues related to ANOVA and lends itself…

Studies and discussions around "good teaching practices" have often identified intentionality as the chief characteristic of outstanding teachers. Intentional teachers are identified as maintaining the habit of informed reflection as they plan, teach, reflect on, and revise the effectiveness of their practices. Intentional teaching strategies are…

Scaffolding is an important tool for meeting the challenging needs of heterogeneous groups of students in inclusive classrooms. It is especially useful when supporting low achievers. A video study (funded by the Swiss National Science Foundation, Project Nr. 134652) of 36 inclusive classes, (3rd grade, aged 9 years), was conducted to examine how…

Manipulatives are considered a best practice for educating students with disabilities, but little research exists which examines virtual manipulatives as tool for supporting students in mathematics. This project investigated the use of a virtual manipulative through the National Library of Virtual Manipulatives--polynominoes (i.e., tiles)--as a…

Children's literature involving mathematics provides a common, natural context for the sharing of mathematics. To learn more about how preservice teachers included children's literature in their mathematics lessons, a study was conducted over two semesters during a required field experience component of an undergraduate teacher education program.…

Teaching physics concepts with the basic materials that are around us is one of the beauties of physics. Without expensive lab materials and long experiments, many physics concepts can be taught to students using simple tools. Demonstrations with these tools can be presented as discrepant events that surprise, amaze, or puzzle students. Greenslade…

Multi-touch tablets allow users to interact with computers through intuitive, natural gestures and direct manipulation of digital objects. One advantage of these devices is that they can offer a large, collaborative space where several users can work on a task at the same time. However the lack of privacy in these situations makes standard…

A well-known optimization problem is the Popcorn Box investigation, which involves a movie theater snack container. The problem has been tailored for classroom investigations by the Ontario Association for Mathematics Education. The exploration was designed for students in grades 9 through 12. A common strategy proposed for algebra students is to…

Teachers in early childhood and elementary classrooms (grades K-5) have been using ten-frames as an instructional tool to support students' mathematics skill development for many years. Use of the similar five-frame has been limited, however, despite its apparent potential as an instructional scaffold in the early elementary grades. Due to scant…

This case study analyzed the impact of a concrete manipulative program on the understanding of quadratic expressions for a high school student with a learning disability. The manipulatives were utilized as part of the Concrete-Representational-Abstract Integration (CRA-I) intervention in which participants engaged in tasks requiring them to…

When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…