Education Commons^™

Pre-Service Elementary Teachers' Use Of Spatial Diagrams: Investigations Of Unbounded Shearing On Solid Figures, Camden G. Bock

Electronic Theses and Dissertations

Mithala and Balacheff (2019) describe three difficulties with two-dimensional representations of three-dimensional geometrical objects: “it is no longer possible to confuse the representation with the object itself,” visually observed relationships can be misleading, and analysis of the representation requires the use of lower-dimensional theoretical properties. Despite these difficulties, students are routinely expected to learn about three-dimensional figures through interacting with two-dimensional inscriptions. Three-dimensional alternatives include diagrams realized through various spatial inscriptions (e.g., Dimmel & Bock, 2019; Gecu-Parmaksiz & Delialioglu, 2019; Lai, McMahan, Kitagawa & Connolly, 2016; Ng and Sinclair, 2018). Such diagrams are three-dimensional in the sense that they occupy …

Online Mathematics Homework Increases Student Achievement, Jeremy Roschelle, Mingyu Feng, Robert F. Murphy, Craig A. Mason

STEM Faculty Scholarship

In a randomized field trial with 2,850 seventh-grade mathematics students, we evaluated whether an educational technology intervention increased mathematics learning. Assigning homework is common yet sometimes controversial. Building on prior research on formative assessment and adaptive teaching, we predicted that combining an online homework tool with teacher training could increase learning. The online tool ASSISTments (a) provides timely feedback and hints to students as they do homework and (b) gives teachers timely, organized information about students’ work. To test this prediction, we analyzed data from 43 schools that participated in a random assignment experiment in Maine, a state that provides …

Deductive Mathematics: An Introduction To Proof And Discovery For Mathematics Education, Andrew Wohlgemuth

Mathematics and Statistics Faculty Scholarship

Mathematics has two fundamental aspects: (1) discovery/logical deduction and (2) description/ computation. Discovery/deductive mathematics asks the questions:

1. What is true about this thing being studied?

2. How do we know it is true?

On the other hand, descriptive/computational mathematics asks questions of the type:

3. What is the particular number, function, and so on, that satisfies ... ?

4. How can we find the number, function, and so on?

In descriptive/computational mathematics, some pictorial, physical, or business situation is described mathematically, and then computational techniques are applied to the mathematical description, in order to find values of interest. The …