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Garrett Eastman

Core foundations of abstract geometry - 4 views

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    Abstract: "Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry. "
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Maggie Verster

The nature and quality of the mathematical connections teachers make - 4 views

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    Current reforms in mathematics education emphasise the need for pedagogy because it offers learners opportunities to develop their proficiency with complex high-level cognitive processes. One has always associated the ability to make mathematical connections, together with the teacher's role in teaching them, with deep mathematical understanding. This article examines the nature and quality of the mathematical connections that the teachers' representations of those connections enabled or constrained. The researchers made video recordings of four Grade 11 teachers as they taught a series of five lessons on algebra-related topics. The results showed that the teachers' representations of mathematical connections were either faulty or superficial in most cases. It compromised the learners' opportunities for making meaningful mathematical connections. The researchers concluded by suggesting that helping teachers to build their representation repertoires could increase the effectiveness of their instructional practices.
Garrett Eastman

Kill Math - 12 views

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    "Kill Math is my umbrella project for techniques that enable people to model and solve meaningful problems of quantity using concrete representations and intuition-guided exploration. In the long term, I hope to develop a widely-usable, insight-generating alternative to symbolic math."
Garrett Eastman

Touch Trigonometry - 18 views

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    "a visual representation of the trig functions"
Roland O'Daniel

Wolfram Education Portal: Free Resources and Materials for Teachers - 12 views

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    In the portal you'll find a dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more built by Wolfram education experts. Absolutely a great resource. Builds in representations, applets, explanations of variable use etc. Great tool.  Since it is in Beta, I am wondering how long it will be free and what their plans are for the future. 
Garrett Eastman

Probability and Statistics Cookbook | Matthias Vallentin - 3 views

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    "The cookbook contains a succinct representation of various topics in probability theory and statistics. It provides a comprehensive reference reduced to the mathematical essence, rather than aiming for elaborate explanations."
Garrett Eastman

Mathematical Literacy for Everyone using Arithmetic Games - 4 views

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    Abstract: "An innovative mathematics game shown to be effective for low-achieving mainstream students is tested in special education for learners with intellectual disabilities. The game relies on a graphical, intuitive representation for numbers and arithmetic operations to foster conceptual understanding and numbers sense, and provides a set of 2-player games to develop strategic thinking and reasoning skills. The game runs on computers and interactive white boards, and as an augmented reality application at a science centre. We compare its use in special education and mainstream education with respect to usage, performance levels and learning gain. The game has been used by teachers in special educations, with gains in mathematical understanding, strategic thinking and communication skills as effects."
Roland O'Daniel

Illuminations: Using Graphs, Equations, and Tables to Investigate the Elimination of Me... - 2 views

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    Great set of lessons for modeling, recursive functions, real-life application from NCTM Illuminations. The lessons include not only context, but applets that help students visualize the situation and  mathematical model. 
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