Group items tagged

A collection of 279 Math Applets designed by International Education Software. Apps show individual concepts from multiple perspectives, usually conceptually from a diagram and graphically. Not very dynamic in that students wouldn't be able to manipulate multiple variables, but great to use with an interactive white board to show connections between representations and to confirm calculations/predictions.

Discussion of the idea of the flipped classroom. Doesn't just introduce one approach but a variety of well thought out options, and how some schools are scaling the model. Musallam is worth reading.  I do have concerns that Hooper's videos are 25-30 minutes long in his model. I think he's missing the point as far as chunking information in smaller components and letting students interact with the content.  Not a perfect model but it is an innovation, and both teachers do a much better job of using key vocabulary well, introducing multiple representations intentionally and connected, and providing guides for students. Much better than I think Khan does in his videos. 

Great connections between math and "real world" settings. Well developed use of multiple representations. 

New tool for drawing. The drawing can be 'replayed' allowing students/teachers to tell a story or to make connections between parts of the drawing. Great visual imagery tool! Great for modeling multiple representations in mathematics.

Activities from TI. Well designed and include multiple representations, technology and exploration

Great new number sense math app. Cost $0.99 at this time but uses: the capabilities of the iPhone well (motion, graphics), multiple representations including linear and circle models, decimals, fractions, percents. Is fast moving and progresses beyond 0 to 1 to have students estimating values like 0.26 on a number line from 0 to 2.  

In Intelligence Reframed Howard Gardner contends that "literacies, skills, and disciplines ought to be pursued as tools that allow us to enhance our understanding of important questions, topics, and themes." Today's readers become literate by learning to read the words and symbols in today's world and its antecedents. They analyze, compare, evaluate and interpret multiple representations from a variety of disciplines and subjects, including texts, photographs, artwork, and data. They learn to choose and modify their own communication based on the rhetorical situation. Point of view is created by the reader, the audience and the medium.

This problem comprehension or schema knowledge is facilitated when the schema underlying a given text is used as a vehicle to translate the information in the text into a semantic representation. this would involve restating the problem, identifying the problem type (i.e. change), discerning relevant and irrelevant information, determining information that is needed for solution, and representing the problem as a diagram (Mayer, 1999).  Problem solution requires representing the problem as a number sentence or list of operations or identifying subgoals for multistep problems (i.e. strategic knowledge) and carrying out single or chains of calculations (i.e. procedural knowledge; Mayer 1999). Because additive problem structures (i.e. change, group, compare) involve a "family" (e.g. 3, 5, 8), connecting the number family to the problem structures is critical to problem solution (Van de Walle, 2004). Although procedural knowledge is important, it (is extremely limited unless it is connected to a conceptual knowledge base" (Prawat, 1989, p. 10).  SBI- Schema-based instructionGSI- General strategy instruction SBI Components (some not necessarily all) a) SBI that used either number line diagrams to understand the semantic structure of compare word problems or schematic diagrams to solve a range of word problems. b) schema-induction instruction, c) SBI that explicitly taught for transfer by focusing on similar problem types, and d) SBI combined with metacognitive instruction.  different format, different question, unfamililiar vocabulary, irrelevent information, combining problem types, and mixing superficial features

Universal design for learning

"In this article we introduce the free educational mathematics software GeoGebra. This open source tool extends concepts of dynamic geometry to the fields of algebra and calculus. You can use GeoGebra both as a teaching tool and to create interactive web pages for students from middle school up to college level. Specifically designed for educational purposes, GeoGebra can help you to foster experimental, problem-oriented and discovery learning of mathematics. We will illustrate the basic ideas of the software and some of its versatile possibilities by discussing several interactive examples."