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A discussion of early advanced mathematics.

"Schoolhouse Rock may be the standard for music-based educational videos, but YouTube is leading the renaissance of educational songs and dances. Using music as a lure for educational content isn't new, but it's being widely adopted, thanks to the accessible and sharable nature of YouTube."

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Definition of the exponential form. A basic example to understand the system of expressing any number into exponential form on the basis of another number.

Among a number of math related questions on this blog, this post focuses on a particular sequence of integrals

"SRI International, Worcester Polytechnic Institute (WPI), and the University of Maine have received a $3.5 million award from the Institute of Education Sciences at the U.S. Department of Education to evaluate the effectiveness of an online tutoring system for mathematics homework. The research team will study seventh-grade mathematics students and teachers in more than 50 schools throughout Maine using WPI's ASSISTments system. ASSISTments aims to transform homework by giving students instant feedback and tutoring adapted to their individual needs. It also provides teachers with customized reports each morning on their students' nightly progress. Teachers in the study will receive training in how to use these reports to adapt their lesson plans to better suit students' needs."

A Kickstarter project for a children's math and science-oriented detective story: "This is the made up story about two very real girls - Ada, the world's first computer programmer, and Mary, the world's first science fiction author - caught up in a steampunk world of hot-air balloons and steam engines, jewel thieves and mechanical contraptions. For readers 8-12. "This is a pro-math, pro-science, pro-history and pro-literature adventure novel for and about girls, who use their education to solve problems and catch a jewel thief. Ada and Mary encounter real historical characters, such as Percy Shelley, Charles Babbage, Michael Faraday, and Charles Dickens - people whom the girls actually knew. If Jane Austen wrote about zeppelins and brass goggles, this would be the book."

by Penta, Michael K., M.S., UNIVERSITY OF MASSACHUSETTS LOWELL, 2011, 83 pages; 1507796 Abstract record for a thesis completed in December 2011, fulltext requires subscription or purchase. A news story on the departmental blog http://blog.uml.edu/cs/2011/12/penta_ms_video_games_for_math_learning.html describes the kinds of games involved, the participants and the results.

"The revolutionary calculator that shows the answer only when you also enter a suitable mental estimate." (I have no connection with this company or product.)

A study on the efficacy of introducing game-like achievements in classroom learning, with math as one of the examples, see appendices

Abstract:"Prime Climb is an educational game that provides individual support for learning number factorization skills in the form of hints based on a model of student learning. Previous studies with Prime Climb indicated that students may not always be paying attention to the hints, even when they are justified (i.e. based on a student model's assessment). In this thesis we will discuss the test-bed game, Prime Climb, and our re-implementation of the game which allowed us to modify the game dynamically and will allow for more rapid prototyping in the future. To assist students as they play the game, Prime Climb includes a pedagogical agent which provides individualized support by providing user-adaptive hints. We then move into our work with the eye-tracker to better understand if and how students process the agent's personalized hints. We will conclude with a user study in which we use eyetracking data to capture user attention patterns as impacted by factors related to existing user knowledge, hint types, and attitude towards getting help in general. We plan to leverage these results in the future to make hint delivery more effective."

From the abstract (full text requires subscription or purchase): "Though cooperative learning has been a topic of considerable interest in educational research, there has been little study specific to learning in the mathematics content area of geometry. This paper seeks to address that gap through a design experiment featuring a novel small-group computing environment for supporting student learning about quadrilaterals. In this design, each student controls a unique point in a shared geometric space, and those points are linked such that a group of four students collectively forms a quadrilateral. We first present results from pre- and post-measures to show how the students learned from the activities and developed in terms of geometric reasoning. We then present three episodes, elaborated with the notion of appropriation, to explain how students took up ways of using the technological tools and of talking about geometric concepts from one another in the interactive environment. Our study found that students achieved learning gains in this novel environment, that the environment provided rich opportunities for peer interaction around geometric objects, and that student learning opportunities and interactions were characterized by processes of appropriating ways of talking about and using software features."

"The purpose of this study is to determine the effect of supplemental instruction using technology on the attitude toward mathematics of fifth grade students with learning disabilities in a classroom."

forthcoming book from University of Chicago Press, June 2012

Beta of a new TED educational video site, featuring "collaborations between talented educators and animators nominated through the TED-Ed platform," and which are available for use as lessons and evaluating student learning. The above link points to the mathematics section

"Some people love math, some hate it, and some are scared of it. Math for the Frightened provides a trauma-free entry into the world of numeracy, written by someone who is on your side. It even gives away the big secret: math really is useful"

"Fascinating Mathematical People is a collection of informal interviews and memoirs of sixteen prominent members of the mathematical community of the twentieth century, many still active. The candid portraits collected here demonstrate that while these men and women vary widely in terms of their backgrounds, life stories, and worldviews, they all share a deep and abiding sense of wonder about mathematics."

"This book explores 20 geometric diagrams that play crucial roles in visualizing mathematical proofs."

"Complicated mathematics presented in a generally understandable way Examples from everyday life are mathematized Many examples presented with a good sense of humor Small riddles and conjuring tricks garantee an entertaining reading Imagine that you've finally found a parking space after a long and harrowing search, but are now encountering some difficulty in trying to enter this space."

A simple Javascript interface allows you type in the expression and get the derivative