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

"π has fascinated mathematicians, engineers and other people for centuries. It is a mathematical constant that is the ratio of a circle's circumference (C) to its diameter (d); This also explains why and how this number got its name: the lowercase π was first adopted in 1706 as an abbreviation for this number because it is the first letter of the Greek for "perimeter", specifically of a circle." Introduces a video by Numberphile explaining more about the determination of π

Discusses theory of motivational learning in educational games and presents a research study involving 115 elementary school students in math class using digital game-based learning

Abstract: "In traditional mathematics education, students have typically been asked to solve lots of tedious and uninteresting exercises for developing the arithmetic skills of addition and subtraction. The paper provides an account of learning arithmetic skills in a more interesting way through the collaborative playing of a puzzle game. 83 students in three classes in Grade 4 were asked to solve arithmetic problems with three different methods: via playing an adapted "cross number puzzle" game on Group Scribbles (GS) collaboratively, via playing the same game on GS individually, and via the traditional method of teaching and learning, i.e. with no games at all. Analysis of the pre and post learning achievement data reveals that the two classes who played the game performed better than the control class, with the collaborative class students achieving better than the individual class students. By playing the game, low-ability students, in particular, made the most significant progress in arithmetic capability and in building up their confidence in doing arithmetic calculations."

Abstract "The relation between fidelity of implementation and student outcomes in a computer-based middle school mathematics curriculum was measured empirically. Participants included 485 students and 23 teachers from 11 public middle schools across seven states. Implementation fidelity was defined using two constructs: fidelity to structure and fidelity to process".

"Albert Einstein called her the most "significant" and "creative" female mathematician of all time, and others of her contemporaries were inclined to drop the modification by sex. She invented a theorem that united with magisterial concision two conceptual pillars of physics: symmetry in nature and the universal laws of conservation."

Essays and commentaries (full text access requires subscription)

"The participants of this study were undergraduate students at a university in Western Canada. They were enrolled in a Secondary Mathematics methods course as part of their program. A total of 21 students (10 males and 11 females) in the class participated voluntarily, ranging from ages 20 to 45 years old. " Surveyed before and after they design math games for the classroom.

"This book provides insights into how mathematical understanding emerged for primary-aged children (5-13 years) when they investigated mathematical tasks through digital media."

Motivation and Disposition: Pathways to Learning Mathematics - 73rd Yearbook (2011) Product Description Daniel J. Brahier, Volume Editor and William R. Speer, General Editor "Teaching mathematics is a much broader endeavor than simply helping students to acquire skills and problem-solving strategies. ...NCTM's seventy-third yearbook examines such elements as the demographic composition of a school; the role of movies, television, and the Internet; and nontraditional pedagogy as means of promoting and influencing positive student and teacher dispositions." Of particular interest is Chapter 9 "What Motivates Mathematically Talented Young Women?," which evidently reports on high school girls at a summer camp. Available for .pdf download via purchase, or in a library: http://www.worldcat.org/oclc/715171259

Abstract: Educational videogames can be designed to provide instructional feedback that is responsive to specific actions. However, existing research indicates that students tend to ignore videogame feedback and subsequently use less effective help-seeking strategies. Research on help-seeking in learning environments has primarily focused on the role of cognitive factors, the nature of the help, or issues of timing and frequency. There is a noticeable gap in understanding regarding how to motivate and increase the use of feedback for improved learning. Using a pre-algebra videogame, this study examined the relationship between an incentive to use feedback and math achievement. A randomized-control design was employed, which compared learning outcomes of students who received the incentive to those who did not. Results indicated that students given the incentive to use feedback had significantly higher normalized change scores on math items (d = .53), with stronger effects for students with low academic intrinsic motivation (d = .88 - 1.17).

"math behind visual hallucinations"

Abstract: "Shoot x Shoot is the first game for EduTurtle. It's a 6th grade Math game that combines topics like "Multiples", "Cartesian Plane", "International and English measurement systems", "Percentages and fractions". Through a pre game test we obtain a score of the students on the subjects then is a game time and before this time we measure again with a similar test the score of the students in order to measure an influence of the game on the students about this subjects. The online platform EduTurlte offers educational games for elementary schools children. In a near future at http://www.eduturtle.com girls and boys may come to play (and at the same time learn and reinforce their knowledge) by keeping track of their progress in games on various topics at different grades. It is also a way to reinforce the lessons learned in the classroom and/or books through games that capture their attention over entertainment. "

Abstract: "A mobile learning research project was conducted in Trinidad and Tobago to determine if mobile learning can assist high school students in learning mathematics. Several innovative techniques were used in this research to address the problem of high failure rates of mathematics in high schools in the Caribbean. A mobile learning application was developed based on a subset of the high school mathematics curriculum used in the English-speaking Caribbean. Game-based learning, personalization and multiple learning strategies were used in conjunction with mobile learning to assist students in improving their performance in mathematics. Three evaluation studies were conducted with the mobile learning application. During the studies, usage data was captured automatically by the system and this was used to determine the extent to which the students actually used the mobile application. At the end of each study, a questionnaire was used to capture student opinions of the mobile learning application. Questionnaire data is based solely on student responses and there is no guarantee of its accuracy and reliability. This paper focuses on the responses of the students to the questionnaire and seeks to determine if the usage data can increase the reliability of the questionnaire data. It summarizes the behaviour patterns of the students gleaned from the usage logs and compares this to the students' responses to the questionnaire. Generally it was found that the students' responses agreed with the usage data, though there were occasions when the responses diverged."

"Research has been conducted on how to aid blind peoples' perceptions and cognition of scientific data and, specifically, on how to strengthen their background in mathematics as a means of accomplishing this goal. In search of alternate modes to vision, researchers and practitioners have studied the opportunities of haptics alone and in combination with other modes, such as audio."

Video games are hard, and that's official Super Mario, Donkey Kong and other classic games belong to class of hard mathematical puzzles, and could be used to solve real-world problems IF YOU have ever struggled to complete classic Nintendo games, don't feel bad?- they are officially difficult.

Electronic tutoring system, to help students with standardized tests gauges students' responses as they learn, received a ONR grant http://www.umass.edu/newsoffice/newsreleases/articles/148281.php

Demonstrates the utility of exergames for teaching and learning. "Our goal is to design a math game for children aged between 8 and 12. Our focus in basic operations: adding, subtracting, dividing and multiplying. Players must gather a given number of objects in order to properly complete mathematical operations while at the same time avoiding or destroying other objects that cause him to lose energy or reduce the time given to complete the task."

A platform combining a searchable database of the "Jahrbuch �ber die Fortschritte der Mathematik" (1868-1942) and digitized mathematical publications from the Digital Library Göttingen. Cannot tell if the project is active or being updated at the moment.

Kristine Fowler, mathematics librarian at the University of Minnesota, shares results from a survey of mathematicians concerning how they want to be able to reuse their work, discusses alternatives to standard copyright contracts and urges scholars and institutions to be aware of not only their options but the rights they may cede in entering into publishing agreements.