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LOG IN February 22, 2012 at 2pm Eastern US time: http://tinyurl.com/math20event During the event, John Mason will lead a conversation about multiplication as scaling, and answer questions about his books, projects and communities. All events in the Math Future weekly series: http://mathfuture.wikispaces.com/events The recording will be at: http://mathfuture.wikispaces.com/JohnMason Your time zone: http://bit.ly/wQYN1Y Event challenge! What good multiplication tasks about scaling do you know? Share links and thoughts! John writes about elastic multiplication: "It is often said that 'multiplication is repeated addition' when what is meant is that 'repeated addition is an instance of multiplication'. I have been developing some tasks which present 'scaling as multiplication' based around familiarity with elastic bands. Participants would benefit from having an elastic (rubber) band to hand which they have cut so as to make a strip; wider is better than thinner if you have a choice." About John Mason John Mason has been teaching mathematics ever since he was asked to tutor a fellow student when he was fifteen. In college he was at first unofficial tutor, then later an official tutor for mathematics students in the years behind him, while tutoring school students as well. After a BSc at Trinity College, Toronto in Mathematics, and an MSc at Massey College, Toronto, he went to Madison Wisconsin where he encountered Polya's film 'Let Us Teach Guessing', and completed a PhD in Combinatorial Geometry. The film released a style of teaching he had experienced at high school from his mathematics teacher Geoff Steel, and his teaching changed overnight. His first appointment was at the Open University, which involved among other things the design and implementation of the first mathematics summer school (5000 students over 11 weeks on three sites in parallel). He called upon his experience of being taught, to institute active-problem-solving sessions, w

from the abstract: "Mathematics is now at a remarkable in exion point, with new technology radically extending the power and limits of individuals. Crowd- sourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. The Study of Mathematical Practice is an emerging interdisciplinary eld which draws on philoso- phy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question-answering system mathover ow contains around 40,000 mathe- matical conversations, and polymath collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of \soft" aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a \social machine", a new paradigm, identi- ed by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathe- matics, and to transform the reach, pace, and impact of mathematics research."

(Abstract only online, full text requires subscription) "The pipeline toward careers in science, technology, engineering, and mathematics (STEM) begins to leak in high school, when some students choose not to take advanced mathematics and science courses. We conducted a field experiment testing whether a theory-based intervention that was designed to help parents convey the importance of mathematics and science courses to their high school-aged children would lead them to take more mathematics and science courses in high school. The three-part intervention consisted of two brochures mailed to parents and a Web site, all highlighting the usefulness of STEM courses. This relatively simple intervention led students whose parents were in the experimental group to take, on average, nearly one semester more of science and mathematics in the last 2 years of high school, compared with the control group. Parents are an untapped resource for increasing STEM motivation in adolescents, and the results demonstrate that motivational theory can be applied to this important pipeline problem. "

Abstract: "Together, brain science and learning design inform Adaptive Interaction Design (AID), a technique for curriculum planning and development. Mathematics is a particular case in which AID can help. The Way of the Game is vital to learning design. There are many definitions of "game." Here, we mean game to be the means by which spontaneous play becomes responsible learning. That innovative games figure as the centerpiece of many 21st century curricula is no accident. Games are a critical element in modern theories of learning design especially when related to insights from neuroscience and online learning/teaching methods. But beyond simple gamification, can games provide the disruptive transformation to mathematics education that is required to effect substantive and sustainable improvement? Can we game the educational system to ensure students' success in mathematics? To find out, we will look at the AID process and two sample products for the development of mathematical thinking and practice based on the Way of the Game."

"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."

"Several of our classes involve students using mathematical expressions, but there was no way for us to automatically check this work. The stated solution to a problem may be x+y, but if a student answers y+x, our system needs to understand that this is also correct." "sympy, an open source Python library for symbolic mathematics," is proposed as a solution.

U.S. Department of Education report including research that "tested the impact of offering an online Algebra I course on students' algebra achievement at the end of grade 8 and their subsequent likelihood of participating in an advanced mathematics course sequence in high school."

Abstract only online, full text requires subscription or purchase. Results of one study of 10-12 year old children in eight classrooms in three Australian primary schools leads researchers to suggest "educators should carefully consider the application and appropriateness of games before employing them as a vehicle for introducing mathematical concepts. "

Mathematics teachers disagreeing with the math teaching methods espoused by the Khan Academy, including words from a Stanford PhD candidate: ""When you attempt to distribute mathematics through any of these media [such as YouTube videos, digital photos, MP3s, PDFs, blog posts, spoken words, and printed text] it changes the definition of mathematics."

(abstract only, full text requires subscription or purchase) "We analyze the logs of an online mathematics game tournament, played simultaneously by thousands of students. Nearly 10,000 students, coming from 356 schools from all regions in Chile, registered to the fourth tournament instance. The children play in teams of 12 students from the same class, and send their personal bets to a central server every 2 minutes. Each competition lasts about one clock hour and takes place within school hours. Students are pre-registered and trained by their school teacher. The teacher is responsible for reviewing curriculum contents useful for improving performance at the game and coaches students participating in trial tournaments taking place a few weeks before the national tournament. All bets are recorded in a database that enables us to analyze later the sequence of bets made by each student. Using cluster analysis with this information, we have identified three types of players, each with a well-defined strategy. "

"The article reports the main insights gained from a study that implemented a game-enhanced learning environment for the training of pre-service elementary school teachers. Teachers taking an undergraduate mathematics methods course experienced some of the ways in which online educational games could help students internalize key mathematical concepts across the school curriculum while at the same time improving their attitudes towards the subject. The course also familiarized teachers with the design principles for constructivist gaming environments. Findings indicate a positive impact on teachers' competence in selecting, evaluating, and productively using online games as an instructional tool."

During the live online event Saturday January 14th 2pm ET, Shad Moarif, the founder of Karismath, will lead brainstorming about mathematical videos and dynamic mathematics in general. Event challenge! What types of the Grid do you see from the pedagogical perspective? Discussions beginning before the event This wiki: discussion tab http://mathfuture.wikispaces.com/message/list/Karismath LinkedIn: "Math, Math Education, Math Culture" group http://www.linkedin.com/groupItem?view=&gid=33207&type=member&item=88774229&qid=00e42ab4-4f69-453e-8a79-0a181ab07bc9 Facebook: http://www.facebook.com/karismath/posts/334691806549990 Math Future email group: http://groups.google.com/group/mathfuture/browse_thread/thread/071299f3319650cf# In a grid, there is an obvious connection between the product cell and the simultaneity of two bits of information coexisting within it. Shad is exploring ways of breaking this connection down into a sequence of transitional steps by distilling them visually. Shad has categorized the Grid into eleven types according to their uses for storing, sorting, and displaying numerical information (see below). What pedagogical types of the Grid come to your mind? How to join Follow this link at the time of the event: http://tinyurl.com/math20event

From the abstract: "The problem addressed by this study is the need to identify practical predictors of success for community college developmental mathematics students in online, hybrid and seated course delivery formats. This study examined two possible predictors of success, mathematics self-efficacy and technology self-efficacy, in the three delivery formats and how they related to performance on a final assessment. The study used a quantitative research design employing binomial logistic regression to determine if the independent variables (math self-efficacy and technology self-efficacy) were significant in predicting the outcome category (score on the final assessment dichotomized about the mean). Next linear regression analysis was used to build a predictor equation for a particular score on the outcome variable. A previously developed survey and an adapted version of another survey were combined to measure the independent variables; demographic factors were also measured for descriptive purposes. Binomial logistic regression analysis showed that math self-efficacy was a valid predictor of success for the developmental math students in this study but technology self-efficacy was not. Regression analysis produced a valid equation to predict standard score from average math selfefficacy score. When separated into groups according to course format, math self-efficacy was only a valid predictor for students in hybrid courses. The implications of these results are discussed and recommendations are made for further research."

An online college math course under development including the following topics (so far): Sets Math Foundations Linear Equations Solving and Graphing Inequalities Graphing and Factoring Quadratic Equations Properties of Exponents Logarithms and Exponential Equations

Online Communities of Enquiry in Mathematics Education. A free article in a conversational style with practical tips for online communications and learning. Colin McAllister and Rebecca Hanson ask: What is it like to take part in online discussions? How do moderators and contributors create active and successful conversations? How is the technology employed in the management of discussion forums evolving? What could be achieved through discussion forums in the future?

From the abstract: "is research develops around a technological intervention intended to transform a peer produced reference resource into a peer produced learning environment. An early Web 2.0 community for mathematics, PlanetMath.org, will henceforth become a mathematical practicum, and a laboratory for learning science."

Online Mathematics Resources

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"Why Learn It (WLI) aims to address the issue of motivation around learning math by helping students explore the beauty and relevance of what they would otherwise dismiss as inconsequential in school. Targeting late middle-school and early high-school students, WLI takes a hybrid approach to cultivat- ing motivation. It leverages the engagement value of short (approximately three-minute long) videos depicting real people talking about how math and computational thinking are critical to their successes in a number of professional areas. Students then complete a series of interactive exercises that help students explore an application area discussed in the video in more detail. These exercises, however, are not simply drill problems aimed at making students experts in a particular content area. Instead, they are multi-step assignments that require the students to draw upon both detailed mathematical knowledge and a big picture view of how this knowledge can be used to draw useful, meaningful conclusions. The exercises are focused on bridging the worlds of number, images, and sounds in or- der to help students build intuition around a particular topic. Therefore, while some questions have objectively correct responses, others require students to gather knowledge they have built through answering previous questions within the packet to draw new inferences. Hints are provided along the 1 way to ensure students receive assistance when necessary. Finally, WLI is housed online and is oered for free, signifying minimal barriers to usage by educators and students."

(Access to full text requires subscription or purchase.) First volume in a new series, Mathematics Education in the Digital Age, features chapters on collaborative learning and new technologies, abstracts available.

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Abstract: "Why do people contribute content to communities of question- answering, such as Yahoo!Answers? We investigated this issue on MathOverflow, a site dedicated to research-level mathematics, in which users ask and answer questions. Math- Overflow is the first in a growing number of specialized Q&A sites using the Stack Exchange platform for scientific collab- oration. In this study we combine responses to a survey with collected data on posting behavior on the site. User behavior suggests that building reputation is an important incentive, even though users do not report this in the survey. Level of expertise affects users' reported motivation to help others, but does not affect the importance of reputation building. We discuss the implications for the design of communities to target and encourage more contributions."

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