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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

LOGIN: http://tinyurl.com/math20event Mind the Daylight Saving Time! Geoff Roulet and Jill Lazarus will discuss their use of wikis, GeoGebra and Jing with students, and invite participants for an extended DIY exploration. More details concerning the software required are below. All events in the Math Future weekly series: http://mathfuture.wikispaces.com/events The recording will be at: http://mathfuture.wikispaces.com/SupportingCollaborativeMath Your time zone: http://bit.ly/z69yzS About Blended Mathematical Collaboration using a Wiki, GeoGebra and Jing This discussion centers on the use of computer tools in a high school class. The goal was to develop a "math-talk learning community" to establish mathematics communication and collaboration as a classroom norm. In support of this we have combined the use of a wiki, GeoGebra, and Jing. We would like to invite educators who have experience with wikis, GeoGebra and screencasts, or who would like to learn more, to discuss our project and share their ideas. Event Hosts Geoff is the skipper of and Jill a crew member on Jeannie, a J35 racing yacht. When not sailing, they are mathematics educators. After graduate work at the University of Waterloo, Geoff Roulet began teaching mathematics, computer science, and chemistry at Roland Michener Secondary School in Timmins, northern Ontario. In the late 1970s, when personal computers for computer science were placed in the back of his classroom, Geoff began using these to support student learning in mathematics. Since then he has been involved in ICT use in teaching and learning at all grades and in all subjects, but with a particular focus on mathematics. Teaching was followed by a short spell of curriculum development and support work with the Ontario Ministry of Education and then in 1990 a move to the Faculty of Education, Queen's University at Kingston. Along the way Geoff completed M.Ed. and D.Ed. degrees at the Ontario Institute for Studies

LOGIN Wednesday February 15 at 3pm Eastern US time: http://tinyurl.com/math20event During the event, Dr. Keith Still of SaferCrowds.com will introduce his Crowd Sciences work and explain the relevance of mathematics in it: "If you don't do the maths, you could end up in court on a manslaughter charge!" All events in the Math Future weekly series: http://mathfuture.wikispaces.com/events The recording will be at http://mathfuture.wikispaces.com/CrowdSciences Pose questions and comments for Keith before the event Math Future wiki: http://mathfuture.wikispaces.com/message/list/CrowdSciences LinkedIn group: http://www.linkedin.com/groupItem?view=&gid=33207&type=member&item=94871153&qid=b29a6dbc-6474-425f-865a-b319bd33dcb9 Email group: http://groups.google.com/group/mathfuture/browse_thread/thread/931328aab6d87b03 How to join Follow this link at the time of the event: http://tinyurl.com/math20event Wednesday, February 15 2012 we will meet online at noon Pacific, 3 pm Eastern time. WorldClock for your time zone. Click "OK" and "Accept" several times as your browser installs the software. When you see Session Log-In, enter your name and click the "Login" button If this is your first time, come a few minutes earlier to check out the technology. Crowd Modelling + Crowd Monitoring + Crowd Management = Safer Crowds Crowd Modelling is the scientific approach to the development of safe, robust, crowd management plans. This can be achieved without the need for expensive, complex, time consuming computer simulations. In simple terms Crowd Modelling is understanding how, where, when and why crowds arrive, move around and leave an events/venues. The majority of this can be accomplished using tried, tested and simple to apply methodologies. "Keith Still is what I term an intuitive mathematician. He is one of the most creative and original thinkers that I know. He adds drive and determination, as well as considerable intellectual power to any group of which h

"This is an exploration of the hypothesis that unique belief systems depend for their coherence on distinctive patterns typically embodied in geometrical symbols in two dimensions. On the basis of that assumption, the case tentatively explored here is that of the "incommensurability" of the 5-fold Star of Islam and the 6-fold Star of David of Judaism -- both symbols appearing on flags of the nations having those distinct faiths. ... The approach taken here explores the possibility that the "pieces" only fit together on a three-dimensional surface, namely a sphere. It is the spherical geometry that then merits consideration, together with the challenge of how to get from any "mis-fitting" two-dimensional layout to a three-dimensional form. Of course, two-dimensional layouts are far more readily comprehensible. Hence the focus on them. However the three-dimensional layout has the potential of rendering comprehensible a far more elegant layout which may well exemplify intuitions characteristic of the faiths so dramatically opposed. The approach follows from various earlier explorations of the potential of mathematics to offer a new perspectives on these issues" ....

Lure of the Labyrinth is today's innovative catch Lure of the Labyrinth is a game for middle school pre-algebra students designed to improve math and literacy skills. It includes intriguing math-based puzzles embedded in a narrative game in which students work to find their lost pet and save the world from monsters. Linked to mathematics standards, the game gives students a chance to think like mathematicians. Lure of the Labyrinth Home Page In Lure of the Labyrinth, students progress through three sections, or wings each related to a different math strand that is part of a the typical pre-algebra curriculum: * Proportions (including fractions and ratios) * Variables and Equations * Number and Operations (including geometry, order of operations and modular arithmetic) Each of the three wings includes three puzzles, and each of the puzzles has three levels progressing from easy to hard. Students have to successfully solve each puzzle three times before they can advance through the game. Lure of the Labyrinth Library Page A professional development video specifically designed for pre-algebra teachers takes them step-by-step through the things they need to do to make this engaging game the focal point of great classroom learning experiences. Planning resources include links to standards, directions for working with specific puzzles, lesson plans, explanations of the background math, and graphic organizers. Video - Lure of the Labyrinth Lure of the Labyrinth was created by Maryland Public Television and MIT Education Arcade in cooperation with FableVision.

For prealgebra students.

In this lesson, students learn how to measure the area of the tire footprint on a car and to find air pressure using a tire gauge. Students then find the weight of the car using their fraction multiplication skills. Learning Objectives   Students will: Estimate weight of a large object Use a ruler and a tire gauge to take measurements Collect and record data Review square units of measure Calculate area by multiplying fractions Materials   Strips of poster board Ruler Tire gauge How Much Does a Car Weigh? Activity Sheet Computer with internet connection Car Instructional Plan In preparation for this lesson, place a car in a safe lcation for the students to measure the tire footprints and pressure. In case of bad weather, find a covered location. Be sure to measure the tire footprint and the pressure (in PSI) of each tire ahead of time, so that you will be able check the accuracy of students' measurements. Also, check the accuracy of your calculation by comparing to it to the weight of the car listed on the sticker inside the driver's door or in the vehicle manual. By the end of the day, data may change because air has leaked out of the tires while students were using the tire gauge. For safety, check the tires before driving home.

Abstract: "n this study we explored the impact of performing mathematical tasks presented in the context of an "adventure challenge" or a "mathematical challenge" in a videogame. This videogame - "Matemáquina do Tempo" - is being developed to facilitate learning of mathematical skills like counting, grouping, and relating numbers. The videogame consists in various movement control tasks with dynamic (e.g., running) and static (e.g., pointing) interactions. Our goal was to test the impact of the integration of a direct mathematical task versus an indirect mathematical task. A group of 18 five year-old children performed the game in two conditions: a) adventure challenge , which implied movements such as running or climbing trees to perform mathematical tasks of counting and grouping; and b) mathematical challenge , which included swimming after selecting the correct path through counting, followed by a direct mathematical task of pointing to organize numbers in a line. Our assumptions were evaluated according to questionnaires and video analysis of the children playing the game. Results confirmed our hypothesis, showing that players performing the mathematical challenge generally considered that they were learning with the game, and most agreeing that the game was fun. Participants in the adventure challenge condition on the other hand, showed a tendency to evaluate the game as very amusing and were more distributed in the learning evaluation. In conclusion, we suggest that the inclusion of direct mathematical tasks in the videogame might lead to increased perception of learning, although they also seem to result in lower amusement ratings."

From the National Center of Education Statistics: "The Trends in International Mathematics and Science Study (TIMSS) 2011 is the fifth administration of this international comparative study since 1995 when first administered. TIMSS is used to compare over time the mathematics and science knowledge and skills of fourth- and eighth-graders. TIMSS is designed to align broadly with mathematics and science curricula in the participating countries. The results, therefore, suggest the degree to which students have learned mathematics and science concepts and skills likely to have been taught in school. In 2011, there were 54 countries and 20 other educational systems that participated in TIMSS, at the fourth- or eighth-grade level, or both. The focus of the report is on the performance of U.S. students relative to their peers in other countries in 2011, and on changes in mathematics and science achievement since 2007 and 1995. For a number of participating countries and education systems, changes in achievement can be documented over the last 16 years, from 1995 to 2011. This report also describes achievement within the United States by sex, race/ethnicity, and enrollment in public schools with different levels of poverty. In addition, it describes achievement in nine states that participated in TIMSS both as part of the U.S. national sample of public and private schools as well as individually with state-level samples of public schools."

From the abstract: "The purpose of this study was to find out from current high school math teachers, of geometry specifically, what their views of technology are. The goal of the study was to ask these teachers which technologies they use and whether they believe technology has beneficial effects on student learning. Data was collected for the survey by asking teachers to take brief electronic surveys and conduct in-person interviews. All questions in both the survey and interviews were focused on the effects of technology that they see in their classrooms. The scope of the participants was restricted to Columbus, Ohio, and thus, generalizations for any classroom or any school building cannot be made. However, this study did find a consensus among the participants as to which technologies they felt were the most beneficial in their classrooms, as well as those that might not be needed at all in a classroom. The three technologies that these teachers claimed to be the most beneficial were SMART boards, TI-nspire calculators and Geometer's Sketchpad/GeoGebra. Again, this study cannot make solid conclusions, but it is safe to say that this study gives insight into teachers' viewpoints, which, in a sense, are more important than those of outside researchers. The teachers agreed on a few technologies that are the most beneficial and thus future studies should focus on really studying the effects of these technologies as well as focus on getting a wider range of teachers' opinions on this topic."

Published by University of Chicago Press, July 2012. "Math and science hold powerful places in contemporary society, setting the foundations for entry into some of the most robust and highest-paying industries. However, effective math and science education is not equally available to all students, with some of the poorest students-those who would benefit most-going egregiously underserved. This ongoing problem with education highlights one of the core causes of the widening class gap. While this educational inequality can be attributed to a number of economic and political causes, in Empowering Science and Mathematics Education in Urban Communities, Angela Calabrese Barton and Edna Tan demonstrate that it is augmented by a consistent failure to integrate student history, culture, and social needs into the core curriculum. They argue that teachers and schools should create hybrid third spaces-neither classroom nor home-in which underserved students can merge their personal worlds with those of math and science. A host of examples buttress this argument: schools where these spaces have been instituted now provide students not only an immediate motivation to engage the subjects most critical to their future livelihoods but also the broader math and science literacy necessary for robust societal engagement. A unique look at a frustratingly understudied subject, Empowering Science and Mathematics Education pushes beyond the idea of teaching for social justice and into larger questions of how and why students participate in math and science. " Excerpts in Google Books

According to Nancy Kimberly of HASTAC, this set of video games won the 1st National STEM Video Game Challenge: "Numbaland!, produced by graduate students Derek Lomas of Carnegie Mellon University, Dixie Ching of New York University and Jeanine Sun of the University of California at San Diego, was the winner of the Collegiate and Impact Prizes and will receive $50,000 in total. The collection of four games allows children in kindergarten to grade 4 to construct a set of skills that helps develop their sense of number concepts"

" The use of logarithms, an important tool for calculus and beyond, has been reduced to symbol manipulation without understanding in most entry-level college algebra courses. The primary aim of this research, therefore, was to investigate college students' understanding of logarithmic concepts through the use of a series of instructional tasks designed to observe what students do as they construct meaning. APOS Theory was used as a framework for analysis of growth. APOS Theory is a useful theoretical framework for studying and explaining conceptual development. Closely linked to Piaget's notions of reflective abstraction, it begins with the hypothesis that mathematical activity develops as students perform actions that become interiorized to form a process understanding of the concept, which eventually leads students to a heightened awareness or object understanding of the concept. Prior to any investigation, the researcher must provide an analysis of the concept development in terms of the essential components of this theory: actions, process, objects, and schemas. This is referred to as the genetic decomposition. The results of this study suggest a framework that a learner may use to construct meaning for logarithmic concepts. Using tasks aligned with the initial genetic decomposition, the researcher made revisions to the proposed genetic decomposition in the process of analyzing the data. The results indicated that historical accounts of the development of this concept might be useful to promote insightful learning. Based on this new set of data, iterations should continue to produce a better understanding of the student's constructions. " (from the abstract)

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."

Abstract: "This research seeks to look into the design process that promotes the development of an educational computer game that supports teaching and learning processes. The research specifically looks at the design of an educational computer game for teaching and learning of the topic of functions. The topic is essential in the teaching and learning of Mathematics courses such as Discrete Mathematics, Real Analysis and Calculus among others at Jomo Kenyatta University of Agriculture and Technology (JKUAT) Kenya. The computer game was developed using the Basic Unified process (BUP) which is a streamlined version of the rational unified process (RUP). This is an object oriented methodology mostly used for small projects with few end users. Due to the few numbers of end users we used interview method of data collection to gather requirements for the computer game. A paper prototype was used to validate the requirements. Use cases were used for both analysis and design of the game while Class diagrams and activity diagrams were purely used for the design of the game. Owens' six top level design anatomy aided in the design of the computer game. The overall computer game design was based on Crawfords' computer game design sequence model. The well designed and developed game met all its user requirements and was able to facilitate the teaching and learning of functions to Bachelor of Science in Mathematics and Computer Science students who were taking Discrete mathematics in their first year of study at JKUATs' Taita/Taveta campus. Development of heuristics for measuring interest, fun and motivation are recommendations given to aid in the evaluation of user satisfaction of educational computer games."

A systematic search of the research literature from 1996 through July 2008 identified more than a thousand empirical studies of online learning. Analysts screened these studies to find those that (a) contrasted an online to a face-to-face condition, (b) measured student learning outcomes, (c) used a rigorous research design, and (d) provided adequate information to calculate an effect size. As a result of this screening, 51 independent effects were identified that could be subjected to meta-analysis. The meta-analysis found that, on average, students in online learning conditions performed better than those receiving face-to-face instruction. The difference between student outcomes for online and face-to-face classes-measured as the difference between treatment and control means, divided by the pooled standard deviation-was larger in those studies contrasting conditions that blended elements of online and face-to-face instruction with conditions taught entirely face-to-face. Analysts noted that these blended conditions often included additional learning time and instructional elements not received by students in control conditions. This finding suggests that the positive effects associated with blended learning should not be attributed to the media, per se. An unexpected finding was the small number of rigorous published studies contrasting online and face-to-face learning conditions for K-12 students. In light of this small corpus, caution is required in generalizing to the K-12 population because the results are derived for the most part from studies in other settings (e.g., medical training, higher education). ix

A systematic search of the research literature from 1996 through July 2008 identified more than a thousand empirical studies of online learning. Analysts screened these studies to find those that (a) contrasted an online to a face-to-face condition, (b) measured student learning outcomes, (c) used a rigorous research design, and (d) provided adequate information to calculate an effect size. As a result of this screening, 51 independent effects were identified that could be subjected to meta-analysis. ***The meta-analysis found that, on average, students in online learning conditions performed better than those receiving face-to-face instruction.*** The difference between student outcomes for online and face-to-face classes-measured as the difference between treatment and control means, divided by the pooled standard deviation-was larger in those studies contrasting conditions that blended elements of online and face-to-face instruction with conditions taught entirely face-to-face. Analysts noted that these blended conditions often included additional learning time and instructional elements not received by students in control conditions. This finding suggests that the positive effects associated with blended learning should not be attributed to the media, per se. An unexpected finding was the small number of rigorous published studies contrasting online and face-to-face learning conditions for K-12 students. In light of this small corpus, caution is required in generalizing to the K-12 population because the results are derived for the most part from studies in other settings (e.g., medical training, higher education). ix

From the abstract: "We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry." (Full text requires subscription.

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: "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."

"A research team led by Carnegie Mellon University's Robert Siegler has identified a major source of the gap -- U. S. students' inadequate knowledge of fractions and division. Although fractions and division are taught in elementary school, even many college students have poor knowledge of them. The research team found that fifth graders' understanding of fractions and division predicted high school students' knowledge of algebra and overall math achievement, even after statistically controlling for parents' education and income and for the children's own age, gender, I.Q., reading comprehension, working memory, and knowledge of whole number addition, subtraction and multiplication. Published in Psychological Science, the findings demonstrate an immediate need to improve teaching and learning of fractions and division."

GeoGebra: Do the Math is a series of screencast tutorials for teachers and/or students. The tutorials were initiated as a project to support Maine math teachers in the integration of technology in the classroom. What is GeoGebra provides an overview of the program and its capabilities. Several tutorials present the program's menu options and tools in step-by-step format. Another group of tutorials provides examples of GeoGebra learning activities in major math content areas. These tutorials are intended as a visual supplement to printed guides and documentation. GeoGebra users can find a wealth of guidance and examples at www.geogebra.org. A web search such as "GeoGebra Pythagorean Theorem" will yield hundreds of additional articles, examples, and applets.