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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

Abstract:"This paper discusses the results of a pilot st udy that explored how prospective secondary school teachers are shaped by learni ng experiences during their undergraduate mathematics education. The collabora tive study, which was conducted by a mathematician and a mathematics educator, dr ew from the experiences of prospective teachers in a non-traditional undergraduate ma thematics program that makes extensive use of technology. Analysis of data collect ed from detailed questionnaires, journals, and focus group discussions strongly suggests that designing, implementing, and testing Learning Objects promotes prospective teache rs' learning of the mathematics needed for teaching. Furthermore, the analysis shows t hat prospective teachers' experiences of ownership, engagement, and pride are key to positive learning experiences. "

This great maths site has an amazing collection of maths self-marking problem solving questions. Search by age level or topic. This covers both Primary and Secondary levels. Topics include numbers, geometry, algebra, data analysis, probability and more. http://ictmagic.wikispaces.com/Maths

Abstract: This research paper has been designed to develop an online tutoring system for pre - K to middle school Math students. The research methodology applied in this study has used both qualitative and quantitative research methods in terms of external and internal Web or software metrics to obtain the usable parameters to design an effective tutoring system to learn Math. Today online hypermedia applications are increasingly becoming more feature rich, important and also the most popular means for communication among school students for e - learning. This paper is divided into four parts: part 'I' presents the introduction of Kumon based after school education; part 'II' describes the research proposal to identify measures, model, and methodology to develop the Web - based online learning system for Pre - K to middle school math students ; part 'III' elaborates the role of using static analysis, dynamic, and comparative analysis that can be applied to check the characteristics and authenticity of data obtained for each student separately; and finally part 'IV' investigates the behaviour of online tutoring system to find the failure points and to calculate reliability aspects using Web page trace algorithms and We b page replacement policies. In this paper, an attempt has been made to systematically explain the state of the art and their practices to design, analyze, and test the functionality of online learning systems for pre - K to middle school Math students

(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. "

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."

Abstract: "Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry. "

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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."

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

This site helps students practise basic maths skills through short online exercises that are intended to be used each day. Teacher can get analysis of progress and more. Signing up a class is quick and easy. http://ictmagic.wikispaces.com/Maths

" 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)

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."

Yet, another great data analysis, display tool from Google. Implications in helping students organize/display/analyze/evaluate data is incredible. Displaying data through a map has implications in so many content areas. 

Northwestern University scientists created a model to explore food web dynamics towards species conservation. "The goal of this project, funded by the National Science Foundation's Division of Mathematical Sciences, is to develop mathematical methods to study dynamical processes in complex networks. Although the specific application mentioned here may be useful in management of ecosystems, the mathematical foundation underlying the analysis is much more universal. The broad concept is innovative in the area of complex networks because it concludes that large-scale failures can be avoided by focusing on preventing the waves of failure that follow the initial event."

"This book is designed to provide mathematics undergraduates with some historical background to the material that is now taught universally to students in their final years at school and the first years at college or university: the core subjects of calculus, analysis, and abstract algebra, along with others such as mechanics, probability, and number theory. All of these evolved into their present form in a relatively limited area of western Europe from the mid sixteenth century onwards, and it is there that we find the major writings that relate in a recognizable way to contemporary mathematics."

Mathematicians at Ohio State University have developed new equations to "describe the shape and motion of single cells for laboratory analysis."

"Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving" by Sanjoy Mahajan, published in 2010. "Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool-the general principle-from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest." Available as a free download (Creative Commons License), .pdf): http://mitpress.mit.edu/books/full_pdfs/Street-Fighting_Mathematics.pdf

"Don't know much about the French I took..." but this looks like some interesting analysis of shapes in the physics world. Worth looking at if you 

Examining Exemplary Mathematics Instruction in Howard County Purpose: This wiki has been designed as a repository for resources and for sharing of ideas. Each of the seven visitation teams will have an opportunity to share reflections and pose questions for further analysis. This is a public wikispace so please respect norms related to confidentiality. Keep the conversations about the work...do not include school or teacher names.