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Mathematical models of cosmology reconsidered

"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

"Braingenie builds deep mastery and sharpens problem-solving skills. Learn, practice, and quiz yourself on 5,000+ skills. Compete in real-time multiplayer matches. Win badges and go for a top spot on the leaderboard. Sign up now (it's free!) Explore Learning Zone"

"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."

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."

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.

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

"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."

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".

Prometheus Books The Glorious Golden Ratio [978-1-61614-423-4] - "For centuries, mathematicians, scientists, artists, and architects have been fascinated by a ratio that is ubiquitous in nature and is commonly found across many cultures. It has been called the "Golden Ratio" because of its prevalence as a design element and its seemingly universal esthetic appeal. From the ratio of certain proportions of the human body and the heliacal structure of DNA to the design of ancient Greek statues and temples as well as modern masterpieces, the Golden Ratio is a key pattern that has wide-ranging and perhaps endless applications and manifestations. What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. With their talent for elucidating mathematical mysteries, veteran educators and prolific mathematics writers Alfred S. Posamentier and Ingmar Lehmann begin by tracing the appearance of the Golden Ratio throughout history. They demonstrate a variety of ingenious techniques used to construct it and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. They also point out the intriguing relationship between the Golden Ratio and other famous numbers (such as the Fibonacci numbers, Pythagorean triples, and others). They then explore its prevalence in nature as well as in architecture, art, literature, and technology. "

learning guides for operations fractions ratio basic- geometry statistics algebra

(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. "

"the three major sections of the manual will be Fluency with Whole Numbers, Fluency with Fractions, and Particular Aspects of Geometry and Measurement. The Fluency with Whole Numbers section is further broken down into subcategories given the wealth of information for this area. The remaining two sections, Fluency with Fractions, and Particular Aspects of Geometry and Measurement are presented only as broad categories because the amount of available information is considerably limited relative to the whole number literature. Finally, two standard protocol interventions are presented as examples of comprehensive, evidence-based mathematics instruction that have been shown effective at increasing mathematics performance according to the Department of Education's What Works Clearinghouse."

" 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: "The principal aim of this study is to find the weaknesses of secondary school students at geometry questions of measures , angles and shapes , transformations and construction and 3-D shapes. The year 7 curriculum contains 4 geometry topics out of 17 mathematics topics. In addition to this , this study aims to find out the mistakes, 28 , 7th grade students made in the last 4 exams including two midterms and two final exams.To collect data, students were tested on two midterms and two final exams using open-ended questions on geometry to analyze their problem solving skills and to test how much they acquired during the year.Frequency tables were used in data analysis.To fulfill this aim in the first midterm exam the subject measures were tested.In the first final exam which followed the first midterm exam in addition to measures and angles shapes skills were also tested. Following these tests , in the second midterm we tested the students on transformation and construction. A descriptive methodology and student interview were used in the study to analyze and interpret the results. The results from this study revealed that 7th grade secondary school students have a number of misconceptions, lack of background knowledge, reasoning and basic operation mistakes at the topics mentioned above."