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Articles 301 - 330 of 426
Full-Text Articles in Mathematics
Early Insurance Mechanisms And Their Mathematical Foundations, Amy Minto
Early Insurance Mechanisms And Their Mathematical Foundations, Amy Minto
The Mathematics Enthusiast
This article gives a historical survey of early insurance mathematics and its development in relation to the maritime industry and the origins of the life insurance industry. The history of the probability and statistics and its intricate connection to the actuarial sciences and modern insurance can be traced to the time period described in this paper.
Three Strikes, Tom O'Brien, Marianne Smith
Three Strikes, Tom O'Brien, Marianne Smith
The Mathematics Enthusiast
The first part of the paper describes and comments upon three aspects of the back-to-basics movement: the make-up and mindset of the National Mathematics Advisory Panel (NMP), the movement’s history in California, and recent “grassroots” activities of the movement in the state of Washington. The second part reports and comments on the principal findings of the NMP report.
Chess And Problem Solving Involving Patterns, Dores Ferreira, Pedro Palhares
Chess And Problem Solving Involving Patterns, Dores Ferreira, Pedro Palhares
The Mathematics Enthusiast
In this paper we present the context and results from a study, with 3rd to 6th grades children, about the relationship between chess and problem solving involving geometric and numeric patterns. The main result of this study is the existence of a relation between strength of play and patterns involving problem solving. We have included in the beginning an analysis of chess as a context for elementary mathematics problems, also showing its richness historically.
A Case Study Using Soft Systems Methodology In The Evolution Of A Mathematics Module, Jon Warwick
A Case Study Using Soft Systems Methodology In The Evolution Of A Mathematics Module, Jon Warwick
The Mathematics Enthusiast
This paper describes the application of Soft Systems Methodology as a tool for facilitating the review of a taught mathematics module so that the views of those engaged with the module could be captured and conflicting expectations and views highlighted. Checkland’s Soft Systems Methodology is used since it enables the capture of stakeholder views and addresses both ‘hard’ and ‘soft’ aspects of the learning experience. Stages in the application of Soft Systems Methodology are illustrated including the development of a rich picture and conceptual models and the work was conducted using a stakeholder group that included students taking the module …
History Of Mathematics In Mathematics Education: A Saussurean Perspective, Michael Fried
History Of Mathematics In Mathematics Education: A Saussurean Perspective, Michael Fried
The Mathematics Enthusiast
It is not only because of a certain eclecticism in mathematics education research that semiotic ideas have begun to take root there: it is also because of the dawning recognition that key areas of interest in mathematics education genuinely have a semiotic nature. For this, one need only point to research focused on meaning, communication, language, and culture (e.g., Presmeg, 1997; Ernest,1997; Radford, 2001; Brown, 2001). The ways in which semiotics informs cultural aspects of mathematics education, particularly those connected with the history of mathematics, were highlighted in a discussion session at the 2003 meeting of the International Group for …
Comparison Of Geometric Figures, Spyros Glenis
Comparison Of Geometric Figures, Spyros Glenis
The Mathematics Enthusiast
Although the geometric equality of figures has already been studied thoroughly, little work has been done about the comparison of unequal figures. We are used to compare only similar figures but would it be meaningful to compare non similar ones? In this paper we attempt to build a context where it is possible to compare even non similar figures. Adopting Klein’s view for the Euclidean Geometry, we defined a relation “≤ ” as: S1 ≤ S2 whenever there is a Euclidean isometry f :R2 →R2 , so that . This relation is not an order because there are …
Incoherence Of A Concept Image And Erroneous Conclusions In The Case Of Differentiability, Antti Viholainen
Incoherence Of A Concept Image And Erroneous Conclusions In The Case Of Differentiability, Antti Viholainen
The Mathematics Enthusiast
The level of the coherence of a concept image conveys how well the cognitive structure concerning the concept is organized. This study considers the relationship between deficiencies in the coherence of the concept image and erroneous conclusions in the case of differentiability. The study is based on an interview where the student made conclusions contradictory to the formal theory of mathematics. He used an erroneous method to study the differentiability of piecewise defined functions. This method became the key factor which maintained the internal coherence of the concept image. It made it possible to build a cognitive structure whose basis …
Editorial: 2 To 3- An Omnibus Of Features & Policy Issues In Mathematics Education, Bharath Sriraman
Editorial: 2 To 3- An Omnibus Of Features & Policy Issues In Mathematics Education, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
Inverses - Why We Teach And Why We Need Talk More About It More Often!, Woong Lim
Inverses - Why We Teach And Why We Need Talk More About It More Often!, Woong Lim
The Mathematics Enthusiast
This article examines the key role that the notion of inverses plays in numerous mathematical concepts.
Chopping Logs: A Look At The History And Uses Of Logarithms, Rafael Villarreal-Calderon
Chopping Logs: A Look At The History And Uses Of Logarithms, Rafael Villarreal-Calderon
The Mathematics Enthusiast
Logarithms are an integral part of many forms of technology, and their history and development help to see their importance and relevance. This paper surveys the origins of logarithms and their usefulness both in ancient and modern times.
Mathematics And The World: What Do Teachers Recognize As Mathematics In Real World Practice?, Barbara Garii, Lillian Okumu
Mathematics And The World: What Do Teachers Recognize As Mathematics In Real World Practice?, Barbara Garii, Lillian Okumu
The Mathematics Enthusiast
Elementary school teachers are encouraged to better integrate appropriate mathematics pedagogy with deeper, more relevant mathematics content. However, many teach a mathematics they do not fully understand to students who see, recognize, and use less mathematics than ever before. Both teachers and students struggle to articulate the role mathematics plays in society as mathematics becomes more embedded into our technology. In this study, we asked teachers to record the mathematics they used on a daily basis during a 1-week period. Their responses indicate that they do not recognize that mathematics plays any important role in technological and professional practices. This …
Associative Operations On A Three-Element Set, Friðrik Diego, Kristín Halla Jónsdóttir
Associative Operations On A Three-Element Set, Friðrik Diego, Kristín Halla Jónsdóttir
The Mathematics Enthusiast
A set with a binary operation is a fundamental concept in algebra and one of the most fundamental properties of a binary operation is associativity. In this paper the authors discuss binary operations on a three-element set and show, by an inclusion-exclusion argument, that exactly 113 operations out of the 19,683 existing operations on the set are associative. Moreover these 113 associative operations are accounted for by means of their operation tables.
Magic Math Cards, Steve Humble
Magic Math Cards, Steve Humble
The Mathematics Enthusiast
Starting lessons with a good story, captures students imagination. The story then leads nicely into a magic card experiment which can be used to help teach the topic. I have used magic with a variety of age groups and found that they ask different questions of the task, and search for different levels of answers.
Mathematical Cognition And The Final Report Of The National Mathematics Advisory Panel: A Critical, Cultural-Historical Activity Theoretic Analysis, Wolff-Michael Roth
Mathematical Cognition And The Final Report Of The National Mathematics Advisory Panel: A Critical, Cultural-Historical Activity Theoretic Analysis, Wolff-Michael Roth
The Mathematics Enthusiast
In its Final Report, the National Mathematics Advisory Panel has depicted a stark image of mathematical competencies and achievement among U.S. students. The Advisory Panel notes the lack of research with “truly scientific” rigor and, mentioning Vygotsky’s cultural-historical activity theory in passing, suggests its utility to be untested. In reading the report, I noted the limited understanding of the mathematics education literature it articulates and a complete failure to draw on established, “tried and proven,” theory and practice in mathematics education founded upon an encompassing culturalhistorical activity theory. This theory is comprehensive and encompassing, because it retains activity in its …
E(Race)Ing Race From A National Conversation On Mathematics Teaching And Learning: The National Mathematics Advisory Panel As White Institutional Space, Danny Bernard Martin
E(Race)Ing Race From A National Conversation On Mathematics Teaching And Learning: The National Mathematics Advisory Panel As White Institutional Space, Danny Bernard Martin
The Mathematics Enthusiast
In this paper, I wish to argue that several factors support a characterization of the National Mathematics Advisory Panel as an instantiation of the white institutional space (Moore, 2008) that characterizes mathematics education research and policy contexts more generally. In particular, my analysis highlights that mathematics education research and policy contexts such as the National Mathematics Advisory Panel are not immune to the structural and institutional racism that characterize many other areas of U.S. society.
Guest Editorial: Reaction To The Final Report Of The National Mathematics Advisory Panel, Brian Greer
Guest Editorial: Reaction To The Final Report Of The National Mathematics Advisory Panel, Brian Greer
The Mathematics Enthusiast
In 2006, President Bush appointed the National Mathematics Advisory Panel (NMAP henceforth) which issued its Final Report on March 13, 2008. The Final Report (summary), plus reports of three subcommittees and five Task Groups, together with two appendices containing the Presidential Executive Order setting up the panel, and details of the panel membership and other personnel, can be downloaded from www.ed.gov/about/bdscomm/list/mathpanel/index.html
Algebra For All?, Brian Greer
Algebra For All?, Brian Greer
The Mathematics Enthusiast
In 1957, the director of one of the major math curriculum projects in the UK was quoted in a newspaper as saying: "Up went Sputnik and down came all the pure mathematicians saying we must do sets and be saved". The corresponding message from the National Math Panel Final Report is "Up went the economic performance of China and India and down came all the pure mathematicians saying we must do algebra and be saved".
The Political Context Of The National Mathematics Advisory Panel, Eric Rico Gutstein
The Political Context Of The National Mathematics Advisory Panel, Eric Rico Gutstein
The Mathematics Enthusiast
The National Mathematics Advisory Panel needs to be situated in its broader political context to more fully understand it. Who created it, for what purpose, and who will (and will not) benefit from it are key questions I address in this article. My argument is that the NMAP, as part of a larger initiative undertaken by the Bush Administration and US financial/corporate elites, serves capital’s efforts to shore up the US’s weakening economic global position and does not benefit the majority of the US people—particularly marginalized and excluded students of color and low-income students.
New Titles In Mathematics Education
Editorial: Expanding Spheres Of Influence- The Zenith, The Nadir And Everything In-Between, Bharath Sriraman
Editorial: Expanding Spheres Of Influence- The Zenith, The Nadir And Everything In-Between, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
Historical Tidbits, The Shoah, And The Teaching Of Mathematics, Wolff-Michael Roth
Historical Tidbits, The Shoah, And The Teaching Of Mathematics, Wolff-Michael Roth
The Mathematics Enthusiast
In this extended essay, I use cultural-historical activity theory to look at the questions Theodore Eisenberg raises about the inclusion of historical facts, both historical tidbits and ethically questionable tendencies and horrific actions (the Shoah), in the teaching of mathematics. I conclude by suggesting that the ultimate answer has to be one that involves a decision, which means that an answer cannot be provided a priori or be determined by any antecedent. Deciding to include this or that in a mathematical curriculum is an ethical act.
Mathematically Gifted Elementary Students' Revisiting Of Euler's Polyhedron Theorem, Jaehoon Yim, Sanghun Song, Jiwon Kim
Mathematically Gifted Elementary Students' Revisiting Of Euler's Polyhedron Theorem, Jaehoon Yim, Sanghun Song, Jiwon Kim
The Mathematics Enthusiast
This paper explores how the constructions of mathematically gifted fifth and sixth grade students using Euler’s polyhedron theorem compare to those of mathematicians as discussed by Lakatos (1976). Eleven mathematically gifted elementary school students were asked to justify the theorem, find counterexamples, and resolve conflicts between the theorem and counterexamples. The students provided two types of justification of the theorem. The solid figures suggested as counterexamples were categorized as 1) solids with curved surfaces, 2) solids made of multiple polyhedra sharing points, lines, or faces, 3) polyhedra with holes, and 4) polyhedra containing polyhedra. In addition to using the monster-barring …
Final Comments On Eisenberg's Paper, Brian Greer
Final Comments On Eisenberg's Paper, Brian Greer
The Mathematics Enthusiast
I must begin by expressing appreciation for the spirit in which Ted accepted my comments as intended to be intellectually and not personally provocative. Let me also assure him that I was not at all offended by the paper – it would be more accurate to say that I was stimulated by it to voice some strong disagreements. Beyond the particular aspects on which we have different perspectives, I applaud his decision to raise ethical issues, too often ignored in writing about mathematics education.
Flaws And Idiosyncrasies In Mathematicians: Food For The Classroom, Ted Eisenberg
Flaws And Idiosyncrasies In Mathematicians: Food For The Classroom, Ted Eisenberg
The Mathematics Enthusiast
This paper raises an ethical question: should aspects of a mathematician’s personality, political beliefs, physical handicaps, and the ironies surrounding their life be mentioned parenthetically or otherwise in our lessons? What about the political and social norms of the times in the countries in which they lived? There are no hard and fast guidelines on this other than to use good taste; but what is in good taste to one is often in bad taste to another. At the very least this paper presents tidbits of information and innuendo about mathematicians the reader might not know. But hopefully this paper …
Reflections Upon Teaching A Poorly-Conceived Lesson, Yuichi Handa
Reflections Upon Teaching A Poorly-Conceived Lesson, Yuichi Handa
The Mathematics Enthusiast
Using a “failed” mathematics lesson as a mini-case study, I explore some of the challenges inherent in teaching an inquiry-style mathematics lesson. The ensuing discussion centers around two issues: the preparation and subsequent scaffolding involved in guiding students to desired understandings, along with the tension inherent in “telling” and “not telling” in an inquiry-style pedagogy. I resort to personal reflection, as well as to Wenger’s (1998) theoretical construct of participation and reification in revealing the underlying link between the manner of lesson preparation and consequent engagement of students during the enactment of the lesson.
Reaction To The Reactors, Ted Eisenberg
Reaction To The Reactors, Ted Eisenberg
The Mathematics Enthusiast
1. A comment. I discussed the contents of my paper with colleagues on many different occasions. By their reactions they seem to divide themselves into two camps. One camp takes the stance of: Are you crazy to mention such things in the classroom? We are charged to teach mathematics, and that’s it. Who cares if Einstein never learned to swim? The other camp however takes an opposite stance: Such items are really important for students to know because they help students to think about the lives and times of the men who created the material they are studying; our lessons …
Comments Provoked By "Flaws And Idiosyncrasies In Mathematicians: Food For The Classroom?", Brian Greer
Comments Provoked By "Flaws And Idiosyncrasies In Mathematicians: Food For The Classroom?", Brian Greer
The Mathematics Enthusiast
In mathematics classes, it is appropriate for many reasons to discuss mathematicians as people with lives, personal problems, both influenced by and influencing cultural movements and societal issues. Mathematics is a human activity, and mathematicians are human. Eisenberg's paper raises important and fascinating issues, such as the extent to which intellectual achievements can be kept separate from the personality and actions of their creator (such as Wagner). However, in my reactions, I suggest ways in which I believe the discussion needs to be broadened and refocused.