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Peer reviewed
Direct linkNilsson, Per – Journal of Mathematical Behavior, 2009
This study investigates students' conceptual variation and coordination among theoretical and experimental interpretations of probability. In the analysis we follow how Swedish students (12-13 years old) interact with a dice game, specifically designed to offer the students opportunities to elaborate on the logic of sample space,…
Descriptors: Probability, Logical Thinking, Foreign Countries, Games
Montiel, Mariana; Vidakovic, Draga; Kabael, Tangul – Investigations in Mathematics Learning, 2009
The present study was implemented as a prelude to a study on the generalization of the single variable function concept to multivariate calculus. In the present study we analyze students' mental processes and adjustments, as they are being exposed to single variable calculus with polar coordinates. The results show that there appears to be a…
Descriptors: Multivariate Analysis, Calculus, Misconceptions, Mathematical Concepts
Mallett, Susanne; Wren, Steve; Dawes, Mark; Blinco, Amy; Haines, Brett; Everton, Jenny; Morgan, Ellen; Barton, Craig; Breen, Debbie; Ellison, Geraldine; Burgess, Danny; Stavrou, Jim; Carre, Catherine; Watson, Fran; Cherry, David; Hawkins, Chris; Stapenhill-Hunt, Maria; Gilderdale, Charlie; Kiddle, Alison; Piggott, Jennifer – Mathematics Teaching, 2009
A group of teachers involved in embedding NRICH tasks (http://nrich.maths.org) into their everyday practice were keen to challenge common perceptions of mathematics, and of the teaching and learning of mathematics. In this article, the teachers share what they are doing to change these perceptions in their schools.
Descriptors: Mathematics Education, Perception, Mathematics Instruction, Mathematics
Liu, Andy – College Mathematics Journal, 2009
In this paper, we give two unexpected applications of a Hamming code. The first one, also known as the "Hat Problem," is based on the fact that a small portion of the available code words are actually used in a Hamming code. The second one is a magic trick based on the fact that a Hamming code is perfect for single-error correction.
Descriptors: Mathematics Instruction, College Mathematics, Coding, Mathematical Concepts
Zhou, Li – College Mathematics Journal, 2009
The familiar process of synthetic division is extended to much more complicated divisors and turns out, surprisingly, not to be as difficult as one might imagine.
Descriptors: Mathematics Instruction, College Mathematics, Arithmetic, Mathematical Concepts
Norton, Anderson – College Mathematics Journal, 2009
After Peano gave an arithmetic construction, Hilbert developed a geometric construction for space-filling curves. This paper describes the key idea of Hilbert's construction, here called "the nested-squares criterion," implicit in Hilbert's writing but, once explicated, generalizes to a whole class of space-filling curves that correspond to a…
Descriptors: Geometric Concepts, Geometry, Mathematics Instruction, College Mathematics
Vis, Timothy; Petersen, Ryan M. – College Mathematics Journal, 2009
A Latin square of order "n" is an "n" x "n" array using n symbols, such that each symbol appears exactly once in each row and column. A set of Latin squares is c ordered pairs of symbols appearing in the cells of the array are distinct. The popular puzzle Sudoku involves Latin squares with n = 9, along with the added condition that each of the 9…
Descriptors: Problem Solving, Mathematics Instruction, College Mathematics, Games
Zucker, Marc – College Mathematics Journal, 2009
We introduce a simple game made up of a board of coins on a triangular lattice. We then study the possibility of turning the board from one pattern of heads and tails to some other pattern. Given that a solution exists we find a precise answer to the number of solutions possible. We then generalize this to more complex boards with coins of many…
Descriptors: Mathematics Instruction, College Mathematics, Educational Games, Problem Solving
Chen, Hang; Cooper, Curtis – College Mathematics Journal, 2009
Motivated by Fitch Cheney's 5-card trick, we present and analyze several "n"-card tricks. We determine the minimum "n" to perform the trick, with and without timing.
Descriptors: Mathematics Instruction, College Mathematics, Creative Teaching, Mathematical Concepts
Lavy, Ilana; Mashiach-Eizenberg, Michal – Journal of Statistics Education, 2009
Various terms are used to describe mathematical concepts, in general, and statistical concepts, in particular. Regarding statistical concepts in the Hebrew language, some of these terms have the same meaning both in their everyday use and in mathematics, such as Mode; some of them have a different meaning, such as Expected value and Life…
Descriptors: Mathematical Concepts, Oral Language, Vocabulary, Definitions
Shutler, Paul M. E. – International Journal of Mathematical Education in Science and Technology, 2009
We consider Egyptian mathematics from a postmodern perspective, by which we mean suspending judgement as to strict correctness in order to appreciate the genuine mathematical insights which they did have in the context in which they were working. In particular we show that the skill which the Egyptians possessed of obtaining the general case from…
Descriptors: Mathematics Education, Geometric Concepts, Mathematical Concepts, Problem Solving
Kulkarni, Raghavendra G. – International Journal of Mathematical Education in Science and Technology, 2009
We describe a method to extract roots of a reducible quintic over the real field, which makes use of a simple division. A procedure to synthesize such quintics is given and a numerical example is solved to extract the roots of quintic with the proposed method.
Descriptors: Problem Solving, Equations (Mathematics), Mathematics Instruction, Mathematical Concepts
Dwyer, Jerry; Barnard, Roger; Cook, David; Corte, Jennifer – Australian Senior Mathematics Journal, 2009
This paper discusses some common iterations of complex functions. The presentation is such that similar processes can easily be implemented and understood by undergraduate students. The aim is to illustrate some of the beauty of complex dynamics in an informal setting, while providing a couple of results that are not otherwise readily available in…
Descriptors: Undergraduate Study, Mathematics Instruction, College Mathematics, Mathematical Concepts
Download full textScott, Paul – Australian Mathematics Teacher, 2009
These days, multiplying two numbers together is a breeze. One just enters the two numbers into one's calculator, press a button, and there is the answer! It never used to be this easy. Generations of students struggled with tables of logarithms, and thought it was a miracle when the slide rule first appeared. In this article, the author discusses…
Descriptors: Arithmetic, Graphs, Calculus, Mathematics Instruction
Wise, Steven L.; DeMars, Christine E. – Applied Psychological Measurement, 2009
Attali (2005) recently demonstrated that Cronbach's coefficient [alpha] estimate of reliability for number-right multiple-choice tests will tend to be deflated by speededness, rather than inflated as is commonly believed and taught. Although the methods, findings, and conclusions of Attali (2005) are correct, his article may inadvertently invite a…
Descriptors: Guessing (Tests), Multiple Choice Tests, Test Reliability, Computation
