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Griffiths, Martin; MacHale, Des – International Journal of Mathematical Education in Science and Technology, 2017
We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…
Descriptors: Arithmetic, Geometry, Geometric Concepts, Algebra
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Whitacre, Ian; Pierson Bishop, Jessica; Lamb, Lisa L.; Philipp, Randolph A.; Bagley, Spencer; Schappelle, Bonnie P. – International Journal of Mathematical Education in Science and Technology, 2015
We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways.…
Descriptors: Grade 7, Grade 11, Interviews, Mathematical Logic
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Komatsu, Kotaro; Tsujiyama, Yosuke; Sakamaki, Aruta – International Journal of Mathematical Education in Science and Technology, 2014
Proof and proving are important components of school mathematics and have multiple functions in mathematical practice. Among these functions of proof, this paper focuses on the discovery function that refers to invention of a new statement or conjecture by reflecting on or utilizing a constructed proof. Based on two cases in which eighth and ninth…
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Grade 8
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Charpin, J. P. F.; O'Hara, S.; Mackey, D. – International Journal of Mathematical Education in Science and Technology, 2013
In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students.…
Descriptors: Foreign Countries, Mathematical Models, Secondary School Mathematics, Workshops
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Varsavsky, Cristina – International Journal of Mathematical Education in Science and Technology, 2012
Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one…
Descriptors: Program Effectiveness, Calculus, Algebra, Foreign Countries
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Marinos, Andreas – International Journal of Mathematical Education in Science and Technology, 2010
In this work, an attempt is made to evaluate the errors that have to do with the interpretation and construction of graphic representations. Although the students are studying in the second year of technical high school (secondary education), i.e. in schools with an emphasis in technical subjects (post junior secondary), it is observed that they…
Descriptors: Secondary School Mathematics, Mathematics Instruction, Graphs, Measurement
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De Vleeschouwer, Martine – International Journal of Mathematical Education in Science and Technology, 2010
Novice students at the university encounter many difficulties, linked with the secondary-tertiary transition. But what does "transition" mean exactly? We consider it here from an institutional point of view, which leads us in particular to distinguish between two types of transition. We propose a specific perspective, and apply it to the…
Descriptors: Algebra, Case Studies, Transfer Students, Course Content
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Back, Ralph-Johan; Mannila, Linda; Wallin, Solveig – International Journal of Mathematical Education in Science and Technology, 2010
In this article, we present the results from a qualitative study on students' initial reactions to the use of structured derivations in mathematics education. Our findings suggest that the approach increases the clarity of solutions and facilitates debugging of proofs. It also has potential to increase students' self-perceived level of…
Descriptors: Feedback (Response), Mathematics Education, Mathematics Instruction, Student Attitudes
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Arnoux, Pierre; Duverney, Daniel; Holton, Derek – International Journal of Mathematical Education in Science and Technology, 2009
In this article, we start by considering the relevant parts of the French educational system and the data relating to science at the end of secondary school and the early years of university. We show an increase, till 1995, and then a decline in the study of mathematics at baccalaureate and university level. However, our main conclusions relate to…
Descriptors: Mathematics Education, Educational Trends, Trend Analysis, Enrollment Trends
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Abramovich, Sergei; Leonov, Gennady A. – International Journal of Mathematical Education in Science and Technology, 2008
This article demonstrates how within an educational context, supported by the notion of hidden mathematics curriculum and enhanced by the use of technology, new mathematical knowledge can be discovered. More specifically, proceeding from the well-known representation of Fibonacci numbers through a second-order difference equation, this article…
Descriptors: Mathematics Curriculum, Numbers, Educational Technology, Calculus
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Zembat, Ismail Ozgur – International Journal of Mathematical Education in Science and Technology, 2008
The current study compared the effects of technological environments with that of the paper-and-pencil environment on reasoning about the concept of derivatives in the context of maximum and minimum problems. The data consisted of clinical interviews conducted with three pre-service secondary mathematics teachers and a newly registered graduate…
Descriptors: Graduate Students, Mathematics Education, Mathematics Teachers, Mathematical Logic
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Luk, Hing Sun – International Journal of Mathematical Education in Science and Technology, 2005
It seems self-evident that there is a significant gap between secondary school and university mathematics, even though the gap may take different forms, which vary with different education systems in different places and at different times. This paper attempts to capture some common forms of this gap, and in particular, it discusses some core…
Descriptors: Mathematics Education, Student Attitudes, College Mathematics, Secondary School Mathematics
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Graham, Ted; Smith, Paulette – International Journal of Mathematical Education in Science and Technology, 2004
This paper outlines an experiment in which pupils in Key Stage 2 were encouraged to use graphics calculators, in particular two simple programs, which helped them develop recall of their tables and allowed them to practise multiplication. The pupils responded very well to the calculators and seemed to have been motivated by them. The pupils did…
Descriptors: Multiplication, Graphing Calculators, Foreign Countries, Elementary Education