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Shinno, Yusuke; Miyakawa, Takeshi; Iwasaki, Hideki; Kunimune, Susumu; Mizoguchi, Tatsuya; Ishii, Terumasa; Abe, Yoshitaka – For the Learning of Mathematics, 2018
The aims of the present study are two-fold. The first aim is to reveal the cultural and linguistic issues that need to be considered in the development of curricular content and sequencing for teaching mathematical proof in secondary schools in Japan. The second aim is to elaborate an epistemological perspective that may allow us to understand…
Descriptors: Mathematics Instruction, Foreign Countries, Cultural Influences, Language Usage
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Cooper, Jason; Pinto, Alon – For the Learning of Mathematics, 2017
"The root of 18 is closer to 4 than it is to 5 because 18 is closer to 16 than it is to 25". Is this statement, voiced in an 8th grade class, valid? We suggest hypothetical arguments upon which this statement might be based, and analyze them from two complementary perspectives--epistemic and pedagogical--drawing on Toulmin's notion of…
Descriptors: Grade 8, Secondary School Mathematics, Inquiry, Mathematical Logic
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Wasserman, Nicholas; Weber, Keith – For the Learning of Mathematics, 2017
In this article, we consider the potential influences of the study of proofs in advanced mathematics on secondary mathematics teaching. Thus far, the literature has highlighted the benefits of applying the conclusions of particular proofs to secondary content and of developing a more general sense of disciplinary practices in mathematics in…
Descriptors: Mathematics Instruction, Secondary School Mathematics, Mathematical Concepts, Teaching Methods
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Zazkis, Rina – For the Learning of Mathematics, 2017
In many Canadian schools the acronym BEDMAS is used as a mnemonic to assist students in remembering the order of operations: Brackets, Exponents, Division, Multiplication, Addition, and Subtraction. In the USA the mnemonic is PEMDAS, where 'P' denotes parentheses, along with the phrase "Please Excuse My Dear Aunt Sally". In the UK the…
Descriptors: Mnemonics, Mathematics Instruction, Learning Strategies, Teaching Methods
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Armstrong, Alayne – For the Learning of Mathematics, 2017
This article presents a case study of a small group of Grade 8 students performing bricolage during a classroom mathematics task. The data analysis involves the use of 'tapestries', a style of transcript that enables the consideration of both the group and individuals within the group as learning agents. I characterize bricolage as an emergent,…
Descriptors: Mathematics Instruction, Grade 8, Middle School Students, Secondary School Mathematics
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Tillema, Erik; Gatza, Andrew – For the Learning of Mathematics, 2016
We provide a conceptual analysis of how combinatorics problems have the potential to support students to establish non-linear meanings of multiplication (NLMM). The problems we analyze we have used in a series of studies with 6th, 8th, and 10th grade students. We situate the analysis in prior work on students' quantitative and multiplicative…
Descriptors: Mathematics Instruction, Multiplication, Mathematics Skills, Thinking Skills
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Jankvist, Uffe Thomas; Misfeldt, Morten – For the Learning of Mathematics, 2015
In recent years computer algebra systems (CAS) have become an integrated part of the upper secondary school mathematics program. Despite the many positive possibilities of CAS, there also seems to be a flip side of the coin in relation to actual difficulties in learning mathematics, not least because a strong dependence on CAS for mathematical…
Descriptors: Mathematics Instruction, Algebra, Computer Uses in Education, Secondary School Mathematics
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Ulrich, Catherine – For the Learning of Mathematics, 2015
This is the first of a two-part article that presents a theory of unit construction and coordination that underlies radical constructivist empirical studies of student learning ranging from young students' counting strategies to high school students' algebraic reasoning. My explanation starts with the formation of arithmetical units, which presage…
Descriptors: Mathematics Education, Secondary School Mathematics, High School Students, Constructivism (Learning)
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Jankvist, Uffe Thomas – For the Learning of Mathematics, 2014
Based on a study about using original sources with Danish upper secondary students, the paper addresses the potential outcome of such an approach in regard to the so-called recruitment problem to the mathematical sciences. 24 students were exposed to questionnaire questions and 16 of these to follow-up interviews, which form the basis for both a…
Descriptors: Secondary School Mathematics, Secondary School Students, Questionnaires, Followup Studies
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Zazkis, Rina; Mamolo, Ami – For the Learning of Mathematics, 2011
This article extends the notion of "knowledge at the mathematical horizon" or "horizon knowledge" introduced by Ball and colleagues as a part of teachers' subject matter knowledge. Our focus is on teachers' mathematical knowledge beyond the school curriculum, that is, on mathematics learnt during undergraduate college or university studies. We…
Descriptors: Secondary School Mathematics, Mathematics Education, Knowledge Base for Teaching, Colleges
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Hansraj, Sudan – For the Learning of Mathematics, 2010
I argue for the inclusion of topics in high school mathematics curricula that are traditionally reserved for high achieving students preparing for mathematical contests. These include the arithmetic mean--geometric mean inequality which has many practical applications in mathematical modelling. The problem of extremalising functions of more than…
Descriptors: Secondary School Mathematics, Calculus, Arithmetic, Geometry
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Pournara, Craig – For the Learning of Mathematics, 2009
The ability of mathematics teachers to decompress mathematics and to move between representations are two key features of mathematical knowledge that is usable for teaching. This article reports on four pre-service secondary mathematics teachers learning the mathematics of annuities. In working with spreadsheets students began to make sense of…
Descriptors: Mathematics Education, Mathematical Concepts, Mathematics Teachers, Spreadsheets
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Castro, Fernando – For the Learning of Mathematics, 2003
The author shares a story of how Luis Gonz├ílez, an iron artisan, helped the author build a wooden and iron toy truck. The knowledge required to build the skeleton for the parallelepiped in the construction of the truck is not in the mathematical high school curriculum in Venezuela. Although Luis never received a degree beyond high school,…
Descriptors: Metallurgy, Geometry, Geometric Concepts, Mathematics Skills
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Adler, Jill – For the Learning of Mathematics, 1998
Illustrates the complexities of secondary mathematics teaching and learning in contemporary multilingual classrooms. Shows how and why the language of dilemmas provides a powerful explanatory and analytic tool as well as a source of praxis in mathematics education in a changing educational and political context. Contains 21 references. (ASK)
Descriptors: Educational Change, Equal Education, Mathematics Instruction, Multilingualism
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Van Den Brink, Jan – For the Learning of Mathematics, 1995
Shows similarities between realism and radical constructivism by presenting examples of using children's ideas in order to create education in the context of teaching spherical geometry. (18 references) (MKR)
Descriptors: Constructivism (Learning), Geometry, Learning Theories, Mathematics Education
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