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Lai, Yvonne; Jacobson, Erik – For the Learning of Mathematics, 2018

This paper focuses on the design of tasks that situate teachers in the work of mathematics teaching. We examine a simple, yet fundamental feature of pedagogical content knowledge tasks: the extent to which pedagogical warrants are necessitated by the pedagogical context. We argue that this feature has implications for the design of tasks, as well…

Descriptors: Mathematics Instruction, Pedagogical Content Knowledge, Instructional Design, Mathematics Teachers

Boggs, George; Whitacre, Ian; Schellinger, Jennifer; Champagn, Zachary; Schoen, Robert – For the Learning of Mathematics, 2018

The literature concerning students' understanding of the equal sign has focused narrowly within the context of formal mathematics. Researchers have put forth a hierarchy of conceptions of the equal sign with only the top level regarded as correct. Meanwhile, we find that the equal sign is used widely and in a variety of ways in advertising and…

Descriptors: Symbols (Mathematics), Mathematical Concepts, Concept Formation, Teaching Methods

Culligan, Karla; Wagner, David – For the Learning of Mathematics, 2018

When deciding what constitutes students' "on task" or "off task" mathematical communication, teachers and researchers are also making judgements about what is, and what is not, mathematics. In this paper, we question our ability to separate the mathematical from the nonmathematical. We explore intersecting storylines in Grade…

Descriptors: Mathematics Activities, Mathematics Instruction, Relevance (Education), Grade 10

Alshwaikh, Jehad – For the Learning of Mathematics, 2018

This article suggests a tool for analysing diagrams in mathematical texts. The starting point for this tool is Halliday's Systemic Functional Grammar (SFG), which considered language as a social practice. Kress and Van Leeuwen (2006) applied Halliday's SFG to images, suggesting a grammar for reading images. Morgan (1996) adopted Halliday's SFG and…

Descriptors: Mathematics Education, Visual Aids, Semiotics, Grammar

Staats, Susan – For the Learning of Mathematics, 2018

A poetic structure occurs when a speaker's comment repeats some of the syntax and words of a previous comment. During a collaborative algebra task, a student explained a property five times over a few minutes, in slightly different ways. He consistently used poetic structures that were marked elaborately through discursive modes such as pause,…

Descriptors: Algebra, Mathematics Activities, Persuasive Discourse, Poetry

Skovsmose, Ole – For the Learning of Mathematics, 2018

The notion of social justice has been addressed from the perspective of 'ethical realism' and 'ethical anarchistic'. Here, however, the possibility of 'ethical constructivism' becomes formulated. With departure in Rawls' description of an idealised meeting defining social justice, the initial steps into ethical constructivism become taken.…

Descriptors: Social Justice, Ethics, Mathematics Education, Constructivism (Learning)

Komatsu, Kotaro; Fujita, Taro; Jones, Keith; Naoki, Sue – For the Learning of Mathematics, 2018

Kitcher's idea of 'explanatory unification', while originally proposed in the philosophy of science, may also be relevant to mathematics education, as a way of enhancing student thinking and achieving classroom activity that is closer to authentic mathematical practice. There is, however, no mathematics education research treating explanatory…

Descriptors: Mathematics Education, Grade 8, Mathematical Concepts, Thinking Skills

Stott, Debbie – For the Learning of Mathematics, 2018

In this article I provide a preliminary review of Radford's ideas about the poetic role of theory and his work on moments of poesis in terms of its appeal and usefulness in research contexts. In light of the mathematics education community's call for more attention to be given to the aesthetic elements of learning mathematics, I conclude that…

Descriptors: Poetry, Mathematics Instruction, Aesthetics, Teaching Methods

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

Radakovic, Nenad; Jagger, Susan; Jao, Limin – For the Learning of Mathematics, 2018

In this article, we explore the reading and writing of mathematical poetry from our experiences as mathematics teacher educators. First, we outline how our own engagement with mathematical poetry encouraged us to incorporate it into our teaching of pre-service teachers. We describe how our initial disappointment with the mathematical content of…

Descriptors: Mathematics Instruction, Poetry, Content Area Reading, Content Area Writing

Farrugia, Marie Therese – For the Learning of Mathematics, 2017

In this article, I describe a research/teaching experience I undertook with a class of 5-year-old children in Malta. The topic was subtraction on the number line. I interpret the teaching/learning process through a semiotic perspective. In particular, I highlight the role played by the gesture of forming "frog jumps" on the number line.…

Descriptors: Mathematics Instruction, Subtraction, Foreign Countries, Young Children

Yoon, Caroline – For the Learning of Mathematics, 2017

Popular culture casts mathematics and writing as opposites--a false dichotomy, which can be harmful for our discipline of mathematics education. Positioning writing outside the domain of the mathematician's abilities and cultivated skill set can create doubt in the mathematician wishing to write--not that one cannot be both writer and…

Descriptors: Writing Strategies, Writing Skills, Mathematics, Professional Personnel

Kofi-Davis, Ernest – For the Learning of Mathematics, 2017

Mathematics is often positioned as being difficult for Ghanaian teachers to teach and pupils to learn. Although literature point to the educational and scientific relevance of many of the socio-cultural practices in the Ghanaian society, many mathematical concepts are taught out of context in schools. In this paper I will draw on Bishop's (1988)…

Descriptors: Teaching Models, Mathematics Instruction, Elementary School Mathematics, Teaching Methods

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

Geiger, Vince; Margolinas, Claire; Sträßer, Rudolph – For the Learning of Mathematics, 2017

This is a response to the collection of communications in 37(1), two of which cited Vince and Rudolf's article in 35(3). Vince and Rudolf have have been joined here by Claire Margolinas in order to provide a complementary (French) perspective to their Australian and German outlooks on this topic. The comments of the three of us can be grouped into…

Descriptors: Mathematics Education, Educational Research, Multilingualism