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Sian Zelbo – For the Learning of Mathematics, 2025
This essay examines how line graphs functioned as markers of status and authority in early 20th-century America, distinguishing intellectual elites from ordinary citizens. Despite education reformers' efforts to democratize functional thinking and graphical representation in the first decades of the century, line graphs retained their position as…
Descriptors: Mathematics Instruction, Graphs, Mathematics Skills, Educational Change
Jørgen Sjaastad – For the Learning of Mathematics, 2024
Years of failed attempts to engage my mathematics teacher students in exploration and co-creation led me to radically change my teaching approach. Inspired by literature that uses the jazz improv metaphor for teaching, I derived three tenets based on principles from jazz improv. First, I would bring no more than a single problem-solving task to…
Descriptors: Creative Activities, Mathematics Instruction, Teaching Methods, Learner Engagement
Gaya Jayakody; Shelton Perera – For the Learning of Mathematics, 2024
It is widely accepted that the classroom teaching practices of in-service secondary mathematics teachers can benefit from the advanced mathematics they learned during their university education. However, pinpointing explicit instances of how this advanced knowledge informs teaching practices has proven challenging for both teachers and…
Descriptors: Mathematics Instruction, Secondary School Teachers, Knowledge Level, Calculus
Francesco Beccuti – For the Learning of Mathematics, 2025
Research in mathematics education has long identified the ideology of certainty as central to mathematical instruction and to the way in which mathematics is (mis)used in social and political discourses. As we will see, this ideology is not merely a matter of individual beliefs, but is deeply embedded in the material practices and power structures…
Descriptors: Ideology, Mathematics Education, Mathematics Instruction, Politics of Education
Dave Hewitt – For the Learning of Mathematics, 2024
The author has been influenced throughout his time in mathematics education by the work of Caleb Gattegno. Gattegno made extensive use of the word awareness whereas much educational literature from a psychological perspective talks about memory (for example, Justicia-Galiano, MartÌn-Puga, Linares & Pelegrina, 2017). This has, amongst other…
Descriptors: Mathematics Instruction, Teaching Methods, Memory, Mathematics Education
Oi-Lam Ng – For the Learning of Mathematics, 2025
This essay extends beyond the characteristics and discourse of word problems to, more generally, school mathematical problem-solving and the implications entailed by a predominant paper-and-pencil mode of learning and instruction since the modern era of education. Contrasting what I call "one-handed" (with paper-and-pencil) with…
Descriptors: Thinking Skills, Computation, Problem Solving, Mathematics Education
Hicks, Michael D. – For the Learning of Mathematics, 2022
Analogical reasoning has played an important role in the development of modern mathematics. However, there has been critique of analogies for the purpose of learning new mathematics. In this article, I counter that students can productively reason by analogy to learn new mathematics and even develop new mathematics themselves. I display examples…
Descriptors: Logical Thinking, Mathematics Skills, Mathematics Education, Undergraduate Students
Benally, Jessica; Palatnik, Alik; Ryokai, Kimiko; Abrahamson, Dor – For the Learning of Mathematics, 2022
We introduce, motivate, and exemplify a proposed theoretical construct guiding the design and facilitation of collaborative geometry activities, conceptually generative perspectival complementarity (CGPC). Participants in CGPC activities learn content by negotiating their respective perceptions of situated features they manipulate to accomplish…
Descriptors: Mathematics, Mathematics Instruction, Instructional Design, Cooperative Learning
Vroutsis, Nikolaos; Psycharis, Giorgos; Triantafillou, Chrissavgi – For the Learning of Mathematics, 2022
In this article we address the 'educationalization' of authentic marine navigation tasks for upper secondary mathematics classrooms and their potential for students' learning. Our approach is based on boundary crossing and as well as on the distinction between realistic tasks (targeting students' familiarization with the marine navigation…
Descriptors: Navigation, Secondary School Students, Grade 10, Mathematics Instruction
Eva Elise Tvedt; Tamsin Meaney; Toril Eskeland Rangnes; Troels Lange – For the Learning of Mathematics, 2024
Learning mathematics is often justified as supporting students to make rational decisions, an important goal given the misinformation spread through social media every day. However, when asking preservice teachers to engage in a critical mathematics education activity in which they had to produce an argumentation that would persuade people to…
Descriptors: Persuasive Discourse, Credibility, Preservice Teachers, Mathematics Education
Sheena Tan – For the Learning of Mathematics, 2025
The research on mathematical argumentation has mainly adopted a dialectic lens which focuses on understanding the abstract and logical development of reasoning in argumentation. However, this approach may have overlooked other key aspects of mathematical argumentation, including the unfolding of the meaning-making experience and process during…
Descriptors: Dialogs (Language), Mathematics Instruction, Mathematics Skills, Persuasive Discourse
Fellus, Olga; Low, David E.; Guzman, Lynette D.; Kasman, Alex; Mason, Ralph – For the Learning of Mathematics, 2022
We use a multi-dimensional identity theory to examine how children's picturebooks present discourses about what mathematics is and what doing mathematics means. In our critical content analysis of twenty-four picturebooks, we found four recurring hidden messages that frame mathematical ability as preternatural; as having a magic eye; as doing…
Descriptors: Picture Books, Mathematics Instruction, Identification (Psychology), Stereotypes
Teledahl, Anna; Kilhamn, Cecilia; Helenius, Ola; Ahl, Linda Marie – For the Learning of Mathematics, 2023
Mathematical writing in school is difficult to teach. Reasons include that it is a domain in which there are rules for some parts of the writing like for example mathematical notation while others must be negotiated locally in the classroom. Writing is also seldom separated from the process of solving mathematical problems, creating a situation…
Descriptors: Mathematics Instruction, Problem Solving, Teaching Methods, Instructional Design
Cook, John Paul; Dawkins, Paul; Reed, Zackery – For the Learning of Mathematics, 2021
In this paper we analyze common solutions that students often produce to isomorphic tasks involving proportional situations. We highlight some key distinctions across the tasks and between the different equations students write within each task to help elaborate the different interpretations of equivalence at play: numerical, transformational, and…
Descriptors: Equations (Mathematics), Mathematical Concepts, Measurement, Concept Formation
Marie Therese Farrugia – For the Learning of Mathematics, 2025
Mathematics education in post-colonial Malta is experienced bilingually by teachers and students. I was recently involved in the publication of a bilingual (English / Maltese) glossary of mathematics terms relevant to early childhood and elementary classes. Work on the glossary involved compiling already existing Maltese mathematics terms and also…
Descriptors: Foreign Countries, Bilingualism, English (Second Language), Semitic Languages