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Showing 1 to 15 of 71 results Save | Export
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Craig J. Cullen; Lawrence Ssebaggala; Amanda L. Cullen – Mathematics Teacher: Learning and Teaching PK-12, 2024
In this article, the authors share their favorite "Construct It!" activity, which focuses on rate of change and functions. The initial approach to instruction was procedural in nature and focused on making use of formulas. Specifically, after modeling how to find the slope of the line given two points and use it to solve for the…
Descriptors: Models, Mathematics Instruction, Teaching Methods, Generalization
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Theresa Wills; Jennifer Suh; Kate Roscioli; Amanda Guzman; Jennifer Everdale; Sandra Lee – Mathematics Teacher: Learning and Teaching PK-12, 2023
This article describes "Build It!--The Rectangle Game" task that uses the context of a game to develop mathematical generalizations based on strategy. The underlying mathematics in this game-based task is for students to discover factors and prime and composite numbers through 100. The playful use of "The Rectangle Game"…
Descriptors: Educational Games, Teaching Methods, Geometric Concepts, Generalization
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Suzuka, Kara; Venenciano, Linda – Mathematics Teacher, 2019
Fragile understanding is where new learning begins. Students' understanding of new concepts is often shaky at first, when they have only had limited experiences with or single viewpoints on an idea. This is not inherently bad. Despite teachers' best efforts, students' tenuous grasp of mathematics concepts often falters with time or when presented…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Misconceptions
Stephens, Max; Day, Lorraine; Horne, Marj – Mathematics Education Research Group of Australasia, 2022
This paper will elaborate five levels of algebraic generalisation based on an analysis of students' responses to Reframing Mathematical Futures II (RMFII) tasks designed to assess algebraic reasoning. The five levels of algebraic generalisation will be elaborated and illustrated using selected tasks from the RMFII study. The five levels will be…
Descriptors: Algebra, Mathematics Skills, Mathematics Instruction, Generalization
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Roscoe, Matt B. – Mathematics Teacher: Learning and Teaching PK-12, 2021
Investigating symmetric dot patterns provides opportunities for foundational mathematical learning that is not restricted to multiplication alone. Students have opportunities to learn about the properties of symmetry, about the generalization of patterns, about writing and interpreting equations--all areas of study in grades 3-5. And symmetric dot…
Descriptors: Multiplication, Mathematics Instruction, Teaching Methods, Generalization
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Zwanch, Karen; Broome, Bridget – Mathematics Teacher: Learning and Teaching PK-12, 2023
Generalizing patterns is an important feature of algebraic reasoning that is accessible to students across grade-levels because it connects their numerical reasoning to algebraic reasoning. In this article, the authors describe how teachers can use the game Crack the Code to introduce generalizing to their students or can extend students'…
Descriptors: Mathematics Education, Elementary School Mathematics, Grade 6, Mathematics Instruction
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Hallman-Thrasher, Allyson; Strachota, Susanne; Thompson, Jennifer – Mathematics Teacher: Learning and Teaching PK-12, 2021
Inherent in the Common Core's Standard for Mathematical Practice to "look for and express regularity in repeated reasoning" (SMP 8) is the idea that students engage in this practice by generalizing (NGA Center and CCSSO 2010). In mathematics, generalizing involves "lifting" and communicating about ideas at a level where the…
Descriptors: Mathematics Instruction, Generalization, Preservice Teachers, Algebra
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Stupel, Moshe; Sigler, Avi; Tal, Idan – International Journal for Technology in Mathematics Education, 2019
We perform dynamic investigation of two surprising geometrical properties, each of which involves additional properties. In the first task the property belongs to two regular polygons with the same number of sides and with one common vertex. It is found that all the straight lines that connect corresponding vertices of the two polygons intersect…
Descriptors: Mathematics Instruction, Teaching Methods, Validity, Mathematical Logic
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Ahmadpour, Fatemeh; Reid, David; Reza Fadaee, Mohammad – Mathematical Thinking and Learning: An International Journal, 2019
We present a model for describing the growth of students' understandings when reading a proof. The model is composed of two main paths. One is focused on becoming aware of the deductive structure of the proof, in other words, understanding the proof at a semantic level. Generalization, abstraction, and formalization are the most important…
Descriptors: Mathematical Logic, Validity, Mathematics Instruction, Secondary School Mathematics
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Breen, Sinéad; O'Shea, Ann – PRIMUS, 2019
Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that…
Descriptors: Undergraduate Students, Mathematics Instruction, College Mathematics, Learning Activities
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Kovács, Zoltán; Recio, Tomás; Vélez, M. Pilar – International Journal for Technology in Mathematics Education, 2018
This document introduces, describes and exemplifies the technical features of some recently implemented automated reasoning tools in the dynamic mathematics software GeoGebra. The new tools are based on symbolic computation algorithms, allowing the automatic and rigorous proving and discovery of theorems on constructed geometric figures. Some…
Descriptors: Geometry, Mathematics Instruction, Teaching Methods, Comparative Analysis
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Mata-Pereira, Joana; da Ponte, João-Pedro – Educational Studies in Mathematics, 2017
A proof is a connected sequence of assertions that includes a set of accepted statements, forms of reasoning and modes of representing arguments. Assuming reasoning to be central to proving and aiming to develop knowledge about how teacher actions may promote students' mathematical reasoning, we conduct design research where whole-class…
Descriptors: Mathematics Instruction, Mathematical Logic, Generalization, Validity
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Lo, Jane-Jane; Cox, Dana C. – Mathematics Teacher: Learning and Teaching PK-12, 2020
The authors who are mathematics teacher educators, have found that classifying, composing, and transforming shapes (in particular, rotations and reflections) are areas of difficulty for adults as well as for children. However, these are also some of the most important geometric ideas. They are fundamental topics in the K-8 Geometry and Measurement…
Descriptors: Thinking Skills, Mathematics Instruction, Geometry, Standards
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Champanerkar, Jyoti; Jani, Mahendra – PRIMUS, 2015
Mathematical ideas from number theory, group theory, dynamical systems, and computer science have often been used to explain card tricks. Conversely, playing cards have been often used to illustrate the mathematical concepts of probability distributions and group theory. In this paper, we describe how the 21-card trick may be used to illustrate…
Descriptors: Mathematics Instruction, College Mathematics, Number Concepts, Manipulative Materials
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Ghosh, Jonaki B. – Mathematics Teacher, 2016
Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…
Descriptors: Mathematics Instruction, Grade 11, Secondary School Mathematics, Algebra
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