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Ghosh, Jonaki B. – Mathematics Teacher, 2018
The Tower of Hanoi is an old, popular, and engaging puzzle. It is an exceptional puzzle too considering how effective it can be in engendering multiple valuable outcomes when used as a tool for learning. One of the fundamental goals of mathematics teacher preparation is to enable the prospective teacher to develop mathematical habits of mind and…
Descriptors: Mathematics Instruction, Teaching Methods, Puzzles, Preservice Teachers
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Graham, Melissa; Lesseig, Kristin – Mathematics Teacher, 2018
Mathematical argumentation is an essential part of the discipline of mathematics and a key indicator of mathematical proficiency. In the process of constructing arguments and critiquing the reasoning of others, students build their understanding of underlying mathematical ideas and engage in critical sense-making activity (Yackel and Hanna 2003).…
Descriptors: Mathematics Instruction, Persuasive Discourse, Mathematics Teachers, Faculty Development
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Rebholz, Joachim A. – Mathematics Teacher, 2017
Graphing functions is an important topic in algebra and precalculus high school courses. The functions that are usually discussed include polynomials, rational, exponential, and trigonometric functions along with their inverses. These functions can be used to teach different aspects of function theory: domain, range, monotonicity, inverse…
Descriptors: Mathematics Instruction, High School Students, Secondary School Mathematics, Graphs
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Corcoran, Mimi – Mathematics Teacher, 2016
Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…
Descriptors: Statistics, Mathematics Instruction, Mathematical Concepts, Learning Activities
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Ko, Yi-Yin; Yee, Sean P.; Bleiler-Baxter, Sarah K.; Boyle, Justin D. – Mathematics Teacher, 2016
This article describes the authors' three-component instructional sequence--a before-class activity, a during-class activity, and an after-class activity--which supports students in becoming self-regulated proof learners by actively developing class-based criteria for proof. All four authors implemented this sequence in their classrooms, and the…
Descriptors: Mathematics Instruction, Teaching Methods, Validity, Mathematical Logic
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Huang, Rongjin; Prince, Kyle M.; Schmidt, Teresa – Mathematics Teacher, 2014
The importance of developing reasoning and justification has been highlighted in "Principles and Standards for School Mathematics" (NCTM 2000). The Common Core State Standards for Mathematics (CCSSI 2010) further reiterates the importance of reasoning and proof in several standards for mathematical practice. Students of all grades are…
Descriptors: Algebra, Mathematics Education, Mathematics Instruction, Mathematical Applications
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Raje, Sonali; Krach, Michael; Kaplan, Gail – Mathematics Teacher, 2013
Concepts in mathematics are often universally applicable to other fields. A critical aspect for success in high school or college is the ability to transfer content knowledge from one discipline to another. This is especially true for material learned in the sciences and mathematics. Several studies have suggested that strong mathematical skills…
Descriptors: College School Cooperation, Mathematics Instruction, Secondary School Mathematics, Problem Solving
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Kinach, Barbara M. – Mathematics Teacher, 2012
Learning to reason spatially is increasingly recognized as an essential component of geometry education. Generally taken to be the "ability to represent, generate, transform, communicate, document, and reflect on visual information," "spatial reasoning" uses the spatial relationships between objects to form ideas. Spatial thinking takes a variety…
Descriptors: Learning Activities, Teaching Methods, Geometry, Geometric Concepts
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Burger, Lance – Mathematics Teacher, 2010
Constructivism has constituted a predominant philosophical trend in mathematics education, but its implementation in the classroom has proven to be "far more difficult than the reform community acknowledges". This difficulty may be due in part to administrative cultures that might insist on more procedural types of instruction aimed at testing, in…
Descriptors: Constructivism (Learning), Mathematics Education, Mathematics Activities, Biology
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Barnes, Rachael; Hamon, Suzanne – Mathematics Teacher, 2010
The prealgebra curriculum presents many opportunities for encouraging students to justify their inferences. Requiring students to communicate clearly the reasoning behind their solutions, with appropriate mathematical language and notation, helps lay the groundwork for future, proof-based mathematics courses. Prealgebra students can even be…
Descriptors: Learning Activities, Algebra, Inferences, Mathematics Instruction
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Matthews, Michael E.; Gross, Greg – Mathematics Teacher, 2008
The problem of creating lamp shades to specific design parameters allows rich and interesting explorations in the mathematics of circles and triangles. This interactive project helps students build their spatial reasoning and is especially appropriate during a unit on either the Pythagorean theorem or similar triangles. (Contains 7 figures and 1…
Descriptors: Geometric Concepts, Mathematics Instruction, Geometry, Learning Activities
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Edwards, Thomas G.; Chelst, Kenneth R. – Mathematics Teacher, 2007
When studying mathematics, students often ask the age-old question, "When will I ever use this in my future?" The activities described in this article demonstrate for students a process that brings the power of mathematical reasoning to bear on a difficult decision involving multiple criteria that is sure to resonate with the interests of many of…
Descriptors: Decision Making, Mathematics Instruction, Relevance (Education), Learning Activities