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Obara, Samuel – Mathematics Teacher, 2010
The inquiry-based approach to learning has gained popularity in recent times. Those who promote this approach maintain that mathematical investigation should be used to engage students. The National Council of Teachers of Mathematics (NCTM) recommends that problem solving be the center of mathematics teaching in promoting student learning through…
Descriptors: Inquiry, Active Learning, Mathematics Instruction, Investigations
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Keazer, Lindsay M.; Menon, Rahul S. – Mathematics Teacher, 2015
This article argues that the practices of reasoning and sense making are critical for developing students' mathematical literacy. Seven mathematics teachers collaborated throughout a school year to discuss the ideas proposed in Reasoning and Sense Making (NCTM 2009) and put them into practice through action research. Conducting action research,…
Descriptors: Mathematics Instruction, Mathematics Teachers, Mathematical Logic, Teacher Collaboration
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Cetner, Michelle – Mathematics Teacher, 2015
When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…
Descriptors: Mathematics Instruction, Teaching Methods, Geometry, Algebra
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Foley, Gregory D. – Mathematics Teacher, 2011
Ellipses vary in shape from circular to nearly parabolic. An ellipse's eccentricity indicates the location of its foci, but its aspect ratio is a direct measure of its shape. This article takes a careful look at the shape of an ellipse and offers practical suggestions and specific activities to deepen students' understanding of the geometry of an…
Descriptors: Geometric Concepts, Mathematics Instruction, Geometry, National Standards
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Sole, Marla A. – Mathematics Teacher, 2015
Every day, people use data to make decisions that affect their personal and professional lives, trusting that the data are correct. Many times, however, the data are inaccurate, as a result of a flaw in the design or methodology of the survey used to collect the data. Researchers agree that only questions that are clearly worded, unambiguous, free…
Descriptors: Test Construction, Surveys, Student Participation, Design
Graham, Karen; Cuoco, Albert; Zimmermann, Gwendolyn – National Council of Teachers of Mathematics, 2010
This book examines the five key elements (meaningful use of symbols, mindful manipulation, reasoned solving, connection algebra with geometry, and linking expressions and functions) identified in "Focus in High School Mathematics: Reasoning and Sense Making" in more detail and elaborates on the associated reasoning habits. This volume is one of a…
Descriptors: High School Students, Symbols (Mathematics), Geometry, Algebra
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Pritchard, Christine K.; Lamb, John H. – Mathematics Teacher, 2012
NCTM (2000) described geometry as "a means of describing, analyzing, and understanding the world and seeing beauty in its structures" (p. 309). Dossey et al. (2002) captured the essence of this aspect of visualization by stating that geometry fosters in students an ability to "visualize and mentally manipulate geometric objects." (p. 200).…
Descriptors: Teaching Methods, Visual Impairments, Geometry, Geometric Concepts
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Edwards, Michael todd; Quinlan, James; Harper, Suzanne R.; Cox, Dana C.; Phelps, Steve – Mathematics Teacher, 2014
Despite Common Core State Standards for Mathematics (CCSSI 2010) recommendations, too often students' introduction to proof consists of the study of formal axiomatic systems--for example, triangle congruence proofs--typically in an introductory geometry course with no connection back to previous work in earlier algebra courses. Van Hiele…
Descriptors: Mathematics Instruction, Logical Thinking, Validity, Secondary School Mathematics
National Council of Teachers of Mathematics, 2010
Classically, geometry has been the subject in which students encounter mathematical proof based on formal deduction. Attention to proof in the geometry curriculum is strengthened by a focus on reasoning and sense making. This book examines the four key elements (conjecturing about geometric objects, construction and evaluation of geometric…
Descriptors: Geometry, Secondary School Mathematics, High Schools, Geometric Concepts
Breunlin, R. James; Kasper, Timothy A.; Kolet, Michelle; Letzel, Kendra; Letzel, Thomas; Noah, John; Schutte, Jennifer; Williams, Bob; Zickert, Chris – Rowman & Littlefield Education, 2006
This book is the result of the collaborative effort of nine AYA National Board Certified Teachers in Mathematics. It represents a compilation of teacher-tested activities that prompt high school students to explore, conjecture and reflect on their mathematical adventures-- thus "experience mathematics." This edition will educate the teacher…
Descriptors: Student Participation, Student Motivation, Cognitive Psychology, Mathematics Education
Cayton, Charity Sue-Adams – ProQuest LLC, 2012
Technology use and a focus on 21st century skills, coupled with recent adoption of Common Core State Standards for Mathematics, marks a new challenge for mathematics teachers. Communication, discourse, and tools for enhancing discourse (NCTM, 1991, 2000) play an integral role in successful implementation of technology and mathematics standards.…
Descriptors: Algebra, Mathematics Teachers, Geometry, Secondary School Teachers