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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
Small, Marian; Lin, Amy – Teachers College Press, 2010
Teachers know that Differentiated Instruction (DI) helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math…
Descriptors: Mathematics Education, Student Participation, Data Analysis, Mathematics Teachers
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Paoletti, Teo J. – Mathematics Teacher, 2013
To engage students, many teachers wish to connect the mathematics they are teaching to other branches of mathematics or to real-world applications. The lesson presented in this article, which uses the algebraic skill of finding the equation of a line between two points and the geometric axiom that any two points define a line, does both. A…
Descriptors: Mathematics Instruction, Relevance (Education), Algebra, Mathematics Skills
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Ichinose, Cherie Lynn; Martinez-Cruz, Armando M. – Mathematics Teacher, 2018
The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) propose a new vision for the mathematics classroom with updated content standards and Standards for Mathematical Practice (SMP). These practices are founded on NCTM processes (Problem Solving, Reasoning and Proof, Communication, Representation, and Connections) and abilities…
Descriptors: Mathematics Instruction, Teaching Methods, Problem Solving, Common Core State Standards
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Askey, Richard; Matsuura, Ryota; Sword, Sarah – Mathematics Teacher, 2015
NCTM's Connections Standard recommends that students in grades 9-12 "develop an increased capacity to link mathematical ideas and a deeper understanding of how more than one approach to the same problem can lead to equivalent results, even though the approaches might look quite different" (NCTM 2000, p. 354). In this article, the authors…
Descriptors: Arithmetic, Geometry, Mathematics Instruction, Mathematical Concepts
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Sherman, Milan; Cayton, Charity – Mathematics Teacher, 2015
Students' ability to use appropriate tools strategically is an important skill of mathematically proficient students (SMP 5, CCSSI 2010, p. 7). A parallel practice for teachers is using appropriate tools strategically for mathematics instruction. An important element of this practice is that the use of technology depends on the goals of…
Descriptors: Mathematics Instruction, Teaching Methods, Technology Uses in Education, Geometry
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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
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
National Council of Teachers of Mathematics, 2015
Do your students think a triangle can be constructed from any three given line segments? Do they believe that a transformation affects only the pre-image--not the whole plane? Do they understand that examples--no matter how many they find--cannot prove a conjecture but one counterexample is sufficient to disprove it? "What tasks can you…
Descriptors: Geometry, Educational Practices, Secondary School Mathematics, Pedagogical Content Knowledge
Silver, Edward A., Ed.; Kenney, Patricia Ann, Ed. – National Council of Teachers of Mathematics, 2015
This book's 28 chapters are adapted and updated from articles published in NCTM's "Journal for Research in Mathematics Education" between 2000 and 2010. The authors have rewritten and revised their work to make it clear, understandable, and--most of all--useful for mathematics teachers today. To help teachers even more, these articles…
Descriptors: Theory Practice Relationship, Mathematics Education, Educational Research, Common Core State Standards
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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
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Browning, Christine A.; Garza-Kling, Gina – Mathematics Teaching in the Middle School, 2010
Middle school mathematics classrooms are changing. The curriculum has changed as well. Instead of an annual return to previously encountered topics, many middle school students encounter mathematics of a varying nature, characterized in "Principles and Standards for School Mathematics" (NCTM 2000) as the five Content Standards of Number and…
Descriptors: Graphing Calculators, Geometry, Mathematics Instruction, Teaching Methods
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Kelley, Paul – Mathematics Teacher, 1999
Describes an activity on fractal geometry in which students built a 19-foot-tall Sierpinski pyramid in the Minneapolis Convention Center in conjunction with the National Council of Teachers of Mathematics' (NCTM) 75th Annual Meeting in April, 1997. Contains 13 references. (ASK)
Descriptors: Fractals, Geometry, Mathematics Activities, Mathematics Instruction
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
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