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Stegall, Joanna B.; Malloy, Jacquelynn A. – Mathematics Teacher, 2019
The ties between literacy and numeracy exist in the development of vocabulary and language for understanding mathematical concepts. Research indicates that explicit instruction in mathematics vocabulary supports success with mathematics problem solving (Biemiller 2009; Pierce and Fontaine 2009; Rubenstein and Thompson 2002) for native…
Descriptors: Misconceptions, Mathematics Instruction, Algebra, Mathematics
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Wagner, Jennifer; Sharp, Janet – Mathematics Teacher, 2017
Calculus, perhaps more than other areas of mathematics, has a reputation for being steeped with procedures. In fact, through the years, it has been noticed of many students getting caught in the trap of trying to memorize algorithms and rules without developing associated concept knowledge. Specifically, students often struggle with the…
Descriptors: Calculus, Mathematics Instruction, Mathematical Concepts, Concept Formation
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Richardson, Janessa; Bachman, Rachel M. – Mathematics Teacher, 2017
This article describes a preservice teacher's imaginative exploration of completing the square through a process of reasoning and sense making. She recounts historical perspectives and her own discoveries in the process of completing the square. Through this process of sense making, she engaged with the content standard of completing the square to…
Descriptors: Preservice Teachers, Mathematics Instruction, Mathematical Concepts, Mathematical Logic
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Case, Catherine; Whitaker, Douglas – Mathematics Teacher, 2016
In the criminal justice system, defendants accused of a crime are presumed innocent until proven guilty. Statistical inference in any context is built on an analogous principle: The null hypothesis--often a hypothesis of "no difference" or "no effect"--is presumed true unless there is sufficient evidence against it. In this…
Descriptors: Mathematics Instruction, Technology Uses in Education, Educational Technology, Statistical Inference
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Hallman-Thrasher, Allyson; Litchfield, Erin T.; Dael, Kevin E. – Mathematics Teacher, 2016
Matrices occupy an awkward spot in a typical algebra 2 textbook: sandwiched between solving linear systems and solving quadratics. Even teachers who do not base their course timeline and pacing on the class textbook may find a disconnect between how matrices are taught (procedurally) and how other topics are taught (conceptually or with real-world…
Descriptors: Multiplication, Algebra, Mathematics Instruction, Teaching Methods
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Lim, Kien H. – Mathematics Teacher, 2016
Magic captivates humans because of their innate capacity to be intrigued and a desire to resolve their curiosity. In a mathematics classroom, algorithms akin to magic tricks can be an effective tool to engage students in thinking and problem solving. Tricks that rely on the power of mathematics are especially suitable for students to experience an…
Descriptors: Teaching Methods, Mathematics Instruction, Problem Solving, Mathematical Concepts
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Klein, Valerie; Fukawa-Connelly, Timothy; Silverman, Jason – Mathematics Teacher, 2016
Teachers' focus on student thinking--and moving beyond superficial "right or wrong" analysis--is essential to effective teaching (Grossman and McDonald 2008; NCTM 2000; Son and Sinclair 2010). Interpreting and evaluating student thinking and providing high-quality feedback are seen as high-leverage practices and are "likely to lead…
Descriptors: Feedback (Response), Teacher Student Relationship, Teaching Methods, Thinking Skills
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Gurl, Theresa J.; Fox, Ryan; Dabovic, Nikolina; Leavitt, Arielle Eager – Mathematics Teacher, 2016
The implementation of the Common Core's Standards for Mathematical Practice can pose a challenge to all teachers of mathematics but especially to preservice teachers. These standards require teaching in a way that often differs from what preservice teachers have experienced as learners. Standard 1--"Make sense of problems and persevere in…
Descriptors: Teaching Methods, Mathematics Teachers, Preservice Teachers, Teaching Experience
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Sole, Marla A. – Mathematics Teacher, 2016
Every day, students collect, organize, and analyze data to make decisions. In this data-driven world, people need to assess how much trust they can place in summary statistics. The results of every survey and the safety of every drug that undergoes a clinical trial depend on the correct application of appropriate statistics. Recognizing the…
Descriptors: Statistics, Mathematics Instruction, Data Collection, Teaching Methods
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Huhn, Craig – Mathematics Teacher, 2016
When the author was first charged with getting a group of students to understand the correlation coefficient, he did not anticipate the topic would challenge his own understanding, let alone cause him to eventually question the very nature of mathematics itself. On the surface, the idea seemed straightforward, one that millions of students across…
Descriptors: Correlation, Mathematics, Mathematics Education, Mathematics Instruction
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Garofalo, Joe; Trinter, Christine P.; Swartz, Barbara A. – Mathematics Teacher, 2015
One method of proof is to provide a logical argument that demonstrates the existence of a mathematical object (e.g., a number) that can be used to prove or disprove a conjecture or statement. Some such proofs result in the actual identification of such an object, whereas others just demonstrate that such an object exists. These types of proofs are…
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Secondary School Mathematics