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Nabb, Keith; Hofacker, Erick B.; Ernie, Kathryn T.; Ahrendt, Susan – Mathematics Teacher, 2018

This article highlights three of the eight Mathematics Teaching Practices (MTP) published in the National Council of Teachers of Mathematics' (NCTM's) "Principles to Actions: Ensuring Mathematical Success for All" (2014): (1) facilitating meaningful mathematical discourse (MTP 4); (2) posing purposeful questions (MTP 5); and (3)…

Descriptors: Mathematics Instruction, Teaching Methods, Active Learning, Calculus

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

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

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

Lommatsch, Christina W. – Mathematics Teacher, 2017

"Find the extreme values of the function." "At what rate is the distance between A and B increasing after 12 seconds?" Prompts like these can be heard in most first-semester calculus courses. Unfortunately, these cues also tend to prompt students' eyes to glaze over with thoughts of "When will I ever use this?" This…

Descriptors: Mathematics Instruction, Calculus, Relevance (Education), Career Choice

FitzPatrick, Daniel L.; Dominguez, Victoria S. – Mathematics Teacher, 2017

Teaching persistence and problem solving must begin with selecting a problem that can be solved mathematically, that allows for multiple methods of solving, and that generally captures the attention and curiosity of the student (Marcus and Fey 2003; NCTM 1991; Van de Walle 2003). This article shows how a STEM three-dimensional (3D) printing…

Descriptors: Problem Solving, Mathematics Instruction, STEM Education, Preservice Teacher Education

Samuels, Jason – Mathematics Teacher, 2017

Calculus has frequently been called one the greatest intellectual achievements of humankind. As a key transitional course to college mathematics, it combines such elementary ideas as rate with new abstract ideas--such as infinity, instantaneous change, and limit--to formulate the derivative and the integral. Most calculus texts begin with the…

Descriptors: Mathematics Instruction, Calculus, Graphs, Problem Solving

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

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

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

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

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

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

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

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