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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

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

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

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

Berger, Lisa – Mathematics Teacher, 2013

Must two triangles with equal areas and equal perimeters also be congruent? This question was introduced in "Mathematics Teacher" ("MT")by Rosenberg, Spillane, and Wulf in their article "Heron Triangles and Moduli Spaces" (2008), which also described the authors' subsequent investigation of a particular moduli…

Descriptors: Mathematics Instruction, Mathematical Concepts, Geometric Concepts, High Schools

Strayer, Jeremy F. – Mathematics Teacher, 2013

Statistical studies are referenced in the news every day, so frequently that people are sometimes skeptical of reported results. Often, no matter how large a sample size researchers use in their studies, people believe that the sample size is too small to make broad generalizations. The tasks presented in this article use simulations of repeated…

Descriptors: Sampling, Sample Size, Research Methodology, Statistical Analysis

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

Groth, Randall E. – Mathematics Teacher, 2011

The lesson study model of professional development that originated in Japan is becoming increasingly popular in the United States. At its core, lesson study is a means of bringing teachers together to carry out the process of planning a lesson, implementing and observing it, and then examining it during a debriefing session. The debriefing…

Descriptors: Mathematics Education, Secondary School Teachers, Professional Development, Instructional Improvement

Devlin, Keith – Mathematics Teacher, 2010

The mathematics that students see in their textbooks is highly polished. The steps required to solve a problem are all clearly laid out. Thus, students are denied what could be a valuable learning experience. Often when students meet a problem that differs only slightly from the ones in the book, they are unable to proceed and afraid to "play…

Descriptors: Textbooks, Error Patterns, Probability, Learning Experience

Mulekar, Madhuri S.; Siegel, Murray H. – Mathematics Teacher, 2009

If students are to understand inferential statistics successfully, they must have a profound understanding of the nature of the sampling distribution. Specifically, they must comprehend the determination of the expected value and standard error of a sampling distribution as well as the meaning of the central limit theorem. Many students in a high…

Descriptors: Statistical Inference, Statistics, Sample Size, Error of Measurement

Gay, A. Susan – Mathematics Teacher, 2008

A focus on mathematics vocabulary must be part of teachers' instructional plans to develop students' understanding of key ideas. The author presents examples from work with preservice teachers regarding two vocabulary strategies and other related activities that can be used by middle and high school mathematics teachers. (Contains 8 figures.)

Descriptors: Preservice Teachers, Methods Courses, Role Models, Vocabulary Development

Canada, Daniel L. – Mathematics Teacher, 2008

To create an environment in which all students have opportunities to notice, describe, and wonder about variability, this article takes a context familiar to many teacher--sampling colored chips from a jar--and shows how this context was used to explicitly focus on variation in the classroom. The sampling activity includes physical as well as…

Descriptors: Computer Simulation, Sampling, Mathematics Instruction, Manipulative Materials

Sultan, Alan – Mathematics Teacher, 2007

In this article, the author presents some interesting geometric fallacies that were used in a problem-solving course for preservice high school mathematics teachers. He states that presenting these fallacies in ordinary math classes can enrich the class by making the students think hard about both the theorems themselves and the steps in the proof…

Descriptors: Geometric Concepts, Mathematics Teachers, Mathematics Instruction, Problem Solving

Kalder, Robin S. – Mathematics Teacher, 2007

Research has found that teachers of mathematics are more effective when they have a profound understanding of the content that is being taught and the content to which students have previously been exposed. It is clear that professional programs must enable preservice teachers to develop the knowledge and skills they need to teach elementary…

Descriptors: Teaching Methods, Preservice Teachers, Mathematics Instruction, Mathematical Concepts

Marcus, Robin; Fukawa-Connelly, Tim; Conklin, Michael; Fey, James T. – Mathematics Teacher, 2007

This article describes recommendations made by participants in a large project of the Mathematical Association of America (MAA), in which representatives of "partner disciplines" shared what they would like students to learn in the first two years of college mathematics. The article further suggests implications for high school mathematics.…

Descriptors: College Mathematics, Secondary School Mathematics, High Schools, Mathematics Instruction

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