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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

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

Simonovits, Reinhard – International Journal for Technology in Mathematics Education, 2011

This article explains the didactical design of M@th Desktop (MD), a teaching and learning software application for high schools and universities. The use of two types of MD resources is illustrated: notebooks and palettes, focusing on the topic of exponential functions. The handling of MD in a blended learning approach and the impact on the…

Descriptors: Blended Learning, Computer Software, Computer Uses in Education, Mathematics Instruction

Roberts, Sally K.; Tayeh, Carla – Mathematics Teaching in the Middle School, 2010

To focus on mathematical reasoning and what makes a good argument, the authors developed an assignment that requires college students to submit a book of mathematical reasoning as an assessment during the semester. To begin, the authors looked for questions and tasks that lend themselves to developing mathematical arguments and justifications and…

Descriptors: Problem Solving, Mathematical Logic, College Students, College Mathematics

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

Wares, Arsalan – International Journal of Mathematical Education in Science and Technology, 2010

The purpose of this article is to provide examples of "non-traditional" theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The…

Descriptors: Geometry, Mathematical Logic, Validity, Mathematics Instruction

Duranczyk, Irene Mary – NADE Digest, 2007

This article is designed to present an overview of critical theory, research, and evaluation for the developmental mathematics educator. Students caught in the gap between high school mathematics preparation and entry-level college mathematics expectations--developmental mathematics education students--need to have their personal narratives told…

Descriptors: Critical Theory, Educational Research, Evaluation Methods, Developmental Studies Programs

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

Mauch, Elizabeth; Shi, Yixun – Mathematics and Computer Education, 2005

A sequence of number pairs can be used to generate many interesting examples in teaching mathematics subjects at various levels. It is often used in elementary or middle school mathematics classes to illustrate the concept of "patterns." In this paper the authors present a few interesting ways of using this sequence to form examples for high…

Descriptors: Teaching Methods, Geometry, College Mathematics, Calculus