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Cetin, Hatice – Universal Journal of Educational Research, 2019

Many related studies have studied many different models in the teaching of the concept of integer, which have reported that counters failed to completely help with the understanding of the concept of and operation modeling in integers. The purpose of the present research is presenting the "opposite model", which is a quantitative model,…

Descriptors: Numbers, Mathematics Instruction, Elementary School Mathematics, Mathematical Concepts

Crawford, Lindy; Quebec Fuentes, Sarah; Huscroft-D'Angelo, Jacqueline; Higgins, Kristina N. – Intervention in School and Clinic, 2019

Meaningful inclusion of quantitative reasoning into mathematics instruction requires meaningful ways to evaluate it. Few formative assessments exist to evaluate the strategies students use when reasoning mathematically. The Framework for Evaluating Quantitative Reasoning Strategies presented in this article provides teachers with categories for…

Descriptors: Fractions, Mathematics Instruction, Mathematical Logic, Student Evaluation

Rodgers, Wendy J.; Weiss, Margaret P. – TEACHING Exceptional Children, 2019

Nearly 63% of students with disabilities are included in general education classrooms for some part of their day, and at the high school level, 79% participate in state reading and math assessments (U.S. Department of Education, 2016). Middle and high school classes pose particular challenges because, unlike elementary classrooms, they are usually…

Descriptors: Teaching Methods, Team Teaching, Disabilities, General Education

Bush, Sarah B. – Mathematics Teaching in the Middle School, 2019

In April 2018, the National Council of Teachers of Mathematics (NCTM) released "Catalyzing Change in High School Mathematics: Initiating Critical Conversations," a long-needed and well-articulated position for transforming the core purposes, structures, instructional practices, essential mathematics concepts, and organization of high…

Descriptors: Mathematics Instruction, Secondary School Mathematics, Educational Change, Mathematical Concepts

Ahmadpour, Fatemeh; Reid, David; Reza Fadaee, Mohammad – Mathematical Thinking and Learning: An International Journal, 2019

We present a model for describing the growth of students' understandings when reading a proof. The model is composed of two main paths. One is focused on becoming aware of the deductive structure of the proof, in other words, understanding the proof at a semantic level. Generalization, abstraction, and formalization are the most important…

Descriptors: Mathematical Logic, Validity, Mathematics Instruction, Secondary School Mathematics

Willingham, James C.; Strayer, Jeremy F.; Barlow, Angela T.; Lischka, Alyson E. – Mathematics Teaching in the Middle School, 2018

Middle-grades teachers and students can have different perspectives on the value of discussing students' mathematical mistakes, despite various classroom evidence that such discussions can help foster strong conceptual understanding. Some teachers consider student mistakes to be an opportunity to correct errors in individual student thinking.…

Descriptors: Mathematics Instruction, Misconceptions, Mathematical Concepts, Middle School Students

Lim, Kien H.; Wilson, Ashley D. – Mathematics Teaching in the Middle School, 2018

More teachers are trying out the flipped classroom model in which content is delivered outside of class time, typically through online videos and "homework," and follow-up activities are done in class. This model frees up more class time for inquiry and discussion. This article focuses on the self-learning portion of the flipped learning…

Descriptors: Mathematics Instruction, Homework, Video Technology, Educational Technology

Schifter, Deborah; Bastable, Virginia; Russell, Susan Jo – National Council of Teachers of Mathematics, 2018

The "Reasoning Algebraically about Operations Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The thirty-four cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation into the…

Descriptors: Mathematics Instruction, Elementary Schools, Middle Schools, Teaching Methods

Poling, Lisa L.; Naresh, Nirmala; Goodson-Espy, Tracy – Mathematics Teaching in the Middle School, 2018

The authors explore how one teacher uses play and enacts the Effective Teaching Practices as a way to increase student engagement and autonomy and to meet learning goals when teaching mathematics with interactive simulations.

Descriptors: Mathematics Instruction, Teaching Methods, Learner Engagement, Personal Autonomy

Cengiz, Nesrin; Rathouz, Margaret – Mathematics Teaching in the Middle School, 2018

A framework using contexts, language, and representations can support middle school students' justifications. This article introduces classroom tasks and student work to provide a vision of framework implementation in classroom settings. Although the students in this article are future elementary and middle school teachers, the framework tasks and…

Descriptors: Mathematical Concepts, Mathematics Instruction, Preservice Teachers, Elementary School Teachers

Safi, Farshid; Bush, Sarah B.; Desai, Siddhi – Mathematics Teaching in the Middle School, 2018

In this article, the authors engage middle-grades students in a series of tasks to develop the mathematical idea of equal versus equivalent, culminating in a gerrymandering task with social, political, economic, and educational implications. The primary mathematical goals of this exploration were to involve students in solving real-world problems…

Descriptors: Mathematics Instruction, Middle School Students, Mathematical Concepts, Concept Formation

Lowe, James; Carter, Merilyn; Cooper, Tom – Australian Mathematics Teacher, 2018

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

Descriptors: Mathematics Instruction, Mathematical Models, Algebra, Mathematics Teachers

Livy, Sharyn; Muir, Tracey; Sullivan, Peter – Australian Primary Mathematics Classroom, 2018

Productive struggle leads to productive classrooms where students work on complex problems, are encouraged to take risks, can struggle and fail yet still feel good about working on hard problems (Boaler, 2016). Teachers can foster a classroom culture that values and promotes productive struggle by providing students with challenging tasks. These…

Descriptors: Mathematics Instruction, Problem Solving, Mathematics, Professional Personnel

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

Coomes, Jacqueline; Lee, Hyung Sook – Mathematics Teaching in the Middle School, 2017

Mathematics teachers want to empower students as mathematical thinkers and doers (NCTM 2000). Specific ways of thinking and doing mathematics were described in the Process Standards (NCTM 2000); they were further characterized as habits of mind (Mark, Goldenberg, and Sword 2010); and more recently, they were detailed in the Common Core's Standards…

Descriptors: Mathematics Instruction, Student Empowerment, Formative Evaluation, Mathematics Skills