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Buchheister, Kelley; Jackson, Christa; Taylor, Cynthia E. – Mathematics Teaching in the Middle School, 2019

With an increased focus on using social discourse to enhance students' mathematical thinking and reasoning (NCTM 2014, Staples and King 2017), teachers are looking for discussion strategies that encourage middlelevel students to make sense of mathematical concepts. However, structuring these valuable discussions is complex. Teachers must carefully…

Descriptors: Mathematics Instruction, Middle School Teachers, Teaching Methods, Classroom Environment

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

Moore, Kimberly – Mathematics Teaching in the Middle School, 2018

Minecraft is an open world survival computer game that was originally created in Sweden in 2011 and later purchased by Microsoft® in 2014. It is among the most popular computer games with students of all ages because it gives players a sense of ownership and opportunities for creative exploration. The game has three unique features: (1) no clear…

Descriptors: Middle School Students, Grade 8, Secondary School Mathematics, Mathematics Instruction

Roy, George J.; Eli, Jennifer A.; Hendrix, Leslie; Graul, LuAnn – Mathematics Teaching in the Middle School, 2018

Students who are adept in modeling with mathematics have the capability to use mathematics in situations that arise in everyday life. The German Tank problem described in this article created the expectation that student reasoning was rooted in logical deductions (NCTM 2000). By engaging in this problem, students grappled with challenging…

Descriptors: Mathematics Instruction, Word Problems (Mathematics), Problem Solving, Mathematical Logic

Hallman-Thrasher, Allyson; Koestler, Courtney; Dani, Danielle; Kolbe, Amanda; Lyday, Katie – Mathematics Teaching in the Middle School, 2018

As a group of middle school mathematics teachers and teacher educators, the authors have focused their attention on using innovative practices coupled with high cognitive demand tasks to engage students, pique their interest in mathematics, and promote conceptual understanding. This article explores their three-act task design. In act 1, students…

Descriptors: Mathematics Instruction, Secondary School Mathematics, Middle School Teachers, Teaching Methods

Jensen, Jessica Lynn – Mathematics Teaching in the Middle School, 2018

Watching a debate can help people understand multiple points of view. At the conclusion of a debate, a consensus might occur after a deep analysis and discussion of the issues. Most students will participate in a class debate at some point in their schooling, but chances are that debate will not take place in math class. What could there be to…

Descriptors: Mathematics Instruction, Teaching Methods, Debate, Critical Thinking

Dunleavy, Teresa K. – Education Sciences, 2018

This article continues to challenge the robust myth that mathematical smartness is exemplified in individuals who consistently complete mathematics problems quickly and accurately. In so doing, I present a set of counterstories from three students in one ninth-grade Algebra 1 classroom. These students described transformative experiences in their…

Descriptors: High School Students, Secondary School Mathematics, Algebra, Mathematics Skills

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

Czocher, Jennifer A.; Moss, Diana L. – Mathematics Teacher, 2017

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

Descriptors: Mathematical Models, Problem Solving, Mathematics Instruction, High School Students

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

Burton, Lauren – Mathematics Teaching in the Middle School, 2017

When teaching algebra concepts to middle school students, the author often hears questions that echo her own past confusion as a young student learning to write linear equations using data tables that show only input and output values. Students, expected to synthesize the relationship between these values in symbolic representation, grow…

Descriptors: Algebra, Middle School Students, Mathematics Instruction, Secondary School Mathematics

Carter, Cynthia J. – Mathematics Teaching in the Middle School, 2017

The author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing…

Descriptors: Middle School Students, Secondary School Mathematics, Multiplication, Fractions

Edwards, Michael Todd; Meagher, Michael S.; Özgün-Koca, S. Asli – Mathematics Teaching in the Middle School, 2017

Middle school students need opportunities to craft informal mathematical arguments beyond justification of steps in an algorithm. Pentominoes provide an excellent vehicle for such activity. In this article, the authors describe an exploration with pentominoes that engaged a group of ninth-grade students in proportional reasoning, dilation, and…

Descriptors: Middle School Students, Secondary School Mathematics, Teaching Methods, Persuasive Discourse

de la Cruz, Jessica A.; Garney, Sandra – Mathematics Teaching in the Middle School, 2016

It is beneficial for students to discover intuitive strategies, as opposed to the teacher presenting strategies to them. Certain proportional reasoning tasks are more likely to elicit intuitive strategies than other tasks. The strategies that students are apt to use when approaching a task, as well as the likelihood of a student's success or…

Descriptors: Mathematics Instruction, Mathematical Logic, Teaching Methods, Learning Strategies