We Reason & We Prove for ALL Mathematics

Building Students’ Critical Thinking, Grades 6-12

Fran Arbaugh,

We Reason & We Prove for ALL Mathematics: Building Students’ Critical Thinking, Grades 6-12
 
 

Sharpen concrete teaching strategies that empower students to reason-and-prove

How do teachers and students benefit from engaging in reasoning-and-proving? What strategies can teachers use to support students’ capacity to reason-and-prove? What does reasoning-and-proving instruction look like?

We Reason & We Prove for ALL Mathematics helps mathematics teachers in grades 6-12 engage in the critical practice of reasoning-and-proving and support the development of reasoning-and-proving in their students. The phrase "reasoning-and-proving" describes the processes of identifying patterns, making conjectures, and providing arguments that may or may not qualify as proofs – processes that reflect the work of mathematicians. Going beyond the idea of "formal proof" traditionally relegated only to geometry, this book transcends all mathematical content areas with a variety of activities for teachers to learn more about reasoning-and-proving and about how to support students’ capacities to engage in this mathematical thinking through:

  • Solving and discussing high-level mathematical tasks
  • Analyzing narrative cases that make the relationship between teaching and learning salient
  • Examining and interpreting student work that features a range of solution strategies, representations, and misconceptions
  • Modifying tasks from curriculum materials so that they better support students to reason-and-prove
  • Evaluating learning environments and making connections between key ideas about reasoning-and-proving and teaching strategies

 We Reason & We Prove for ALL Mathematics is designed as a learning tool for practicing and pre-service mathematics teachers and can be used individually or in a group. No other book tackles reasoning-and-proving with such breadth, depth, and practical applicability. Classroom examples, case studies, and sample problems help to sharpen concrete teaching strategies that empower students to reason-and-prove!




  • ;
  • ISBN:
  • Edition:
  • Title:
  • Series:
  • Author:
  • Imprint:
  • Language:

In The Press


About The Author


Customer Reviews

Verified Buyer

Read online

If you’re using a PC or Mac you can read this ebook online in a web browser, without downloading anything or installing software.

Download file formats

This ebook is available in file types:

This ebook is available in:

After you've bought this ebook, you can choose to download either the PDF version or the ePub, or both.

DRM Free

The publisher has supplied this book in DRM Free form with digital watermarking.

Required software

You can read this eBook on any device that supports DRM-free EPUB or DRM-free PDF format.

Digital Rights Management (DRM)

The publisher has supplied this book in encrypted form, which means that you need to install free software in order to unlock and read it.

Required software

To read this ebook on a mobile device (phone or tablet) you'll need to install one of these free apps:

To download and read this eBook on a PC or Mac:

  • Adobe Digital Editions (This is a free app specially developed for eBooks. It's not the same as Adobe Reader, which you probably already have on your computer.)

Limits on printing and copying

The publisher has set limits on how much of this ebook you may print or copy. See details.

  • {{ format_drm_information.format_name }} unrestricted {{ format_drm_information.format_name }} {{format_drm_information.page_percent}}% pages every day{{format_drm_information.interval}} days {{ format_drm_information.format_name }} off
Read Aloud
  • {{ read_aloud_information.format_name }} on {{ read_aloud_information.format_name }} off
Subject categories
  •  > 
ISBNs