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5 Practices for Orchestrating Productive Mathematics Discussions

In the book 5 Practices for Orchestrating Mathematics Discussions, the authors describe how teachers can facilitate "mathematically productive discussions that are rooted in student thinking." In the links below, a math teacher blogs about his experiences implementing the strategies in the book.

TAGS: MTBOS, productive math discussions, 3 Act Math

Balancing the Equation

Matt Larson addresses the historic pendulum swing in instructional practice, addresses recent concerns about national academic standards, and suggests what math educators might advocate for today in this 5-minute talk

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TAGS: new math, common core standards, CCRS, ignite

Classroom Clock

In this 5-minute talk, Andrew Stadel addresses strategies for dealing with the limited time each teacher must face. How do we make best use of time in our classroom? How can we approach “squeezing great content into short segments”?

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TAGS: Stadel, video, MTBOS, time management, ignite

Designing Systems of Teacher Learning around Student Work

Description of this recorded webinar: "How do we develop sustained growth in teacher practice in a department? One way is to design a system of teacher learning based on student artifacts. Join Geoff Krall (@emergentmath) as he shares experiences and models of student work analysis that lead to better instructional choices and departmental coherence."

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TAGS: assessment, Global Math Department, webinar

Ever Wonder What They'd Notice?

Asking the right questions and making space for student thinking can change outcomes for students. What can we do as teachers to faciliate their critical thinking and engagement? In this 5-minute Ignite talk, Annie Fetter addresses giving students to space to notice and wonder.

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TAGS: video, MP1, MP3, MP7, MP8, Mathematical Practice 1, Mathematical Practice 3, Mathematical Practice 7, Mathematical Practice 8, Annie Fetter

Global Math Department

A community of smart, skilled instructors who teach math at all levels, and share their materials and ideas. Go to the website and sign up for their email newsletter. Great free resources will come to you each week! The newsletter will bring you information about free, terrific webinars on math instruction.

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TAGS: MTBOS, #mtbos, webinar, blogs, learning about instruction

Great Estimations by B. Goldstone

This picture book both describes estimation strategies and gives interesting, appealing images to practice on. An ABE teacher may scaffold the book by focusing an instructional activity around certain pages. Goldstone has a series of similar math-related books, including Greater Estimations - which considers estimating larger quantities.

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TAGS: estimation

How to Edit Your Math Pessimism

Students and teacher often have beliefs that are counter producitve to learning. In this blog post, the author "edits" common statements about learning math to re-frame them in ways that are encouraging and honest.

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TAGS: growth mindset, perseverance, habits of mind, confidence, math anxiety

How to Learn Math

How to Learn Math is a free, self-paced class for learners of all levels of mathematics. It combines information on the brain and learning with research on the best ways to approach and learn math effectively. It is open to anyone learning math, and is good for instructors as well as students.

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TAGS: Jo Boaler, fixed mindset, growth mindset, learning about instruction

Ignite Videos - Math Forum

Ignite is a presentation format where each presenter speaks for 5 minutes. This site has some excellent talks from the Math Forum at Drexel. Recommended talks include: 

Ever Wonder What they’d Notice? - Annie Fetter
Fun with Trig Identities – Max Ray

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TAGS: video, Math Forum, Max Ray, Annie Fetter, #mtbos, MTBOS, learning about instruction

Let's Laugh About Math

In this 11-minute video is Laila Nur's talk from Shadow Con 2015. In it she suggests using humor to build students' relationship with Math.

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TAGS: Danielson, MTBOS, TMWMK, Shadowcon

Listen to Your Students

In this 12 minute video is Christopher Danielson's talk from Shadow Con 2015. Here is the description from the website: "Teachers are busy—so busy we often don’t hear what students say. Sometimes we hear things that students don’t say. I’ll make a case for the importance of listening carefully to students of all ages. I’ll encourage you to make time to listen more carefully, and I’ll give you some simple strategies for doing it."

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TAGS: Danielson, MTBOS, TMWMK, Shadowcon

Problem Strings

Pamela Weber Harris gives a knockout webinar on Problem Strings. Problem Strings are an instructional strategy where the teacher facilitates students working through and thinking aloud about a set of math problems (for example: 5 x 6, then 5 x 60, and so on...) as a method for students to learn from each other about math strategies. The strategy offers a way to pack significant math learning into a short time in class.

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TAGS: Pamela Weber Harris, number strings, problem strings, Global Math Department, MTBOS, #MTOBS, Mathisfigureoutable, building powerful numeracy, teaching strategy, instruction, progression, intentional

Rethinking How We See Mistakes

A math teacher writes about encouraging students to make and learn from mistakes. She recommends specific strategies for changing a classroom's culture around mistakes.

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TAGS: MTBOS, blog, error, growth mindset, chemical equations, McLaren, McSquared

Students with Disabilities Can Do Math

Slides, detailed resources and a record of Twitter discussion around this important topic.

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TAGS: disability, mainstream, inclusion

The Best Way to Learn Math is to Learn to Fail Productively

Manu Kapur's research finds that students are more successful when teachers allow them to have a period of (teacher-planned) productive struggle with material before the teacher provides direct instruction on the math strategies. "Students have to figure out three critical things: what they know, the limits of what they know, and exactly what they do not know. Floundering first elevates the learning from knowing a formula to understanding it, and applying it in unfamiliar contexts." This article addresses Kapur's research and his suggested instructional approach - which seems to increase students' conceptual understanding.

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TAGS: mistakes, Singapore, productive struggle, research

The Problem with Math is English

The Problem with Math is English. Molina, Concepcion (2012). Available at many libraries, bookstores, through Amazon and Powell's, etc. (ISBN-13: 978-1118095706)

Molina explores the relationship between mathematical instruction and language. There is also a recording of a webinar with Molina here

From the publisher:

Published in partnership with SEDL, The Problem with Math Is English illustrates how students often understand fundamental mathematical concepts at only a superficial level. Written to inspire "aha" moments, this important new book offers teachers the tools they need to help their students identify and comprehend the nuances and true meanings of essential math concepts—such as multiplication, division, fractions, place value, and much more—by exploring them through the lenses of language and symbolism.

The Problem with Math Is English explains how language-focused conceptual instruction leads students to a deeper understanding than traditional procedural-based teaching methods. By placing emphasis on truly understanding math concepts, Dr. Molina shows that teaching math becomes easier when teachers are able to communicate the language, symbolism, and representation of math to all of their students.

"Teachers of mathematics of all levels who read and spend time with this fun and challenging book will strengthen their content knowledge and find confidence in their own ability to think and reason. When teachers truly understand and embrace the mathematics/language connections so richly illustrated in the book, they will be able to pass on to all of their students a depth of mathematical insight and joy they may never have imagined before." (See more at Powell's)

TAGS: book, Como Molina, vocabulary, language learner, ESL, ELL

Why Before How

Why Before How: Singapore Math Computation Strategies. Hazekamp, Jana (2011). Available at many libraries, bookstores, through Amazon and Powell's, etc. (ISBN-13: 978-1934026823)

Hazekamp explores strategies for building number sense around place value and basic operations. 

From the publisher:

Jana Hazekamp introduces a wide variety of computation strategies, adapted from the acclaimed Singapore approach, that will bring students a real understanding of number relationships and the meaning behind the math. The guided-conversation format is designed for quick reading, and Jana's question-and-answer style is particularly well suited to encouraging students to focus on the why and to begin using math terminology correctly and fluently.

Teachers can use this book to build the concept of place value, encourage students to consider multiple methods for solving problems, and build real understanding of the meaning behind addition, subtraction, multiplication, and division paving the way to beginning algebra.

These strategies can be used for whole-class instruction and also for small intervention groups. The book does not have to be read cover to cover; the reader can dip in as needed to help a student who's struggling with a particular concept. (See more at Powell's)

TAGS: book, number sense, operations, CCRS, Level A, Level B, Level C, conceptual understanding

Youcubed.org

The site explains itself this way: “Our main goal is to inspire, educate and empower teachers of mathematics, transforming the latest research on math learning into accessible and practical forms.” Jo Boaler is a professor and author focused on math instruction. This nonprofit offers free, easy-to-use resources. Since there are many great resources here, you may want to start with TASKS to find for instructional, ready-to-use materials. Because many of these tasks are “Low Floor, High Ceiling,” students at different levels can thoughtfully engage on the same work. The tasks are searchable by math topic, grade and mathematical practice.

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TAGS: activities, printable, growth mindset, Jo Boaler