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Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 6



Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 6 PDF

Author: Jo Boaler , Jen Munson

Publisher: Jossey-Bass

Genres:

Publish Date: January 7, 2019

ISBN-10: 1119358833

Pages: 272

File Type: PDF

Language: English

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Book Preface

I still remember the moment when Youcubed, the Stanford center I direct, was
conceived. I was at the Denver NCSM and NCTM conferences in 2013, and I had
arranged to meet Cathy Williams, the director of mathematics for Vista Unified
School District. Cathy and I had been working together for the past year improving
mathematics teaching in her district. We had witnessed amazing changes taking
place, and a filmmaker had documented some of the work. I had recently released my
online teacher course, called How to Learn Math, and been overwhelmed by
requests from tens of thousands of teachers to provide them with more of the same
ideas. Cathy and I decided to create a website and use it to continue sharing the ideas
we had used in her district and that I had shared in my online class. Soon after we
started sharing ideas on the Youcubed website, we were invited to become a Stanford
University center, and Cathy became the codirector of the center with me.

In the months that followed, with the help of one of my undergraduates,
Montse Cordero, our first version of youcubed.org was launched. By January 2015,
we had managed to raise some money and hire engineers, and we launched a revised
version of the site that is close to the site you may know today. We were very excited
that in the first month of that relaunch, we had five thousand visits to the site. At the
time of writing this, we are now getting three million visits to the site each month.
Teachers are excited to learn about the new research and to take the tools, videos,
and activities that translate research ideas into practice and use them in their
teaching.

Low‐Floor, High‐Ceiling Tasks

One of the most popular articles on our website is called “Fluency without Fear.”
I wrote this with Cathy when I heard from many teachers that they were being made
to use timed tests in the elementary grades. At the same time, new brain science was
emerging showing that when people feel stressed—as students do when facing a
timed test—part of their brain, the working memory, is restricted. The working
memory is exactly the area of the brain that comes into play when students need to
calculate with math facts, and this is the exact area that is impeded when students
are stressed. We have evidence now that suggests strongly that timed math tests in
the early grades are responsible for the early onset of math anxiety for many students.
I teach an undergraduate class at Stanford, and many of the undergraduates are math
traumatized. When I ask them what happened to cause this, almost all of them will
recall, with startling clarity, the time in elementary school when they were given
timed tests. We are really pleased that “Fluency without Fear” has now been used
across the United States to pull timed tests out of school districts. It has been
downloaded many thousands of times and used in state and national hearings.
One of the reasons for the amazing success of the paper is that it does not just
share the brain science on the damage of timed tests but also offers an alternative to
timed tests: activities that teach math facts conceptually and through activities that
students and teachers enjoy. One of the activities—a game called How Close to
100—became so popular that thousands of teachers tweeted photos of their students
playing the game. There was so much attention on Twitter and other media that
Stanford noticed and decided to write a news story on the damage of speed to
mathematics learning. This was picked up by news outlets across the United States,
including US News & World Report, which is part of the reason the white paper has
now had so many downloads and so much impact. Teachers themselves caused this
mini revolution by spreading news of the activities and research.

How Close to 100 is just one of many tasks we have on youcubed.org that are
extremely popular with teachers and students. All our tasks have the feature of being
“low floor and high ceiling,” which I consider to be an extremely important quality
for engaging all students in a class. If you are teaching only one student, then a
mathematics task can be fairly narrow in terms of its content and difficulty. But
whenever you have a group of students, there will be differences in their needs, and
they will be challenged by different ideas. A low‐floor, high‐ceiling task is one in
which everyone can engage, no matter what his or her prior understanding or knowledge, but also one that is open enough to extend to high levels, so that all students can be deeply challenged. In the last two years, we have launched an
introductory week of mathematics lessons on our site that are open, visual, and low
floor, high ceiling. These have been extremely popular with teachers; they have had
approximately four million downloads and are used in 20% of schools across the
United States.

In our extensive work with teachers around the United States, we are
continually asked for more tasks that are like those on our website. Most textbook
publishers seem to ignore or be unaware of research on mathematics learning, and
most textbook questions are narrow and insufficiently engaging for students. It is
imperative that the new knowledge of the ways our brains learn mathematics is
incorporated into the lessons students are given in classrooms. It is for this reason
that we chose to write a series of books that are organized around a principle of
active student engagement, that reflect the latest brain science on learning, and that
include activities that are low floor and high ceiling.


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