Changing our Mindset about Math

Meg ConnorsInternational School Stuttgart

True or False? ● I am good at math.

● Some people are born good at math.

● Math is about creativity.

● It’s important to get the right answer in math.

● School math should connect to the “real world”.

● Memorizing procedures and rules is critical to math success.

● Boys are usually better at math than girls.

● Everyone needs to learn math.

● Math is about performing and being able to compute quickly.

● My students are all mathematicians.

What are the challenges?

What are the challenges?-Students struggle to meet international standards in mathematics.

-Students lack confidence in their mathematical ability or feel stressed about their performance in math class.

-Parents worry about their children’s progress in mathematics.

-Teachers feel unprepared to teach math.

-Parents/Teachers unintentionally convey messages that math is a difficult subject and “not meant for everyone”.

-Our world is changing at a rapid pace.

Math Class circa. 1966?

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Math Class circa. 2016

What do mathematicians do? A brief survey of 3-5 graders (2014)

-add, subtract, multiply and divide

-do math problems/ work on math

-take tests

-try to figure out hard math

-go to math competitions like Math Quest

What would your students say?

What is mathematics, really?

What does the PYP think? “In the same way that students describe themselves as “authors” or “artists”, students

are given the opportunity to see themselves as “mathematicians”, where they enjoy and

are enthusiastic when exploring and learning about mathematics.”

“In the IB Primary Years Programme (PYP), mathematics is also viewed as a vehicle to

support inquiry, providing a global language through which we make sense of the world

around us.”

Retrieved from “PYP Mathematics Scope and Sequence”

How do many schools view math?

A Mathematician's Lament

What do REAL mathematicians think and do? Ray Peacock (research director for Phillips Laboratories in the UK)

“Lots of people think knowledge is what we want, and I don’t believe that, because knowledge is surprisingly transitory…we employ people to actually do things or solve things...the things are flexibility, team working, communications and sheer persistence.”

Maryam Mirzakhani (first woman to win the Fields Medal)“Of course, the most rewarding part is the "Aha" moment, the excitement of discovery and enjoyment of understanding something new the

feeling of being on top of a hill and having a clear view...”

Terry Tao (widely considered one of the greatest mathematicians of our time)

“Early encounters with math can be misleading. The subject seems to be about learning rules — how and when to apply ancient tricks to arrive at an answer. Four cookies remain in the cookie jar; the ball moves at 12.5 feet per second. Really, though, to be a mathematician is to

experiment. Mathematical research is a fundamentally creative act...”

Conrad Wolfram (director of Wolfram-Alpha, one of the most important mathematical companies in the world)

“Learning by rote is not the answer – unlocking the creative power of problem-solving is what will enthuse British schoolchildren and make them world-class…”

Conrad Wolfram- TED talk

What do REAL mathematicians think and do? Ray Peacock (research director for Phillips Laboratories in the UK)

“Lots of people think knowledge is what we want, and I don’t believe that, because knowledge is surprisingly transitory… we employ people to actually do things or solve things...the things are flexibility, team working, communications and sheer persistence.”

Maryam Mirzakhani (first woman to win the Fields Medal)“Of course, the most rewarding part is the "Aha" moment, the excitement of discovery and enjoyment of understanding something new the

feeling of being on top of a hill and having a clear view...”

Terry Tao (widely considered one of the greatest mathematicians of our time)

“Early encounters with math can be misleading. The subject seems to be about learning rules — how and when to apply ancient tricks to arrive at an answer. Four cookies remain in the cookie jar; the ball moves at 12.5 feet per second. Really, though, to be a mathematician is to

experiment. Mathematical research is a fundamentally creative act...”

Conrad Wolfram (director of Wolfram-Alpha, one of the most important mathematical companies in the world)

“Learning by rote is not the answer – unlocking the creative power of problem-solving is what will enthuse British schoolchildren and make them world-class…”

How did you experience math?

How do we want our students to experience MATH?

What do our students need to be successful mathematicians?

Growth Mindset Number Sense

What is a Growth Mindset?Benjamin Barber

(sociologist/City University of NY)

“I don’t divide the world into the weak and the strong, or the successes and the failures…. I divide the world into the learners and nonlearners.”

Carol S. Dweck, Ph.D.

(psychologist/ Stanford University)

“In a growth mindset, people believe that their most basic abilities can be developed through dedication and hard work—brains and talent are just the starting point. This view creates a

love of learning and a resilience that is essential for great accomplishment,”

Carol Dweck- Growth Mindset

How do students get a FIXED MINDSET about math?

-”Messages” from the media about math

-”Messages” from parents and teachers about math

-Math work that is “right” or “wrong”

-Repeated failures in math

-The belief that math ability is innate

How can we encourage a GROWTH MINDSET in math?

Brain Growth and Mistakes

What is a Number Sense?“A student with a strong number sense understands numbers, ways to represent numbers, relationships among numbers, and number systems. This student makes reasonable estimates, computes fluently, uses reasoning strategies, and uses visual models to figure out problems.”

“Number Sense Routines: Building Numerical Literacy Every Day” by Jessica Shumway

Jo Boaler- Number Sense

How do we build Number Sense in our students? -Provide many opportunities for students to “play” with numbers.

-Ask students to calculate mentally.

-Model and discuss different strategies for computing.

-Make estimation an integral part of computing.

-Question student about how they reason.

-Pose questions with more than one possible answer.

About Teaching Mathematics. A K-8 Resource, 3rd Edition, Marilyn Burns (2007)

“Number Talks”...a mini-lesson -Select a special location close to your students allowing for informal observations and interactions.

-Have a large space to record students’ thinking and ideas.

-Provide appropriate wait time to ensure most students have accessed the problem.

-All answers are accepted, respected, and considered.

-Encourage student communication throughout the number talk.3rd Grade Number Talk 1st Grade Number Talk

Setting up Positive Norms in Math Class(Professor Jo Boaler- Stanford University “How to Learn Math”)

1. Everyone can learn math to the highest level.

2. Mistakes are valuable.

3. Math class is about learning, not performing.

4. Depth is more important than speed.

5. Math is about connections and communicating.

6. Questions are really important.

7. Math is about creativity and making sense.

Resources

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