Power of Mindsets In Math

Written by Marsi Quarin-Wright, Instructional Coach

Online Teacher Course by Jo Boaler: youcubed.com

I was recently introduced to the work of Jo Boaler and the website youcubed.org. What caught my interest is where she says math learning begins. Her starting point is fundamental to the vison of FSD and the role relationships play in learning. To me, this is not a typical starting point in understanding math. What furthered my curiosity was watching this approach to math instruction in a classroom.  I listened to the teacher’s positive talk and how engaged students were in the lessons.  The most impressive is listening to how students in her class love math, describe 3-D shapes with excitement and apply proper math vocabulary. I knew I had to investigate more. I went on to the website and found that there was an online course I could take. I signed up!

I was nervous and fearful; what was I doing taking a math course? What if I had to add or multiply something?  To my surprise, as I logged in and found the first sections of the course were on Math Mindset, Mistakes and Persistence, and Teaching for a Growth Mindset. Dr. Boaler quickly dispelled the myths of math, such as:

·         math is only for smart people

·         you either get math or you don’t.

Taken from youcubed.com - Growth Mindset by Jo Boaler: retrieved from https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/2017/05/When-You-Believe-in-Your-Students-They-Do-Better.pdf

She uses brain research to show that everyone is capable of learning math to high levels. I quickly realized that math has a bad reputation and my own worries about taking this class fed into that bad reputation. I quickly understood and turned my worries into wonders and began to see math in a new light.

Over the years I have heard from friends, family, parents and students – “I hate math” or “I’m no good at math”. I think it is vitally important that we become more aware of how these passing comments can affect how students’ view and ultimately learn math. We need to focus on the positives and not create unnecessary anxiety in students by continuing to discuss math in a negative way.  Using a growth mindset can offset many of these fears for our students. We need to use mistakes as a path to a deeper understanding of math. Having students see that persevering through difficult tasks is a way to make our math brain grow.

Where to start? I encourage everyone to take a look at youcubed.org.

In particular, look under Tasks and More à Week of Inspirational Math.

This starts that switch in mindset in math. You can check out the online student class on youcubed.org called, “How to Learn Math: For Students;” its free and another great place to start for everyone. The whole site is really amazing and provides practical, easy to use lessons for all teachers – even for those who think they “aren’t good at math”…

Math Tools

By Julie Julian, Instructional Coach
Guided Math & Running Record, CRC Session with Dr.Nicki Newton

Math tools help students scaffold their thinking. All learners should be able to access them at any given moment, regardless of grade level.

“Good problem solvers usually construct a representation of the problems to help them comprehend it “(van Gardener & Montague, 2003), but representing mathematical information visually does not come naturally to most students. Visual representation should be explicitly taught and then practiced using a variety of tools.

Both hands-on manipulatives and virtual tools:

·        Help convey concepts

·        Help visualize mathematical ideas

·        Model number relationships

Classroom Manipulatives

Manipulatives Tip Sheets http://www.edugains.ca/newsite/math/manipulative_use.html
The tip sheets for each of the listed manipulatives include a description of what they are, how they can help students, how many are recommended and sample activities. Unfortunately, many of the weblinks at the bottom of these PDF files aren’t active, but the tip sheets themselves are very helpful.

Algebra Tiles (pdf)

Base 10 Blocks (pdf)

Coloured Tiles (pdf)

Connecting Cubes (pdf)

Connecting Cubes (pdf)

Five and Ten Frames (pdf)

Fraction Circles (pdf)

Fraction Strips and Towers (pdf)

Geoboards (pdf)

Pattern Blocks (pdf)

Rekenreks (pdf)

Relational Rods (pdf)

Tangrams (pdf)

Beaded Number Line

https://guidedmath.wordpress.com/2016/09/01/the-beaded-number-line/

Have each student created a 100-bead beaded number line alternating colours every 10 beads This can be used for counting, skip counting, place value, rounding, adding, subtracting, number patterns, multiplication, division, and decimals.

Virtual Manipulatives

There are lots of fantastic interactive virtual math tools and apps for Smartboards, computers, tablets, and phones.

Graph Paper:

https://www.desmos.com/calculator/als0wdo8d4

Number Frames:

https://apps.mathlearningcenter.org/number-frames/

Cuisenaire Rods:

https://www.mathplayground.com/mathbars.html

Fractions:

https://apps.mathlearningcenter.org/fractions/

Geoboards:

https://apps.mathlearningcenter.org/geoboard/

Number Line:

https://apps.mathlearningcenter.org/number-line/

Rekenrek (number rack):

https://apps.mathlearningcenter.org/number-rack/

Pattern Shapes:

https://apps.mathlearningcenter.org/pattern-shapes/

Problem Solving in Math

By Darla Milford, Instructional Coach
Running Record, CRC Session with Dr.Nicki Newton

Real World Connection:

Problem solving in math should not be taught separately from the mathematical skills, processes, and understanding.  In fact, according to Dr. Nicki Newton, everything ‘math’, should be attached to the real world with a story attached to it.   In order to intellectually engage our students in math, it is essential we approach problem solving from a real world context with personalization being key.  

On Dr. Newton’s Guided Math Blog, she quotes Bailey saying students “don’t care how many apples
Bob gave to Suzy. They’re much more interested in things like music, video games, movies, trading
cards, money, and friends” (Bailey, 2002, p. 61) so make it personal!!!

Here are some sites with engaging problems ready to use with your own students:

*Greg Tang Math

*South Dakota Counts

*Math Playground Story Math

Cue Words/Keywords

We often fall into the trap of teaching our students to pick out ‘cue words’ or ‘keywords’ within a
problem to figure out the answer.  Some of these words may include ‘how many in all’ referring to
addition or ‘what is the difference’ suggesting subtraction. This strategy is essentially a quick ‘trick’
to help students solve the problem but it is important not to focus entirely on keywords without
considering the contextual information within the problem.  Focusing on words alone takes away
from the mathematical reasoning and understanding that is required in higher level or multi-step
problems students will encounter as they move forward in math.

Here’s an example:

Joe has 8 marbles, which is 2 times more than his brother. How many marbles do they have
altogether?

If kids focus primarily on key mathematical vocabulary, it may lead to a misunderstanding that the
term ‘times’ means that we multiply 8 X 2, when, in fact, if you read the problem in context you will
figure out that you already know that Joe has 8 marbles but you need to figure how many marbles
Joe’s brother had before adding these numbers together to get our answer.

Joe-8 marbles

Brother-½ of Joe’s 8 marbles = 4

So,

8+4=12 marbles altogether

Open-Ended Problem Solving

Dr. Nicki Newton emphasizes that math is best learned in contextual situations and that it is
important to provide opportunities for kids to demonstrate their mathematical understanding through
the use of ‘Open’ word problems.  ‘Open’ word problems are just that, open-ended, with a variety
of questions that could be asked as well as proven.  She suggested using a ‘3 Reads Protocol’
reading strategy to help make the problem more about the math than the reading  component.

Here’s an ‘Open’ problem example using the ‘3 Reads Protocol’ Reading Strategy.

The Smith Family Vacation Problem

The Smith family went on vacation. They drove 201 km on Monday, 177 km on Tuesday and 99 km
on Wednesday.

Write a story problem that includes the information given with an answer that makes sense.

When using this strategy, which can be used for whole group or guided math instruction there are 3
steps:

1. Begin by reading the problem altogether out loud.

     2) Reread the problem altogether again, this time, unpacking the math.

     3) Read the problem a 3rd time and have students create possible problems linked to the  
information and have them figure out the answer.

Here is an interesting article about open-ended questions and the value in having students write their
own problems to increase engagement and metacognition.  

The Answer is 20 Cookies

Dr. Nicki Newton’s authentic approach to teaching math problem solving in real world contexts makes
sense.  When students are connected to their learning and they can see the implications in the world
around them, they become much more invested.  Make sure you check out Dr. Nicki’s blog and if you
have any questions about her material, be in touch with the Instructional Coach in your building!

What Exactly is Math Fluency Anyways?

Written by Shelly Read, Curriculum & Instruction Facilitator

"Guided Math and Running Records" session with Dr. Nicki Newton through CRC

A few years ago, as part of our curriculum redesign journey, I had the opportunity to meet with math professors from the University of Lethbridge to discuss student learning. The conversation centred around their valid concern that students were struggling in university math courses, mainly due to a lack of number fluency. As Bjorklund et al found back in 1990, “student brains are exhausted with these ‘small things’ and so can't work on the more complex problems”. This conversation has stuck with me and is one lens I use when designing math with a focus on conceptual learning. Although we know not ALL students go to university,  we also recognize the importance of understanding numbers in our everyday lives and the world of work.

So, what are these ‘small things’ that provide evidence that students know and understand
the ‘basics’ of basic facts?

There are four pillars around math fluency that teachers should consider:

1. Automaticity

• Can students recall the answer instantaneously or do they have to stop and

think?

• As a general rule, automaticity is answering in 2-3 seconds without thinking

about it or hesitating.

• No actual timer should be used by the teacher.
• 
  

2. Accuracy

• Teachers should consider both a student’s oral and written responses.
• Does the student self-correct if they provide an incorrect answer?
• Be aware of counting strategies a student may use to solve facts mentally,

such as finger counting or counting in their head.

3. Flexibility

• Flexible thinking about numbers reveals a student’s depth of understanding.
• Does the student have a variety of strategies at their disposal?
• Teachers and students, as mathematicians, should know the names of the

strategies they are using.

4. Efficiency

• Students have a repertoire of strategies to choose from and choose the best

one for the situation.

• Students may have more developed strategies but often resort back to simple

methods.

• Both the teacher and the student should monitor progress and use of the most

appropriate strategies.

Together, these four criteria are used by students when they develop their individual
mathematical disposition. Having math talks with individual students is invaluable, as it
“provides teachers with a richer portrait of who they are helping to learn.” (p. 17)

In her book, Math Running Records in Action,Dr. Nicki Newton has created a framework
teachers can use to assess basic fact fluency that goes beyond memorization or speed and
instead helps to make students’ thinking visible by providing evidence of the child’s
computational thinking. “Designed to go way beyond merely capturing answers, these
assessments reveal how students are arriving at solutions, where they are breaking down,
and how they feel about themselves in the context of math. Ask yourself, can a timed test
do all that?” (page xiii)