Engaging Students in Learning Mathematics

Grade 5Session 1

Pam HutchisonAugust/September, 2015

AGENDA• Mindset and Learning Math• GO Math

– Chapter 1 – Place Value, Multiplication, and Expressions• questions and comments

– Chapter 2 – Divide Whole Numbers– Chapter 3 – Add and Subtract Decimals

Expectations• We are each responsible for our own

learning and for the learning of the group.• We respect each others learning styles and

work together to make this time successful for everyone.

• We value the opinions and knowledge of all participants.

Qualities Needed in High Tech Workplace – Ray Peacock, Phillips Laboratories

Lot’s of people think knowledge is what we want… and I don’t believe that, because knowledge is astonishingly transitory. We don’t employ people as knowledge bases, we employ people to actually do things or solve things. Knowledge bases come out of books.

Qualities Needed in High Tech Workplace – Ray Peacock, Phillips Laboratories

So I want flexibility and continuous learning…. [A]nd I need teamworking. And part of teamworking is communications. …the tasks are not 45 minutes max, they’re usually 3-week dollops or one-day dollops, or something, and the guy who gives up, you don’t want him.

Qualities Needed in High Tech Workplace – Ray Peacock, Phillips Laboratories

So the things therefore are the flexibility, the teamworking, the communication, and the sheer persistence.

What’s Math Got To Do With ItJo Boaler, Professor, Stanford University

Mindset

The Brain and Learning• Understanding brain research is a key

– What does the brain do while learning?– How does learning occur?– How do we maintain/develop new learning?– How do we use and connect prior knowledge?

What do you think?• In just a minute I am going to ask you a few

questions about what you believe about learning and math.

• Please jot your answers on a piece of paper.

What do you think?• You can learn new math skills but you can’t

really change your basic level of math ability.– Strongly Agree– Agree– Disagree– Strongly Disagree

What do you think?• I like math best when I can do it perfectly

without any mistakes.– Strongly Agree– Agree– Disagree– Strongly Disagree

What do you think?• When I have to work hard on a math

problem, it makes me feel as though I am not very smart.– Strongly Agree– Agree– Disagree– Strongly Disagree

What do you think?• I like math problems that I’ll learn from

even if I make a lot of mistakes.– Strongly Agree– Agree– Disagree– Strongly Disagree

Brain Plasticity • Jo Boaler, Benjamin Bloom, and Carol Dweck

research• Neuroplasticity—the ability for the brain to

grow and rewire itself

WIM Day 1 – Video

The Brain and Learning• Experiences and making sense of the

experiences• Providing many experiences for children

allow their brains to work and make sense of the situation in new ways

Benjamin Bloom

After 40 year of intensive research… major conclusion is:

• “What any person in the world can learn, almost all persons can learn if provided with the prior and current conditions of learning.”

Mindset

mindsetThe New Psychology of Success• By Carol Dweck:

Growth Mindset• A belief system that suggests that one’s

intelligence can be grown or developed with persistence, effort, and a focus on learning

Fixed Mindset• A belief system that suggests that a

person has a predetermined amount of intelligence, skills, or talents

Interview with Carol Dweck• https://

www.youtube.com/watch?v=wh0OS4MrN3E

Fixed vs Growth Mindset

Look smart

No

Give up

Lower

Learn

Yes

Work harder

Higher

What do you think?• You can learn new math skills but you can’t

really change your basic level of math ability.Fixed Mindset Growth Mindset– Strongly Agree– Agree

– Disagree– Strongly Disagree

What do you think?• I like math best when I can do it perfectly

without any mistakes.Fixed Mindset Growth Mindset– Strongly Agree– Agree

– Disagree– Strongly Disagree

What do you think?• When I have to work hard on a math

problem, it makes me feel as though I am not very smart.Fixed Mindset Growth Mindset– Strongly Agree– Agree

– Disagree– Strongly Disagree

What do you think?• I like math problems that I’ll learn from

even if I make a lot of mistakes.Fixed Mindset Growth Mindset

– Strongly Agree– Agree

– Disagree– Strongly Disagree

What do you think?• I like math problems that I’ll learn from

even if I make a lot of mistakes.Fixed Mindset Growth Mindset

– Strongly Agree– Agree

– Disagree– Strongly Disagree

What Can We Do?

Work to change students beliefs and mindsets.

Ned the Neuron• Teach children about the brain and the role

that challenges play in helping the brain grow.

Books about the Brain• Young Genius Brains by Kate Lennard• Think, Think, Think: Learning About Your

Brain by Pamela Hill Nettleton• Your Fantastic Elastic Brain – Stretch It,

Shape It by JoAnn Deak, Ph.D.• My First Book About the Brain by Donald M.

Silver and Patricia J. Wynne

Students• Week of Inspirational Math• Jo Boaler website: youcubed

https://www.youcubed.org/week-of-inspirational-math/

Week of Inspirational Math

• Different tasks that involve deep thinking with growth mindset messages that will help them persist with open and difficult problems and embrace mistakes and challenge.

• All tasks are low floor and high ceiling – they are accessible to all students and they extend to high levels.

Week of Inspirational Math• Meant to inspire students through

“open, beautiful and creative math”• Students learn important growth mindset

messages that will help them – feel confident, – try harder all year, – persist with open and difficult problems and – embrace mistakes and challenge.

WIM Day 1

What Can We Do?

Remove the idea that “speed” corresponds to how smart you

are in math!

Why does it matter?

Jo Boaler• … the number of highly qualified individuals

who have been really harmed by mathematics– Tales of trauma– Scarring experiences

Vivienne Parry, OBE(Order of the British Empire)

Jump to 2:40

Vivienne Parry

What Can We Do?

Set up positive norms!

What Can We Do?

Provide a wide variety of strategies and activities that allow all students to achieve.

Classroom Practices• Hands-On Activities• Allowing students to explore and investigate

math• Developing students’ conceptual

understanding• Number Talks and Daily Math• Alernate Algorithms• Emphasis on problem solving and word

problems/real world problems

GO Math!

Overall Program• Need to spend time in class on word

problems and problem solving• Send basic practice problems for homework

ONCE students are ready to work independently

• Send a reasonable number of problems for homework (about 10) – pick and choose which ones to send home

Overall Program• The “Advanced Learners” activities can

frequently be used for all students and is frequently more engaging

Chapter 1• Any comments, questions, or concerns?

Chapter 2• Lesson 2.1 Example #1 (63)

• Why 160?

Lesson 2.1

Estimate 128 ÷ 8• An alternative

– Do you have enough to make 1 group of 8?– Do you have enough to make 10 groups of 8?– Do you have enough to make 100 groups of 8?

10 groups 100 groups 80 800

Lesson 2.1

4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Lesson 2.1• Students may still need to draw or use

concrete objects at first• Lesson 2.1 jumps right to abstract

– Attend to precision• Connect to place value language• Alternative to erasing – record above• Area Models and Partial Quotients

Area Models

Partial Quotients

Lesson 2.5• Compatible Numbers (p 81)

Lesson 2.5• Multiplication

Lesson 2.6• Students can continue to use partial

quotients or area models• They do not have to use the traditional

algorithm shown in the text (see standard)

Lesson 2.7• This lesson is important• Students need to understand what the

remainder means and whether or not it is relevant to the problem.

Lesson 2.8• Again, students do not have to use

traditional algorithm• Students can use

“stacking” if theirestimate is toolow.

Chapter 2• Briefly look over Chapter 2• Any additional questions or concerns at this

time?

Chapter 3• Lessons 3.1 and 3.2 extend place value to

thousandths– 4th grade introduced tenths and

hundredths– Primary models should have been

number lines and area models– Lessons 3.1 and 3.2 connect to area

models

Lesson 3.2• Fraction/Decimal Connection (p113)

Lesson 3.3

Connect to prior knowledge• What would you do to compare the

following 2 numbers?234,108 and 98,978

LINE UP THE PLACE VALUES!

Lesson 3.3

Connect to prior knowledge• So what do you think you should do to

compare the following 2 numbers?2.34 and 5.9

LINE UP THE PLACE VALUES!

Lesson 3.3 (p 117)• Emphasize line up by place value, not by

decimal point• Decimal point can be an “Oh, yeah, what do

we notice?”

Lesson 3.3 (p 117)

Lesson 3.4

Rounding• Keep language of closer to (not rote rule)• Vertical (or horizontal) number line• Having to find the “middle” between 4.3 and

4.4 – Forces students to pay attention to equivalent

decimals (4.30 and 4.40)– Calls attention to the concept that there are

always more numbers between any 2 numbers

Lesson 3.7• Be sure you connect back to place value and

the models they used in Lessons 3.5 and 3.6

Lesson 3.8• Be sure to emphasize place value (not line

up the decimals)• Some students may still need to draw first

(not as a check – see p 139) – that is okay

Lesson 3.8 (p 139)

Lesson 3.9• Many students need a lot more time with

manipulatives and drawings to prevent common errors

• For example: 14.2 – 8.63

14.2 – 8.63

• Order of numbers

• Why did you place a “0”?

• Why didn’t the “3” just come down?

C – R – A • One of the weaknesses of the program is

that they (frequently) do not allow enough time at the concrete and representational stages

• You need to make sure that you allow extra time with manipulatives or drawing if needed

• Pay attention to standards

Chapter 3• Briefly look over Chapter 3• Any additional questions or concerns at this

time?