**How to Learn Math**

**Jo Boaler's EDUC115N**

**WHY AM I SHARING THIS WITH YOU?**

I have been taking a free online course taught by a Stanford University Professor named Jo Boaler. Jo teaches math at college- level. *Has anyone heard of Stanford University? It is a prestigious, highly ranked and respectfully well-known, university that is in Palo Alto, a city that is South of San Francisco. *map of California that includes both SF and Stanford*

It is a prestigious, highly ranked and respectfully well-known, university that is in Palo Alto, a city that is South of San Francisco.

BSc (Psychology) Liverpool University

1985

MA (Mathematics Education) King's College, London University

1991

PhD (Mathematics Education) King's College, London University

1996

Faculty at Stanford University from 1998-2006

Professor at Stanford University during 2006 and from 2010- Present

1998-present

BECAUSE IT TURNS OUT ALL OF YOU HAVE THE POTENTIAL TO BE MATH GENIUSES

I remember from last school year, for ExCEL, I was helping out during homework time. I remember that some for those students who did their math homework first have either told me that they enjoyed it more or were better at it than other subjects that they were learning in school.

SURVEY

LET'S SEE A HAND RAISE FROM ANYONE WHO HAS BEEN TOLD OR ASKED ANY ONE OF THE FOLLOWING:

You're not a Math

person, are you?

Math isn't your thing,

but it's okay because

maybe you're better

at other subjects?

Something that we SUPPOSE something is true in order for the observed statements to hold true.

Whoever uses "math person" organizes students into types or categories which are defined by their current abilities.

NOTE: This way of labeling students devalues their potential for growth. Jo says that teachers should place more value on effort than results. (Therefore, standardized testing

Jo says she has two teenage daughters who watch tv shows that often portray math to be hard.

MATH IS

JO

Little

JO #1

Little

JO #2

I haven't followed up with the tv shows that are aired and that you watch so let's get hands for examples of something that you've seen on tv, either a commercial, movie, or tv program that send negative messages about math.

**BECAUSE OF THE FOLLOWING:**

REAL LIFE EXAMPLES OF NEUROPLASTICITY

TAXI DRIVER EXAMPLE

HALF A BRAIN 9 YEAR OLD GIRL EXAMPLE

MENTAL HEALTH INSTITUTION

Hi, I'm Jo. And I believe

that these are all

untrue.

Neuroplasticity- n. the lifelong capacity of the brain to change and rewire itself.

Example of Brain Growth #1: Taxi Drivers and Bus Drivers in London

Taxi drivers' brains were compared to bus drivers' brains in London. They discovered that taxi drivers' hippocampus is bigger than bus drivers'. Taxi drivers in London have to remember many very complex routes whereas bus drivers do not.

Conclusion

: There's a correlation between the physical structure of your brain and how much you learn and remember. Most importantly, challenges seem to expand brain power.

What you learn is like a footprint. The footprint is molded into the sand but if you don't keep stepping on it, it will be washed away by the waves. In other words, you need to keep using and applying what you learn or else you will forget it.

VOCABULARY

Hippocampus- n. this sea horse-like shape part of the brain that controls memory and spatial memory (memory of anything that relates to space, like remembering the location of things)

Example of Brain Growth #2: Girl with Half a Brain

A one month year old girl had a rare illness called Aicardi syndrome that didn't let her right and left hemispheres collaborate with each other, causing her to experience seizures 50 times a day. Because medication failed to stop these seizures, she underwent hemispherectomy, a removal of half her brain, specifically, the right side. They had concerns of her losing all the functions of the left side of the body (each side of the brain controls opposite sides of the body). However, once she woke up, her left arm moved, which was an indication of what was left of her brain taking over the roles of the part that's missing.

Conclusion:

Despite physical removal of a brain, she hardly showed any long term damages of her functions proves that the brain is very malleable.

Example of Brain Growth #3: Patients at Mental Institutions

Mental illnesses can be reflected in the brain. Mental patients' brain structures have shown change throughout weeks of treatment.

Conclusion

: Again, this shows how flexible a brain is.

**Sum Up**

Basically, these examples are evidence for two points, the brain is very modifiable. You can train it to do many things. Maybe you're not a math genius today, but if believing that you can if you want to be is the important initial step in getting there.

TWO STUDENTS OF DIFFERENT STRUCTURED ATTITUDES TOWARDS LEARNING

FIXED MINDSET

Given a set of math problems, this student would prefer to approach a problem that they can solve easily because this student places a lot of value in a correct answer.

A fixed mindset student who has been used to being told that they are smart will not take their mistakes very well.

GROWTH MINDSET

With this student, he or she would like to take on a challenging problem. Because getting the right answer to that problem is less important than how much that problem makes him or her think.

Whereas for a growth mindset student, mistakes are embraced as a part of their learning process.

Mathematics Process

1.Stop/think/say/draw

2.Talk

3. Estimate

4. Mathematize

5.Try, refine, revise

6.Make sense

MISTAKES IS TO YOUR BRAIN AS MILK IS TO YOUR BONES (except if you're lactose intolerant)

Example #1

A man is on a diet and goes into a shop to buy some turkey slices. He is given 3 slices which together weight 1/3 of a pound, but his diet allows 1/4 of a pound.

How much of the 3 slives can he eat while staying true to his diet?

Example #2

Charmaine and Tesha each have a number of cards in the ratio 2:3. Tesha and Holly have a number of cards in the ratio 2:1.

If Tesha has 4 more cards than Charmaine, how many cards does Holly have?

Example #3

Jo takes 3 hours to paint a house and Sam takes 5 hours to paint a house.

How long do they take if they paint it together?

Example #1

A man is on a diet and goes into a shop to buy some turkey slices. He is given 3 slices which together weight 1/3 of a pound, but his diet allows 1/4 of a pound.

How much of the 3 slices can he eat while staying true to his diet? (Assuming every slice weighs the same can we really answer this question)

1. Let's THINK

by DRAWING

*Reminder: the 2:3 ratio says this. Thinking a little outside of this problem, if Charmaine has 6 cards. For every 2 cards in the 6 that she has, Tesha has 3. Let's try to make sense of this.

1/3 lb

1 lb

2. Mathematize

9 slices/4= 1/4 lb

3 slices= 1/3 lb

9 slices= 1 lb

3.

Make sense

1/3 lb > 1/4 lb

answer has to be less than 3 slices

Answer: 2 and 1/4 slices of turkey (

which is less than 3 slices

)

Charmaine

Tesha

Holly

1. Think by drawing

If they both work on a house together, assuming their working together doesn't affect either one's painting rate, how much of the house will they have painted in an hour?

Let's make sense out of this

If it takes them an hour to paint a little more than half of the house, it should take them under an hour to paint the rest of it.

The problem tells us that Tesha has four more cards than Charmaine.

Notes: In this problem, we are trying to find the exact number of cards that Holly has. We are not given the exact number of cards that any person has except for this for every 2 cards, Tesha has three. *Reminder: the 2:3 ratio says this. Thinking outside of this problem, if Charmaine has 6 cards. For every 2 cards in the 6 that she has, Tesha has 3.

Charmaine

Tesha

How do we know if Charmaine has 2 cards and Tesha has 3?

Charmaine

Tesha

The problem tells us that Tesha and Holly have cards in the ratio of 2:1, meaning for every 2 cards that Tesha has, Holly has 1.

In other words, Holly has half of the number of cards that Tesha has. Does it make sense for Holly to have have half of 3 cards?

Tesha

Holly

Why is it okay for me to do this, to pretend there is one card under each card?

We were also given another piece of information from the problem.

Let's refer back to the previous slide.

Holly

Tesha

Charmaine

Does Tesha have four more cards than Charmaine? How many cards does Holly have?

Jo can paint 1/3 of a house.

Sam can paint 1/5 of a house

In 1 hour...

1/3 house+1/5house= 8/15 house

8/15 of a house in 1 hr

8/15 of a house

1/15 of a house takes how long to paint? (1hr/8 and then multiply by 15 because the house is divided into 15 parts)