Building Math Confidence: Presentation #1

Building Math Confidence Presented by

Christopher S. Vaughen

Mathematics Professor, MCCC [email protected]

Building Math Confidence Presentation Topics

• Personality Types and Learning Styles

• Math Anxiety and Negative Self-Talk

• Problem Solving

• Building Math Confidence Strategies

Personality Types & Learning Styles

An age old debate…

Nature vs. Nurture

Math skills: are you born with it or is it your upbringing?

Personality Types & Learning Styles •  Is there a mathematical mind? A non-mathematical mind?

• Are men better at math than women?

• Are certain personality types better at math than others? Do people with certain learning styles find math more difficult?

• Are some people “left-brain” logical types while others are “right-brain” creative types?

Common Myths What do you believe?

§ Math requires logic, not intuition.

§ Math is not a creative endeavor.

§  In math, there is one way to get the answer.

§ Math is done by working intensely until the problem is solved.

§ To be good at math, you have to be good at calculating.

§  If you are good at math, you skip steps and do most of the work in your head.

Personality Types & Learning Styles •  I believe problem solving requires creativity and that creativity is

essential to learning math and that math is full of beauty, surprises, paradoxes and mystery and that is is more about ideas than calculation.

•  I believe learning mathematics is valuable to everyone and everyone can improve in mathematics.

•  I don’t believe in general that men or women are better at mathematics.

Personality Types & Learning Styles In 1992, a study of attitudes about success in math in the U.S. and in Japan revealed an interesting difference:

When asked to explain why some children do better in math than others, Japanese children, parents and teachers pointed to hard work as the reason some students did better than others, while their American counterparts pointed to the student’s ability as the explanation.

-Department of Education, the Nations Report Card, 1992


Another study revealed an interesting difference in attitudes toward math among men and women.

A math test was given to a group of men and women. There was no significant correlation between gender and performance on the test but there was a strong correlation between gender and attitude toward performance…

-Psychology Today, November/December (1995)


The men, in general, were more confident in their performance. The women, however, generally had less confidence in their own performance.

In other words, while each group performed about the same on the test, the men had a more positive opinion about how well they did.

Personality Types & Learning Styles Only in the past few years scientists working in the field of

genetics have begun to realize a fascinating truth: Gene expression is modified by experience. That is, the genes you were born with are changing and

adapting based on your life experiences.


“This is a new understanding of the fundamental building blocks of life based on the discovery that genes are not immutable things handed down from our parents like Moses’ stone tablets but are active participants in our lives, designed to take their cues from everything that happens to us from the moment of our conception.”

-Time Magazine, June 2, 2003


Becoming Who We Are

Personality Types & Learning Styles • Personality types and learning styles may be nothing more than a reflection of how you see yourself now based on experiences you have had.

• Having different experiences might change the way you see yourself.

• Seeing yourself or the world differently might effect the choices you make, which then might effect the experiences you have.

Learning Styles • Everybody benefits from instruction that includes all of the

modalities: visual, auditory, reading and writing and tactile or kinesthetic. There’s no need to categorize people in this way.

• The more of these different modalities are used, the more interaction will take place and the more learning can occur for anyone.

•  Teachers can strive to include as many different ways to interact with material as possible and students can learn to adapt to different ways to interact with the material.

Math Anxiety or Confidence

When you make a mistake in something you enjoy, you probably don’t think to yourself:

“Well, there’s more proof I can’t do this…”

Math Confidence Instead, you just say “oops!” (or something stronger) and then you move on…

If you enjoy a subject, you probably still make mistakes - but you don’t dwell on them.

Think of things you enjoy to do – you probably don’t have 100% perfect success all the time.

Mistakes and Failure “Failure is so important. We speak about success all the time. It is the ability to resist failure or use failure that often leads to greater success.” ~ J.K. Rowling "I don't believe I have special talents, I have persistence… After the first failure, second failure, third failure, I kept trying." ~ Carlo Rubbia, Nobel Prize winning Physicist

Mistakes and Failure “You just keep pushing. You just keep pushing. I made every mistake that could be made. But I just kept pushing.” ~ Rene Descartes

"I've missed more than 9000 shots in my career. I've lost almost 300 games, 26 times I've been trusted to take the game winning shot ... and missed. I've failed over and over and over again in my life. That is why I succeed.” ~ Michael Jordan

Math Confidence To be “good at math” … • You don’t have to be perfect. • You don’t have to get every problem right. • You don’t have to make an A on every test.

Math Confidence Doing math is an intensive learning process… §  Mistakes and failures are expected. They are an opportunity for

learning.

§  In fact, if you aren’t making mistakes, perhaps you aren‘t even learning!

§  When learning, it is normal to be confused, to forget things, and to ask basic questions.

§  Be patient with yourself. It takes time to learn complex ideas. Mathematics itself has taken thousands of years to develop.

Negative Self-Talk • Professional mathematicians make plenty of mistakes, forget things and get confused when presented with new and challenging problems.

• When studying, don’t be surprised or frustrated when you find ideas confusing, or when you forget things or make mistakes.

• The more difficulties you can uncover when studying, the less difficulty you will have during the exam.

• When studying, look for trouble! Look for failure as the opportunity to really learn.

Negative Self-Talk Too many people decide they aren’t good at math, only

because they faced the normal failures in math early on. They were turned off and try to avoid more failure. Fears of being wrong, of making mistakes, of forgetting, of

failing, of being unable to understand or to solve a problem are normal but can create anxiety.

Relax! Everyone has these thoughts…

Math Anxiety Failure is a routine part of learning math. It can be intense

and can be frustrating. Not dealing with failure, set backs and frustration in

learning mathematics in a healthy way can lead to math anxiety.

Anxiety is a psychological and physical response to stress. This response can interfere with your ability to perform successfully.

Math Anxiety What are the symptoms of anxiety?

• An inability to focus on a specific task • Overwhelming negative self-talk • Sweaty palms • Racing heart • Memory loss • Headache • Muscle tension

Math Anxiety Where does this anxiety come from? Why do we have it?

Some stress is good. Too much, not so good.

Math Anxiety

When you perceive a threat, your body’s natural and healthy reaction is to prepare to handle the threat – you feel stress. A certain amount of stress is normal, even good.

However, if excessive stress is sustained for too long, for example by a repeating fear of failure, the anxiety can become a real problem itself. The thoughts of failure and the physical reaction it can trigger can become overwhelming. The added anxiety can interfere with your ability to perform.

Negative Self-Talk and Corresponding Emotions, Behaviors, Physical Sensations

Thoughts

I’m not good at math.

Physical Sensations

I tense up when I do math.

Behaviors

I avoid math.

Emotions

I’m frightened by math.

More Healthy and Realistic Approach to Math

Thoughts

I can do some math.

Body Sensations

My body relaxes.

Behaviors

I will make another attempt

Emotions

Relief, satisfaction.

Math Anxiety To avoid math anxiety, maybe you just avoid math. Maybe you tell yourself either “I hate math” or “I like it, but

am just not good at it”. This is not a good solution. In every career, the more math

you know, or the more you are able to think mathematically, the more successful you could be.

Math Anxiety •  If you believe or dwell on the negative self-talk, stress

and anxiety can overwhelm your ability to think clearly.

• When mistakes or failures occur move on. Learn from your mistakes but don’t dwell. Learn and move on.

• Be present in the moment – based on a careful,

complete and honest assessment of the past and future, ask: What must be done now?

• Anxiety is based on fear of what may happen in the future and is based on past experience. Anxiety generally has little to do with the present moment.

Math Anxiety How well do you deal with frustration? Math provides could practice in dealing with frustration! If you believe you will fail you may allow that to happen. If you

feel confident you can find the answer, you might find the way. Obviously confidence alone is not enough, and over-confidence

can lead to mistakes, as well. The key is to be well-prepared, calm and focused on the present

task at hand. This takes time and practice to develop.

Being Present •  Past problems can’t be solved in the past, they can only be solved

now.

•  Future problems aren’t solved by traveling into the future – either they are solved now or they aren’t solved.

•  We can only do what we can do now. •  Test questions, homework problems and studying are all done one

problem at a time, in the present moment.

•  We must learn from the past and prepare for the future but try not to let thoughts of the past or future become distracting, or create negative emotions or anxiety and thus interfere with what you can do now.

Dealing With Problems •  Suppose you walked into a dark room and didn’t know where

the light switch was.

•  If you been there before, you know if you just feel along the wall, eventually you will find the light switch.

•  The same thing can happen when you face a problem in math. If you’ve been in similar situations enough, you know you will find your way to the point where you can make the lights come on.

•  And don’t worry if you have to ask for help with a new problem, even if its several times, eventually you remember where to look for that light switch.

Problem Solving A car travels 20,000 miles. To save wear, the car’s 5 tires are rotated regularly. How many miles will each tire travel in contact with the road?

Problem Solving The difficulties in solving math problems often arise in

recognizing the assumptions in the problem.

Most people would agree: there are 4 tires on a car and 1 in the trunk.

But this assumption was not explicitly stated.

Problem Solving

Is this a trick question?

Problem Solving Memorizing formulas is not enough. In fact, under stress, you may blank-out and forget what you had memorized.

Obviously, some things must be memorized, but it is

important to internalize concepts – to develop skill at thinking mathematically.

That means following logical conclusions, step by step from

given information. Do this when you solve a problem: Write what you know.

Write what that implies. Make each small step clear and complete.

Problem Solving Some ways to get the answer:

1.  Four of the five tires are being used at any given time. Each tire is used 4/5 of the time which implies it travels 4/5 of the distance. 4/5 of 20,000 miles is 16,000 miles.

2.  Each tire will spend 1/5 of the trip in the trunk. Each tire will therefore travel 4/5 of the distance. Thus 4/5 of 20,000 miles is 16,000 miles.

3.  The trip is 20,000 miles. Together, in total, the tires will travel 80,000 on the road (because 4*20,000 = 80,000.) There are 5 tires to divide up this work. Therefore 80,000 tire-miles / 5 tires = 16,000 miles.

Problem Solving 1.  Understand the problem. What is given? What are the

assumptions?

2.  Devise a plan. Is there an equation or formula you can use to describe or model the situation?

3.  Carry out the plan. Follow logical steps carefully and completely, writing everything neatly for each step.

4.  Check the solution. Does this answer make any sense?

Problem Solving •  If it seems like there is missing information, make

something up. Try the problem with the made up information and see where that leads. See if that would change if you changed whatever was made up.

• Math is all about following given information to its logical conclusions.

• You don’t have to get it right on the first try. Just try. See where logic takes you and if its doesn’t make sense, try again. Think carefully, neatly, be organized and know the reasons for each step … and you are thinking mathematically.

Make Practice Routine • Big improvements usually come only after lots of work.

• Before inventing the light bulb, after thousands of failed attempts, a reporter said to Thomas Edison, “What a shame to have no results.”

• Edison responded “I’ve got results! I know 10,000 things that will not work!”

• Of course, he eventually found the solution and created the electric light bulb.

Building Confidence In math, everything has a reason.

When studying, if you come across something and you don’t know the reason, look it up. If you don’t, it’ll probably keep coming back to get you because it was there for a reason.

Understand it, don’t just memorize it.

Building Confidence • Making Math Memories

• Rote memorization is usually not enough.

• We remember by understanding and making mental connections.

• Our mental connections are constantly changing and updating as we learn so we must continue to use them or we lose them.

• Organization is key to everything.

• Have fun, be active.

Building Confidence Strategies Before the Test • Be organized. Know what is on the test. • Begin reviewing several days in advance. • Use flashcards. Be sure you understand what you

memorize. • Keep healthy routines for eating, sleeping, exercising,

working, studying. • Study under conditions similar to the test. Make your own

practice test. • Study in the math lab. •  Take notes from the book. • Practice relaxation techniques.

Building Confidence Strategies During the Test §  Write neatly and you will think neatly. §  Do the easy problems first. §  Stay present and focused, let go of negative thoughts. §  Show all your work, make each step logical and

complete. §  Stay organized, use separate sheets of paper if

necessary and allowed. If your writing gets cramped in a small space, the chance of error increases.

Building Confidence Strategies After the Test § Congratulate yourself on the accomplishment.

§ When you get the test back, learn from the mistakes.

§ Remember it takes time to make significant progress.

It’s up to you to make the right choices and stick with it…

Thank You • The “tire problem,” the accompanying illustration, and

many other ideas in this presentation come from the book “Overcoming Math Anxiety” by Sheila Tobias.

• Other ideas about dealing with anxiety in general come from the book “The Power of Now” by Ekhart Tolle.

• Some ideas on gender and math performance are from Jennifer Gutbezahl ( more info available at http://www.fix.org/jennyg/articles/litreview.html)

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Building Math Confidence: Presentation #1