Brian Beaudrie bpbeaudrie@ Plymouth c.ymcdn.com/sites/ · PDF fileWith very little information & research about quantitative literacy and numeracy in grades K ... find the difference

Brian Beaudrie

[email protected]

New Hampshire Impact Center

Plymouth State University

mailto:[email protected]

Many terms, many meanings: Quantitative Literacy is a term used most often in the

United States and Canada

There are several synonyms, or at least words that are used as synonyms:

Numeracy (used most often internationally, particularly in Great Britain)

Quantitative Reasoning

Statistical Literacy

Innumeracy is defined as the opposite of Numeracy

© 2009 Brian Beaudrie, NH Impact Center

Some Definitions of our term “[Quantitative Literacy is] the knowledge and skills

required to apply arithmetic operations, either alone or sequentially, using numbers embedded in printed material” - – The National Adult Literacy Survey (National Center for Education Statistics, 1993).

“[Quantitative Literacy is] an aggregate of skills, knowledge, beliefs, dispositions, habits of mind, communication, capabilities, and problem solving skills that people need in order to engage effectively in quantitative situations arising in life and work” - The International Life Skills Survey (Policy Research Initiative, Statistics Canada, 2000).


More Definitions “The ability to identify understand and use elementary

mathematics in everyday contexts” – Deborah Hughes Hallett, mathematics professor, University of Arizona

“[Quantitative Literacy includes] confidence in mathematics, cultural appreciation, interpreting data, logical thinking, making decisions, mathematics in context, number sense, practical skills, prerequisite knowledge, symbol sense” – Lynn Arthur Steen, mathematics professor at St. Olaf College, former MAA president, and executive editor, Mathematics and Democracy: The Case for Quantitative Literacy (2001).


Tired of them yet? Quantitative Literacy can be defined as the level of

mathematical knowledge and skills required of all citizens” – John Dossey, mathematics educator at Illinois State University

“The heart of quantitative literacy is real world problem solving – the use of mathematics in everyday life, on the job, and as an intelligent citizen.” – Henry Pollak, Visiting Professor of Mathematics Education, Teacher’s College, Columbia University

“Quantitative Literacy involves understanding the mathematical concepts and skills that are necessary for everyday life”. – Glenda Price, President Emeritus, Marygrove College


What do they seemingly have in common? Quantitative literacy involves real-life situations.

Quantitative literacy involves problem solving.

Quantitative literacy involves a synthesis of several skills.

Quantitative literacy is not a separate skill in and of itself; rather, it is infused in mathematics, and indeed in most areas of curricula and everyday life.

Quantitative literacy seems to involve responsible citizenship in some way, much as we would expect any citizen to be literate.


Why QL? Why Now? As the world economy has shifted from unskilled to

skilled labor, many jobs have become more complex and other jobs have been entirely eliminated.

Many of the new and future jobs require critical thinking & problem-solving.

There is a considerable wage premium for workers with strong quantitative skills, leading to more job security and income stability


Why QL? Why Now? We've shifted from an industrial technology to information-age

technology…Industrial technology required reading and writing literacy; information technology requires quantitative literacy.

“When I was in Mississippi [in the 1960s], I saw very graphically how literacy mattered. Sharecroppers weren't literate, so they were outside the economic arrangement…We're growing young people who are outside the economic arrangements for the information-age technologies. It's not that they don't need reading and writing. They need higher levels of reading and writing because they have to communicate. But they also need the ability to encode and decode information, which is partially encoded with quantitative information.” – Bob Moses, creator of The Algebra Project


Mathematical Illiteracy is a problem in the United States 78% of all adults cannot explain how to

compute the interest paid on a loan

71% cannot calculate miles per gallon on a trip

58% cannot calculate a 10% tip for a lunch bill

(Phillips, 2007)


More evidence of the problem In one study of student writing, one in three students

at a highly selective college failed to use any quantitative reasoning when writing about subjects in which quantitative evidence should have played a central role (Lutsky, 2006).

College students in the natural and social sciences consistently have trouble expressing in precise English the meaning of data presented in tables or graphs (Schield, 2006).


Some examples: developing number sense (measurement)

Joe is five feet tall. How many Joes:

Are needed to cross the width of this room?

Are needed to cross the length of this room?

Are there in a mile?

Carrie is 54 inches tall. How many Carries and how many Joes must be stacked on top of each other until their heights are equal? What is that height (in feet)?

Brett Farve passed for 65,127 yards in his NFL career...until he un-retired…again. Anyway, it’s 40 miles from Plymouth to Concord. Which is a greater distance? By how much?


Some more examples: measurement Nevada is 110,567 square miles in area. About 71.5

“Rhode Islands” would fit inside Nevada. How many of the following states would fit inside Nevada:

New Hampshire?

Ohio?

California?

Alaska?

Answers: NH= 11.8, Ohio = 2.5, CA= .67 (or about 1.5 “Nevadas” would fit inside CA), AK = .167 (or about six “Nevadas” would fit inside Alaska)


It doesn’t have to be restricted to U.S. States Of the following countries, which are bigger than

Nevada? Which are smaller? Which one is closest in size to Nevada?

France?

Belgium?

Italy?

United Kingdom?

Answers: France = 260,558 sq. mi.; Belgium = 11,787 sq. mi.; Italy = 116,346 sq. mi.; UK = 94,526 sq. mi.


A very large number example A thousand seconds ago was:

16 2/3 minutes ago

A million seconds ago was:

11 days, 13 hours and 47 minutes ago (about)

A billion seconds ago was:

April, 1978 (roughly 31.5 years)

A trillion seconds ago was:

29,500 B.C. (give or take a few years)


A very small number example According to its web site (www.powerball.com), the

probability of winning the Powerball jackpot is one in 195,249,054. How small is that?


Correlation doesn’t imply Causation

Found at: http://montaraventures.com/blog/2007/09/14/pirates-cause-global-warming/


What do you notice about all of these examples? They involve real life situations and real data

They involve problem solving

They synthesize several math skills, not a separate skill all to itself

Many of them are important for us to truly understand a situation involving quantities

AND, I would dare to add:

They are relevant

They are interesting

They are fun!© 2009 Brian Beaudrie, NH Impact Center

Numbers should help students: Articulate their ideas.

Express themselves with precision.

Ground their observations in evidence.

Test claims and hypotheses.

Participate in civil discourse.

Represent what they are ill-equipped to see.

Recognize and weigh uncertainty.

Construct a context to attract interest and to inform critical thinking

(NNN Annual Meeting, 2008)


Our challenge as teachers in developing Quantitatively Literate students: How do we teach students to: Read from a text, or newspaper, or article, or handout,

about a quantitative situation?

Penetrate below the surface level when reading the situations?

Ask good questions?

Identify critical ideas?

Challenge conclusions?

Identify the underlying assumptions?

Identify the domains of applicability?


The Numeracy Action Plan: A Case for Quantitative Literacy in the State of

New Hampshire A project that began in April, 2008.

The goal is to create a plan (document) for the schools of New Hampshire to follow that help develop quantitative literacy in all high school/college graduates.

The document is written, in final stages of approval.

It will soon be sent to every school and district across the state of New Hampshire.


One big problem…one big solution With very little information & research about

quantitative literacy and numeracy in grades K-12, the creation of this document was a daunting task.

To begin the process, the writers for each grade level were asked to address the following:

Determine the 3 to 5 “big” math ideas for your grade level & why they are the “big” ideas

Choose sample problems that illustrate a quantitatively literate approach to teaching those “big” ideas

Think about ways teachers can help their students become quantitatively literate.


Example from PreK-2Problem: Choose a number & have students write a

numerical expression equal to that number, given various parameters.

For example, express the number 21 by writing an expression with 1) 3 addends or 2) with as many addends as possible.


Another Example from PreK-2 Students are given a variety of objects (such as pattern

blocks) with which to show a pattern. Each child is then asked one or more of the following questions:

What is your pattern?

How did you come up with your pattern?

Could your pattern be extended?

How could you change your pattern?


Example from 3-5: Multiplication Mark has four bags of apples. There are six apples in

each bag. How many apples does Mark have?

Pete has 24 apples. He wants to share them equally among his four friends. How many apples does each friend receive?

Jill picked 6 apples; Tara picked 3 times more. How many apples did they pick altogether?

Without doing any multiplication, find the difference between 16 x 7 and 16 x 8 and explain how you know.


Examples from 3-5Problem: Flash the following problem(s) on an

overhead for 10 seconds, asking students to “estimate” their answer:

Jack and Jill ordered two identical-sized pizzas, one cheese and one pepperoni. Jack ate 5/6 of a pizza and Jill at ½ of a pizza. How much pizza did they eat together?

You are going to a birthday party. You order 6 pints of ice cream. If you serve ¾ of a pint of ice cream to each guest, how many guests can be served?


Example from 6-8 Maria and Stephanie were playing Monopoly. In

Monopoly, you get an extra turn when you throw a double. Maria remarked that she was a lucky Monopoly player because she was able to roll doubles about 1/4th of the time.

Decide for yourself, using the theory of probability, and have evidence that either proves Maria is lucky or that it was not luck to throw doubles 1/4th of the time. Explain your reasoning.


Example from 6-8 Traditional Problem: What is the probability of

drawing a blue marble from a bag containing 3 green, 5 yellow, 6 blue and 10 red?

Numeracy Problem: How many blue marbles would you need to add to the original bag of marbles to make the probability of drawing a blue marble:

Greater than 0.25?

Exactly 0.5?

Exactly 0.75?

What if you added an equal amount of blue and green marbles…will the probability of drawing a blue ever equal 0.5? If so, after how many added marbles?


Ways all teachers can help allstudents develop NumeracyMost methods are useful across the grades:

Developing Problem Solving

Encouraging Habits of Mind

Using Technology Appropriately

Using Formative Assessment

Promoting Discourse (Communicating mathematically)

Using an “Active” Curriculum

Possessing Strong Content Knowledge


What happens next? “Grand Unveiling” April 6th 2010 at NHTM Conference

Dissemination Meetings will follow, held across the state, beginning in April 2010 and continuing throughout the next academic year.

Course(s) will be offered to help teachers understand how to implement numeracy ideas into their classrooms.

Association of Teachers of Mathematics in New England (ATMNE) 2010 conference in Nashua, NH: November 8th and 9th, 2010

Note that this is the same week as AMATYC 2010!


Final Thoughts… “You cannot get students to become quantitatively

literate with just one class, or even a sequence of courses…it is something you need to develop in them to use beyond the classroom. They have to develop the Habit of Mind.” – Bernie Madison, Professor Emeritus of Mathematics, Arkansas

The essence of Quantitative Literacy is to usemathematical and logical thinking in context". - Lynn Steen, St. Olaf College

“Quantitative Literacy is less about the manipulation of numbers than it is about the evaluation and construction of arguments” - Neil Lutsky, Carleton College © 2009 Brian Beaudrie, NH Impact Center

Acknowledgements Emily Ricard, Associate Director of the NH-Impact

Center, without whom this project would have never been finished!

The NH Department of Education

The New England Comprehensive Center

The members of the Writing Team: Susan Deese, Andrea Lancey, Erin Kilrain, Kathy Fowler, Betty Erickson, Connie Upshulte, Deborah Luszey, David Gilcreast, Greg Superchi, Rich Andrusiak, Teresa Magnus, Dick Evans, and Judy Buck


Questions? Brian Beaudrie – [email protected]

NH-Impact Center Website:

http://www.plymouth.edu/graduate/nhimpact


mailto:[email protected]

http://www.plymouth.edu/graduate/nhimpact

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Brian Beaudrie bpbeaudrie@ Plymouth c.ymcdn.com/sites/ · PDF fileWith very little information & research about quantitative literacy and numeracy in grades K ... find the difference