Mathematics

The Bigger Picture

Mathematics is not arithmetic…

• Arithmetic is about – math facts– computation– algorithms– word problems

• Mathematics is about– conceptual understanding– problem solving– application of facts & computation

An Arithmetic Testof the Past

456 x 56

782 x 49

652 x 98

803 x 67

356 x 63

789 x 45

908 x 72

504 x 37

867 x 29

345 x 89

731 x 76

519 x 64

784 x 48

468 x 76

706 x 98

623 x 84

735 x 39

451 x 99

805 x 64

668 x 77

608 x 58

345 x 72

777 x 36

382 x 49

Mrs. Jones is collecting money for a field trip. Each student has to pay $9.99 to go. If all 23 students pay, how much will she collect in all? Bobby has 257 sheets of paper. How many 36-page books can he make?

Today’s Math Assessments

Connecticut Mastery TestMarla and Janie are on the same basketball team. In the first 4 games of the season, Marla scored a total of 24 points and Janie scored a total of 21 points as shown on the table below.

Player 1st Game

2nd Game

3rd Game

4th Game

Total Points

Marla 24 Janie 21

• In the 1st game, Marla and Janie scored 11 points together. • In the 2nd game, together they scored fewer than 10 points. • In the 3rd game, together they scored more than 12 points. • In the 4th game, they each scored at least 3 points.

Complete the table above to show how Marla and Janie could have scored their points in the 4 games. Show your work or explain how you found your answers.

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Arithmetic is necessary,

but not sufficient.

NAEPNational Assessment of Educational Progress

The Nation’s Report Card

• Mathematics performance improved for the nation, for the majority of states, and for many student groups. – Fourth-graders’ average score was 3 points

higher and eighth-graders’ average score was 1 point higher in 2005 than in 2003…

– …on a 0 to 500 point scale.

TIMSSTrends in International Mathematics and Science Study

• NEW INTERNATIONAL ASSESSMENT FINDS ASIAN COUNTRIES AGAIN DOMINATE IN STUDENT MATH AND SCIENCE ACHIEVEMENT

– Grade 4 - Singapore 1st, USA 12th– Grade 8 - Singapore 1st, USA 15th– Grade 4 - Singapore 594, USA 518– Grade 8 - Singapore 605, USA 504

PISA Program for International Student Assessment

• 30 “developed”countries participate as well as 11 additional countries

• Assesses 15-year olds, the age when compulsory schooling ends in most countries

• Considered more rigorous than TIMSS or NAEP

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US Results on PISA• The United States ranks 29th in

math.• US performance on math literacy and

on problem solving was lower than the average for “developed” countries

• US had fewer students at the highest proficiency levels on math literacy and on problem solving than other developed countries

While change is uncomfortable,

it appears necessary.

21st Century Expectations• Math Literacy -

– Identify and understand role of math in the world

– Use math to make judgments– Use math in life situations

• Problem Solving - – Capacity “to confront and resolve cross-

disciplinary situations where the solution is not immediately obvious…”

The World Is Flat By Thomas Friedman

• An astronaut, a doctor, an author, a pediatrician, a detective, a surgeon, chemistry and physics

• Too few replacements for American mathematicians, scientists, engineers

• “We cannot hope to fight jobs lost to international competition without a well-trained and educated workforce.”

Business Week, 1/12/06• “The challenge facing the U.S. now is twofold. On one

hand, the country must breed more top-notch mathematicians at home, especially as foreigners find greater opportunities abroad. This will require revamping education, engaging more girls and ethnic minorities in math, and boosting the number of students who make it through calculus, the gateway for math-based disciplines. "It's critical to the future of our technological society," says Michael Sipser, head of the mathematics department at Massachusetts Institute of Technology. At the same time, school districts must cultivate greater math savvy among the broader population to prepare it for a business world in which numbers will pop up continuously. This may well involve extending the math curriculum to include more applied subjects such as statistics.”

Arithmetic (the old math)is necessary,

but not sufficient.