How is the mathematics that we teach changing?

Johnny W. Lott

Past President

National Council of Teachers of Mathematics

Is mathematics curriculum changing?

What was your first grade class like?What math did you learn?Has that changed?Should we be changing?Why?

Is the mathematics curriculum changing?

What was your middle school like?What math did you learn?Has that changed?Should we be changing?Why?

Is the mathematics curriculum changing?

What was your high school like?What math did you learn?Has that changed?Should we be changing?Why?

How did you answer?If your school is very much like today’s

school, then…

It was very progressive when you were there, or…

Today’s school is very backward, or…You’re very young!

From grade school

• How many different ways did you learn to add?

• Did you learn geometry?

• Did you learn about statistics?

From middle school

• Did you learn how to add, subtract, multiply and divide whole numbers every year?

• Did you learn how to compute with fractions, percents and decimals?

• Did you learn geometry?

• Did you learn about statistics?

From high school

• Did you learn to multiply binomials?• Did you learn to factor?• Did you learn to do two-column proofs?• Did you learn to do flow proofs?• Did you ever see a proof?• Was geometry anything but proofs?

• Did you learn about statistics?

Your age can be judged by your answers, or…

• You went to a progressive school, or…

• Your school was backward, or…

• You lie, or…

• You truly have Alzheimer's.

How should we be changing today?

• Students still have to learn the basics!– Do we want them to be able to add,

subtract, multiply, and divide?

– Silly question--of course!

Do we want them to learn by rote?

• That is a possibility!

• So is learning different methods of computing.

• So is using technology to learn about numbers and computing.

Fact:

• Research tells us that students learn when four-function calculators are used.

• They still learn to compute as well as they ever did.

• They are better problem solvers.

• Hembree and Dessart, 1986 and 1992

What else can they be learning with numbers that wasn’t done in the past?

• They can be learning why they are doing what they are doing at the same time!

• They can be learning algebraic thinking at the same time!

Computation problem

• What happens when you multiply any two-digit number by 101?

• This one is for the purists!

Computation problem

• No-Cal candy bars cost $2.09. If the original price each was $0.12 but the price has been inflated, how much does each cost now?

Message

• Problems have changed and teaching strategies have changed!

• Basic basic skills did not!

• But basic skills have changed!!!!

New/old Problem

• What is the pattern below if it continues?

7, 13, 19, 25, 31, …

What is the pattern?

• Add 6.

• Skip count by 6.

• Arithmetic sequence with a difference of 6.

• Others?

What is a formula for the pattern?

• First term is 7

• Next is current + 6

• Recursive formulas were not heard of when I was in school!

Questions

• Would you accept this as a formula for the pattern?

• Up to grade 3?

• Up to grade 6?

• Up to grade 9?

• Up to college seniors?

What did many of you expect?

• Remember: 7, 13, 19, 25, 31, …

• What is the common “add 6” pattern?

6, 12, 18, 24, 30, What is the pattern here that 3rd graders know?

Number of term with term below1 2 3 4 5 6… n6 12 18 24 30 36…7 13 19 25 31 37…

Does this process work for any arithmetic sequence?

• This is algebraic thinking!

• Does this type of process have a use in today’s world that did not exist when I was in school?

Think

SPREADSHEETS

What else might be changing?

• Transformational geometry--flips, slides, turns, and glide reflections

• Matrices

• Data Analysis– Did you know that only bar graphs and

circle graphs existed when I was in school?

Some graphical representations are true infants!• Stem and Leaf Plots

• Box plots

• Dot plots

• Every grade school child should know how to use these by the end of middle school.

Where do we go from here?

• I don’t know;

• NCTM doesn’t know;

• Mathematicians don’t know;

• No one does, but…

All know that we can’t go backward.

• Well, nearly all!

• Can we sit still?

• Unfortunately, no!

What can we do?

• Realize that WE must continue learning.

• Realize that FAMILIES must continue learning.

• Realize that Principles and Standards is the most visionary document on the math scene today.

Realize that neither NCTM nor you can sit still.• Go to conferences.• Read the literature.• Read newspapers.• Read literature of today.

• LEARN HOW THE WORLD AROUND YOU IS CHANGING.

• YOUR CLASSROOM WILL BE AFFECTED.

Johnny W. LottDepartment of Mathematical

SciencesThe University of Montana

Missoula, MT 59812jlott@mso.umt.edu