- If my son uses Prelude to Algebra for pre-algebra, will this cause him
trouble when he takes a regular algebra class next year? Will his teacher
criticize him for writing “weird” things on his paper? [Answer]
- My daughter is currently using Prelude to Algebra in her class. When she has
questions and asks me for help, I’m not sure what to say. It seems different
from what I learned. What can I do? [Answer]
- Is Prelude
to Algebra harder or easier than the traditional 8th grade
curriculum?
[Answer]
- I am a home-schooling parent. Can I buy a copy of Prelude to Algebra to
use with my children? [Answer]
- How can the math teachers at my children’s school get trained to
use the Prelude to
Algebra approach? [Answer]
- I have talked to my son’s teacher about Prelude to Algebra and she says she
would like to know more about it. Is there some way she can obtain more
information than what’s on the web site? [Answer]
- If my school were to use Prelude to Algebra, would it replace the book
they are now using? [Answer]
- Is Prelude
to Algebra just for middle school pre-algebra, or can it be used in a
high school “Foundations” class as well? [Answer]
- Has Prelude
to Algebra been used with special education students? [Answer]
- If Prelude
to Algebra is so simple that students of below average ability can
understand it, won’t advanced students get bored? [Answer]
- What is the main thing about Prelude to Algebra that makes it unique? [Answer]
- The web site seems to imply that the usual definition of
exponents is not correct. What’s wrong with it? [Answer]
- If Prelude to Algebra is so good, and the Prelude approach has been used in one form or another for 40 years, why doesn’t everyone teach middle school math this way? [Answer]
If my son uses Prelude to Algebra for pre-algebra, will this cause him trouble when he takes a regular algebra class next year? Will his teacher criticize him for writing “weird” things on his paper?
There should be no problem for him to take a “regular” algebra class next year. In fact, based on past experience, he should find it easier than the other students do. The difference in Prelude is how the students think, not what they write on the paper.
My daughter is currently using Prelude to Algebra in her class. When she has questions and asks me for help, I’m not sure what to say. It seems different from what I learned. What can I do?
Yes, much of it is different from what you learned. If you have a specific question about a lesson, you can contact us at parentquestions@preludetoalgebra.com. We will try to answer in a timely manner, but realistically, it may not be before your daughter’s test if she has one the next day.
For the long haul, there are two possibilities. If you have the time and the interest, try studying the book along with your daughter. Ask her to explain as much as she can of each lesson to you. This will be a great review for her. Then read the book together and look at the examples. They will give you a pattern to follow in the exercises. You will need to do this on a regular basis because it is very hard to jump in and out with a math book.
Another possibility is to talk with your daughter’s teacher. He/she has been specially trained to use Prelude to Algebra, and most of the teachers are very willing to provide extra help and explanations to motivated students (and their parents).
Is Prelude to Algebra harder or easier than the traditional 8th grade curriculum?
Interesting question. Students usually find it easier than the traditional approach because it makes better sense to them. On the other hand, having studied from the Prelude book, they are able to work harder problems than the traditionally trained students can.
I am a home-schooling parent. Can I buy a copy of Prelude to Algebra to use with my children?
The approach in Prelude is so different from the traditional approach that we don’t recommend using the book without being trained. It would be very difficult for home-schooling parents to use it on their own without additional instruction. For that reason we don’t usually make the book available for individual purchases.
If you live near Cleveland, TN, however, there is one possibility. You could take the class MATH098 at Lee University. The Prelude approach is used in this class and you would gain the necessary training to use the book effectively with your children.
How can the math teachers at my children’s school get trained to use the Prelude to Algebra approach?
Have your school principal or one of the math teachers contact us at INAT@preludetoalgebra.com We are willing to set up an INAT summer training institute at their school if there is enough interest.
I have talked to my son’s teacher about Prelude to Algebra and she says she would like to know more about it. Is there some way she can obtain more information than what’s on the web site?
Yes, there is. Have her contact us at INAT@preludetoalgebra.com. INAT staff are available to visit your son’s school and give a short presentation to the math teachers about the approach.
If my school were to use Prelude to Algebra, would it replace the book they are now using?
No. At this time Prelude to Algebra is a supplementary text. It would be used it in addition to the regular text. Prelude only covers about two-thirds of the material in the regular 8th grade curriculum. An expanded version that covers all the TN curriculum standards for the 8th grade is in the development stage.
Is Prelude to Algebra just for middle school pre-algebra, or can it be used in a high school “Foundations” class as well?
Prelude can be used very effectively in a Foundations class. It has the advantage of being different from what the students have tried before unsuccessfully. It also has the advantage of being easier to understand, so the students don’t have to just memorize rules.
Has Prelude to Algebra been used with special education students?
Yes it has. Because Prelude starts at a very basic level without fractions or negative numbers, special education students have a chance to benefit from its simple, clear explanations. The approach is also visually oriented with real-life illustrations of riding an elevator, giving and receiving money, and many others. Of course, a student’s ability level will influence how far and how fast they will progress, but if they can master the addition and multiplication facts for positive whole numbers, they can take a giant step toward algebra by studying Prelude.
If Prelude to Algebra is so simple that students of below average ability can understand it, won’t advanced students get bored?
Not at all. While the primary setting for Prelude is the positive whole numbers (without fractions and negatives) and this makes it easier to understand, the questions that are asked are new, even for the most advanced students. So everyone is challenged to think, and everyone can experience success.
What is the main thing about Prelude to Algebra that makes it unique?
It’s hard to single out just one thing, since it presents many new ideas. But the fundamental difference is the way it explains the basic arithmetic operations. For example, the traditional way of thinking about the sum of 5 and 3 is to think of the two numbers 5 and 3 being combined together by addition to form a third number, their sum 5 + 3 or 8.
In the operator approach as developed in Prelude, we think of starting with the number 5 and applying the increase operator + 3 to get the sum 5 + 3 or 8. So we don’t combine two numbers to get a third number, we start with one number and change it into a second number by joining an operator, in this case an increase of 3. While this change of perspective is subtle, it turns out to be really significant in how it simplifies everything from multiplication and exponents to canceling and solving equations.
It also anticipates the properties of signed numbers. Long before children encounter -1 as a mysterious negative number, they are already comfortable with the concept of decreasing by 1 if they have ever ridden on an elevator or had to share a toy with a friend. Recent research has shown that this “operator” point of view is effective in introducing algebraic concepts to children as early as grades 2 – 4. [Carraher; 2006]
For the mathematically inclined, I would also add the following: The traditional view of addition can be symbolized by the function f (x, y) = x + y. Our example is the case f (5, 3) = 5 + 3 = 8. The operator approach can be symbolized by the function g(x) = x + 3, and our example
is g(5) = 5 + 3 = 8.
Mathematicians speak of addition and subtraction as being inverse operations. But the function
f (x, y) = x + y does not have an inverse. It is not one-to-one. The function g(x) = x + 3, on the other hand, is one-to-one. It has an inverse. (Its inverse is the function that subtracts 3.) So our approach is better mathematically. Of course, none of this “higher” mathematics is included in the text itself.
For additional unique features [click here].
The web site seems to imply that the usual definition of exponents is not correct. What’s wrong with it?
Glad you asked. There are two common definitions of exponents. The first one is never true and the second one is only true part of the time.
Some books (and math teachers) will explain an expression like 53 by saying it is “5 times itself 3 times.” But that’s not true. They will write
53 = 5 ´ 5 ´ 5,
and then say this shows that 53 is 5 times itself 3 times. But how many multiplications are there? Only two! And is 52 equal to 5 times itself twice? No, it’s 5 times 5. You only multiply once. So this commonly used definition is never true.
Other books (and math teachers) try to be more careful. They say
“53 is a product where there are 3 factors of 5.”
This is marginally better. It works for 53 and 52, but what about 51? Is 51 a product where there is one factor of 5? Not really. To have a product at all, you have to have at least two factors. So explaining 51 as a product of factors makes no sense. And what about 50? What does a product of no factors of 5 produce? It produces nonsense (or the incorrect answer of 0 which plagues many students).
In Prelude (Lesson 5.1) we explain a simple, correct definition of exponents that includes the cases of 1 and 0. Moreover, it has a natural extension to negative exponents (in Chapter 9).
If Prelude to Algebra is so good, and the Prelude approach has been used in one form or another for 40 years, why doesn’t everyone teach middle school math this way?
That’s a very good question. When the early versions of the text were used in California in the 60s and 70s, it was very popular with the teachers and the students. [Click here for testimonials] But beginning about that time, the focus of math educational reform shifted from trying to improve the content to looking for better pedagogy—new ways to package the same old product. The “professional” educators simply were not interested in better ways to explain the concepts.
Fortunately, this has changed in recent years. For example, Dr. H. Wu, professor of mathematics at UC Berkeley and a member of the President’s National Mathematics Advisory Panel, argues forcefully that “great pedagogy lavished on incorrect mathematics makes bad education.” [Wu; 2005, p. 27] In other words, if we want to improve math education, we need to improve the math. This is exactly what Prelude to Algebra does.