Bloggers.PreAlgebraIsBunkLogPage (r1.1 vs. r1.16)
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 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.16 - 19 Feb 2006 - CatherineJohnson)

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 Phase 4 topic list, grade 6 class
comments thread on pre-algebra as algebra
death march to algebra
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>		 NYU ed textbooks; NY math test


 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.15 - 19 Feb 2006 - CatherineJohnson)

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 U.S. fourth graders not doing as well as thought
Phase 4 topic list, grade 6 class
comments thread on pre-algebra as algebra
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>		 death march to algebra


 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.14 - 30 Jan 2006 - CatherineJohnson)

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 What elements of Algebra 1 are missing here?

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applications

 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.13 - 11 Jan 2006 - CatherineJohnson)

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applications
applying equations and inequalities

 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.12 - 11 Jan 2006 - CatherineJohnson)

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>		 Summer Supplement Time
linking decline in high school scores to elementary school
research on summer regression
the time costs of not teaching to mastery
U.S. fourth graders not doing as well as thought
Phase 4 topic list, grade 6 class
comments thread on pre-algebra as algebra

-- CatherineJohnson - 09 Jan 2006


 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.11 - 09 Jan 2006 - CatherineJohnson)

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 negativeexponent.jpg


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<		 Ken left this comment, about the negative exponent problems Christopher was trying (and failing) to do
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>		 Ken left this comment about the negative exponent problems Christopher was trying (and failing) to do

Er, isn't this algebra and not "pre-algebra"?

 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.10 - 09 Jan 2006 - CatherineJohnson)

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Both courses are algebra, and both courses cover the same material.

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<		 This is the only explanation we can come up with for the torture that is Phase 4 math. (OK, there's the This was supposed to be a course for gifted children, but then high achievers jumped on board and ruined everything meme, which could be true. That's a side issue I'm curious about: are the one or two gifted kids learning well in this course? I'd love to know.)
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>		 This is the only explanation we can come up with for the torture that is Phase 4 math. (OK, there's the This was supposed to be a course for gifted children, but then the high achievers jumped on board and ruined everything meme, which could be true. That's a side issue I'm curious about: are the one or two gifted kids learning well in this course? I'd love to know.)

Leaving gifted children aside, Prentice Hall Mathematics: Explorations and Mathematics was not written for gifted children. As I understand it, it's intended for use in the regular 8th grade pre-algebra course. (Of course, if that's true, then the good news is: WE'VE BEEN TEACHING ALGEBRA TO 8TH GRADERS FOR QUITE SOME TIME NOW.)


 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.9 - 09 Jan 2006 - CatherineJohnson)

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Glencoe's Table of Contents
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<		 The Glencoe pre-algebra text, which I believe is the other 'big,' widely used pre-algebra book, has a terrific Parent abd Student Guide available online.
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>		 The Glencoe pre-algebra text, which I believe is the other 'big,' widely used pre-algebra book, has a terrific Parent and Student Guide available online.

The book has 14 chapters:


 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.8 - 09 Jan 2006 - CatherineJohnson)

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 probability of compound events

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how would a mathematically gifted child handle this course?

What do you think?

One more 'data point': the class does no word problems.


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>		 Just the extended response problems.

These concepts are taught as isolated procedures with no application to problem-solving.




 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.7 - 09 Jan 2006 - CatherineJohnson)

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  • 1 year of Algebra 1
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<		 Both courses are algebra.
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>		 Both courses are algebra, and both courses cover the same material.

This is the only explanation we can come up with for the torture that is Phase 4 math. (OK, there's the This was supposed to be a course for gifted children, but then high achievers jumped on board and ruined everything meme, which could be true. That's a side issue I'm curious about: are the one or two gifted kids learning well in this course? I'd love to know.)


 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.6 - 09 Jan 2006 - CatherineJohnson)

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Pre-algebra is called pre-algebra, we both think, because it's the beginning of the Second Spiral in an American child's life.

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<		 The Algebra Spiral.
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>		 The Algebra Spiral.

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<		 In K-6 or K-7, kids experience the Arithmetic Spiral.
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>		 In K-6 or K-7, kids experience the Arithmetic Spiral.

Then, starting somewhere in middle school, they move on to the Algebra Spiral.


 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.5 - 09 Jan 2006 - CatherineJohnson)

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Pre-algebra is algebra.

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<		 Pre-algebra is called pre-algebra, we both think, because it's the beginning of the Second Spiral in an American child's life: the Algebra Spiral.
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>		 Pre-algebra is called pre-algebra, we both think, because it's the beginning of the Second Spiral in an American child's life.

The Algebra Spiral.


In K-6 or K-7, kids experience the Arithmetic Spiral.


 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.4 - 09 Jan 2006 - CatherineJohnson)

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Ken beat me to it.
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<		 Saturday night, after Ed had lived through his first Screaming Pre-teen session, he said, "This is spiralling."
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>		 Saturday night, after Ed had lived through his first Screaming Pre-teen Math Test Study Session, he said, "This is spiralling."

What he meant was, pre-algebra is not pre-algebra.


 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.3 - 09 Jan 2006 - CatherineJohnson)

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Added:
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>		 Ken beat me to it.

Saturday night, after Ed had lived through his first Screaming Pre-teen session, he said, "This is spiralling."

What he meant was, pre-algebra is not pre-algebra.


 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.2 - 09 Jan 2006 - CatherineJohnson)

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<		 Great minds think alike.

Ken left this comment, about the negative exponent problems Christopher was trying (and failing) to do,

>
>		 Great minds think alike.

negativeexponent.jpg


Ken left this comment, about the negative exponent problems Christopher was trying (and failing) to do

Er, isn't this algebra and not "pre-algebra"?

 <<O>>  Difference Topic PreAlgebraIsBunkLogPage (r1.1 - 09 Jan 2006 - CatherineJohnson)
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Great minds think alike.

Ken left this comment, about the negative exponent problems Christopher was trying (and failing) to do,

Er, isn't this algebra and not "pre-algebra"?

I suppose pre-algebra now is pick an algebra lesson (and I use that term loosely) at random, teach it poorly or not at all, and ask the student to memorize the answer solve the problem.



Saturday night, after Ed had lived through his first Screaming Pre-teen session, he said, "This is spiralling."

What he meant was, pre-algebra is not pre-algebra.

Pre-algebra is algebra.

Pre-algebra is called pre-algebra, we both think, because it's the beginning of the Second Spiral in an American child's life: the Algebra Spiral.

In K-6 or K-7, kids experience the Arithmetic Spiral.

Then, starting somewhere in middle school, they move on to the Algebra Spiral.

They spend two years learning Algebra 1:

  • 1 year of Pre-algebra

  • 1 year of Algebra 1

Both courses are algebra.

This is the only explanation we can come up with for the torture that is Phase 4 math. (OK, there's the This was supposed to be a course for gifted children, but then high achievers jumped on board and ruined everything meme, which could be true. That's a side issue I'm curious about: are the one or two gifted kids learning well in this course? I'd love to know.)

Leaving gifted children aside, Prentice Hall Mathematics: Explorations and Mathematics was not written for gifted children. As I understand it, it's intended for use in the regular 8th grade pre-algebra course. (Of course, if that's true, then the good news is: WE'VE BEEN TEACHING ALGEBRA TO 8TH GRADERS FOR QUITE SOME TIME NOW.)

Christopher is trying to learn one whole brand-new topic in algebra a day, every day.

He can't do it. Period. I'm assuming the gifted kids can, but I'd bet the ranch they're the only ones.

What we're doing now is the equivalent of forcing an 11-year old to cram for tests every single day of his school week. We're ramming rules, numbers, notations & mathematical conventions into his head so he can — yes — regurgitate them on a test, knowing all the while that he'll forget everything we're 'teaching' as soon as the test is over.

Why would a textbook present this much new material in one year's time?

J.D. will have an answer, I'm sure. Perhaps this book is intended to be used over two years' time?

However, I have the Teacher's Edition, and I don't get the sense that's the case.

I think the book is set up to 'cover' a vast amount of basic algebra in 1 year.



Glencoe's Table of Contents

The Glencoe pre-algebra text, which I believe is the other 'big,' widely used pre-algebra book, has a terrific Parent abd Student Guide available online.

The book has 14 chapters:

Chapter 1 - Tools for Algebra and Geometry

Chapter 2 - Exploring Integers

Chapter 3 - Solving One-Step Equations and Inequalities

Chapter 4 - Exploring Factors and Fractions

Chapter 5 - Rationals: Patterns in Addition and Subtraction

Chapter 6 - Rationals: Patterns in Multiplication and Division

Chapter 7 - Solving Equations and Inequalities

Chapter 8 - Functions and Graphing

Chapter 9 - Ratio, Proportion, and Percent

Chapter 10 - More Statistics and Probability

Chapter 11 - Applying Algebra to Geometry

Chapter 12 - Measuring Area and Volume

Chapter 13 - Applying Algebra to Right Triangles

Chapter 14 - Polynomials



That's a lot.

Each chapter has 8 to 10 separate lessons, all of which cover new material.

Approximately 130 separate items of brand-new material for students to learn in a 180-day school year?

This weekend I pulled out all of the individual topics, so I could try to keep track of them — so I could try to figure out quickly what Christopher needs to practice today.

Here's the list.

What elements of Algebra 1 are missing here?

applications
applying equations and inequalities

arithmetic sequences
geometric sequence

coordinate plane
ordered pairs

data
circle graphs

estimation Estimating sums and differences

equations
solve using inverse operations
solve using addition & subtraction
solve using multiplication and division
one-step equations
two-step equations
one-step equations with whole numbers
two-step equations with integers
one-step equations with fractions
two-step equations with negative fractions
one-step equations with decimals
two-step equations with decimals
one step-equations complex (positive & negative fractions, distributive property, solve by addition, subtraction, multiplication, division)
solve equations with variables on both sides
writing two-step equations

expressions & variables
simplify expressions
write expressions

exponents
negative exponents

factors
factors
greatest common factor
least common multiple
monomials
negative exponents
powers & exponents
prime factors
multiplying & dividing monomials

formula
using formulas

fractions

functions and graphs
relations & functions
scatter plots
graphing linear relations
equations as functions
draw a graph
slope
intercept
systems of equations
graphing inequalities

geometry
circles & circumference
area and perimeter
geometry terms
angles & parallel lines
triangles
congruent triangles
similar triangles & indirect measurement
quadrilaterals
polygons
transformations
area: parallelograms, triangles, trapezoids
area: circles
geometric probability
surface area: prisms and cylinders
surface area: pyramids and cones
volume: prisms and cylinders
volume: pyramids & cones

inequalities
solving inequalities by adding or subtracting
solving inequalities by multiplying or dividing
writing inequalities
solving multi-step inequalities

integers
absolute value
comparing and ordering
adding integers
subtracting integers
multiplying integers
dividing integers

measurement
metric system

order of operations

polynomials
adding polynomials
subtracting polynomials
powers of monomials
multiplying a polynomial by monomial
multiplying binomials

problem solving
Draw a Diagram
Make a plan
Look for pattern
Eliminate the possibilities
Use logical reasoning
Work backwards
Make a table
Use a simulation
Make a model or drawing
Venn diagrams

Properties
Distributive
Commutative
Associative

Ratio & proportion
Ratios & rates
Simple probability
Using proportions
Using the percent proportion
Using statistics to predict
Fractions decimals & percents
Percent & estimation
Using percent equations
Percent of change

Rational numbers (decimals & fractions)
Adding & subtracting decimals
Multiplying and dividing decimals
Estimating sums and differences
Estimate products
Fraction to decimal
add subtract like fractions
add subtract unlike fractions
multiply fractions
divide fractions
solving equations with rational numbers
solving inequalities w/rational numbers

right triangles
squares & square roots
real number system
Pythagorean Theorem
Special right triangles
Sine, cosine, & tangent ratios
Using trigonometric ratios

statistics
scientific notation
measure central tendency
stem and leaf plots
measures of variation
displaying data
misleading data
misleading statistics
counting
permutations & combinations
odds
probability of compound events

-- CatherineJohnson - 09 Jan 2006

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Topic: PreAlgebraIsBunkLogPage . { View | Diffs | r1.16 | > | r1.15 | > | r1.14 | More }

Revision r1.1 - 09 Jan 2006 - 18:33 - CatherineJohnson
Revision r1.16 - 19 Feb 2006 - 18:14 - CatherineJohnson