Navigate KTM
- KitchenTableMath
- What's New
- FAQ
- Book-style Index
- Ask a Question
- Search Comments
- Search Blog Posts
- Monthly Archives
- Search by Category
- Register as a User
- Register as our Guest
Kitchen Table Math
KTM User Pages
Service Groups
- Mathematically Correct
- WhatWorksClearinghouse
- Progressive Policy Institute
- Education Trust
- Illinois Loop
- Fordham Foundation
- New York City HOLD
Parent Groups
- Plano Parent Rights
- Informed Residents of Reading
- Teach Us Math
- Save Our Children from Mediocre Math
Personal Pages
Blogs
- Animals In Translation
- Eduwonk
- The Education Wonks
- Instructivist
- Jenny D
- Joanne Jacobs
- Learning Curves
- Math And Text
- MathMan
- Number 2 Pencil
- Oh, snap!
- Parent Pundit
- Vlorbik
- D-Ed Reckoning
- Teens And Tweens
Special lists
Help
09 Jan 2006 - 18:01
Great minds think alike.
Ken left this comment about the negative exponent problems Christopher was trying (and failing) to do
Ken beat me to it. 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. 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:
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 and Student Guide available online. The book has 14 chapters:
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?
how would a mathematically gifted child handle this course? What do you think? One more 'data point': the class does no word problems. Just the extended response problems. These concepts are taught as isolated procedures with no application to problem-solving.
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
death march to algebra
NYU ed textbooks; NY math test
Back to main page.
Please consider registering as a regular user.
Look here for syntax help.
How would a mathematically gifted child handle this course, in 6th grade? Of course, it depends how mathematically gifted the child is, but I think someone who's moderately gifted would probably choke on the pace. For comparison, in my graduate courses this past semester, we covered approximately 6 or 7 chapters worth of material in each course. I'd say there were probably about 5 or 6 broad concepts per chapter or so. Given that, I'd say the pace of a course using this textbook for a 1 year course for 6th graders is approximately the same as a graduate level course. BTW, what is an "extended response" problem? -- PaulMiller - 11 Jan 2006
it depends how mathematically gifted the child is, but I think someone who's moderately gifted would probably choke on the pace well, thanks for answering that's what I was thinking.....but I just don't have a solid feel for mathematically gifted kids Engelmann says gifted kids learn exactly twice as fast as non-gifted kids — but even by that standard one-new-topic-a-day sounds way too fast to me. otoh, there are kids getting good grades in the class. Of course, they're probably doing what we're doing, only more successfully, which is cramming like mad for every test (or, rather, being crammed by their parents). I'd say the pace of a course using this textbook for a 1 year course for 6th graders is approximately the same as a graduate level course. When you say it's the pace of a graduate level course.....do you mean any grad level course in any area of mathematics? -- CatherineJohnson - 11 Jan 2006
-- CatherineJohnson - 11 Jan 2006
-- CatherineJohnson - 11 Jan 2006
-- CatherineJohnson - 11 Jan 2006
Find all the numbers that satisfy all of the following conditions: 1. Positive whole numbers less than 100,
2. Four more than each number is a multiple of 6
3. The sum of the digits of each number is a multiple of 4. -- CatherineJohnson - 11 Jan 2006
-- CatherineJohnson - 11 Jan 2006
What is the digit in the hundreds places of the sum of the following addition problem: 7 + 77 + 777 + 7777 + ... + 77777777777777777777 (The final number has 20 7s) -- CatherineJohnson - 11 Jan 2006
Extended response problems are problems that are usually far above the student's level, which require an answer and an extended response, meaning that the child shows all his work and can explain it if asked. -- CatherineJohnson - 11 Jan 2006
I'm willing to bet there's not a single child in the class who has done all of these problems on his own. I certainly have never heard of a child doing Extended Response problems on his own. -- CatherineJohnson - 11 Jan 2006
pre-algebra is bunk
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 tomemorize the answersolve the problem.
Ken beat me to it. 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. 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
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 and 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
how would a mathematically gifted child handle this course? What do you think? One more 'data point': the class does no word problems. Just the extended response problems. These concepts are taught as isolated procedures with no application to problem-solving.
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
death march to algebra
NYU ed textbooks; NY math test
Back to main page.
Comments
After entering a comment, users can login anonymously as KtmGuest (password: guest) when prompted.Please consider registering as a regular user.
Look here for syntax help.
How would a mathematically gifted child handle this course, in 6th grade? Of course, it depends how mathematically gifted the child is, but I think someone who's moderately gifted would probably choke on the pace. For comparison, in my graduate courses this past semester, we covered approximately 6 or 7 chapters worth of material in each course. I'd say there were probably about 5 or 6 broad concepts per chapter or so. Given that, I'd say the pace of a course using this textbook for a 1 year course for 6th graders is approximately the same as a graduate level course. BTW, what is an "extended response" problem? -- PaulMiller - 11 Jan 2006
it depends how mathematically gifted the child is, but I think someone who's moderately gifted would probably choke on the pace well, thanks for answering that's what I was thinking.....but I just don't have a solid feel for mathematically gifted kids Engelmann says gifted kids learn exactly twice as fast as non-gifted kids — but even by that standard one-new-topic-a-day sounds way too fast to me. otoh, there are kids getting good grades in the class. Of course, they're probably doing what we're doing, only more successfully, which is cramming like mad for every test (or, rather, being crammed by their parents). I'd say the pace of a course using this textbook for a 1 year course for 6th graders is approximately the same as a graduate level course. When you say it's the pace of a graduate level course.....do you mean any grad level course in any area of mathematics? -- CatherineJohnson - 11 Jan 2006
-- CatherineJohnson - 11 Jan 2006
-- CatherineJohnson - 11 Jan 2006
-- CatherineJohnson - 11 Jan 2006
Find all the numbers that satisfy all of the following conditions: 1. Positive whole numbers less than 100,
2. Four more than each number is a multiple of 6
3. The sum of the digits of each number is a multiple of 4. -- CatherineJohnson - 11 Jan 2006
-- CatherineJohnson - 11 Jan 2006
What is the digit in the hundreds places of the sum of the following addition problem: 7 + 77 + 777 + 7777 + ... + 77777777777777777777 (The final number has 20 7s) -- CatherineJohnson - 11 Jan 2006
Extended response problems are problems that are usually far above the student's level, which require an answer and an extended response, meaning that the child shows all his work and can explain it if asked. -- CatherineJohnson - 11 Jan 2006
I'm willing to bet there's not a single child in the class who has done all of these problems on his own. I certainly have never heard of a child doing Extended Response problems on his own. -- CatherineJohnson - 11 Jan 2006
| WebLogForm | |
|---|---|
| Title: | pre-algebra is bunk |
| TopicType: | WebLog |
| SubjectArea: | AboutCurricula, IrvingtonMath, IrvingtonSchools, MiddleSchoolMath |
| LogDate: | 200601091301 |