kitchen table math, the sequel: 3/27/11 - 4/3/11

Thursday, March 31, 2011

"The Death and Life of the Great American School System"

Ravitch suspects, with good reason, that her favorite teacher, the intelligent, exacting, and highly literary Mrs. Ratliff, would languish under NCLB. But would Mrs. Ratliff even have become a teacher in today's world? Would someone who is "stifled by the jargon, the indifference to classical literature, and the hostility to her manner of teaching" last through even one week of ed school pabulum, projects, peer-group activities, and proselytizing about Balanced Literacy?
An excerpt of my review of Diane Ravitch's latest book at the Nonpartisan Education Review. You can access the entire review here.

In this book Ravitch brings up her next most recent book: The Language Police. Intrigued (and embarrassed that I hadn't yet read it) I devoured that one a few days ago. If you haven't read it yet, it's a great read.

Monday, March 28, 2011

number sense

from Number Sense with Whole Numbers
Some adults lack a sense of the "equal distance of 1" between the whole numbers (the numbers on a number line). Without this concept, addition makes no sense. All math including basic addition is learned by rote as a mechanical process.
I have a memory of Dehaene arguing that people have an "innate" number line inside their minds.



It was Dehaene:
I propose that the foundations of arithmetic lie in our ability to mentally represent and manipulate numerosities on a mental “ number line ”, an analogical representation of number ; and that this representation has a long evolutionary history and a specific cerebral substrate. “ Number appears as one of the fundamental dimensions according to which our nervous system parses the external world. Just as we cannot avoid seeing objects in color (an attribute entirely made up by circuits in our occipital cortex, including area V4) and at definite locations in space (a representation reconstructed by occipito-parietal neuronal projection pathways), in the same way numerical quantities are imposed on us effortlessly through the specialized circuits of our inferior parietal lobe. The structure of our brain defines the categories according to which we apprehend the world through mathematics. ” (TNS, p. 245).

Précis of “The number sense”
Stanislas Dehaene
Service Hospitalier Frédéric Joliot
4 Place du Général Leclerc
91401 cedex Orsay
Phone +33 1 69 86 78 73
Fax +33 1 69 86 78 16
Makes people who don't seem to possess an internal number line interesting.

I've been relying on number lines to explain things to myself and to C. ever since coming across Dehaene's work.

The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition

how to remember

FedUpMom on remembering area vs circumference:
I had the following brainstorm at an embarrassingly advanced age:

For a long time, I knew there were two formulas that were somehow relevant to circles, namely 2πr and πr2, but I could never remember which one was area and which one was circumference.

I finally realized that  πr2 must be the formula for area, because area is described in square units. 
Tell your kids.

progress report

C. and I just took a timed math section in the College Board book.

I missed one question and skipped none.

The question I missed was number 4 out of 16, which means it was super-easy. It was so easy, that I'm not going to tell you what the question was. Too embarrassing.

I had brain freeze. Number 4 was one of those "which value can't be the answer?" items. I took a quick look at the 5 possibilities, spotted the one value that was glaringly different from all the other values, and then eliminated that answer because it was different from all the others.


Then I spent precious minutes trying to figure out how all the other answers, which obviously could be the answer, could conceivably not be the answer.

oh, man

I think I'll go spend some quality time with Dr. Chung.

Dr. John Chung's SAT Math

Jo in Oklahoma on exercises vs problems

re: SAT problems, Jo in OKC said...
I asked my daughter today. She took the SAT this fall and got a score in the range you mention.

She said the questions are all routine exercises.

She would agree the AMC questions and AIME questions are problems.

One of her favorite areas of math is counting. :-) I remember covering permutations and combinations in high school math. However, what I learned was just a small fraction of what's covered in Art of Problem Solving's Intro to Counting and Probability course or book.
Introduction to Counting & Probability (The Art of Problem Solving)

Carnegie Hall

from Dr. John Chung's SAT Math:
Achieving a perfect score on any math exam is quite simple. Though this may sound cliched, all it takes is practice. Practice by taking as many mock tests as you can, and take the time to go through and correct all of your incorrect answers. Keep your mistakes in mind as you take your next mock test.

Since 1992,1 have personally helped more than 50 students each year achieve perfect scores on the SAT Math, SAT II Math I & II, and AP Calculus AB & BC exams. As you might imagine, during my many years of teaching, I have gone through almost every single SAT Math test preparation book out there. I have come to realize that every book is loaded down with explanations and not enough tests! What a waste of money!

Therefore, it is my honor to introduce to you my first test preparation book, Dr. John Chung's SAT Math. There are no tricks or fast-track methods in this book. I have put together 20 mock exams, complete with answers and explanations, to help you PRACTICE your math test taking skills. These are the mock exams that I have used in my private tutoring sessions with my own students, most of whom have gone on to achieve perfect scores on the SAT Math exam.

Special thanks to my latest star students, Angela Lao, Priya Vohra, Devi Mehrotra, Donna Cheung, Jennifer Wong, Amos Han, and Shalini Pammal, who provided invaluable feedback on the format of this book and assisted in the final proofreading session. They all achieved a perfect score on the math section of the PSAT, SAT Math, and SAT II Math I and H.

I hope this book helps you as much as it has helped my students.

Dr. John Chung
President, NYEA
Dr. John Chung's SAT Math