MathNotations: The Number Warrior and the Mysterious Minds of Students!
Robin Schwartz said...
Negative exponents, fractional exponents, the zero exponent, exponent rules, logs – these should turn on the ALERT indicator – be careful -- danger ahead!! Even armed with a calculator, students will get tricked by these types of problems…Jason, did your students use calculators for this exam?Studying multiple choice questions can help refine thinking skills (and analyze potential errors) through the strength of the comparative.
An example from “Using ‘Good Wrong Answers’ To Achieve Math Confidence and Success” is:
What’s the value of 3^-2?
A) -2/3
B) -9
C) 1/9
D) -6
If they are comfortable with the zero power, they can write 3^-2 = (3^0)/(3^2). Since exponents (and logs) are not logical, I work with learners on extra alertness with this type of content. Unlike some content where they know they are guessing, here they feel sure they have done it right. Another exercise is shown below:
16^1 =
16^.5 =
16^0 =
16^-.5 =
16^-1 =
By increasing awareness of their thinking process, students can build confidence and enjoyment of Math and even improve their scores.
Robin A. Schwartz
Founder, www.mathconfidence.com
www.blogspot.mathconfidence.com
December 24, 2008 11:32 PM
Tuesday, December 30, 2008
Friday, December 12, 2008
Re: The Opportunities of Test Prep – learning, studying, Life skills: response to Slatalla article 12/4/08
To the Editor:
Thank you for the article on the College Board’s new program (Michelle Slatalla’s “My Child’s Fate, All Laid Out by 13”, 12/4/08). While there can be an overemphasis on testing, as a parent and Math educator, I try to focus on the positive opportunities that studying and learning can offer.
While some see multiple choice tests as counterproductive, the “good wrong answers” (the tempting ones that test takers may choose due to being tricked or not reading carefully) can help students see their mistakes and learn from them. Identifying potential errors leads to more metacognition (thinking about thinking), stronger comprehension, better grades, improved problem-solving skills and more enjoyment of the process.
In addition to content, the study of Math has other benefits:
· instilling values of discipline and excellence
· improving memory and focus
· preparing students for success in the ‘knowledge economy’
This positive perspective can help students, parents, teachers, and administrators meet the challenges of ‘teaching to the test’ by viewing it as an opportunity to address knowledge gaps and common errors while sharpening critical thinking and gaining confidence.
The testing of 8th graders can lead to strengthening of knowledge and skills to build a strong foundation so learners can realize their potential. This may alleviate remediation at the college level while inspiring lifelong learning in the next generation.
Robin A. Schwartz
link to NYT article
http://www.nytimes.com/2008/12/04/fashion/04spy.html
To the Editor:
Thank you for the article on the College Board’s new program (Michelle Slatalla’s “My Child’s Fate, All Laid Out by 13”, 12/4/08). While there can be an overemphasis on testing, as a parent and Math educator, I try to focus on the positive opportunities that studying and learning can offer.
While some see multiple choice tests as counterproductive, the “good wrong answers” (the tempting ones that test takers may choose due to being tricked or not reading carefully) can help students see their mistakes and learn from them. Identifying potential errors leads to more metacognition (thinking about thinking), stronger comprehension, better grades, improved problem-solving skills and more enjoyment of the process.
In addition to content, the study of Math has other benefits:
· instilling values of discipline and excellence
· improving memory and focus
· preparing students for success in the ‘knowledge economy’
This positive perspective can help students, parents, teachers, and administrators meet the challenges of ‘teaching to the test’ by viewing it as an opportunity to address knowledge gaps and common errors while sharpening critical thinking and gaining confidence.
The testing of 8th graders can lead to strengthening of knowledge and skills to build a strong foundation so learners can realize their potential. This may alleviate remediation at the college level while inspiring lifelong learning in the next generation.
Robin A. Schwartz
link to NYT article
http://www.nytimes.com/2008/12/04/fashion/04spy.html
Sunday, November 30, 2008
Invert and multiply...which one????
Oh, just flip it upside down and then multiply (“invert and multiply”).
But they are not sure which one to flip!!
Students learn this in late elementary, but when asked “Why?”,
they will say “Oh, it’s the rule”.
An example such as “How much is 12 divided by ½?” can illustrate the concept and learners can follow this example rather than a rule!!
How many half dollars are in $12?
How many half inches in 1 foot?
12 x 2/1 = 24!! ;)
But they are not sure which one to flip!!
Students learn this in late elementary, but when asked “Why?”,
they will say “Oh, it’s the rule”.
An example such as “How much is 12 divided by ½?” can illustrate the concept and learners can follow this example rather than a rule!!
How many half dollars are in $12?
How many half inches in 1 foot?
12 x 2/1 = 24!! ;)
Friday, November 28, 2008
Subject: Trig homework can be pleasant ;)
Dear Professor Fisman:
Your Slate (NYT, http://www.nytimes.com/2008/06/15/weekinreview/15read.html?_r=1&scp=5&sq=trigonometry&st=cse) article from June about One Laptop Per Child has some terrific points, however,
“Perhaps not surprisingly, the lesson from Romania’s voucher experiment is not that computers aren’t useful learning tools, but that their usefulness relies on parents being around to assure they don’t simply become a very tempting distraction from the unpleasantness of trigonometry homework.”
The role of a Math peak performance coach goes beyond the algebra and trig knowledge and focuses on the benefits of brain fitness, ‘flow’, persistence and critical thinking – assets for academic, professional and personal success.
Math could sure use some good PR – last month, the headline for a New York Times article read: "Video Game Helps Math Students Vanquish an Archfiend: Algebra"
Trig homework can be pleasant! Many learners find that there is enjoyment in the engagement or ‘flow’ of studying and that brain fitness can be challenging and sometimes even fun!
Robin A. Schwartz, MBA, BSEE
CEO, Math Confidence
Thanks. I loved this message. I was a math guy until I got to graduate school, but I know I’m not normal. Anything you can do on this front is all to the greater good.
Best, ray fisman, Lambert Family Professor of Social Enterprise, Columbia Business School
Dear Professor Fisman:
Your Slate (NYT, http://www.nytimes.com/2008/06/15/weekinreview/15read.html?_r=1&scp=5&sq=trigonometry&st=cse) article from June about One Laptop Per Child has some terrific points, however,
“Perhaps not surprisingly, the lesson from Romania’s voucher experiment is not that computers aren’t useful learning tools, but that their usefulness relies on parents being around to assure they don’t simply become a very tempting distraction from the unpleasantness of trigonometry homework.”
The role of a Math peak performance coach goes beyond the algebra and trig knowledge and focuses on the benefits of brain fitness, ‘flow’, persistence and critical thinking – assets for academic, professional and personal success.
Math could sure use some good PR – last month, the headline for a New York Times article read: "Video Game Helps Math Students Vanquish an Archfiend: Algebra"
Trig homework can be pleasant! Many learners find that there is enjoyment in the engagement or ‘flow’ of studying and that brain fitness can be challenging and sometimes even fun!
Robin A. Schwartz, MBA, BSEE
CEO, Math Confidence
Thanks. I loved this message. I was a math guy until I got to graduate school, but I know I’m not normal. Anything you can do on this front is all to the greater good.
Best, ray fisman, Lambert Family Professor of Social Enterprise, Columbia Business School
Algebra as an Archfiend?
Education is about stretching knowledge, skills and attitude.
Last month, the headline of a New York Times article about a Math video game for middle schoolers designed by Dimension M:
"Video Game Helps Math Students Vanquish an Archfiend: Algebra"speaks volumes about attitudes about Math! In the print verson, the word "foe" was used.
How about "ally", "comrade", "challenge", "opportunity"?
"Students at Intermediate School 30 in Brooklyn played a video game on Monday, and learned a little algebra at the same time. " was the caption on a photo.
The juxtaposition of this sentence would be:
"Students at Intermediate School 30 in Brooklyn learned algebra on Monday and played a little bit of video game at the same time. "
http://www.nytimes.com/2008/10/08/nyregion/08video.html
Education is about stretching knowledge, skills and attitude.
Last month, the headline of a New York Times article about a Math video game for middle schoolers designed by Dimension M:
"Video Game Helps Math Students Vanquish an Archfiend: Algebra"speaks volumes about attitudes about Math! In the print verson, the word "foe" was used.
How about "ally", "comrade", "challenge", "opportunity"?
"Students at Intermediate School 30 in Brooklyn played a video game on Monday, and learned a little algebra at the same time. " was the caption on a photo.
The juxtaposition of this sentence would be:
"Students at Intermediate School 30 in Brooklyn learned algebra on Monday and played a little bit of video game at the same time. "
http://www.nytimes.com/2008/10/08/nyregion/08video.html
Wednesday, November 26, 2008
Linked In Question:
How did you succeed in a difficult course while in high school or college?
Students all over the country are getting ready for major tests and final examinations. It seems that students always have one difficult course or instructor. I would like to hear about strategies that you used to get through a difficult course. What are some of the best study habits? I would like to share your strategies with students. Please confirm that I can share your suggestions.
Math Confidence Response:
As a peak performance Math coach (and a former Engineering and Finance student who made it through Electromagnetics and Corporate Finance), there are key questions for test takers that raise awareness of their thinking process:
How did you get your answer?
Was it Easy? Medium? Hard?
Is that your final answer? (courtesy of Who Wants to Be a Millionaire?)
Other Success Factors:
Study Groups turn up the volume of thinking through discussion
Read over the entire test at the beginning
Do not leave anything blank -- write something :)
Know examples rather than formulas (12 divided by 1/2 = 24 is better than invert and multiply) Keep review sheets clean -- do not write the answers on the review sheet! This will force reworking of the problems --increasing the chance of success on the test
View the test as a learning opportunity -- test takers are making new connections while they are in the exam
While studying for finals may not have an exact parallel in the workplace, gaining math (and other academic) confidence can help with the following Life Skills:
Problem-Solving
Critical Thinking
Optimizing Your Potential
Escaping the Perfectionism Trap
Appreciating Effort vs. Obsessing about Ability
Financial / Medical Information Fluency
Expanding your self-teaching Skills
Finding a (new) career
Lifelong Learning
Brain Fitness
Posted by
Robin A. Schwartz, 11/26/08
http://www.mathconfidence.com/
mathconfidence@aol.com
How did you succeed in a difficult course while in high school or college?
Students all over the country are getting ready for major tests and final examinations. It seems that students always have one difficult course or instructor. I would like to hear about strategies that you used to get through a difficult course. What are some of the best study habits? I would like to share your strategies with students. Please confirm that I can share your suggestions.
Math Confidence Response:
As a peak performance Math coach (and a former Engineering and Finance student who made it through Electromagnetics and Corporate Finance), there are key questions for test takers that raise awareness of their thinking process:
How did you get your answer?
Was it Easy? Medium? Hard?
Is that your final answer? (courtesy of Who Wants to Be a Millionaire?)
Other Success Factors:
Study Groups turn up the volume of thinking through discussion
Read over the entire test at the beginning
Do not leave anything blank -- write something :)
Know examples rather than formulas (12 divided by 1/2 = 24 is better than invert and multiply) Keep review sheets clean -- do not write the answers on the review sheet! This will force reworking of the problems --increasing the chance of success on the test
View the test as a learning opportunity -- test takers are making new connections while they are in the exam
While studying for finals may not have an exact parallel in the workplace, gaining math (and other academic) confidence can help with the following Life Skills:
Problem-Solving
Critical Thinking
Optimizing Your Potential
Escaping the Perfectionism Trap
Appreciating Effort vs. Obsessing about Ability
Financial / Medical Information Fluency
Expanding your self-teaching Skills
Finding a (new) career
Lifelong Learning
Brain Fitness
Posted by
Robin A. Schwartz, 11/26/08
http://www.mathconfidence.com/
mathconfidence@aol.com
Math Confidence's Robin Schwartz's Letter to the Editor
The New York Times
LETTERS; Ups, Downs and America's Mind-Set
Published: September 29, 2008
To the Editor:
Positive thinking is not about always getting what you want; it is making the best of what you have while planting seeds to create opportunities in the future.
My role as an educator and parent is to empower the learner with independence, knowledge, skills and attitude to achieve personal, professional and academic success.
Motivational speakers like Tony Robbins, Jim Rohn and Stephen R. Covey have helped millions of people stay on course, some of whom might have turned to other coping mechanisms, like alcohol. Their messages may not resonate with all audiences, but they help to motivate and inspire millions of people to persevere through life's (and the financial markets') inevitable ups and downs.
Robin A. Schwartz Bronx, Sept. 25, 2008
The writer is the founder of mathconfidence.com.
The New York Times
LETTERS; Ups, Downs and America's Mind-Set
Published: September 29, 2008
To the Editor:
Positive thinking is not about always getting what you want; it is making the best of what you have while planting seeds to create opportunities in the future.
My role as an educator and parent is to empower the learner with independence, knowledge, skills and attitude to achieve personal, professional and academic success.
Motivational speakers like Tony Robbins, Jim Rohn and Stephen R. Covey have helped millions of people stay on course, some of whom might have turned to other coping mechanisms, like alcohol. Their messages may not resonate with all audiences, but they help to motivate and inspire millions of people to persevere through life's (and the financial markets') inevitable ups and downs.
Robin A. Schwartz Bronx, Sept. 25, 2008
The writer is the founder of mathconfidence.com.
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