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
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