10 ways to solve a quadratic equation
13 views
Skip to first unread message
Don Cohen- The Mathman
Nov 2, 2010, 10:03:37 AM11/2/10
to natur...@googlegroups.com
Maria,
It's all possible, as shown in my books. And see Jenny on youtube Don Cohen "Solving a quadratic equation by iteration".
Don
--
809 Stratford Dr.
Champaign, IL 61821-4140
Tel. 217-356-4555
Fax: 1 217 356 4593
Email: doncohe...@gmail.com
Don's Mathman website URL: http://www.mathman.biz
--
"Learning, Living and Loving mathematics.."- the core of Don's teaching and books, observed by Seth Nielson.
Don Cohen -The Mathman809 Stratford Dr.
Champaign, IL 61821-4140
Tel. 217-356-4555
Fax: 1 217 356 4593
Email: doncohe...@gmail.com
Don's Mathman website URL: http://www.mathman.biz
See Don's new clickable A Map to Calculus with student works and sample problems from Don's books at every node
Our Shaklee website:
http://marilynanddoncohen.myshaklee.com
Our Shaklee website:
http://marilynanddoncohen.myshaklee.com
Maria Droujkova
Nov 2, 2010, 6:12:59 PM11/2/10
to natur...@googlegroups.com
The wonderful video is here: http://www.youtube.com/watch?v=NkPfW40DFyk
Video with text comments (e.g. "Jenny starts to program her calculator at 2:35") is probably the best of existing ways to capture and to share our mathematical practices.
Cheers,
Maria Droujkova
Make math your own, to make your own math.
Video with text comments (e.g. "Jenny starts to program her calculator at 2:35") is probably the best of existing ways to capture and to share our mathematical practices.
Cheers,
Maria Droujkova
Make math your own, to make your own math.
Maria Droujkova
Nov 3, 2010, 7:40:53 AM11/3/10
to natur...@googlegroups.com
I have added the following piece by Don, and the video, to the growing Flow Channel collection about balances in mathematics: http://naturalmath.wikispaces.com/Flow+Channels
From a local parent whose 2 children came to work with Don for a number of years:
"Typical approach studies one simple concept at a time- boring- isolated, irrelevant. Instead- have a more interesting, complicated problem, that uses these concepts in finding the answer. This leads the student through math concepts, seeing them in their natural context and usefulness. Also, when the problem is finally solved, the "Look what I can do!" feeling spurs further exploration of math."
In trying to solve the complicated problem, the student needs to use the simple concepts to understand the whole thing.
An example
I give a 4th grader a quadratic equation like x^2 - 5x + 6 = 0
Before I do this I make sure they know 5^2=25 and 3-4 = -1
Then we guess a number (need the rule for substitution and order of operations). So they give me a guess number, say 1.
1->x 1^2 - 5*1 + 6 =? 0
So they are squaring a number, multiplying, subtracting,adding negative and positive numbers, and deciding if the sentence is true - all without thinking about it. When they find the 2 numbers that work, they really feel like they have accomplished a great feat! And when they see a pattern of how the 2 numbers relate to the adding number and coefficient of x WOW - this is not busy work! Then I give them a few others to solve... Then they have to make a quadratic equation for Mom and Dad and one for me. And they make up really hard ones for me! "Look what I can do!" feeling spurs further exploration of math." That's the real payoff.
Simple exercises and complex problems
by Don CohenFrom a local parent whose 2 children came to work with Don for a number of years:
"Typical approach studies one simple concept at a time- boring- isolated, irrelevant. Instead- have a more interesting, complicated problem, that uses these concepts in finding the answer. This leads the student through math concepts, seeing them in their natural context and usefulness. Also, when the problem is finally solved, the "Look what I can do!" feeling spurs further exploration of math."
In trying to solve the complicated problem, the student needs to use the simple concepts to understand the whole thing.
An example
I give a 4th grader a quadratic equation like x^2 - 5x + 6 = 0
Before I do this I make sure they know 5^2=25 and 3-4 = -1
Then we guess a number (need the rule for substitution and order of operations). So they give me a guess number, say 1.
1->x 1^2 - 5*1 + 6 =? 0
So they are squaring a number, multiplying, subtracting,adding negative and positive numbers, and deciding if the sentence is true - all without thinking about it. When they find the 2 numbers that work, they really feel like they have accomplished a great feat! And when they see a pattern of how the 2 numbers relate to the adding number and coefficient of x WOW - this is not busy work! Then I give them a few others to solve... Then they have to make a quadratic equation for Mom and Dad and one for me. And they make up really hard ones for me! "Look what I can do!" feeling spurs further exploration of math." That's the real payoff.
Reply all
Reply to author
Forward
0 new messages