Showing posts with label word problems in math and science. Show all posts
Showing posts with label word problems in math and science. Show all posts
Thursday, July 19, 2007
Problem complexity and higher-order thinking
Burger King math (silly to post it on both blogs).
Tuesday, June 26, 2007
help desk, part 2
I need a royal road to geometry.
Tomorrow I begin Lesson 88 in Saxon Algebra 2.
I won't finish the book until the very end of the summer, which means I will have taken 12 months to get through the thing.
Next I start Saxon Advanced Mathematics, which will take me another year to get through if I'm lucky.
fyi: Saxon publishes four high school books:
Geometry and trigonometry are integrated throughout the first 3 books.
So I'll spend next year working my way through Advanced Mathematics while Christopher, who will be in 8th grade, finishes Math A: algebra and some geometry. (Math A is still a 1 1/2 year course, as far as I can tell, though people keep saying NY is going back to the old algebra 1 - geometry - algebra 2 sequence. His class began Math A in January.)
Freshman year, if he stays on the fully accelerated track which I expect he will, he'll be taking geometry - real geometry, with proofs. Or so I hear. (Is this a separate, souped-up geometry course that's neither Math A nor Math B? Don't know! I get all my info from my neighbor, whose son is a year ahead in school.)
Assuming you aren't hopelessly confused by now,* you may see the problem.
He's catching me.
I'm 2/3 of the way through Saxon Algebra 2, and I have yet to do a proof. Unless there are a lot of proofs in Advanced Mathematics (which there may be - don't know)** I'm going to be starting geometry-with-proofs the same time Chris does.
That's not good.
I need a royal road.
Does anyone know whether Tammi Pelli's Proofs Workbook might work?
At 64 pages, it's the right length.
(large image)
(large image)
**update: proofs in Advanced Mathematics
Just checked the scope and sequence for Advanced Mathematics:
Proofs
Elements of Proofs
Understand basic logic and reasoning
State the contrapositives of conditional statements
State the converses and inverses of conditional
statements
Do proof outlines
Do formal proofs
Theorems
Prove the chord-tangent theorem
Prove theorems about secants and tangents
Prove theorems about chord products
Prove the Pythagorean theorem
Prove similarity of triangles
Prove the law of sines
Prove that equal angles imply proportional sides
questions about Math A
Math A Regents exams (archived)
Math A Toolkit
Home Instruction Schools Regents Exam Review
sample Saxon Math lessons
Saxon scope and sequence
* I'm hopelessly confused, but I'm used to it
Tomorrow I begin Lesson 88 in Saxon Algebra 2.
I won't finish the book until the very end of the summer, which means I will have taken 12 months to get through the thing.
Next I start Saxon Advanced Mathematics, which will take me another year to get through if I'm lucky.
fyi: Saxon publishes four high school books:
Geometry and trigonometry are integrated throughout the first 3 books.
So I'll spend next year working my way through Advanced Mathematics while Christopher, who will be in 8th grade, finishes Math A: algebra and some geometry. (Math A is still a 1 1/2 year course, as far as I can tell, though people keep saying NY is going back to the old algebra 1 - geometry - algebra 2 sequence. His class began Math A in January.)
Freshman year, if he stays on the fully accelerated track which I expect he will, he'll be taking geometry - real geometry, with proofs. Or so I hear. (Is this a separate, souped-up geometry course that's neither Math A nor Math B? Don't know! I get all my info from my neighbor, whose son is a year ahead in school.)
Assuming you aren't hopelessly confused by now,* you may see the problem.
He's catching me.
I'm 2/3 of the way through Saxon Algebra 2, and I have yet to do a proof. Unless there are a lot of proofs in Advanced Mathematics (which there may be - don't know)** I'm going to be starting geometry-with-proofs the same time Chris does.
That's not good.
I need a royal road.
Does anyone know whether Tammi Pelli's Proofs Workbook might work?
At 64 pages, it's the right length.
(large image)
(large image)
**update: proofs in Advanced Mathematics
Just checked the scope and sequence for Advanced Mathematics:
Proofs
Elements of Proofs
Understand basic logic and reasoning
State the contrapositives of conditional statements
State the converses and inverses of conditional
statements
Do proof outlines
Do formal proofs
Theorems
Prove the chord-tangent theorem
Prove theorems about secants and tangents
Prove theorems about chord products
Prove the Pythagorean theorem
Prove similarity of triangles
Prove the law of sines
Prove that equal angles imply proportional sides
questions about Math A
Math A Regents exams (archived)
Math A Toolkit
Home Instruction Schools Regents Exam Review
sample Saxon Math lessons
Saxon scope and sequence
* I'm hopelessly confused, but I'm used to it
Friday, June 1, 2007
on charts and word problems in math and science
I just went back to read the article by A. Toom , in which he explains how he taught word problems to Algebra class students. He gives an example of the chart and stresses the importance of organized and clear writing.
When I was in school, I was taught to organize all problems in chemistry and physics in a chart. This skill is extremely useful when dealing with word problems.
Our teachers taught us to use the following chart (in math, physics, and chemistry alike):
Given:
Asked
Formula:
Solution:
Answer:
Consider the following problem: A block of unknown material weighs 100g and has the volume of 25 cm3. What is the density of the block?
Given:
m=100g
V=25cm3
Asked:
d=?
Formula:
d=m/V
Solution:
d=100g/25cm3=4g/cm3
Answer:
Density of a given block is 4g/cm3
So I used this type of chart routinely and could see clearly what is given in the text, what I have to find, what formula will suit my purpose, check if the units are correct, and a teacher could easily check my reasoning on each step.
When I went to a Community College in NY (confession - I didn't show my DVM diploma so I could be allowed to take undergraduate courses in English and get the financial aid in the beginning), I observed many students struggling with simplest chemistry problems because they could not organize them , and were lost in words. I tutored at least 20 Chemistry students during my years in college, and all troubles were gone as soon as they got the habit of using the chart.
When I started teaching physics to my 7th graders and, recalling my own physics classes in school, started giving them word problems, I faced the necessity of teaching them an organized manner of analysis. Yes, using the chart can be considered an analysis of a problem. It took me a month and 3 quizzes until they got it. I modeled the chart on the board for every problem we did (again, since American textbooks in physics do not have problems!, I had to make most of them myself or translate from the Russian text), I took points off for absence of the chart of absence of steps in solution, but we did it. By the end of physics part (oh, I hate general science! nothing is complete!), ALL 31 of them could solve word problems using the chart. Their math teacher told me that some of them were using the chart in math HW problems (obviously, she was giving some word problems, too)
I still didn't beat their sloppy handwriting, even though I had some students' works returned with F because I couldn't read it... It takes consistency and discipline. And math is the great helper in disciplining the mind.
When I was in school, I was taught to organize all problems in chemistry and physics in a chart. This skill is extremely useful when dealing with word problems.
Our teachers taught us to use the following chart (in math, physics, and chemistry alike):
Given:
Asked
Formula:
Solution:
Answer:
Consider the following problem: A block of unknown material weighs 100g and has the volume of 25 cm3. What is the density of the block?
Given:
m=100g
V=25cm3
Asked:
d=?
Formula:
d=m/V
Solution:
d=100g/25cm3=4g/cm3
Answer:
Density of a given block is 4g/cm3
So I used this type of chart routinely and could see clearly what is given in the text, what I have to find, what formula will suit my purpose, check if the units are correct, and a teacher could easily check my reasoning on each step.
When I went to a Community College in NY (confession - I didn't show my DVM diploma so I could be allowed to take undergraduate courses in English and get the financial aid in the beginning), I observed many students struggling with simplest chemistry problems because they could not organize them , and were lost in words. I tutored at least 20 Chemistry students during my years in college, and all troubles were gone as soon as they got the habit of using the chart.
When I started teaching physics to my 7th graders and, recalling my own physics classes in school, started giving them word problems, I faced the necessity of teaching them an organized manner of analysis. Yes, using the chart can be considered an analysis of a problem. It took me a month and 3 quizzes until they got it. I modeled the chart on the board for every problem we did (again, since American textbooks in physics do not have problems!, I had to make most of them myself or translate from the Russian text), I took points off for absence of the chart of absence of steps in solution, but we did it. By the end of physics part (oh, I hate general science! nothing is complete!), ALL 31 of them could solve word problems using the chart. Their math teacher told me that some of them were using the chart in math HW problems (obviously, she was giving some word problems, too)
I still didn't beat their sloppy handwriting, even though I had some students' works returned with F because I couldn't read it... It takes consistency and discipline. And math is the great helper in disciplining the mind.
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