Tips How to Create and Teach a Calculus Prerequisite Course
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Khaled Omran
Mar 31, 2013, 6:10:04 PM3/31/13
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Article Title: Tips How to Create and Teach a Calculus Prerequisite Course
Author: Khaled Omran
Word Count: 728
Article URL: http://www.isnare.com/?aid=1828280&ca=Education
Format: 64cpl
Contact The Author: http://www.isnare.com/eta.php?aid=1828280
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It is essential to have a calculus prerequisite course that gathers all the topics covered in pre calculus just in one subject. This subject is overwhelming for many students. This is because they have to have thorough knowledge of several other subjects. The student should have solid base in algebra, geometry, and trigonometry. Special attention should be given to binomial theorem, conic sections, complex numbers and real numbers.
Calculus is the branch of science that deals with rates of change. In algebra the student is taught about a function that represents a physical quantity, for example the amount of water in a tank relative to time. However; in calculus the interest is in the rate at which water is changing in a tank relative to time. One can see clearly how calculus completes the picture after algebra. Algebra answers one question and calculus answers a different question and they together give the whole picture.
Calculus requires that the student have a good knowledge of algebra. A good tactic in teaching algebra in a calculus prerequisite course is to point out the points that most students have problems with. Students studying algebra have particular problems with exponents and logarithms.
It is good to use calculators to do laboratory experiments to get the students to understand exponents. For example the teacher can ask the students to use their calculators to find the exponents of 0, 2, 4, 100, and 200. The students will see how the change of the output gets very steep with small changes in the input. Then the teacher should ask the students to use their calculator to plot the graph of an exponent function. The students should examine the curve and see how little change in input cause a dramatic change in output. The same experiments should be done with logarithms. The teacher should choose a base and chooses values to take the logarithms of. The teacher should let students try forbidden values like negative values and see how the calculator responds. Also the teacher should let the students plot a logarithmic function and spot the forbidden values on the graph.
Geometry is very important for calculus. The most important concept in geometry related to calculus is the area. The student should see how he can find the area of a shape by slicing it into simpler shapes and then adding the individual areas of these shapes. The student should see that we can simplify the circumference calculation by simplifying the circle by considering it a polygon. This simplification causes some error margin. However; the error decreases as we increase the number of sides of the polygon. The error becomes null when the number of sides become infinite.
Although the need of trigonometry does not come at the beginning of a calculus class students should know the basic trigonometric functions and their relations. The students should appreciate that the cosine is a sine with a shift and the sine is a cosine with a shift. They should see their graphs simultaneously on a calculator.
After knowing what should be taught in a calculus prerequisite course one should choose a suitable textbook to be assigned to the class. Choosing a textbook is not an easy task. Some students would not do well in a course only because the textbook was not friendly or easy to understand. The textbook should be easy to understand with lots of examples and starts right from the beginning. The teacher explanation of concepts should be in close resemblance to the textbook so the students do not get confused.
Foe every new concept or idea the teacher should solve several demonstration problems. This really allows the student to follow up with the ideas discussed in class.
The teacher should allow the students to ask as many questions as needed to understand. The students should know that their questions are welcome and that it is important for the teacher that they understand the concepts.
Throughout the course the students should do laboratory experiments using calculators to dissolve the concepts. They would need an algebra calculator, a basic scientific calculator and a graphing calculator. There are many new innovative software calculators like kinematics calculators and many others. These calculators allow the teacher to be creative in how he creates mathematics laboratory experiments.
About The Author: Check out these calculators at http://www.software-hitech.com
Please use the HTML version of this article at:
http://www.isnare.com/html.php?aid=1828280
*********************** ARTICLE END ***********************
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Message delivered directly to members of the group:
publish-the...@googlegroups.com
*****************************************************************
Please consider this free-reprint article written by:
Khaled Omran
*****************************
IMPORTANT - Publication/Reprint Terms
- You have permission to publish this article electronically in free-only publications such as a website or an ezine as long as the bylines are included.
- You are not allowed to use this article for commercial purposes. The article should only be reprinted in a publicly accessible website and not in a members-only commercial site.
- You are not allowed to post/reprint this article in any sites/publications that contains or supports hate, violence, porn and warez or any indecent and illegal sites/publications.
- You are not allowed to use this article in UCE (Unsolicited Commercial Email) or SPAM. This article MUST be distributed in an opt-in email list only.
- If you distribute this article in an ezine or newsletter, we ask that you send a copy of the newsletter or ezine that contains the article to http://www.isnare.com/eta.php?aid=1828280
- If you post this article in a website/forum/blog, ALL links MUST be set to hyperlinks and we ask that you send a copy of the URL where the article is posted to http://www.isnare.com/eta.php?aid=1828280
- We request that you ask permission from the author if you want to publish this article in print.
The role of iSnare.com is only to distribute this article as part of its Article Distribution feature ( http://www.isnare.com/distribution.php ). iSnare.com does NOT own this article, please respect the author's copyright and this publication/reprint terms. If you do not agree to any of these terms, please do not reprint or publish this article.
*****************************
Article Title: Tips How to Create and Teach a Calculus Prerequisite Course
Author: Khaled Omran
Word Count: 728
Article URL: http://www.isnare.com/?aid=1828280&ca=Education
Format: 64cpl
Contact The Author: http://www.isnare.com/eta.php?aid=1828280
Easy Publish Tool: http://www.isnare.com/html.php?aid=1828280
*********************** ARTICLE START ***********************
It is essential to have a calculus prerequisite course that gathers all the topics covered in pre calculus just in one subject. This subject is overwhelming for many students. This is because they have to have thorough knowledge of several other subjects. The student should have solid base in algebra, geometry, and trigonometry. Special attention should be given to binomial theorem, conic sections, complex numbers and real numbers.
Calculus is the branch of science that deals with rates of change. In algebra the student is taught about a function that represents a physical quantity, for example the amount of water in a tank relative to time. However; in calculus the interest is in the rate at which water is changing in a tank relative to time. One can see clearly how calculus completes the picture after algebra. Algebra answers one question and calculus answers a different question and they together give the whole picture.
Calculus requires that the student have a good knowledge of algebra. A good tactic in teaching algebra in a calculus prerequisite course is to point out the points that most students have problems with. Students studying algebra have particular problems with exponents and logarithms.
It is good to use calculators to do laboratory experiments to get the students to understand exponents. For example the teacher can ask the students to use their calculators to find the exponents of 0, 2, 4, 100, and 200. The students will see how the change of the output gets very steep with small changes in the input. Then the teacher should ask the students to use their calculator to plot the graph of an exponent function. The students should examine the curve and see how little change in input cause a dramatic change in output. The same experiments should be done with logarithms. The teacher should choose a base and chooses values to take the logarithms of. The teacher should let students try forbidden values like negative values and see how the calculator responds. Also the teacher should let the students plot a logarithmic function and spot the forbidden values on the graph.
Geometry is very important for calculus. The most important concept in geometry related to calculus is the area. The student should see how he can find the area of a shape by slicing it into simpler shapes and then adding the individual areas of these shapes. The student should see that we can simplify the circumference calculation by simplifying the circle by considering it a polygon. This simplification causes some error margin. However; the error decreases as we increase the number of sides of the polygon. The error becomes null when the number of sides become infinite.
Although the need of trigonometry does not come at the beginning of a calculus class students should know the basic trigonometric functions and their relations. The students should appreciate that the cosine is a sine with a shift and the sine is a cosine with a shift. They should see their graphs simultaneously on a calculator.
After knowing what should be taught in a calculus prerequisite course one should choose a suitable textbook to be assigned to the class. Choosing a textbook is not an easy task. Some students would not do well in a course only because the textbook was not friendly or easy to understand. The textbook should be easy to understand with lots of examples and starts right from the beginning. The teacher explanation of concepts should be in close resemblance to the textbook so the students do not get confused.
Foe every new concept or idea the teacher should solve several demonstration problems. This really allows the student to follow up with the ideas discussed in class.
The teacher should allow the students to ask as many questions as needed to understand. The students should know that their questions are welcome and that it is important for the teacher that they understand the concepts.
Throughout the course the students should do laboratory experiments using calculators to dissolve the concepts. They would need an algebra calculator, a basic scientific calculator and a graphing calculator. There are many new innovative software calculators like kinematics calculators and many others. These calculators allow the teacher to be creative in how he creates mathematics laboratory experiments.
About The Author: Check out these calculators at http://www.software-hitech.com
Please use the HTML version of this article at:
http://www.isnare.com/html.php?aid=1828280
*********************** ARTICLE END ***********************
- To distribute your articles go to http://www.isnare.com/distribution.php
- For more free-reprint articles go to http://www.isnare.com
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