The Instigator
Pellerin12
Con (against)
Losing
0 Points
The Contender
UndeniableReality
Pro (for)
Winning
28 Points

Calculus at 4 grade why ? I haven't learned that yet

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Post Voting Period
The voting period for this debate has ended.
after 5 votes the winner is...
UndeniableReality
Voting Style: Open Point System: 7 Point
Started: 10/8/2014 Category: Education
Updated: 2 years ago Status: Post Voting Period
Viewed: 1,452 times Debate No: 62933
Debate Rounds (3)
Comments (22)
Votes (5)

 

Pellerin12

Con

Why would a fourth grader need calculus especially when there brains aren't developed yet and I haven't learned it yet
UndeniableReality

Pro

No terms or rules were declared by Con in the first round. Thus it is unclear (to me) whether an argument should be fully presented. Since Con did not begin with a fully argument, I will simply take this opportunity to define terms and state my position more precisely, leaving the main argument for Rounds 2 and 3. Apologies if the content of this post extends beyond the expectations for the first round of this debate.

Calculus can be defined as the mathematical study of limits [1], and/or the mathematical study of change [2].

A limit is a concept in mathematics which is used to describe the behaviour of a function or a system as its inputs approach a particular set of values. Limits are of particular interest where the behaviour of the function or system is not obvious (often when the inputs are zero, negative infinity, or positive infinity).

My position is that the basics of calculus can, and should, be taught in the 4th grade. My argument will consist mainly of two basic points: (1) children of that age are capable of understanding the basic concepts of calculus, and (2) an understanding of the basic concepts of calculus is beneficial for children of that age.

To premise the argument, I would like to differentiate between a few levels of understanding in calculus.
(1)A basic understanding of the concepts of calculus involve a conceptual understanding of limits, working with infinity, rates of change and changing rates of change, and accumulation (integration) of quantity.
(2)A further level of understanding in calculus is the learned ability to compute derivatives and integrals.
(3)A deeper level of understanding in calculus implies the ability to generate and manipulate mathematical expressions to make derivatives and integrals easier to compute, but also to describe different aspects of real world problems.
(4)A deep understanding of calculus implies the ability to derive theorems and produce mathematical proofs relating to the concepts and principles of calculus.

A basic understanding is sufficient to allow one to appreciate the significance of calculus in the world to a valuable degree, and to gain a deeper understanding of reality. Therefore, I will be arguing for teaching the basic concepts of calculus to 4th grade students. I will also give examples of how the concepts of calculus can be taught to a student who has only a 4th grade level of mathematical ability and why even this rudimentary level of understanding is beneficial for their conceptual understanding of the world, their development, and their future success.

I look forward to an interesting debate and hope for the best from both sides!

Cheers.

[1] Verberg, D.; Purcell, E. J.; Rigdon, S. E. (2007). Calculus, 9th Edition. Pearson Education Inc., New Jersey. Chapter 1, p. 55.
[2] Latorre, D. R.; Kenelly, J. W.; Reed, I. B.; Biggers, S. (2007). Calculus Concepts: An Applied Approach to the Mathematics of Change. Cengage Learning. Chapter 1, p 2
Debate Round No. 1
Pellerin12

Con

It's hard for them to understand it the way teenagers do. So why do they need it anyway I'm 12 and I haven't learned that yet
Or used it
UndeniableReality

Pro

The concepts of calculus can easily be explained with visual examples that a 4th grader can understand.

Infinity implies a quantity that is large to an unlimited degree, while infinitesimal is a quantity that is small to an unlimited degree. Here is a simple illustration: if you start drawing a straight line and just go on forever, the length of the line is infinite. Or, if you keep dividing a line in half, you will get smaller and smaller lines but you can always divide it in half forever.

Limits: Draw a triangle. Then a square. Continue to add one side to the polygon. By adding sides, the shape becomes closer and closer to a circle. Indeed, the limit of a polygon as the number of sides approaches infinity is a circle. Similarly, if you collapse one side of a triangle, you get two lines on top of each other (2 sides). Collapsing one of the lines gives you a line again (1 side). And if you collapse that line, you get a dot (0 sides). So the limit of a polygon as the number of sides approaches 0, is a dot. This is the essence of limits.

Differentiation tells you how much a quantity is changing at a specific point. Understanding this only requires knowledge of basic division, which all 4th graders have. Take a right-angle triangle and color it in. Ask how much the height of the triangle changed from the start to the end. This is of course the height of the triangle divided by the length. Now erase some of the color from the beginning and the end, and ask the same question. Keep erasing to get smaller and smaller slices of the triangle and repeat the calculation. The limit as the colored slice gets infinitely thin is the derivative at the point along the length where the triangle is still colored.

Integration: Integration is basically the generalized concept of area or volume for any shape. Draw an irregular shape and explain how you can roughly estimate the area by drawing thing rectangles side by side with the tops touching the curve and adding up the areas. Now make the rectangles thinner and show that the estimated area is slightly more precise (color the part of the rectangle that is inside the shape blue, and the parts outside the shape red, and as you make the rectangles thinner, you can see the amount of red decreasing). The integral is what you get when you take the limit of the total area of all the rectangles as their widths become infinitesimally small (which also means the number of rectangles approaches infinity).

These together are the essentials of understanding calculus. With this, equations become more intuitive. But equations are only descriptions and not calculus itself, in much the same way that the word 'dog' is not actually a dog. Therefore, conceptually and visually understanding the above examples is actually understanding calculus, just like a toddler understands what a dog is before they can read and write 'dog'.

I will explain why these concepts are important for 4th graders in the final round.
Debate Round No. 2
Pellerin12

Con

Pellerin12 forfeited this round.
UndeniableReality

Pro

It doesn't seem right to present the final portion of my argument. I will instead summarize very briefly and state some reasons understanding calculus can be beneficial for children.

Calculus is the foundation of all modern scientific understanding, even in fields which are not typically associated with mathematics, such as biology and medicine. Underlying the principles and methods used in all fields of science, whether directly or indirectly, is calculus. For example, see the Noyers Whiter equation for calculating dosage rates (https://bhcc.digication.com...), or see hypothesis testing in statistics, which is used in most scientific studies and clinical trials to establish whether acquired data supports or fails to support a particular hypothesis. As someone with a mathematics degree specializing in statistics, I can say that almost all of probability and statistics is based upon calculus.

Calculus itself is not the symbols and calculations most people associate with it. Calculus, in reality, is the set of concepts, ideas, and principles which give meaning to those symbols and allow us to develop methods for those calculations. Therefore I have argued that this level of understanding calculus should be the focus of education. I have also argued that a basic level of each of the essential concepts of calculus (infinity, limits, derivatives, integrals) is within reach of children at the 4th grade level and I have provided basic sketches of how these concepts can be taught to children.

However, the question of this debate is 'why' teach calculus to children, not whether or not it is possible. I will presume that establishing benefits from learning calculus for children in the 4th grade which outweigh the effort involved in learning the concepts involved is sufficient to answer the question.

As I said at the beginning of this post, I will not put in the effort to establish the validity of these benefits when my opponent has not taken the time or effort to argue his side. I will simply list these benefits and invite any reader to take up this debate with me if they disagree.

Benefits:
1) Improved ability to understand scientific concepts, including such things as velocity and acceleration in physics, which are currently taught in high school without calculus, even though calculus is required for learning the actual concepts.
2) Improved understanding of the natural world around them (all sorts of phenomena involving rates of change and accumulation).
3) Understanding infinity and limits in a concrete sense have great potential to expand the mind and develop the brain for higher level concepts.
4) Greater appreciation of math and science.

I will conclude by thanking Con for setting up this debate. It is a topic in which I am very interested, and I strongly advocate teaching calculus to children of this age. I personally intend to teach my children calculus starting from the first grade.
Debate Round No. 3
22 comments have been posted on this debate. Showing 1 through 10 records.
Posted by UndeniableReality 1 year ago
UndeniableReality
I just wanted to formalize my thoughts on this question a little bit, even if it wasn't a debate =P
Posted by Atmas 1 year ago
Atmas
Geez, Reality. Way to crush a 12 year old ;)
Posted by UndeniableReality 2 years ago
UndeniableReality
With who?
Posted by volcan 2 years ago
volcan
id like to debate this topic with you
Posted by Tweka 2 years ago
Tweka
I agree with UndeniableReality.
Posted by UndeniableReality 2 years ago
UndeniableReality
But I still think it should be taught earlier =)

I just posted. 3000 characters is extremely limiting and challenging. I was only able to say about 25% of what I hoped to say this round.
Posted by Pellerin12 2 years ago
Pellerin12
Exactly
Posted by UndeniableReality 2 years ago
UndeniableReality
When I was in high school, it was a grade 12 course.
Posted by Pellerin12 2 years ago
Pellerin12
Calculus should be an extra class for 9-12 grades
Posted by UndeniableReality 2 years ago
UndeniableReality
I was really looking forward to a debate. Sadly, it isn't really a debate at this point. But I want to finish my argument because one major reason for doing this debate was to formalize my thoughts on this topic. Hopefully anyone reading the debate will find it useful on some level. Maybe Con will find some value in my posts as well.

To Con, I sincerely hope you will try to make the best argument you can on your next post =)

By the way, could anyone inform me if it inappropriate for me to comment on this forum while the debate is still active, as long as I don't further my arguments?
5 votes have been placed for this debate. Showing 1 through 5 records.
Vote Placed by n7 2 years ago
n7
Pellerin12UndeniableRealityTied
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Total points awarded:07 
Reasons for voting decision: FF and Con ignored everything by Pro
Vote Placed by Blade-of-Truth 2 years ago
Blade-of-Truth
Pellerin12UndeniableRealityTied
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Total points awarded:07 
Reasons for voting decision: Conduct - Pro. This is due to Con's forfeit in R3 which is rarely acceptable behavior in any debate setting. S&G - Pro. Con failed to use proper grammar throughout the debate. Arguements - Pro. Con failed to provide rebuttals to most of Pro's arguments. This allowed Pro to continue debating unchallenged and in doing so, fully affirmed the resolution. Sources - Pro. Con failed to utilize sources or cite anything throughout the debate, whereas Pro did. Due to this, Pro is awarded source points. This is a solid 7-point win for Pro.
Vote Placed by zmikecuber 2 years ago
zmikecuber
Pellerin12UndeniableRealityTied
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Reasons for voting decision: FF
Vote Placed by Ragnar 2 years ago
Ragnar
Pellerin12UndeniableRealityTied
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Reasons for voting decision: Forfeit, and ouch (too little of a showing by con, for me to read pro's arguments... thus can't really award that)
Vote Placed by lannan13 2 years ago
lannan13
Pellerin12UndeniableRealityTied
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Total points awarded:06 
Reasons for voting decision: Forfeiture