Difference between revisions of "Word Problems"

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{|style="margin-left: auto; margin-right: auto; border: 1px; font-style: italic;"
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{|style="margin-left: auto; margin-right: auto; border: none; width: 70%; font-style: italic;"
 
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|The origins of mathematics lie in the desire to solve problems of a practical nature.[…]<br>
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|'''The origins of mathematics lie in the desire to solve problems of a practical nature.[…]'''<br>
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Solving practical problems provides the only reason the vast majority of the population needs to learn mathematics at all, and adds variety and interest to learning the rote methods of calculation.
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'''Solving practical problems provides the only reason the vast majority of the population needs to learn mathematics at all, and adds variety and interest to learning the rote methods of calculation.'''<br>
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Problems serve to exercise our minds (both young and old) in the techniques of mathematical thinking and problem solving. They are the reason we first do mathematics.<br>
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'''Problems serve to exercise our minds (both young and old) in the techniques of mathematical thinking and problem solving.'''<br>
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It is a necessary consequence of this situation that the making and solving of mathematical problems constitutes the longest continuing tradition in the history of mathematics.
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'''They are the reason we first do mathematics.'''<br>
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'''It is a necessary consequence of this situation that the making and solving of mathematical problems constitutes the longest continuing tradition in the history of mathematics.'''
 
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(Warren Van Egmond, "Types and Traditions of Mathematical Problems: A Challenge for Historians of Mathematics", p.379)<br>
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{|style="margin-left: auto; margin-right: auto; border: none; width: 75%;"
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In his article Warren Van Egmond calls for an international multilingual and multicultural project of writing the history of mathematical word problems.
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|-
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|Warren Van Egmond, "Types and Traditions of Mathematical Problems: A Challenge for Historians of Mathematics", in: Menso Folkerts ed., ''Mathematische Probleme im Mittelalter: Der lateinische und arabische Sprachbereich'', Wiesbaden: Harrassowitz Verlag, 1996, (pp. 379-428), p.379
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|}
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In his article Warren Van Egmond calls for an international multilingual and multicultural project of writing the history of mathematical word problems.<br>
 
In his words:
 
In his words:
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"Elementary mathematics represents the core of the mathematical experience. It is the first level of mathematics that every person learns, providing the foundation for all the superstructures that are built upon it, and it is the first part of mathematics that passed from one culture to another when scientific ideas are shared; it is the surest sign of continuity from author to author and culture to culture. If we want to trace the paths by which mathematical ideas are passed from one culture to another or, in their absence, fix the origins of new mathematics, then these are some of the most important sources we have." (pp.381-2)
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{|style="margin-left: auto; margin-right: auto; border: none; width: 70%; font-style: italic;"
 +
|-
 +
|'''Elementary mathematics represents the core of the mathematical experience.'''<br>
 +
'''It is the first level of mathematics that every person learns, providing the foundation for all the superstructures that are built upon it, and it is the first part of mathematics that passed from one culture to another when scientific ideas are shared; it is the surest sign of continuity from author to author and culture to culture'''.<br>
 +
'''If we want to trace the paths by which mathematical ideas are passed from one culture to another or, in their absence, fix the origins of new mathematics, then these are some of the most important sources we have'''.(pp.381-2)
 +
|}
 
Van Egmond offers some guidelines for such a project, saying:
 
Van Egmond offers some guidelines for such a project, saying:
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"Identifying problems for the purpose of tracing influences cannot be based entirely on their specific texts, the particular situations they pose, or their mathematical form alone; it must instead be based on some combination of all those features that characterize a particular problem. Only a comparison based on these essential features will allow us to identify true similarities and differences among problems and so trace their common lineage". (p. 386)
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{|style="margin-left: auto; margin-right: auto; border: none; width: 70%; font-style: italic;"
 +
|-
 +
|'''Identifying problems for the purpose of tracing influences cannot be based entirely on their specific texts, the particular situations they pose, or their mathematical form alone; it must instead be based on some combination of all those features that characterize a particular problem'''.<br>
 +
'''Only a comparison based on these essential features will allow us to identify true similarities and differences among problems and so trace their common lineage.''' (p. 386)
 +
|}
 
Inspired by Van Egmond's words and with the help of the classification system he offers we present here a pool of word problems collected from the texts that are included in our database, in the hope that it will be extended to other languages as well.
 
Inspired by Van Egmond's words and with the help of the classification system he offers we present here a pool of word problems collected from the texts that are included in our database, in the hope that it will be extended to other languages as well.
  
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:*Measures
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:*[[Measures Problems]]
 
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:*[[Find the Time Problems]]
 
:*[[Find the Time Problems]]
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:*[[Find the Fund Problems]]
 
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:*Compound interest
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:*[[Compound Interest Problems]]
 
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*Divide a Number
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*[[Mixture and Alligation Problems]]
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*[[Find a Number Problems]]
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*[[Divide a Number Problems]]
 
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:*Multiple quantities
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:*[[Multiple Quantities Problems]]
 
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:*Simple division
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:*[[Simple Division Problems]]
 
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:*Simultaneous division
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:*[[Simultaneous Division Problems]]
 
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:*Twins
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:*[[Twins]]
 
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:*Too much and too little
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:*[[Too Much and Too Little]]
 
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:*The found purse
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:*[[The found purse]]
 
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*Partial payment
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*[[Partial payment]]
 
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*[[Boiling Problems]]
 
*[[Boiling Problems]]
 
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!Series: Sums; Products
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*Series
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:*[[Sums]]
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:*Products
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*[[Ordering Problems]]
 
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!Ordering problems
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*[[Guessing Problems]]
 
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!Geometrical problems
 
!Geometrical problems
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:*Areas
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:*[[Area of a Figure]]
 
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:*Volumes
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:*[[Volume of a Figure]]
 
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:*Sides
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:*[[Side of a Figure]]
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:*[[Perimeter of a Figure]]
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:*[[Diagonal of a Figure]]
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:*[[Height of a Figure]]
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:*[[Point of a Figure]]
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:*[[Divide a Figure]]
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:*[[Transformation Problems]]
 
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*Construction problems
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*[[Construction problems]]
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*[[Gaging problems]]
 
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*Gaging problems
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*[[Magic Square]]
  
 
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Latest revision as of 04:47, 15 October 2022

The origins of mathematics lie in the desire to solve problems of a practical nature.[…]

Solving practical problems provides the only reason the vast majority of the population needs to learn mathematics at all, and adds variety and interest to learning the rote methods of calculation.
Problems serve to exercise our minds (both young and old) in the techniques of mathematical thinking and problem solving.
They are the reason we first do mathematics.
It is a necessary consequence of this situation that the making and solving of mathematical problems constitutes the longest continuing tradition in the history of mathematics.

Warren Van Egmond, "Types and Traditions of Mathematical Problems: A Challenge for Historians of Mathematics", in: Menso Folkerts ed., Mathematische Probleme im Mittelalter: Der lateinische und arabische Sprachbereich, Wiesbaden: Harrassowitz Verlag, 1996, (pp. 379-428), p.379

In his article Warren Van Egmond calls for an international multilingual and multicultural project of writing the history of mathematical word problems.
In his words:

Elementary mathematics represents the core of the mathematical experience.

It is the first level of mathematics that every person learns, providing the foundation for all the superstructures that are built upon it, and it is the first part of mathematics that passed from one culture to another when scientific ideas are shared; it is the surest sign of continuity from author to author and culture to culture.
If we want to trace the paths by which mathematical ideas are passed from one culture to another or, in their absence, fix the origins of new mathematics, then these are some of the most important sources we have.(pp.381-2)

Van Egmond offers some guidelines for such a project, saying:

Identifying problems for the purpose of tracing influences cannot be based entirely on their specific texts, the particular situations they pose, or their mathematical form alone; it must instead be based on some combination of all those features that characterize a particular problem.

Only a comparison based on these essential features will allow us to identify true similarities and differences among problems and so trace their common lineage. (p. 386)

Inspired by Van Egmond's words and with the help of the classification system he offers we present here a pool of word problems collected from the texts that are included in our database, in the hope that it will be extended to other languages as well.


  • Pricing Problems
  • Exchange Problems
  • Barter Problems
  • Interest and Discount Problems
  • Simple discount
  • Compound discount
  • Partnership Problems
  • Find a Quantity
  • Divide a quantity
  • Purchase
  • Joint Purchase
  • Motion problems
  • Series
  • Products
Geometrical problems
  • Figure problems
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