Difference between revisions of "Word Problems"

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{|style="margin-left: auto; margin-right: auto; border: none; width: 70%; font-style: italic;"
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|-
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|'''The origins of mathematics lie in the desire to solve problems of a practical nature.[…]'''<br>
 +
'''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>
 +
'''Problems serve to exercise our minds (both young and old) in the techniques of mathematical thinking and problem solving.'''<br>
 +
'''They are the reason we first do mathematics.'''<br>
 +
'''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.'''
 +
|}
 +
{|style="margin-left: auto; margin-right: auto; border: none; width: 75%;"
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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:
 +
{|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:
 +
{|style="margin-left: auto; margin-right: auto; border: none; width: 70%; font-style: italic;"
 +
|-
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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'''.<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)
 +
|}
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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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{|class="wikitable"
 
{|class="wikitable"
 
|-
 
|-
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!Pricing Problems
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|
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*Pricing Problems
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|-
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|
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:*[[Find the Price Problems]]
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|-
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|
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:*[[Find the Amount Problems]]
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|-
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|
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:*[[Tare and Tret Problems]]
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|-
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|
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*Exchange Problems
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|-
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|
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:*[[Currencies Problems]]
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|-
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|
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:*[[Measures Problems]]
 
|-
 
|-
 
|
 
|
−
*[[Find the Price Problems]]
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*[[Payment Problems]]
 
|-
 
|-
 
|
 
|
−
*[[Find the Amount Problems]]
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*Barter Problems
 
|-
 
|-
 
|
 
|
−
*[[Tare and Tret Problems]]
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:*[[Cash Barter Problems]]
 
|-
 
|-
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!Exchange Problems
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|
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:*[[Simple Barter Problems]]
 
|-
 
|-
 
|
 
|
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*Currencies
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:*[[Compound Barter Problems]]
 
|-
 
|-
 
|
 
|
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*Measures
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*Interest and Discount Problems
 
|-
 
|-
−
![[Payment Problems]]
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|
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:*[[Find the Interest Problems]]
 
|-
 
|-
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!Interest and Discount Problems
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|
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:*[[Find the Time Problems]]
 
|-
 
|-
 
|
 
|
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*Find the Interest Problems
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:*[[Find the Fund Problems]]
 
|-
 
|-
 
|
 
|
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*Find the Time Problems
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:*Simple discount
 
|-
 
|-
 
|
 
|
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*Simple discount
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:*[[Compound Interest Problems]]
 
|-
 
|-
 
|
 
|
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*Compound interest
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:*Compound discount
 
|-
 
|-
 
|
 
|
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*Compound discount
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*[[Rent Problems]]
 
|-
 
|-
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!Divide a Number
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|
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*Partnership Problems
 
|-
 
|-
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!Find a Quantity
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|
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:*[[Partnership Problems - for the Same Time]]
 
|-
 
|-
 
|
 
|
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*[[How Much Problems]]
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:*[[Partnership Problems - for Different Times]]
 
|-
 
|-
 
|
 
|
−
*[[How Many Problems]]
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*[[Mixture and Alligation Problems]]
 
|-
 
|-
 
|
 
|
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*[[Whole from Parts Problems]]
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*[[Find a Number Problems]]
 
|-
 
|-
 
|
 
|
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*[[First from Last Problems]]
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*[[Divide a Number Problems]]
 
|-
 
|-
 
|
 
|
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*Multiple quantities
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*Find a Quantity
 
|-
 
|-
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!Divide a quantity
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|
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:*[[How Much Problems]]
 
|-
 
|-
 
|
 
|
−
*Simple division
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:*[[How Many Problems]]
 
|-
 
|-
 
|
 
|
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*Proportional division
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:*[[Whole from Parts Problems]]
 
|-
 
|-
 
|
 
|
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*Simultaneous division
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:*[[First from Last Problems]]
 
|-
 
|-
 
|
 
|
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*Twins
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:*[[Multiple Quantities Problems]]
 
|-
 
|-
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!Purchase
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|
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*Divide a quantity
 
|-
 
|-
 
|
 
|
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*Equal amount
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:*[[Simple Division Problems]]
 
|-
 
|-
 
|
 
|
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*Unequal amount
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:*[[Proportional Division Problems]]
 
|-
 
|-
 
|
 
|
−
*[[Buy and Sell Problems]]
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:*[[Simultaneous Division Problems]]
 
|-
 
|-
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!Joint purchase
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|
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:*[[Twins]]
 
|-
 
|-
 
|
 
|
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*Too much and too little
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*Purchase
 
|-
 
|-
 
|
 
|
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*"If you give me"
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:*[[Purchase Equal Amount Problems]]
 
|-
 
|-
 
|
 
|
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*The found purse
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:*[[Purchase Unequal Amount Problems]]
 
|-
 
|-
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!Partial payment
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|
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:*[[Buy and Sell Problems]]
 
|-
 
|-
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![[Shared Work Problems]]
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|
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*Joint Purchase
 
|-
 
|-
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!Motion problems
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|
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:*[[Too Much and Too Little]]
 
|-
 
|-
 
|
 
|
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*[[Pursuit Problems]]
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:*[[Joint Purchase Problems - "if you give me"]]
 
|-
 
|-
 
|
 
|
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*[[Encounter Problems]]
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:*[[The found purse]]
 
|-
 
|-
 
|
 
|
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*To and from
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*[[Partial payment]]
 
|-
 
|-
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!Give and take
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|
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*[[Shared Work Problems]]
 
|-
 
|-
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!Series: Sums; Products
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|
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*Motion problems
 
|-
 
|-
−
!Ordering problems
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|
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:*[[Pursuit Problems]]
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|-
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|
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:*[[Encounter Problems]]
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|-
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|
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:*[[To and From Problems]]
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|-
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|
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*[[Give and Take Problems]]
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|-
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|
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*[[Boiling Problems]]
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|-
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|
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*Series
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|-
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|
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:*[[Sums]]
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|-
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|
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:*Products
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|-
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|
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*[[Ordering Problems]]
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|-
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|
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*[[Guessing Problems]]
 
|-
 
|-
 
!Geometrical problems
 
!Geometrical problems
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|-
 
|-
 
|
 
|
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:*Areas
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:*[[Area of a Figure]]
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|-
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|
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:*[[Volume of a Figure]]
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|-
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|
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:*[[Side of a Figure]]
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|-
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|
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:*[[Perimeter of a Figure]]
 
|-
 
|-
 
|
 
|
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:*Volumes
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:*[[Diagonal of a Figure]]
 
|-
 
|-
 
|
 
|
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:*Sides
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:*[[Height of a Figure]]
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|-
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|
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:*[[Point of a Figure]]
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|-
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|
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:*[[Divide a Figure]]
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|-
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|
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:*[[Transformation Problems]]
 
|-
 
|-
 
|
 
|
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|-
 
|-
 
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*Construction problems
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*[[Construction problems]]
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|-
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|
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*[[Gaging problems]]
 
|-
 
|-
 
|
 
|
−
*Gaging problems
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*[[Magic Square]]
  
 
|}
 
|}

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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