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.'''
 +
|}
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{|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;"
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|-
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|'''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)
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|}
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Van Egmond offers some guidelines for such a project, saying:
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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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|'''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>
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'''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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|}
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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]]
 
|-
 
|-
 
|
 
|
−
*[[Find the Price Problems]]
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:*[[Find the Amount Problems]]
 
|-
 
|-
 
|
 
|
−
*[[Find the Amount Problems]]
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:*[[Tare and Tret Problems]]
 
|-
 
|-
 
|
 
|
−
*[[Tare and tret problems]]
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*Exchange Problems
 
|-
 
|-
−
!Exchange Problems
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|
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:*[[Currencies Problems]]
 
|-
 
|-
 
|
 
|
−
*Currencies
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:*[[Measures Problems]]
 
|-
 
|-
 
|
 
|
−
*Measures
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*[[Payment Problems]]
 
|-
 
|-
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!Payment Problems
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|
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*Barter Problems
 
|-
 
|-
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!Divide a Number
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|
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:*[[Cash Barter Problems]]
 
|-
 
|-
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!Find a Quantity
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|
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:*[[Simple Barter Problems]]
 
|-
 
|-
 
|
 
|
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*How much or how many?
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:*[[Compound Barter Problems]]
 
|-
 
|-
 
|
 
|
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*Whole from parts
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*Interest and Discount Problems
 
|-
 
|-
 
|
 
|
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*First from last
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:*[[Find the Interest Problems]]
 
|-
 
|-
 
|
 
|
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*Multiple quantities
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:*[[Find the Time Problems]]
 
|-
 
|-
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!Divide a quantity
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|
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:*[[Find the Fund Problems]]
 
|-
 
|-
 
|
 
|
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*Simple division
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:*Simple discount
 
|-
 
|-
 
|
 
|
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*Proportional division
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:*[[Compound Interest Problems]]
 
|-
 
|-
 
|
 
|
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*Simultaneous division
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:*Compound discount
 
|-
 
|-
 
|
 
|
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*Twins
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*[[Rent Problems]]
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!Purchase
 
 
|-
 
|-
 
|
 
|
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*Equal amount
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*Partnership Problems
 
|-
 
|-
 
|
 
|
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*Unequal amount
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:*[[Partnership Problems - for the Same Time]]
 
|-
 
|-
 
|
 
|
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*Buy and sell
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:*[[Partnership Problems - for Different Times]]
 
|-
 
|-
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!Joint purchase
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|
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*[[Mixture and Alligation Problems]]
 
|-
 
|-
 
|
 
|
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*Too much and too little
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*[[Find a Number Problems]]
 
|-
 
|-
 
|
 
|
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*"If you give me"
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*[[Divide a Number Problems]]
 
|-
 
|-
 
|
 
|
−
*The found purse
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*Find a Quantity
 
|-
 
|-
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!Partial payment
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|
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:*[[How Much Problems]]
 
|-
 
|-
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!Shared work
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|
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:*[[How Many Problems]]
 
|-
 
|-
−
!Motion problems
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|
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:*[[Whole from Parts Problems]]
 
|-
 
|-
 
|
 
|
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*Pursuit
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:*[[First from Last Problems]]
 
|-
 
|-
 
|
 
|
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*Encounter
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:*[[Multiple Quantities Problems]]
 
|-
 
|-
 
|
 
|
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*To and from
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*Divide a quantity
 
|-
 
|-
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!Give and take
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|
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:*[[Simple Division Problems]]
 
|-
 
|-
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!Series: Sums; Products
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|
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:*[[Proportional Division Problems]]
 
|-
 
|-
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!Ordering problems
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|
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:*[[Simultaneous Division Problems]]
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|-
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|
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:*[[Twins]]
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|-
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|
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*Purchase
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|-
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|
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:*[[Purchase Equal Amount Problems]]
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|-
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|
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:*[[Purchase Unequal Amount Problems]]
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|-
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|
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:*[[Buy and Sell Problems]]
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|-
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|
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*Joint Purchase
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|-
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|
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:*[[Too Much and Too Little]]
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|-
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|
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:*[[Joint Purchase Problems - "if you give me"]]
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|-
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|
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:*[[The found purse]]
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|-
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|
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*[[Partial payment]]
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|-
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|
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*[[Shared Work Problems]]
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|-
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|
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*Motion problems
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|-
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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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|-
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|
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:*[[Diagonal of a Figure]]
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|-
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|
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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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:*Volumes
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:*[[Transformation Problems]]
 
|-
 
|-
 
|
 
|
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:*Sides
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*[[Triangulation Problems]]
 
|-
 
|-
 
|
 
|
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*Triangulation problems
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*[[Construction problems]]
 
|-
 
|-
 
|
 
|
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*Construction problems
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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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