Mathematics and Society - OS X Lion Server

INSTQUM~NTSWIT~ CLRSSClassification is important in mathematics,biology, chemistry, music and many otherfields of study.In mathematics numbers areclassified as whole numbers, rational numbers,irrational numbers,.•• and geometric figuresare classified as polygons, polyhedra, curves,squares, '"Biologists classify plants andanimals and chemists classify the elements andMATHEMATICALLY,'IOU l-ll\V£ MORECLA~'" 'l-lA\Il I DO,compound substances. Music and instruments ,-----,each have their classifications. Althoughclassification is used in many subject areas~,----;===~~~==JC::~the study of classes, often called sets, is abranch of mathematics and logic.(BUT '/OU PLAYSUc.t\ Bt:AUTIF'ULMUSIC,RECTA\IlGLEPARALLELOGRAMQUADRJLAT£R.ALAttributes such as number, size, color or shape can be used to classify objects.Students can decide how to classify a large group of objects, determine relationshipsbetween the sets (the class of whole numbers is a subset of the class of rational numbers)and operate on the sets (what numbers belong to both the set of prime numbers andthe set of odd numbers?).(Focussing on properties or attributes allows for more flexible or creative problemsolving. If an object is unfamiliar to someone, its name alone does not help describethe object. A list of its properties will help someone visualize the object. Also,if you need an object that is not available, a list of its properties could suggest asuitable replacement.(Trombones can play some cello parts and have been used as "substitutes"in small orchestras.)A collection of musical instruments can become that large group that needs to beclassified by students.Most people tend to think about only the names of the instruments,but their use is really a function of their many attributes.The activity onthe next page suggests that students explore the classification of instruments and howthese classes relate to each other.Further Sources: Learning Logic, Logical Games, Vol. I (First Years in Mathematics)by Z.P. Dienes and E.W. Golding, New York: Herder and Heider, 1971Describingmatics andversity of& Classifying, Unit 3 (Minnemast) by Minnesota Mathe-Science Teaching Project, Minneapolis, Minnesota: Uni­Minnesota, 1967('274