MAE2240 Lecture Notes - Lecture 9: Lev Vygotsky, Egocentrism, Operant Conditioning
29 May 2018
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!WEEK!9!
Using!learning!theory!to!help!us!understand!how!children!learn!mathematics.!
!
Behaviourism!
Skinner:!Skinner!is!one!of!the!most!influential!thoerist!of!the!20th!century.!!
Skinners)box:!More!productive!to!study!observable!behaviour!rather!than!attempt!to!
discern!internal!mental!events,!such!as!feeling,!motives,!and!intentions,!which!are!not!easily!
seen.!!
Operant)conditioning:!proposed!that!behaviour!could!be!changed!by!the!use!of!
reinforcement,!given!directly!after!a!desired!response.!!
Thorndike:!asserted!that!mathematics!should!be!explicitly!taught!with!lots!of!drill!and!
practice.!!
Constructivist)theory:!according!to!piaget,!children!need!concrete!experienes!to!'construct;!
their!own!learning.!He!believed!that!children!learn!differently!to!adults!and!move!through!a!
series!of!stages!of!cognitive!development.!Egocentrism!is!central!to!his!theory,!that!is,!
young!children!can!only!understand!the!world!through!their!own!eyes.!!
!
Piagets!four!stages:!1.!sensorimotor!
!!!!!!!2.!preoperational!
!!!!!!!3.!concrete!operational!
!!!!!!!4.!formal!operations!
!
Equilibration!
Assimilation!and!accommodation,!we!adjust!our!ideas!to!make!sense!of!reality!
• Assimilation:!process!of!matching!external!reality!to!an!existing!cognitive!structure.!!
• Accommodation:!when!there's!an!inconsistency!between!the!learner's!cognitive!
structure!and!the!thing!being!learned!the!child!will!recognise!her!thoughts.!!
Piaget!in!maths!classroom:!children!can!engage!individually!in!discovering!mathematics,!
teacher!role!is!reduced.!Children!need!to!be!given!individual!attention!and!cannot!all!be!
treated!in!the!same!way,!children!should!not!be!taught!things!until!they!are!developed!
enough!intellectually!to!cope!with!them.!!
!!
Vygotsky!-!Socio!cultural!theory!
Children!can!think!for!themselves!rather!than!rote!learning,!culture!and!environment!is!how!
we!understand!the!world!around!is,!important!components!for!cognitive!development,!it!is!
a!historical!process,!it!is!social!in!nature,!it!is!enabled!by!the!idea!of!mediation!by!employing!
tools!of!language,!numbers!and!symbols.!!
*Children!construct!their!knowledge,!the!learning!is!mediated!-!tools,!language!plays!a!
central!role!in!mental!development,!learning!appears!twice;!social!and!personal!level.!!
!!
Participationist!view!of!learning!in!mathematics,!the!teacher!provides!opportunities!for!the!
learner!to!enter!in!mathematical!discourse!with!teachers,!other!learners,!and!themselves.!!
!
Document Summary
Using learning theory to help us understand how children learn mathematics. Skinner: skinner is one of the most influential thoerist of the 20th century. Skinners box: more productive to study observable behaviour rather than attempt to discern internal mental events, such as feeling, motives, and intentions, which are not easily seen. Operant conditioning: proposed that behaviour could be changed by the use of reinforcement, given directly after a desired response. Thorndike: asserted that mathematics should be explicitly taught with lots of drill and practice. Constructivist theory: according to piaget, children need concrete experienes to "construct; their own learning. He believed that children learn differently to adults and move through a series of stages of cognitive development. Egocentrism is central to his theory, that is, young children can only understand the world through their own eyes. Piaget in maths classroom: children can engage individually in discovering mathematics, teacher role is reduced.
