ESH 250 Lecture Notes - Lecture 8: Australian Curriculum, Numeracy, Inductive Transfer
9 Jun 2018
School
Department
Course
Professor
Reading
---Access&the Australian&Curriculum:&Mathematics.&For&each&of&the&year&levels,&
read&what&the&descriptors&say&about&understanding&and&fluency.&Visit&
the ACARA&site that&contains&further&information&about&all&the&proficiencies.
---Siemon&et&al&(2015)&Chapter&4,&'Thinking&mathematically'&
---McIntosh,&A.&(2002) principles&for&improving&numeracy&in&schools
•
Introduction
You&should&have&achieved&the&following&learning&outcomes:
---Apply&strategies&to&solve&a&range&of&problems
---Distinguish&between&understanding,&fluency,&problem&solving&and&
reasoning
---Identify&the&difference&between&a&problem&and&an&exercise
---Identify&the&difference&between&open&and&closed&questions&and&the&
purpose&of&questioning
•
Understanding
•
---Students&build&a&robust&knowledge&of&adaptable&and&transferable&
mathematical&concepts.&They&make&connections&between&related&concepts&
and&progressively&apply&the&familiar&to&develop&new&ideas.&They&develop&an&
understanding&of&the&relationship&between&the&why&and&the&how&of&
mathematics.&Students&build&understanding&when&they&connect&related&ideas,&
when&they&represent&concepts&in&different&ways,&when&they&identify&
commonalities&and&differences&between&aspects&of&content,&when&they&
describe&their&thinking&mathematically&and&when&they&interpret&mathematical&
information&(ACARA,&2016)
Fluency
---Students&develop&skills&in&choosing&appropriate&procedures,&carrying&out&
procedures&flexibly,&accurately,&efficiently&and&appropriately,&and&recalling&
factual&knowledge&and&concepts&readily.&Students&are&fluent&when&they&
calculate&answers&efficiently,&when&they&recognise&robust&ways&of&answering&
questions,&when&they&choose&appropriate&methods&and&approximations,&
when&they&recall&definitions&and®ularly&use&facts,&and&when&they&can&
manipulate&expressions&and&equations&to&find&solutions&(ACARA,&2016).
•
Problem6Solving•
---Students&develop&the&ability&to&make&choices,&interpret,&formulate,&model&
and&investigate&problem&situations,&and&communicate&solutions&effectively.&
Students&formulate&and&solve&problems&when&they&use&mathematics&to&
represent&unfamiliar&or&meaningful&situations,&when&they&design&
investigations&and&plan&their&approaches,&when&they&apply&their&existing&
strategies&to&seek&solutions,&and&when&they&verify&that&their&answers&are&
reasonable&(ACARA,&2016).
Reasoning•
---Students&develop&an&increasingly&sophisticated&capacity&for&logical&thought&
and&actions,&such&as&analysing,&proving,&evaluating,&explaining,&inferring,&
justifying&and&generalising.&Students&are&reasoning&mathematically&when&they&
explain&their&thinking,&when&they&deduce&and&justify&strategies&used&and&
conclusions&reached,&when&they&adapt&the&known&to&the&unknown,&when&they&
transfer&learning&from&one&context&to&another,&when&they&prove&that&
something&is&true&or&false&and&when&they&compare&and&contrast&related&ideas&
and&explain&their&choices&(ACARA,&2016).
---According&to&AAMT's&top&drawer&resource,&reasoning provides&the&
opportunity&for&students&to&engage&in&mathematics&in&a&thought-provoking&
and&intellectual& way.
---Good&teaching&of&reasoning&involves&embedding&it&in&all&mathematics&
classes.&Like&the&other&proficiencies&(understanding,&problem-solving&and&
fluency),&reasoning&is&at&the&heart&of all mathematics&learning&and&teaching.
---Some&key&elements&of&good&teaching&of&reasoning&include:&challenging&all&
students&to&reason,&using&effective&questioning&to&prompt&reasoning,&
encouraging&deep&thinking,&making&reasoning&a&routine&element&of&every&
class,&making&mathematical&connections.
Teaching6Through6Problem6Solving
---Students&learn&mathematics&through&real&contexts,&problems,&situations&
and⊧&skills&emerge&through&working&through&the&problems.
---Must&begin&where&students&are&at
---The&engaging&aspect&of&the&problem&must&be&due&to&the&mathematics&that&
the&students&are&to&learn
---It&must&require&justifications&and&explanations&for&answers&and&methods
•
Teaching6About6Problem6Solving
---Involves&teaching&students&how&to&problem&solve,&including&teaching&the&
problem&solving&process&and&problem&solving&strategies.
•
Polya's646step6Problem6Solving6Process
---As&you&teach&through&problem&solving,&use&the&steps&to&guide&your&
students.
---1:&Understand&the&problem&(what&is&the&problem&about?)
---2:&Devise&a&plan&(What&strategy&will&you&use?)
---3:&Carry&out&the&plan&(Implement&your&strategy)
---4:&Look&back&(determine&whether&or¬&your&answer&makes&sense,&does&it&
answer&the&problem?)
•
What6is6a6Problem?
---“Any&task&or&activity&for&which&the&students&have&no&prescribed&or&
memorised&rules&or&methods,&nor&is&there&a&perception&by&students&that&there&
is&a&specific&‘correct’&solution&method”&(p.&33,&Van&de&Walle,& et&al.,&2010)&
---There&is&a&goal&to&be&reached
---An&obstacle&prevents&ready&solution&
---The&solver&is&motivated&to&reach&a&solution
---A&question&for&which&you&do¬&immediately&know&the&answer,&or&how&to&
obtain&it&
---What&is&a&problem&for&one&person,&may¬&be&a&problem&for&another
•
Benefits6of6Problem6Solving
---Focuses&students’&attention&on&ideas&and&sense&making&
--- Develops&student&confidence&
---Provides&a&context&
---Allows&an&entry&point&for&a&range&of&students&
---Allows&for&extensions&and&elaborations&
---Engages&students
•
Week$8-Developing$the$Proficiencies
Wednesday,& 2&August&2017
12:09&am
