Moving between discourses: from learning-as-acquisition to learning-as-participation

Moving between discourses:from learning-as-acquisition to learning-as-participation AAPT & PERC bridging session Ann Arbor, 29 September 2008 Anna Sfard The University of Haifa &The Michigan State University

Answer: This is the Dove of Peace Question: What is this? 4/1/2014 2

Question: What is happening here? Question: What is this? 4/1/2014 3

Answer: People are moving according to certain rules Question: What is happening here? Question: What is it? 4/1/2014 4

conclusion • It changes what we see How we talk about things matters: • and may thus change what we do

Meta-question on learning Howto talkaboutlearning mathematic(physics)?

Basic assumptions • How we talk about learning matters • We need more than one way of talking

Meta-question on learning - refined How should I Howto talkaboutlearning mathematic (physics)? so as to answer my questions?

an exampleof the questions I ask

Learning mathematics in school:The case of negative numbers Study with Sharon Avgil and her 7th grade students

Learning mathematics in school:The case of negative numbers Study with Sharon Avgil and her 7th grade students Whenever I say mathematics, you think physics, ok? and when I say negativenumber, you think force, ok?

Some facts about the study • The teacher opted forre-inventionwithconcrete models • Expected difficulty: the rule for “minus times minus” • The students re-invented adding and subtracting signed numbers • First difficulty: the rule for “plus times minus”

When asked about 2 ּ (-5) Roi:2 times -5 is -10 because 5 is the bigger number Adva:it is like 2 times -5, so it is -5 plus -5. It gives -10

And the class followed… Roi The teacher asked about6 ּ (-2) Vladis: Me too: Plus 12 because 6 is bigger. Teacher: Why this rule? Yoash: Because this is what Roi said. Teacher: But Roi did not explain … Leah: The bigger is the one that decides.

…and Roi concluded Roi: I am more charismatic… I managed to influence them all.

And when the teacher presented her argument • The childrenopenlydisbelieved • Especially when the teacher tried to explain the rule “minus times minus is plus” • And they kept beingskeptical all along the way

example of Questionabout learningI am asking in my research What went wrongin this classroom? What could/should be done differently?

Plan of this talk • Two ways of talking about learning:acquisitionist & participationist B. Commognition as a special case of participationist approach: School learning as developing discourses C. Applying commognitive discourse: back to th question on learning negatives Aalborg Nov 2006

If learning means change, what is it that changes when a person learns mathematics (physics)?

Acquisitionist answer What is it that changeswhen one learns? One’s knowledge / concepts / mental schemas which one acquires/ constructs

Acquisitionist answer Participationist answer What is it that changeswhen one learns? One’sparticipationin anactivity, form of life, practice… One’s knowledge / concepts / mental schemas which one acquires/ constructs

Examples of historically established human activities: cooking, dressing, talking, drawing, making/using tools… uniquely human learning: individualization of patterned, historically established ways of doing things 4/1/2014 22

Individualization: development of one’s agency as a participant in a given form of doing uniquely human learning: individualization of patterned, historically established ways of doing things 4/1/2014 23

Just to remind: If learning means change, what is it that changes? ACQUISITIONIST answer: Student’sconceptions PARTICIPATIONIST answer: Form of activity (way of performing some well defined tasks) There is much space in learning for contingency and for human agency individual learning is a matter of human biological makeup and external constraints 4/1/2014 24

Acquisitionism vs. participationism – a number of remarks • What’s the relation between them?They are incommensurable, not incompatible • Why both are useful?Each has its relative advantages and weaknesses • Which to choose?Depends on the nature of one’s enterprise

My choice:participation metaphor and as I’ll try to show, this helps to answer my questions Why?Because it leaves more space forhuman agency

Fotnote 1: Sources of ideas not just Vygotsky but also Wittgenstein 4/1/2014 28

This approach shows family resemblance to that of Rom Harré(discursive psychology) and Michael Halliday(functional linguistics) 4/1/2014 29

Question 1 School learningmeans a change inthinking. Butwhat is thinking? 4/1/2014 30

participationists:uniquely human skills and abilities develop by individualization of historically established collective activities Question: which collective activity is the best candidate for the precursor of thinking? Taking participationism one step further Communication! 4/1/2014 31

participationists:uniquely human skills and abilities develop by individualization of historically established collective activities Taking participationism one step further Commognition= communication + cognition conclusion: Human thinking is an individualized form of inter-personal communication Communication does not have to be verbal 4/1/2014 32

Question 2 What is mathematics (physics)?

So, what is mathematics (or history,or physics, or..)? mathematics way of thinking physics physics mathematics a discourse 4/1/2014 34

What makes discourses of mathematics (physics) distinct?

keywords and their use Threefunction derivative triangle Visual mediators symbols ¼ x2 dx/dy  Discourses ofmathematics are made distinct by  endorsed narratives • “2+2=4”, “(x2)’ = 2x” • “In triangle, equal sides face equal angles.”  routines how to look, how to convince, how to inscribe, how to prove, etc. 

keywords and their use Threefunction derivative triangle symbols ¼ Ω ρ x2 dx/dy Visual mediators symbols ¼ x2 dx/dy  Discourses of mathematicsare made distinct by physics Force Big Bang quark energy work  endorsed narratives • “2+2=4”, “(x2)’ = 2x” • “In triangle, equal sides face equal angles.” • E=mc2F=ma • “the loss in weight of an object immersed in a fluid …”  routines how to look, how to convince, how to inscribe, how to prove, etc. 

But can discourse be all there is to mathematic? For example, what is the number (negative or otherwise)? Number is a discursive construct people created to communicate about the world. It is to be found in the discourse, not in the world Is it any different for force?

Question 3 And what does it mean to learnmathematics(physics)?

mathematics (physics) a discourse learning mathematics [physics] developing the discourse What does it mean to learn mathematics (physics)? Important! We’re in thebusiness of defininghere, not of finding the truth about the world!

criteria for assessing the quality of the definitions • coherence consistency with other elements of the system • adequacygood fit with the informal use of the word • operationalitycommunicational effectiveness • usefulnesscapability to bring abut new insights & re-/dis-/solve old quandaries 

Questionabout learning What went wrongin this classroom? What could/should be done differently?

Alternatively: What was the nature of the expected learning? Was it possible for this learning to happen by re-invention?

Two levels of learning Example: one already knows whatfunctionis and now learns about properties of differenttypes of functions • object – level • Adding endorsed narratives about existing objects or narratives, built according to existing meta-rules

Two levels of learning Example:transition fromAristotelian toNewtonian discourse on force and motion Example:transition from the discourse onunsigned numbersto the one onsigned numbers • meta – level • adding new objects • changing meta-rules • changing use of words • object – level • Adding endorsed narratives about existing objects or narratives, built according to existing meta-rules

New objects negative numbers  New meta-rule: What is the source of mathematical truth? Consistency with formerly endorsed narratives  From unsigned to signed numbersWhat changes in the discourse? Meta-level learning results in discourse incommensurable with the previous one

What was the nature of the expected learning? Was it possible for this learning to happen by re-invention?

Just to remind, in our study the teacher tried to honor the principle of inventive learning: The learners should have as much agency over their learningas possible

Is there room for inventive learning? object-level learning can happen by (re-)invention meta-level learning Not that simple! The nature of discourse change: logically necessary The nature of the required meta-discursive change: contingent

Moving between discourses: from learning-as-acquisition to learning-as-participation