creativity in schools: mathematics, identity & motivation€¦ · creativity in schools:...

Creativity in Schools:Mathematics, Identity &

Motivation

Stephen Hegedus, PhDProfessor, STEM Education Depm

Director, Kaput Center

Sunday, September 23, 12

OVERVIEW1. Introduction: Do Schools Kill Creativity?

2. Robinson Report, 1999

3. My reflections on Creativity ... establishing a research program

4. Remarks from my own work - situating creativity in the context of Math Ed Research


DO SCHOOLS REALLY KILL CREATIVITY?

Interview with Sir Ken RobinsonEducation Today, Issue: 9 May 2009

“One of the problems is that the organisation of education in most countries was developed to meet the needs of an industrial economy and that’s simply not suited to the 21st century.”

“We educate people in a very linear way. The whole assumption is based on a 1950s model, whereby children have to be processed in an orderly fashion through the curriculum and eventually go to university, get a good degree and then they’ll get a job for life!


Luka Hegedus Age 7


He will retire in 2070

What will his world look like then?

Are we educating him for that future?


2000

233 MHz

2012

A6 1.02GHz (2 cores)


His identity is projected into the world

He can see things and be part of things invisible before

He positions himself relative to the world

He defines himself, his creativity and his education


1999, Robinson Report

National Advisory Committee on Creative and

Cultural Education

All Our Futures: Creativity, Culture

and Education

Sir Ken Robinson


This report argues that no education system can be world-class without valuing and integrating creativity

in teaching and learning, in the curriculum, in management and leadership and without linking this

to promoting knowledge and understanding of cultural change and diversity.


THE CHALLENGES FOR EDUCATION

The Economic ChallengeTo develop in young people the skills, knowledge and personal qualities they need for a world where work is undergoing rapid

and long-term change.


The Technological ChallengeTo enable young people to make their way with confidence in a world that is being shaped by technologies which are evolving

more quickly than at any time in history.


The Social ChallengeTo provide forms of education that enable young people to

engage positively and confidently with far-reaching processes of social and cultural change.


The Personal ChallengeTo develop the unique capacities of all young people, and to provide a basis on which they can each build lives that are

purposeful and fulfilling.


WHAT IS CREATIVITY?

Creativity is obviously to do with producing something original. But there are different views of what is involved in

this process and about how common the capacity for creativity is.


Sectoral DefinitionThe ‘creative arts’ are often contrasted with the sciences, which

tend to be thought of as uncreative.

It is equally fundamental to advances in the sciences, in mathematics, technology, in politics, business and in all areas of

everyday life.


Elite DefinitionIt is sometimes thought that only very rare people are creative

and that creativity involves unusual talents


Democratic DefinitionIn our view, all people are capable of creative achievement in

some area of activity, provided the conditions are right and they have acquired the relevant knowledge and skills


MY DEFINITION

Imaginative activity fashioned so as to produce outcomes that are both original and of value to

others.


MY DEFINITION

Imaginative activity fashioned so as to produce outcomes that are both original and

of value to others.


In teaching for creativity, teachers should aim to:

Encourage self expression that is oriented towards a given task


MOST IMPORTANT ISSUE IS IDENTITY OF THE SELF (AS A LEARNER)

Dynamics of social

The individual as a corporate entityCo-action: we guide and are guided by our collective self

Not just about self-efficacy but identification of self vis-a-vis others

How do we participate and represent our thinking to others?

How are we represented by and perceived of by others?


How do we participate and represent our thinking to others?

How are we represented by and perceived of by others?


John Henry Clippinger shows that we are, in fact, much less individualistic that we have been taught. Our personal identity, like our biological

identity, is derived from our relationships to others, knowing how to recognize social signals of trust and deceit; security comes not from

exclusion or narrow self-interest but a capacity to recognize and embrace mutual self-interest.

The hardwiring of our brains has predisposed us to derive a sense of self through our interactions with others; in isolation, a child's growth is

stunted, and those qualities we deem most distinctly human--language and empathy--fail to develop.

There is no such thing as the noble savage; we are a crowd of one.


“Being in their element takes them beyond the ordinary experiences of enjoyment or happiness. We're not simply taking about laughter, good

times, sunsets, and parties. When people are in their Element, they connect with something fundamental to their sense of identity, purpose, and well-being. Being there provides a sense of self-revelation, of defining who they really are and what they're really meant to be doing with their

lives.”

Ken Robinson, The Element


Educating our children means educating ALL our children ...


4th Grade Achievement Gap between White students and Black students

In 2007, Massachusetts

narrowed the gap between students - gains by 4th grade

Black students outpaced those of

White students

8th Grade Achievement Gap between White students and Black students

In 2007, the achievement gap

between 8th grade White and Black students was the

largest it has been in 15 years


Big Problems

1. Algebra Problem (RAND Report 2002)

2. Student motivation and alienation in the nation’s schools, especially urban secondary schools (National Research Council, 2003)

3. Widely acknowledged unfulfilled promise of technology in education, especially mathematics education (e.g., Cuban, 2001)

4. Problems for K-12 and Higher Education - the STEM problem


Big Issue #1

Algebra


100 years later it is necessary for all children to

learn algebra in order to graduate

from high school

At the end of the 19th century, barely 3% of the 18-year-old cohort was expected to

graduate from high school, so less than 2% were expected to take some form of

algebra Source: NCES, 1994


Result .... abrupt introduction of algebra in

high school

in superficial ways

resulting in high student failure and dropout Shopkeeper-Arithmetic


Why can we not do algebra sooner ... like, in the elementary grades ...?


Big Issue #2

Motivation and Alienation


so far the answer is: to incentivize students that math and science is

important in life ... well it does not work

problem of student motivation and alienation in the nation’s high schools,

especially urban high schools Source: NRC, 2003


MotivationExtrinsic motivation such as rewards can have an undermining

effect and decrease intrinsic motivation

Intrinsic motivation reflects the propensity for humans to engage in activities that interest them

Key factors for motivation but have been orthogonal to the development and instruction of content

Motivational strategies have been in the form of incentivizing students because it is fun


A new approach

Students can be motivated because they want to participate more fully in what their classroom is doing now

Link motivation and mathematics through participation

But before we say we just need new technology ....


SOME HISTORICAL PERSPECTIVES

The history of writing, from pictographs to alphabets, alphabets to the printing press, teaches us:

How the presence of a new technology transforms the practice and redefines the nature of that practice…


Clay

Paper

Papyrus

Biological mini-Screen

The development of portability of information and knowledge

As media became more malleable man’s efforts to communicate evolved in more expressive ways

Screen


FROM STATIC TO DYNAMIC MATHEMATICS

What happens with mathematics when it is transcribed/embedded in a digital media?

Are new mathematical phenomena waiting to be represented?

New representations transform mathematical thinking

Technology should not serve as a prosthetic device to prop up old practices but transform the educational landscape


Big Issue #3

Unfulfilled Role of Technology


what are we using technology for in our schools?

the widely acknowledged unfulfilled promise of technology in education.

Source: Cuban, 2001


2

Exhibit ES-1. Percentage of Students With Access to Computers for Mathematics Instruction in 2004–05

55%

74%

30%

44%

79%

36%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

In classroom In computer lab/

media center

Students do not

use computers in

mathematics

Grade 4

Grade 8

Exhibit reads: Fifty-five percent of fourth-graders and 44 percent of eighth-graders had access to computers in mathematics classrooms. Seventy-four percent of fourth-graders and 79 percent of eighth-graders had access to computers for mathematics in school computer labs or media centers. Thirty percent of fourth-graders and 36 percent of eighth-graders did not use computers in mathematics. Source: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment.

There was variability among states in students’ access to classroom computers in 2004–05. In

some states, 20 percent or more of fourth- and eighth-grade students were in mathematics

classrooms with computers; in other states, 60 percent or more of fourth- and eighth-graders

were in mathematics classrooms that had computers (Exhibit ES-2).

Perc

en

tag

e o

f S

tud

en

ts

Most 4th and 8th graders have access to computers

Source: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National

Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment.


4

Exhibit ES-3. Percentage of Students Whose Teachers Used Computers in Mathematics Instruction at Least Once a Week in 2004–05

9% 11%13%

32%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

To present mathematics

concepts

To post homew ork,

assignment, or schedule

information on the Web

Grade 4

Grade 8

Exhibit reads: The teachers of 9 percent of fourth-graders and 13 percent of eighth-graders used computers at least once a week to present mathematics concepts. The teachers of 11 percent of fourth-graders and 32 percent of eighth-graders used computers at least once a week to post homework, assignment, or schedule information on the Web. Source: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment.

• In mathematics classes, technology was more likely used by students than by their

teachers.

Thirty percent of fourth-grade students and 11 percent of eighth-grade students used computers

at least once a week to practice or review mathematics topics, and roughly 25 percent to 30

percent, respectively, used computers to extend mathematics learning with enrichment

activities (Exhibit ES-4). There was considerable variation in student use across states,

however. In some states, as many as 70 percent of fourth-grade students used computers at least

once a week for practice or review in mathematics; in others, fewer than 10 percent did.

Perc

en

tag

e o

f S

tud

en

ts

When they have frequent access they use computers for simple not conceptual tasks


Teachers are propping up their old teaching styles with new technology

Technology is not just a tool but a partner

to transform our classroom, to change the way we communicate, and to change the way

we interact

2


19th century curriculum

20th century methodologies

by the way we are in the ...

21st century


Big Issue #4

STEM is not a Pathway


In general, test-takers with higher SAT math scores are more interested in STEM majors than test-takers with lower SAT math scores.

Interest in STEM Majors by Test-Taker SAT Math Score

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

2005 2006 2007 2008

600 orHigher

550 to590

AllTest-Takers

500 to540

400 to490

390 orLower

However, also in general, test-takers from higher performing MCAS schools are less interested in STEM majors than test-takers from lower performing MCAS schools.

Interest in STEM Majors by School 10th Grade Math MCAS Level

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

2005 2006 2007 2008

Test-Takersfrom Schoolswith Low 10thGrade MathMCAS Scores

Test-Takersfrom Schoolswith Middle-Low 10thGrade MathMCAS Scores

All Test-Takers

Test-Takersfrom Schoolswith Middle-High 10thGrade MathMCAS Scores

Test-Takersfrom Schoolswith High 10thGrade MathMCAS Scores

Page 3 DRAFT

Test takers with higher SAT scores are more interested in STEM majors

Analyzed and prepared by the UMass Donahue Institute based on College Board SAT & SAT II Registration Questionnaire responses by MA public school test-takers from 2005-2008 graduation cohorts.


Need to put the student back at the

center of the classroom

Curriculum and assessment have dominated the classroom

Important but need to refocus

1


Results of large Research and Development Projects at the Kaput Center

1. SimCalc MathWorlds

2. Haptics Project


SIMCALC PROJECTSSimCalc MathWorlds(R) is

used by over 15,000 students in 12

countries

Integrates dynamic visualization with

wireless connectivityto transform

communication in the classroom

56


Stephen Hegedus, PhD (PI)Professor, Mathematics Education

Director, Kaput CenterUMass Dartmouth

Sara DaltonResearch Assistant

Math Ed PhD CandidateUMass Dartmouth

Arden BrooksteinResearch Assistant


John Tapper, PhDResearch Manager

UMass Donahue Institute

Eric Heller, PhDDirector, Research &

EvaluationUMass Donahue Institute


SimCalc MathWorlds(r)


Studies in MA showed that SimCalc can

impact motivation as well as learning

through participation INSIDE the classroom

Changes in modes of expressionGesture, Talk, Action ...

New levels of engagement


Instruments

Mathematics Algebra 1 Content Test 1 & 2

Student Attitude Survey

Teacher Background Survey

Teacher Attitude Survey

SimCalc Teacher Daily Logs

Logs measuring implementation (for measuring fidelity)


Gains by each class


Student Attitude SurveyFour Constructs:

1. Positivity towards math and school (α=.717)• “I think mathematics is important in life.”

2. Working collaboratively & related affect (α = .692)• “I sometimes feel nervous talking out-loud in front

of my classmates.”

3. Working privately (α = .727)• “I learn more about mathematics working on my

own.”

4. Technology (α = .674)• “Technology can make mathematics easier to

understand.”

66


Content x Attitude

No significant correlations for the comparison group


CASE STUDIESClassroom from each group

demonstrating high pre-post test student gains

Veteran teacher and well-experienced teacher (5 yrs) - both used SimCalc but the comparison is not in this study.


No significant correlations for the comparison group


Cluster Randomized Study

Algebra 1 Pilot Study 1 (Year 1)6 districts - total sample: 48 classesN(classrooms) = 14 (7 Treatment & 7 Control) n(students) = 254 (136 Treatment & 130 Control)SimCalc replacement curriculum for 8-12 weeks

Algebra 2 Pilot Study 3 (Year 2)3 districtsN(classrooms) = 7 (4 Treatment & 3 Control) n(students) = 149 (78 Treatment & 71 Control)SimCalc replacement curriculum for 6-8 weeks

Algebra 1 Main Study 2 (Year 2) & Algebra 2 Main Study 4 & 5 (Years 3 & 4)7 districts - total sample: 60 classesN(classrooms) = 28 (14 Treatment and 14 Control)n(students) ≈ 700 (350 Treatment; 350 Control)Algebra 1 SimCalc replacement curriculum for 8-12 weeksAlgebra 2 SimCalc replacement curriculum for 6-8 weeks


Change on M1 & M2 Items

72

n=268

n=298 n=31

n=24

Experimental GroupSimCalcComparison

Me

an C

han

ge f

or

M1

& M

2 I

tem

s

2

1

0

School 1

Class 65 - SimCalc

Class 80 - Comparison

5

4

3

2

1

0

Change in M2 Score

Change in M1 Score


Tes

t 2

Gai

n4

2

0

-2

-4Class

TC

Group

Algebra 1


Free or Reduced Lunch

Denied Free or Reduced Lunch

Tes

t 2

Gai

n1.25

1.00

0.75

0.50

0.25

0.00

TC

Group


Test 2 M2 GainTest 2 M1 Gain

Mea

n

0.50

0.25

0.00

TC

Group


TC

Mea

n T

est

2 G

ain

2

1

0

Honorsnon-Honors

Class Level


Gain

3

2

1

0

-1

-2

-3

-4

-5Class

TC

Group

Algebra 2


SimCalcComparison

Gai

n2

1

0

M2 GainM1 Gain


TC

Mea

n G

ain

4

3

2

1

0

Honorsnon-Honors

Class Level

79


Denied Reduced Lunch

Reduced LunchFree Lunch

Gain

2

1

0

TC

Group

SAVE OUTFILE='/Users/kaputcenter/Desktop/AY0910 Student Content Test Data from wiki.sav' /COMPRESSED.RECODE ses ('D'=0) ('F'=1) ('R'=1) INTO Free_Red.EXECUTE.SORT CASES BY group#.SPLIT FILE LAYERED BY group#.FREQUENCIES VARIABLES=ses Free_Red /ORDER=ANALYSIS.

Frequencies

Page 14

80


Gain

3

2

1

0

-1

-2

-3

AsianAfrican American

WhiteOther

Hispanic

TC

Group

SORT CASES BY group#.SPLIT FILE LAYERED BY group#.FREQUENCIES VARIABLES=ethnicity ethnicity_2 /ORDER=ANALYSIS.

Frequencies

Page 25

81


ORRDHSNBHSWaHSWeHSGNBV

Cha

nge

in C

onfid

ence

1.00

0.75

0.50

0.25

0.00

-0.25

TC

Group

82


Impact on student interactionUsing the physical structure of the classroom to naturally vary students’ mathematical work and thinking

Focus student attention from single functions to parameterized families of functions

Provide opportunity for generalization and expose common thought-patterns (including errors in a positive way)

Students personally identify themselves with their work

Math and social experience are deeply intertwined

Teachers play in a central role in orchestrating the activity of the whole class (effective questioning part of our curriculum materials)

It can impact motivation and attitude


http://www.kaputcenter.umassd.edu/products/curriculum_new/




WHAT DO TEACHERS DO?focus on reasoning across multiple representations

Perform procedures/solve routine problems


DYNAMIC HAPTIC GEOMETRY(2009 - 2013)

Research and Evaluation on Education in Science and Engineering Program#REC-0835395

Stephen Hegedus (PI): Kaput CenterNick Jackiw (Co-Pi): KCP Technologies, Inc.


Stephen Hegedus, PhD (PI)Professor, Mathematics Education

Director, Kaput CenterUMass Dartmouth

Ryan RobidouxResearch Associate

Math Ed Doctoral StudentUMass Dartmouth

James BurkeResearch Assistant


Nicholas Jackiw (Co-PI)Chief Operating OfficerKCP Technologies, Inc.

Beste Güçler, PhDAssistant Professor,

Mathematics EducationUMass Dartmouth

Jonathon Brooks & Matthew LitwinSenior Software Engineers

KCP Technologies, Inc.


MULTI-MODAL ENVIRONMENTS

Support student interaction and reasoning using multiple communication channels

Haptic technologies: physical force-feedback & touch

Dynamic geometry: dynamic visuals


RESEARCH GOALS

What are the affordances of haptic technology in elementary classrooms?

Development of multi-modal learning experiences


PARTICIPANTS

Seven fourth-grade classrooms

Middle-class elementary school in the southeast region of Massachusetts

150 students, working in groups


MULTI-MODAL ENVIRONMENTS

PHANTOM Omni® Haptic Device

SketchExplorer on the iPad


SKETCHEXPLORER ON THE IPAD• Multi-touch environment, little to no interface

• Compatible with Geometer’s Sketchpad® sketches

• Geometric Transformations

• Estimation

• Measurement

• Complex procedures


Conclusion


CREATIVITY AND SCHOOLSIt exists in schools - how it exists is problematic

It exists in the dialogical and social relationships between key players in schools (student to student, student to teacher,

teacher to administrator in terms of ‘offered’ infrastructure)

It is not an it but a form of expression

Mediated by technology through representational forces

Is a process of identification of the self in a meaningful way that can impact learning and motivation

Is a personal revelation of self development and positioning in the world


Need to understand under what conditions we see effect – not one-size fits all which is a reaction to the

mile-wide inch-deep metaphor which is based in assessment vs a deep epistemological treatment (21st century mathematics education) with pedagogically

flexible teachers


His identity is projected into the world

He can see things and be part of things invisible before

He positions himself relative to the world

He defines himself, his creativity and his education

3


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