Creativity in Schools: Mathematics, Identity & Motivation€¦ · Creativity in Schools:...
Transcript of Creativity in Schools: Mathematics, Identity & Motivation€¦ · Creativity in Schools:...
Creativity in Schools:Mathematics, Identity &
Motivation
Stephen Hegedus, PhDProfessor, STEM Education Depm
Director, Kaput Center
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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
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
Sunday, September 23, 12
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!
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Luka Hegedus Age 7
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He will retire in 2070
What will his world look like then?
Are we educating him for that future?
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2000
233 MHz
2012
A6 1.02GHz (2 cores)
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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
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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
Sunday, September 23, 12
1999, Robinson Report
National Advisory Committee on Creative and
Cultural Education
All Our Futures: Creativity, Culture
and Education
Sir Ken Robinson
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Elite DefinitionIt is sometimes thought that only very rare people are creative
and that creativity involves unusual talents
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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
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MY DEFINITION
Imaginative activity fashioned so as to produce outcomes that are both original and of value to
others.
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MY DEFINITION
Imaginative activity fashioned so as to produce outcomes that are both original and
of value to others.
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In teaching for creativity, teachers should aim to:
Encourage self expression that is oriented towards a given task
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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
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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?
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How do we participate and represent our thinking to others?
How are we represented by and perceived of by others?
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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.
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“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
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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
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Educating our children means educating ALL our children ...
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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
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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
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Big Issue #1
Algebra
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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
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Result .... abrupt introduction of algebra in
high school
in superficial ways
resulting in high student failure and dropout Shopkeeper-Arithmetic
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Why can we not do algebra sooner ... like, in the elementary grades ...?
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Big Issue #2
Motivation and Alienation
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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
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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
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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 ....
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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…
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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
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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
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Big Issue #3
Unfulfilled Role of Technology
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what are we using technology for in our schools?
the widely acknowledged unfulfilled promise of technology in education.
Source: Cuban, 2001
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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.
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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
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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
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19th century curriculum
20th century methodologies
by the way we are in the ...
21st century
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Big Issue #4
STEM is not a Pathway
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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.
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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
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Results of large Research and Development Projects at the Kaput Center
1. SimCalc MathWorlds
2. Haptics Project
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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
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Stephen Hegedus, PhD (PI)Professor, Mathematics Education
Director, Kaput CenterUMass Dartmouth
Sara DaltonResearch Assistant
Math Ed PhD CandidateUMass Dartmouth
Arden BrooksteinResearch Assistant
Math Ed PhD CandidateUMass Dartmouth
John Tapper, PhDResearch Manager
UMass Donahue Institute
Eric Heller, PhDDirector, Research &
EvaluationUMass Donahue Institute
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SimCalc MathWorlds(r)
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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
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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)
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Gains by each class
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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
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Content x Attitude
No significant correlations for the comparison group
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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.
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No significant correlations for the comparison group
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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
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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
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Tes
t 2
Gai
n4
2
0
-2
-4Class
TC
Group
Algebra 1
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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
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Test 2 M2 GainTest 2 M1 Gain
Mea
n
0.50
0.25
0.00
TC
Group
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TC
Mea
n T
est
2 G
ain
2
1
0
Honorsnon-Honors
Class Level
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Gain
3
2
1
0
-1
-2
-3
-4
-5Class
TC
Group
Algebra 2
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SimCalcComparison
Gai
n2
1
0
M2 GainM1 Gain
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TC
Mea
n G
ain
4
3
2
1
0
Honorsnon-Honors
Class Level
79
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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
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80
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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
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ORRDHSNBHSWaHSWeHSGNBV
Cha
nge
in C
onfid
ence
1.00
0.75
0.50
0.25
0.00
-0.25
TC
Group
82
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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
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WHAT DO TEACHERS DO?focus on reasoning across multiple representations
Perform procedures/solve routine problems
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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.
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Stephen Hegedus, PhD (PI)Professor, Mathematics Education
Director, Kaput CenterUMass Dartmouth
Ryan RobidouxResearch Associate
Math Ed Doctoral StudentUMass Dartmouth
James BurkeResearch Assistant
Math Ed PhD CandidateUMass Dartmouth
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.
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MULTI-MODAL ENVIRONMENTS
Support student interaction and reasoning using multiple communication channels
Haptic technologies: physical force-feedback & touch
Dynamic geometry: dynamic visuals
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RESEARCH GOALS
What are the affordances of haptic technology in elementary classrooms?
Development of multi-modal learning experiences
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PARTICIPANTS
Seven fourth-grade classrooms
Middle-class elementary school in the southeast region of Massachusetts
150 students, working in groups
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MULTI-MODAL ENVIRONMENTS
PHANTOM Omni® Haptic Device
SketchExplorer on the iPad
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SKETCHEXPLORER ON THE IPAD• Multi-touch environment, little to no interface
• Compatible with Geometer’s Sketchpad® sketches
• Geometric Transformations
• Estimation
• Measurement
• Complex procedures
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Conclusion
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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
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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
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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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