Cliff Konold

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Designing a Data Analysis Tool for Learners

Cliff Konold Scientific Reasoning Research
Institute University of Massachusetts, Amherst
The 33rd Carnegie Symposium on Cognition "Thinking
with Data" June 4-6, 2004
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Overview
1. General observations about designing for
students. 2. Research that informed many design
decisions. 3. Demonstrate tool
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Why all the interest in statistical reasoning?

• Why the effort to get it into the K-12
  curriculum?
• Why all the funded projects exploring statistical
  reasoning?
• Why this conference?

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Have you got any data?
Ease of collecting and sharing information and
mounds of data
New tools for handling and analyzing large data
sets
More use of data for forecasting, decision
making,consensus building
The Age of Accountability
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Its just the beginning
Ease of collecting and sharing information and
mounds of data
New tools for handling and analyzing large data
sets
More use of data for forecasting, decision
making,consensus building
The Age of Accountability
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What kind of data analysis tool do young students
need?
1. Where are they coming from how do they
reason about data?

• 2. Where are they headed how do we want
  them to reason about data?

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Bottom-up vs. Top-down Design
Novicesneed a tool that is designed from their
bottom-up perspectiveand can develop in various
ways into a full professional tool (not vice
versa). Biehler, 1995, p. 3
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Research Foci

Conceptual aspects of seeing data as signal vs.
noise Konold Pollatsek (2002) Different
perspectives students use in reasoning about
data Konold Higgins (2003) Konold, Higgins,
Russell, Khalil (2004) How experts vs. novices
visually scan graphs Khalil (MA thesis in
progress) How students compare two
groups Konold, Pollatsek, Well, Gagnon
(1997) How students describe and summarize data
Konold et al. (2002)
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What Kind of Tool Does Data Analysis Require?
Data analysis is a give-and-take conversation
between our hunches about some phenomenon and
what the data have to say about those hunches.
This sort of flexible exploration requires a tool
that lets us quickly change and refine our point
of view.
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Graph Construction Set Primitives not graph
types but ?
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Curriculum Collaborators
Connected Mathematics Project, Michigan State
University Mathematics in Context, University of
Wisconsin MathScape, Educational Development
Center MATH Thematics, University of Montana
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Design Objective for multiple users and uses
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Why This Approach?

• Experience of DataScope

A stripped down, professional tool.
Novicesneed a tool that is designed from their
bottom-up perspectiveand can develop in various
ways into a full professional tool (not vice
versa). Biehler, 1995, p. 3

• Results of research on how people reason about
  data

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Design Objective let students start where they
are
and build towards expertise
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Comparing Groups
Give students information about two groups and
ask them which group is better

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Backpack Weights Pre-Post Assembly
Based on these data, what would you conclude
about the question of whether or not the assembly
was effective?
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Modal Clump An Informal Average
A range of values located in the heart of a
distribution used to indicate what is typical,
usual, or average. Konold, Robinson, Khalil,
Pollatsek, Well, Wing, Mayr (2002)

The bulk of the backpacks weighed between 8 and
12.
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Comparing Using Modal Clumps
The cluster is between 8 and 12 before, and
between 8 and 12 after the assembly. I dont
think that there was that much of a ---Theres a
little bit.
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Locating and Comparing Centers of Aggregates
Khalil, in preparation
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Local Methods of Comparison
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Creating and Comparing Slices/Extremes
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Viewing and Comparing Distributions Aggregate
vs. Classifier
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What ideas in data analysis should figure
centrally in K-9 instruction?
Candidate Idea Data as an aggregate, a group
with emergent, distributional characteristics.

• What are the building blocks?
• How are they put together?

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Juan likes red
Half like red
Three like red
We said our favorite colors
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I looked at the chart of favorite colors
wondering why do I so clearly see the
information in the red column as being
interesting and important? Do the children see
it as I do? In the end, they seemed to attend
to names on the chart and the information that
was recorded about each person. They did not
seem to pull the individual pieces of information
together to share ideas about the data as a whole
i.e., as an aggregate. What do the data
reveal to the children?
Kindergarten teacher, DMI Casebook p. 28
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Seeing Data As
Pointer
Case value
Classifier
Aggregate
Konold, Higgins, Russell, Khalil (2003)
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Data as Pointer Data records point to the
entire event. Used, like string tied around
a finger, to aid recall.
In drawings, children depict not what they see
but what they know (Vygotsky, 1978 p. 112).
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Data as Pointer Example
Favorite colors of students in a kindergarten
class What does the graph show?
We learned English and Chinese colors.
My shirt is blue.
My favorite color is red.
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Data as Case Value
Associating a value with an individual case.
My favorite color is red.
With numeric data, used to identify
largest/smallest cases.
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Data as Case Value Example
Number of years your family has lived in town.
(Grades 3-4)
The longest someone lived in our town is 37
years. The shortest time is 0 years.
A lot of people have lived here for three years.
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Grade 2 From DMI Casebook
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Data as Classifier
Treating cases with similar values as the
same. Used to compare category frequencies
(most and least popular case-types).
A lot of people have lived here for three
years.
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Classifier vs. Case Value
Kindergarten
Teacher What does our survey tell us? Linda
That 3 people said yes. 2 people said no. 8
said super-duper...
Teacher So do you think someone else could tell
something about us from our survey? Rhea Yes,
they know most of us like computers a lot.
Amanda Not me, I said no. Melinda Me either, I
said I never played before. Rhea I said most of
us!
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From the classifier and case value perspectives,
data displays should facilitate accurate reading
of values.
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8th Grader, Val
I How do you think the researchers organized
the data? Val Probably in a graph, because
most adults like graphs instead of charts. But I
would probably do it in a chart just so it'd be
easier to read, so you can take a specific person
and know just about that person without having to
know about all the other people.
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Val, cont.
Because no matter if you gave it to me or
somebody else, they would always see
thatAngela would have 21 and 61.
But if you gave somebody just like this
scatterplot, I could say thathe had 30
something, and another person would say that he
had 40 something, because there's no marks.
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Data as Aggregate Example
Teacher So what does this data tell us about how
many years the families in our class have lived
in this town?
Kevin Most of the xs are between 0 and
6. Teacher How did you decide that? Kevin Its
the biggest clump.
About half of the families have been here between
0 and 6 years.
Teacher How many xs families are in that
clump? Anna Theres 11. Thats almost
half. Teacher Almost half of what? Anna Well
theres 23 altogether, and its almost half of
that.
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Funded by The National Science Foundation Grant
No. ESI-9818946
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High-Level Design Objectives
1. Accommodate novice and teacher goals -
design for multiple users and uses - base on
research of student thinking 2. A construction
set - build graphs from basic operators 3.
Capitalize on visual abilities (EDA)
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Progressive organization
By ordering, stacking, and separating data
icons, students gradually organize data to answer
their questions.
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Gounding in the Case
1. Case as physical object animation
2. Case-salient data structure
3. Case-icon as graph building block
4. Linking/highlighting
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Design Objective
1. Intuitive Operators 2. Accessible
binning 3. Animating between plot types
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Design Objective for multiple users and uses
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Tools should let students
begin where they are
Axis as label shelf Locate a case. Sight to axis
and read off value.
Values of individual cases
and progress towards expertise.
Axis as dimension Map values into a space.
Systematically scan space in search of patterns.
Features of aggregates