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The Research Basis for Graphing and Data
Analysis Software Tools to Support Instruction in Grades K–8
In our informationdriven world, the ability to graph and
interpret data is a critical skill. Every day, we are confronted
with graphs and tables conveying important information—from
election results to social trends to fluctuations in the stock
market. In school, students evaluate data not only in math
class but across a range of subject areas—whether analyzing
graphs of historical trends or charting results from a science
experiment.
Not surprisingly, statistical literacy has become "a
major goal of the school curriculum" (BenZvi, 2000).
Once the province of college curricula, statistics and data
analysis are now considered important topics in all grades,
beginning in the primary years. The National Council of Teachers
of Mathematics has recommended greater emphasis on data analysis
within the mathematics curriculum at every grade level, and
national standardized tests, such as the National Assessment
of Educational Progress, have increased the proportion of
test items in this area (Shaughnessy & Zawojewski, 1999).
However, data analysis remains a challenge for students (Lajoie
& Romberg, 1998). At the primary level, students typically
have trouble making the transition from concrete "object
graphs" to abstract representations of data. In later
elementary and middle school, they often fail to develop the
deep conceptual understanding necessary to perform higherlevel
data analysis skills. Many students have difficulty drawing
inferences or making predictions, identifying appropriate
ways to display data, or recognizing when a graph’s
scale has been manipulated to mislead. In short, they struggle
with "exactly the [skills] that people need in their
everyday lives" (Shaughnessy & Zawojewski, 1999).
Developing data analysis skills takes time. These skills
must be learned early and reinforced often. Research reveals
several important areas of the graphing and data analysis
curriculum where elementary students struggle:
 The transition from concrete to abstract
 Data representations
 Classification
 Scale
 Graph interpretation
 Mean, Median, and Mode
The Transition from Concrete to Abstract
When primary students are introduced to graphing, they typically
begin by creating “object graphs” in which physical
objects (e.g., shoes, milk cartons, attribute blocks) are
sorted and lined up to form a reallife picture graph. However,
students often have trouble connecting these real objects
to abstract representations (Friel, Curcio, & Bright,
2001).
Research shows that computer software plays an important
role in bridging the gap between concrete and abstract representations.
In contrast to physical manipulatives, software can provide
immediate visual or auditory feedback—linking students’
physical experiences with corresponding symbolic representations
(Clements & McMillen, 1996).
In The Graph Club 2.0, for example, each category
of data is represented by a graphic symbol that functions
much like the physical objects in an object graph. Students
drag these symbols one at a time from the “symbol bins”
to the appropriate location on the graph. The program reinforces
the addition of each new symbol by counting aloud. This concrete
approach to manipulating data in a graph helps students connect
the real objects in an object graph to abstract representations
(pictures of objects in a picture graph, or the height of
a bar in a bar graph). As students begin to understand these
representations, The Graph Club 2.0 lets them progress
to more abstract and efficient methods of adding data, such
as dragging the top of a bar to the desired height, or simply
typing a numerical value in a table.
Data Representations
Studies show that students have difficulty recognizing the
same data when it is presented in different ways (Kerslake,
1981; Bright & Friel, 1998). To address this problem,
teachers should provide students with numerous opportunities
“to compare multiple representations of the same data
set” and engage students in “rich discourse on
what each of the representations shows” (Bright &
Friel, 1998). Older students have particular difficulty understanding
the relationship between raw and grouped representations of
data (Bright & Friel, 1998). Tallying raw data helps students
better understand the transition between raw and grouped data
(Bright & Friel, 1998).
Tom Snyder Production’s The Graph Club 2.0 and
GraphMaster make it easy for students to view and compare
different representations of the same data. Whenever students
open a new file using The Graph Club 2.0, they are presented
with two sidebyside representations of the same data. As
students make a change to one graph (for example, by dragging
additional symbols into a picture graph), the other graph
changes dynamically, helping students see the relationship
between the two representations. This feature also supports
students as they make the transition from more concrete to
more abstract types of graphs (e.g., picture to bar). The
GraphMaster program’s Tally feature allows students
to tally columns of raw data. The resulting Tallied Data display
provides a conceptual link between the data table and the
final graph.
Classification
Students who develop sorting and classification skills during
kindergarten (along with related skills such as sequencing)
are significantly more likely than their peers to succeed
academically throughout elementary school (Dudek, Strobel,
& Thomas, 1987; Silliphant, 1983). Teachers can help students
develop classification skills by giving them many practice
opportunities with a wide variety of objects.
The Graph Club 2.0 reinforces sorting and classification
skills. Unlike some other elementary graphing programs, which
sort data automatically, The Graph Club 2.0 provides
students with a handson sorting experience each time they
make a graph. When students create a graph using the program,
they add data to a category by dragging symbols into the corresponding
column (for example, the cat symbol must be dragged to the
cat column). A reinforcing sound confirms that students have
dragged a symbol to the correct location. The program’s
extensive library of symbols allows students to sort and graph
everything from animals or food to hair color or weather —
reinforcing classification skills in a wide variety of contexts.
Scale
Understanding a graph’s scale is essential to making
sense of the data it displays, yet many students assume that
every “tick mark” on a scale represents a single
unit and misread graphs in which the scale uses a different
increment (Dunham & Osborne, 1991). Increments of more
than one unit can be particularly challenging for young students,
who often have a limited ability to count by 2s, 5s, 10s,
etc. (Friel, Curcio, & Bright, 2001).
Students also frequently fail to understand how the proportions
of a graph are affected by scale (Goldenberg et al., 1988;
Kerslake, 1981). When a graph’s proportions change,
students assume that the data has changed. They don’t
realize that the same data can look radically different when
displayed with a different scale.
Research shows that extensive practice exploring and describing
the effects of scale helps students develop “scale sensitivity”
and become more critical of misleading graphs (BenZvi, 2000).
The Graph Club 2.0 allows students to change a graph’s
scale easily, making it simple for students to explore how
scale changes can affect a graph’s appearance and can
distort trends. Graph Master requires students to make
a decision about scale whenever they create a graph. In contrast
to Excel and other standard spreadsheet programs, Graph
Master can be set so that default values for scale minimum,
maximum, and step size are not provided; students must identify
appropriate values on their own. This focuses students’
attention on scale and reinforces the idea that a graph’s
step size can be greater than one.
Graph Interpretation
A critical goal of the data analysis curriculum is to teach
students to interpret data in order to make decisions and
solve problems. However, studies show that students struggle
with all but the most basic interpretive tasks.
Researchers have identified three levels of graphinterpretation
skill that students should master (Curcio, 1987;Wainer, 1992).
The first level involves extracting specific values from a
graph: How many books did Jessie read in November?
The second level requires integrating information from different
parts of the graph: How many more books did Jessie read
in February than in September? The third level involves
understanding the data set as a whole, making predictions
or noticing trends: How many books do you think Jessie
might read in March, and why? While students generally
can extract data values from a graph (a lower level task),
they perform poorly on higherlevel tasks that involve additional
computation or inference (Shaughnessy & Zawojewski, 1999).
Students also have difficulty expressing their mathematical
ideas in writing. This is particularly true for younger students.
One study found that “the quality of students’
written work [was] inferior to their verbal reasoning”
on statistics questions (Jacobs, 1993). Providing opportunities
to speak as well as write about their statistical ideas helps
all students demonstrate their understanding.
The Graph Club 2.0 and GraphMaster were designed
to support students as they build skills in data analysis
and interpretation. The programs include a builtin notebook
feature, encouraging students to interpret and write about
their graphs. This process makes student thinking explicit
and external, helping to build conceptual understanding. Notebook
text can be printed with graphs and assessed. The notebook
also includes an audio feature that lets students record their
ideas orally. This provides a scaffold for students to express
more complex ideas, as well as an alternative for younger
students or those whose writing skills are less developed.
As students write and talk about their graphs, they develop
a better understanding of their data.
Center: Mean, Median, Mode
An important statistical skill identified by the NCTM Principles
and Standards (2000) is the ability to interpret and summarize
what is “typical” in a set of data using measures
of center—mean, median, and mode. Many students display
poor conceptual understanding of these measures (Mokros &
Russell, 1995). Although they may have memorized algorithms
for calculating the mean or median, students fail to understand
what these values communicate about the data, and view them
as arbitrary procedures rather than useful analytical tools.
Graph Master allows students to display statistics
(including mean, median, and mode) for graphs containing numerical
data. The program displays these values in both numerical
and graphical form. This display helps students make a visual
connection between the values of the data and the mean or
median. For example, students may note that the mean is never
greater than the highest data value (an easy mistake to make
when applying the algorithm without understanding). Students
can view a data table and graph side by side and explore how
changing the data will affect the mean, median, and mode.
As they do so, students build a conceptual, rather than formulaic,
understanding of these measures.
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Clements, D. H., & McMillen, S. (1996). Rethinking "concrete"
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Tom Snyder Productions
Tom Snyder Productions, a Scholastic company, is a leading
developer and publisher of educational software for K–12
classrooms. The company was founded over 20 years ago by Tom
Snyder, a former science and music teacher who pioneered the
use of technology in the classroom to enhance teaching and
learning. Today we are proud to carry over 140 awardwinning
software titles covering each curriculum area, developed with
strict adherence to our high standards for quality and innovation.
Our products help teachers meet curriculum goals in over 400,000
classrooms, improving student performance and understanding.
Our mission is to create innovative products and services
to inspire great teaching and improve student learning.
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