ERIC EJ967476: Teaching Data Analysis to Elementary Students with Mild Disabilities

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by  ERIC

Teaching Data Analysis to Elementary Students
with Mild Disabilities
Pamela J. Hudson
Marcia Shupe
Eleazazr Vasquez
Susan P. Miller
An Article Published in
TEACHING Exceptional Children Plus
Volume 4, Issue 3, January 2008
Copyright © 2008 by the author. This work is licensed to the public under the Creative Commons Attri-
bution License
Teaching Data Analysis to Elementary Students
with Mild Disabilities
Pamela J. Hudson
Marcia Shupe
Eleazazr Vasquez
Susan P. Miller
Abstract
The purpose of this manuscript is to describe the implementation of an action research
project in a fifth grade resource classroom. Students with mild disabilities were taught
how to conduct surveys using three data collection methods, display the data collected in
tables and graphs, and use the data to answer survey questions.
Keywords
data analysis, mathematics instruction, data collection, surveys
SUGGESTED CITATION:

Hudson, P. J., Shupe, M., Vasquez, E., & Miller, S. P. (2008). Teaching data analysis to elemen-
tary students with mild disabilities. TEACHING Exceptional Children Plus, 4(3) Article 5. Re-
trieved [date] from http://escholarship.bc.edu/education/tecplus/vol4/iss3/art5
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! The six students in Mrs. Shupe's fifth (NCTM) expectation for students to formu-
grade mathematics group were working to late questions that can be subsequently an-
meet Annual Yearly Progress (AYP) expecta- swered through data collection, organiza-
tions identified by state standards. The state tion, and visual display (NCTM 2000; NCTM
standards were aligned to AYP expectations 2006).
stated in the No Child Left Behind Act of 2001
(NCLB). The students have been identified as Many students with disabilities strug-
having math disabilities and qualified for gle to apply mathematics knowledge to real-
special education services using the Individu- world situations. The NCTM expectation for
als with Disabilities Education Act of 2004 data collection is included in the standards to
(IDEA) categories of learning disabilities and develop and promote application of mathe-
communication disordered. Of the six stu- matics knowledge and skill to real-world
dents, five had specific learning disabilities situations. The data collection expectation
and one had a communication disorder. goes beyond the traditional focus of teaching
The mathematics goals written in each students to read and interpret tables and
student’s Individualized Education Plan (IEP) graphs, and adds an important dimension that
were designed to provide each prepares students to be collec-
student access to the general tors and consumers of research.
education mathematics cur- Empowering stu- Beginning in kindergarten, stu-
riculum. According to school dents are introduced to con-
dents to answer
district policy, these students cepts of data and methods of
questions paves the
left their general education data collection. In subsequent
way to informed
classroom on a daily basis for grades, these concepts become
decision-making and
one hour to attend Mrs. more complex and sophisti-
is the foundation of
Shupe’s special education re- cated. Empowering students,
responsible
source room for mathematics such as Mrs. Shupe's math stu-
citizenship.
instruction. The students had dents, to ask questions and col-
been doing well with grade lect data to answer questions
level expectations for the Data paves the way to informed
Analysis standard, so when a situation arose decision-making and is the foundation of re-
that required Mrs. Shupe to survey all of her sponsible citizenship and consumer know-
resource students, she asked these students to how. Based on years of research related to
help her plan and conduct the survey. She was the effectiveness of explicit instructional ap-
surprised that even though these students proaches for teaching students with mathe-
were able to answer questions on the state matics disabilities (Butler, Miller, Lee, &
core mathematics exam about data collection Pierce, 2001; Hudson & Miller, 2006; Kroes-
methods and displaying data in graphs and bergen & Van Luit, 2003; Maccini & Hughes,
tables, they did not know how to formulate a 1997; Mastropieri, Scruggs, & Shiah, 1991;
question or plan how to collect the data using Miller, Butler, & Lee, 1998), Mrs. Shupe,
a survey approach. This gap between know- along with university researchers, designed
ledge and application provided an ideal seven phases that would help her students
teaching opportunity that was aligned to the meet the NCTM expectation (Table 1).
National Council of Teachers of Mathematics
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Phase 1: Identify Instructional Goals and tions, measurement).
Objectives
The state data analysis standard was Phase 2: Select an Instructional Approach
examined related to the NCTM expectation, Based on previous experience teach-
and two main goals with related objectives ing these particular students and based on our
were identified for each goal (see Table 2). knowledge of beneficial teaching approaches
Goals and objectives were limited to ensure for students with disabilities, Mrs. Shupe de-
opportunities for student mastery of the data cided to use an explicit or direct teaching ap-
analysis concepts while still preserving in- proach. She believed this approach would
structional time for other important mathe- likely result in success for her students.
matics standards (e.g., numbers and opera-
Table 1: Seven Phase Instructional Approach
Phase 1: Identify Instructional Goals and Objectives
Phase 2: Select an Instructional Approach
Phase 3: Select a Data Investigation Strategy
Phase 4: Plan and Teach Students How to Conduct Surveys Using the Hand Raising
Method (Objective 1a)
Phase 5: Plan and Teach Students How to Plan and Conduct Surveys Using a Ballot
Method (Objective 1b)
Phase 6: Plan and Teach Students How to Conduct Surveys Using the Ballot Method and
Unlimited Response Questions (Objective 1c)
Phase 7: Plan and Teach Students How to Develop Tables and Graphs to Display Survey
Data (Goal 2)
t h e
Explicit instruction has been consis-
importance of the new lesson (Williams &
tently validated as an effective approach for
Butterfield, 1992; Miller, 2002). Once the ad-
teaching mathematics to students with special
vance organizer is completed, the teacher
needs (Kroesbergen & Van Luit, 2003; Swan-
moves to the demonstration. The demonstra-
son & Hoskyn, 2001). In the explicit or direct
tion consists of the teacher modeling the overt
instruction approach, each lesson includes
actions as well as decision-making to solve a
four stages: advance organizer, demonstra-
problem or complete a task. The teacher en-
tion, guided practice, and independent prac-
gages students verbally with a high level of
tice (Miller & Hudson, 2007). In the first
questions and prompts (Rosenshine, 1995). In
stage, the advance organizer, prerequisite
the third stage, guided practice, the teacher
knowledge is reviewed, essential vocabulary
provides students with opportunities to prac-
is pre-taught, the lesson objective is stated in
"kid language," and students are helped to see
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tice the problems. The teacher assists and accurately and without teacher assistance, the
supports students as they begin to apply the teacher moves to the independent practice
steps modeled by the teacher. Students are stage of instruction where students solve
highly engaged, and the teacher uses students' problems independently. The explicit teaching
verbal and written responses to monitor per- sequence has been used successfully to teach
formance, and provide positive and corrective all types of mathematics problems to students
feedback. Once students complete problems with disabilities.
Table 2: Goals and Objectives
Goal 1: Given questions requiring limited and unlimited* responses, students will conduct inves-
tigations using hand raising and ballot survey methods, and summarize the results to answer the
questions.
Objective a: Given a question requiring limited responses, students will conduct a survey
using the hand raising method, and summarize the data to answer the question.
Objective b: Given a question requiring limited responses, students will conduct a
survey using a ballot method and summarize the data to answer the question.
Objective c: Given a question requiring unlimited* responses, students will
conduct a survey using a ballot method and summarize the data to answer the
question.
Goal 2: Given questions requiring limited responses, students will collect the data, summarize
the results, and display the data in a table or bar graph to answer the question.
Objective a: Given a question and a limited response data set, students will display the
data in a table.
Objective b: Given a question and a limited response data set, students will display the
data in a bar graph.
* Students initially worked with survey questions that had limited or set answers for respondents to
choose from, e.g., "Is pink or blue the favorite class color?" Later, students worked with survey ques-
tions with an unlimited or open-ended response format, e.g., "What is your favorite color?"

Phase 3: Select a Data Investigation veys using a variety of data collection meth-
Strategy ods. Second, the four-step strategy can be eas-
Mrs. Shupe and the university re- ily adapted for a specific data collection
searchers selected a data investigation strat- method by adding sub-steps that guide stu-
egy (Hudson & Miller, 2006) that involved dents in the data collection process.
four strategy steps (see Figure 1). These strat-
egy steps were selected for several reasons.
First, they are appropriate for conducting sur-
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Phase 4: Plan and Teach Students How to answer certain kinds of questions. Students
Conduct Surveys Using the Hand Raising volunteered the types of survey questions
Method (Objective 1a) they were curious about (e.g., What is the
The four-step data investigation strat- group’s favorite winter sport?) and the type of
egy was adapted for the hand raising method data that would be collected (e.g., the name of
with three sub-steps added under Step 2 (See the student's favorite winter sport). Mrs.
a, b, and c). These sub-steps guided Mrs. Shupe then stated the objective for the lesson.
Shupe’s students in the collection of the data. After the first lesson, the advance organizer
Step 1: Formulate the question. included reviewing the data investigation
Step 2: Plan and collect the data steps, and stating the lesson objective.
(a) list choices Following the advance organizer, Mrs.
(b) call for a vote Shupe demonstrated each of
(c) write a tally the four data investigation
for each hand Figure 1: Data Investigation steps and modeled how to
raised Strategy formulate the question, plan
Step 3: Count and Step 1: Formulate the and collect the data, count and
write the totals question write the totals on a data col-
Step 4: Answer the lection form, and answer the
Step 2: Plan and collect the
question question. Once the demonstra-
data
tion was complete, Mrs.
Only questions Step 3: Count and write the Shupe provided opportunities
allowing for limited re- totals for guided practice related to
sponses were used for the the steps she had just demon-
Step 4: Answer the question
hand raising lessons. For strated. Initially, Mrs. Shupe
example, if the question provided many prompting
was "What is the favorite school lunch?" Mrs. questions to ensure student success with the
Shupe helped students narrow the range of strategy steps, but gradually she shifted more
possible responses or choices to pizza, ham- and more responsibility to the students. For
burgers, and hot dogs, and then reworded the example, during step one, Mrs. Shupe and the
question to be more specific: "Is pizza, ham- students began by discussing what the ques-
burgers, or hot dogs the favorite school tion was and how to word it. At first, she
lunch? Limiting the choices helped students wrote the question on the board and students
manage and organize the data as it was col- copied, but as the students became more pro-
lected. Use of a data collection form also ficient with the process, they were expected
helped students during this phase of the in- to formulate and write their research ques-
structional process (see Figure 2 in appendi- tions independently. Similarly, for steps 2, 3,
ces). and 4, Mrs. Shupe initially provided prompts
The lesson began with an advance or- to facilitate students through the process, and
ganizer. For the first hand raising lesson, Mrs. then faded the prompts. It is important to note
Shupe began the advance organizer by intro- that each practice opportunity required a new
ducing the concepts of data and survey. This research question, so that students had the
led to a discussion of when students might opportunity to follow the process all the way
find it useful to collect data with a survey to through from beginning to end.
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By independent practice, all students matically sorted for totaling. One question
were able to complete all of the data investi- used for the ballot survey was "Is blue, red, or
gation steps without teacher assistance. The green the favorite color of students in our
configuration of the independent practice was class?" To collect the data in step 2, three sub-
unique. When a survey topic was proposed, steps were added: (a) label a container for
all students independently formulated and each choice, (b) provide each voter with an
wrote a question on a piece of paper (step 1), object for voting, and (c) take turns voting
however, in step 2, only one student planned (see Figure 4 in appendices). The previously
and conducted the survey: listing discussed lesson procedures (i.e.,
the choices, calling for the vote, advance organizer, demonstra-
and writing a tally for each hand The performance tion, guided practice, independent
raise. All students completed of all students practice) were used to teach the
steps 3 and 4 by counting the tal- improved to an first ballot method for surveying
lies on the board from the vote, average of 90%. groups. Six data investigations
and then answering the question. were conducted at the independ-
Each new question practiced al- ent practice level with students'
lowed another student to conduct step 2 inde- performance averaging 92% accuracy
pendently. The reason the independent prac-
tice was configured this way was to maximize Phase 6: Plan and Teach Students How to
the engagement and practice of all students in Conduct Surveys Using the Ballot Method
the group for each new question. Six data in- with Unlimited Response Questions
vestigations were conducted in this fashion (Objective 1c)
with students' performance averaging 91% Following instruction and practice
accuracy. The final application of the four with the first ballot method, we adapted the
data investigation steps occurred around Val- four-step data investigation strategy for a sec-
entine's Day, and students worked in pairs to ond type of ballot survey. Table 3 shows the
survey other instructional groups in the class four data investigation steps with added sub-
as to their favorite Valentine's Day candy. steps for steps 2 and 3. This ballot method
Figure 3 (in appendices) shows the data col- required written responses from those being
lection sheet used for the Valentine's Day sur- surveyed. Each written response was placed
vey. in a single container to be totaled. This
method offers two advantages over the previ-
Phase 5: Plan and Teach Students How to ous two survey methods. First, it provides a
Conduct Surveys Using the Ballot Method record of each person's vote, and second, this
(Objective 1b) method is suitable for unlimited response
When students had mastered conduct- questions. An unlimited response question is
ing surveys with the hand raising method, one that allows the person surveyed to re-
Mrs. Shupe decided students were ready to spond with any possible choice related to the
move on to the ballot method. Two ballot question. For example, with the question
methods were taught. The first ballot method "What is your favorite cookie?" the person
was similar to the hand raising method in that surveyed can answer with any type of cookie.
the questions had limited responses or choices However, totaling the votes (step 3) is more
and the method allowed for votes to be auto- difficult because students must organize the
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data before it can be counted. Mrs. Shupe’s 3. Represent the data in bars
instruction for this ballot method followed the 4.Name the graph
explicit teaching approach previously de-
scribed for the other two surveying methods. Guided practice followed the demon-
Six data investigation lessons were conducted stration. Here Mrs. Shupe prompted students
in this fashion with students' performance av- to recall one step at a time and then perform
eraging 89% accuracy. the step. For example:
Mrs. Shupe: What's the first step,
everyone?
Phase 7: Plan and Teach Students How to Students: Draw the x and y axis
Develop Tables and Graphs to Display Mrs. Shupe: Good remembering! Go
Survey Data (Goal 2) ahead and do that on your graph
Once instruction related paper (teacher circulates, moni-
to goal one was complete, the Independent tors, and provides feedback).
emphasis shifted to goal two
practice was
(i.e., Given questions requiring During the independent
configured this way
limited responses, students will practice part of the lesson, stu-
to maximize
collect the data, summarize the dents were given a set of data
engagement and
results, and display the data in (previously collected in Goal 1
practice for all
a table or bar graph to answer activities) and directed to record
students.
the question). Student perform- the data in a specified visual
ance data revealed that students display (i.e., table or bar graph).
knew how to pose questions, collect data, and When students had mastered the objective of
summarize the results, but now they needed representing a set of data in a visual display,
to learn how to display the data in a visual Step 4 of the Data Investigation Strategy (see
display (i.e., table or bar graph). Tables and Figure 1) was altered slightly. Students were
bar graphs were selected for instruction be- now expected to first record the data in a vis-
cause the survey data collected in goal 1 ual display, and then answer the question.
would best be represented in these types of Four sets of data were recorded in visual dis-
visual displays. To teach students how to de- plays. Student performance for recording data
velop and record a set of data in a table or bar in tables and bar graphs averaged 90% ac-
graph (see Objectives 2a and 2b in Table 2), curacy.
Mrs. Shupe worked with one type of visual After teaching the six math students to
display at a time. In the advance organizer, represent their data visually, another opportu-
she reviewed the characteristics of the visual nity arose for students to conduct a real-life
display being taught in the lesson (see Figure survey. Mrs. Shupe used an incentive pro-
5 in appendices). When students were firm on gram to reward students for completing
the characteristics, Mrs. Shupe demonstrated homework, improving math and reading tim-
how to develop the visual display using a ings, and following the class rules. All of
simple procedural strategy. The strategy for Mrs. Shupe’s students, including the six math
developing a bar graph included four steps. students, had the opportunity to earn partici-
1. Draw the x and y axis pation in an ice cream float party. Once the
2. Mark and label each axis party had been earned, Mrs. Shupe engaged
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the six math students in determining the type type of ice cream float students preferred that
of ice cream float students preferred (i.e., root provided an opportunity for the math students
beer or Sprite). It was the need to identify the to conduct a meaningful survey.
Table 3: Data Investigation Steps for Ballot Surveys using Unlimited Response Questions
Step 1: Formulate the question.
Step 2: Plan and collect the data.
a. get a container
b. each person writes their choice
c. take turns voting
Step 3: Count and write the totals.
a. sort the votes
b. write the choices
c. count and write totals for each choice
Step 4: Answer the question.
A discussion was held with the stu- day, the eligible voters wrote their choice on
dents in the math group to determine what the provided paper, signed their name, and
type of survey would be most appropriate to placed their vote in the designated container.
conduct. The hand-raising method was elimi- The following day, students counted the
nated because not all of the students that had votes, and because this was a group project,
earned the ice cream float party were present Mrs. Shupe showed the students how to use
in the classroom at the same time. They came Microsoft Excel, a program to record and pre-
to her resource room at different times of the sent the data in a bar graph (see Figure 6 in
day. Thus, the ballot method was selected. appendices). By counting the votes and dis-
Because the responses were limited, students playing the data in bar graph form, the stu-
suggested the first ballot method that in- dents learned that root beer was the favorite
volved having one container for root beer kind of ice cream float. Mrs. Shupe’s students
floats and one container for Sprite floats, with had a great time at their ice-cream party!
each qualified student placing a bean in the
container of their choice. However, Mrs. Final Thoughts
Shupe was concerned that some voting stu- Teaching students to collect data to
dents would change their minds. Therefore, answer questions is an important life skill that
the group agreed to go with the second ballot will serve them well throughout their adult
method because it would provide a record of lives. The instructional goals, objectives and
the students’ votes. lesson procedures described in this article
To conduct the survey, students pre- provided an important foundation for under-
pared a voting area in the room with a single standing the concepts of data and data collec-
container, and cut up pieces of paper to dis- tion. This instruction helped students see the
tribute to each eligible voter. Throughout the important connection between collecting data
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and answering questions. Students also works for teaching data analysis.
learned strategies for conducting data investi- A third practical implication that Mrs.
gations and recording the data in a variety of Shupe learned was that students with mathe-
visual displays. The performance of all stu- matics disabilities enjoy being actively en-
dents improved to an average of 90% accu- gaged in the instructional process and they
racy on all objectives and goals which helped can succeed in mathematics skills associated
students not only meet their IEP goals, but with the general education curriculum. She
also AYP expectations. In addition, students now understands the value of linking mathe-
said that collecting the data and making the matics to real-world applications. She is
visual displays "Was really fun!" pleased that her students learned an important
Several implications for practice skill that will be used throughout her stu-
emerged from Mrs. Shupe’s experiences with dents’ future lives. As these concepts and
her six math students. First, she realized that skills are developed further in subsequent
just because students can answer questions grades, these students will be better prepared
about data collection methods, graphs, and to pursue complex questions, use sophisti-
tables on a state mathematics exam does not cated methods of data collection, and make
ensure that they understand and/or can apply wise data-based decisions.
the bigger ideas associated with the use of
various data collection and data analysis pro- References
cedures to answer real life questions. It is Butler, F. M., Miller, S. P., Lee, K., & Pierce,
insufficient to teach students to answer test T. (2001). Teaching mathematics to
questions accurately without ensuring that students with mild-to-moderate mental
retardation: A review of the literature.
they can apply the information in real world
Mental Retardation, 39(1), 20-31.
settings. Fortunately, Mrs. Shupe understood
this and was willing to allocate additional in-
Hudson, P. and Miller, S. P. (2006). Designing
structional time to be sure that her students
and Implementing Mathematics In-
could use what they had learned in meaning-
struction for Students with Diverse
ful ways.
Learning Needs, Boston: Allyn & Ba-
A second practical implication that
con, an imprint of Pearson Education.
Mrs. Shupe learned was the importance of
using explicit instruction for teaching an im- Individuals with Disabilities Education Im-
portant mathematics skill that has been provement Act of 2004, 20 U. S.
somewhat overlooked in the mathematics lit- ! C. § 614 et seq.
erature. Recent changes in litigation (e.g.,
NCLB and IDEA) mandate that students with Kroesbergen, E. H. & Van Luit, J. E. H.
disabilities have access to and progress (2003). Mathematics interventions for
children with special educational
through the general education curriculum.
needs. Remedial and Special Educa-
This means that students with disabilities now
tion, 24, 97 - 114.
face a broader mathematics curriculum that
includes content areas such as data analysis.
Maccini, P., & Hughes, C. A. (1997). Mathe-
Mrs. Shupe now realizes that using explicit
matics interventions for adolescents
instruction, an approach frequently used for
mathematics skills such as computation, also
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