Quantitative Literacy for Elementary and Middle Schools
(Alias: Using Real Data to Motivate Students to Learn
SMED 769 F
Dates: January 20 - May 5 1998(Queen Rachael Hopes Every Coward Gains Courage.)
Location: Ruth Patrick Science Education Center
Objectives: Students completing this course should be able
1.0 Solve problems using real data.
1.1 Identify the key components or factors in a problem and formulate
questions about them.
1.2 Suggest ways to obtain the data needed in order to begin solving
1.3 Comprehend variables as attributes.
1.4 Distinguish between qualitative and quantitative
1.5 Distinguish between variables and values of a variable.
1.6 Identify five basic variables used in elementary science classes
(e.g., length, area, volume, mass, and temperature).
1.7 Apply a problem solving process.
2.0 Gather and explore data.
2.1 Analyze the source and method of data collection for possible
2.2 Gather data in a variety of ways, including sorting and counting
or measuring, surveys or simple experiments, or from the media or
other resources within the student's environment.
2.3 Interpret the data collected by the student and understand what
the numbers actually represent.
2.4 Record data in tables or frequency charts using tallies and other
techniques to gain a rough feel for the shape of the data.
3.0 Organize and represent data.
3.1 Organize data in a frequency distribution, table or chart.
3.2 Display the distribution of a single variable or compare two sets
of data using counts or relative frequencies.
3.3 Distinguish between real, representational and abstract
3.4 Make and interpret graphs such as pictographs, bar graphs,
3.5 Construct, either manually or by using software, plots such as
line plots, stem-and-leaf plots (simple, back-to-back,
truncated/rounded, or spread out), box-and-whiskers plots,
histograms, and scattergrams.
3.6 Recognize the importance of the unit of measure and choosing an
appropriate scale when graphing.
3.7 Explain the pros and cons of various graphical methods and
determine when to use which one to achieve a desired result.
3.8 Distinguish between bivariate and single variable data.
3.9 Distinguish between independent and dependent variables.
4.0 Describe data.
4.1 Estimate, describe numerically and recognize the role of measures
of center, measures of variability and percents/percentiles.
4.2 Determine the center of a set of data by finding the mean, median
4.3 Compare and contrast the value of using the mean vs. the median
as a numerical summary of a set of data.
4.4 Qualify the spread of a set of data by finding the range,
quartiles, interquartile range, and outliers.
4.5 Recognize linear patterns in scatterplots.
4.6 Discuss the role of the linear equation as a summary measure for
bivariate data and the significance of the line y=x.
4.7 Recognize non-linear patterns in bivariate data.
4.8 Describe the overall shape of a distribution using words such as
symmetrical, rectangular, skew, J-shape, U-shape, bimodal, etc.
4.9 Relate the mean, median, mode and range to the graphical
representation of a set of data.
5.0 Interpret data.
5.1 Use patterns in data to make predictions, decisions or
5.2 Recognize the presence of variation.
6.0 Discuss critical attributes of sound sampling
6.1 Explain the concept of random sampling and how it relates to
6.2 Distinguish between a population and a sample.
6.3 Comprehend the significance of sample size and the impact of
randomness in an investigation.
6.4 Identify possible sources of bias in a set of data.
7.0 Plan experiments and surveys.
7.1 Select an appropriate method (experiment, survey, etc.) to
collect the data necessary to solve a problem.
7.2 Operationally define a population.
7.3 Design an experiment to answer a specific question.
7.4 Design and conduct a survey of a fixed population to determine a
7.5 Recognize that experimental design may influence the results when
conducting a survey or experiment and identify those factors which
will have an influence.
7.6 Distinguish between a survey, poll and a census.
8.0 Support inferential thinking.
8.1 Distinguish between observation and inference.
8.2 Make observations and draw conclusions from single variable
8.3 Fit a line to a scatterplot and use it to make predictions when
appropriate (interpolation and extrapolation).
8.4 Construct a median-median best fit line.
8.5 Use a sample proportion as an estimator for a population
9.0 Recognize the role of statistics in society.
9.1 Relate statistical ideas to the world around them.
9.2 Evaluate advertising claims which use statistics for accuracy and
9.3 Discuss data collected by the Census Bureau and through polls and
surveys and their impact on society.
9.4 Express a critical attitude toward information presented in the
media (advertising particularly) and ask relevant questions before
making judgments based on that information.
10.0 Apply elementary probability terminology.
10.1 Use the language of probability to describe the likelihood of an
10.2 Correctly use terms such as likelihood, chance, assumption,
expected outcome, actual outcome.
11.0 Use probability as a measure.
11.1 Recognize probability as a number between 0 and 1 with this
number expressed as a fraction, a decimal, or percent.
11.2 Apply simple probability concepts to data organized in tables
11.3 Use techniques such as tree diagrams or Venn diagrams to
determine theoretical probabilities.
11.4 Describe the outcomes of an event and the relation between two
or more events in probabilistic terms.
11.5 Use the concept of expected value.
12.0 Compute experimental probabilities.
12.1 Estimate the probability of an event (experimental probability)
by collecting and observing real data.
12.2 Simulate real situations and use the results to estimate
probabilities and expected values.
12.3 Recognize that probability predicts the long-run chance of an
12.4 Recognize that the empirical probability becomes more stable as
more data is collected.
12.5 Distinguish between fair and unfair games using a knowledge of
elementary probability concepts.
13.0 Use two technologies commonly applied in statistics.
13.1 Use basic scientific calculators.
13.2 Use graphing calculators.
13.3 Use computer applications such as spreadsheets and
Assignments and Evaluation for "Real Data"
1. Attendance and Active Participation (40%) Students are
expected to attend all classes and complete homework assignments.
During most classes, students will work in cooperative groups and are
expected to participate appropriately. Absences and/or
non-participation will affect the grade. Students will have
opportunities to gather, organize, represent, describe and analyze
data during each class session. Students will have opportunities to
use performance assessment techniques such as scoring rubrics for
evaluating group work and/or student projects.
2. Individual Assignments (15%) On an individual basis,
students are required to prepare a portfolio of real samples of
statistics used in the media (newspaper/magazine clipping, audio or
video tapes, etc.). Samples should be ones that may be used by
teachers to connect quantitative literacy with the everyday lives of
their students. The samples must be collected weekly, labeled and
mounted in a three ring binder. The full collection should contain a
good variety of uses relating to local, state, national and
3. Team Projects and Presentations (25%) Teams of not
more than three (3) teacher-participants will be formed in order to
develop and conduct a statistics/probability project with students in
their classrooms. Good projects will involve students actively in
finding quantitative ways to answer one or more questions of interest
to the students. In addition, good projects will:
Written materials summarizing the completed project should
include a minimum of the following: project title, student learning
outcomes, level(s), materials, procedure for at least one hands-on
mathematics experience, raw data, summarized and represented data,
and a narrative conclusion. The contributions of each team member
should be clearly documenthe ed in an acknowledgements section.
Written materials should be organized in a tabbed three-ring
a. apply the ASA Principles for Teaching Statistics
discussed in class.
b. involve K-12 students in age-appropriate activities for gathering
and exploring data, organizing and representing data, describing
data, and interpreting data.
c. use sound sampling/questionnaire designs to collect data via a
survey, a poll, an experiment, consumer product labels or a reference
d. include classroom instructions that make real world
e. contain visuals and a complete report submitted during the
All members of each team will participate in some significant way
in a 15-30 minute presentation of the project to the class. Materials
for at least one of the hands-on activities should be gathered for
use during the class presentation. Presentations must include visuals
of your students' involvement in the project, such as photographs,
slides, videotapes and samples of student work. Although only one
copy of the project will be submitted for evaluation, it is advisable
that each member keep a copy in her/his notebook.
4. Final Exam (20%) Students will be assigned teams to
complete tfirst part of a three part exam. Part I will involve a
hands-on data collection and analysis activity. Each team will
complete the activity/experiment in class and answer questions as a
team. One team paper will be submitted. Part II will involve
questions related to Part I that will be answered and submitted on an
individual basis. Part III will cover topics unrelated to the
activity and will be completed individually.
The University of South Carolina
Copyright © 2001 by the Board of Trustees of the
University of South Carolina.
Ruth Patrick Science
Center of Excellence in Educational
University of South Carolina
471 University Parkway
Aiken, SC 29801