Quantitative Literacy for Elementary and Middle Schools

(Alias: Using Real Data to Motivate Students to Learn Mathematics)

SMED 769 F

Spring 1998

Dates: January 20 - May 5 1998
Location: Ruth Patrick Science Education Center Classroom
Instructors: Ms. Gwen Johnson, Ms. Gloria Allen and Dr. Jeffrey M. Priest

Objectives: Students completing this course should be able to:

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 a problem.
1.3 Comprehend variables as attributes.
1.4 Distinguish between qualitative and quantitative observations.
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.

(Queen Rachael Hopes Every Coward Gains Courage.)

2.0 Gather and explore data.
2.1 Analyze the source and method of data collection for possible bias.
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 graphs.
3.4 Make and interpret graphs such as pictographs, bar graphs, broken-line 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 and mode.
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 comparisons.
5.2 Recognize the presence of variation.

6.0 Discuss critical attributes of sound sampling techniques.

6.1 Explain the concept of random sampling and how it relates to bias.
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 particular characteristic.
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 data.
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 proportion.

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 reasonableness.
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 event.
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 and graphs.
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 event.
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 databases.

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 international issues.
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:

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 (e.g., almanac).
d. include classroom instructions that make real world connections.
e. contain visuals and a complete report submitted during the presentation.

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 binder.
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.

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URL: http://rpsec.usca.sc.edu/courses/SMED769Syl.html(February, 1998)

Ruth Patrick Science Education Center
Center of Excellence in Educational Technology
University of South Carolina Aiken
471 University Parkway
Aiken, SC 29801