El Camino College - Division of Mathematical Sciences

Math 115
Probability and Statistics for Prospective Elementary School Teachers
4 units; 4 hours lecture

Catalog Description Course Objectives and Methods of Evaluation
Outline of Subject Matter Planned Instructional Activities

Grading Method: Letter

Associate Degree Credit --- Transfers to CSU
                                           Transfer to UC is pending

Prerequisite: Mathematics 70 with a minimum grade of C or equivalent.

Catalog Description:
  This course is designed for students who plan to become elementary school teachers and will emphasize group and hands-on activities, the use of computer software, and graphing calculators in the exploration of statistics and probability. Topics include creating and interpreting graphs, random variables and sampling, measures of central tendency and dispersion, analysis of experiments including hypothesis testing, design of experiments, and data gathering. In addition, basic laws of probability, logic and set theory including dependent, independent, and mutually exclusive events, odds, and expected values will be explored.

 Course Objectives and Methods of Evaluation:

  1. Course objectives (list the major objectives stated as student outcomes in behaviorally measurable terms.)
    1. Explain and distinguish the differences among various types of data, random variables, and sampling techniques
    2. Design and analyze experiments involving data gathering in order to draw meaningful conclusions from studies
    3. Create and interpret line graphs, pie charts, histograms, bar graphs, stem and leaf plots, scatter plots, and box plots
    4. Calculate, interpret, and explain measures of central tendency, measures of dispersion, and measures of position
    5. Explain the differences between population and sample
    6. Implement simple random samplings
    7. Calculate and solve application problems involving the normal distribution of data
    8. determine the appropriate statistical procedure, such as hypothesis testing, to analyze and draw inferences regarding populations
    9. Calculate and explain the probability and odds of given events
    10. Calculate and explain the meaning of expected values for real world applications
    11. Solve problems involving probability and statistics using both computer software and graphing calculators, and explain the results
    12. Perform basic operations on sets using set notation
    13. Apply basic principles of logic to justify valid arguments
    14. Solve problems involving dependent, independent, and mutually exclusive events
  1. Methods of Evaluation - Associate Degree Credit Course
    1. Substantial writing assignments, including:
      1. Written homework
      2. Term or other paper(s)
    2. Substantial writing assignments are inappropriate for this degree applicable course because:
      1. The course is primarily computational in nature
      2. The course primarily involves skill demonstrations or problem solving.
    3. Computational or non-computational problem-solving demonstrations, including:
      1. Exam
      2. Quizzes
      3. Homework problems

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Outline of Subject Matter
 

Approximate Time

Major Topic

36 hours

I. Statistics

4 hours
 		(i) Different classifications of data, variables, and distributions
4 hours
 		(ii) Visual displays of distributions; bar graphs, line graphs, pie charts, stem and leaf plots, histograms, box and whisker plots, scatter plots
4 hours
 		(iii) Design and analysis of experiments; data gathering, random variables, population vs. sample, bias in sampling methods
4 hours
 		(iv) Measures of central tendency; mean, median, mode, midrange
4 hours
 		(v) Measures of dispersion:   range, variance, standard deviation
2 hours
 		(vi) Measures of position; quartiles and percentiles
4 hours (vii) Comparing and contrasting different distributions
8 hours
 		(viii) Normal distribution; properties and graph, z-scores and t-scores
2 hours
 		(ix) Uses and misuses of statistics

8 hours

II. Hypothesis Testing

  1. Appropriate choice of null and alternative  hypotheses
  2. Level of significance
  3. Analysis of experiments, interpretation and conclusion

16 hours

III. Probability

  1. Experiments to determine the number of possible outcomes
  2. Counting methods; basic counting law, combinations and permutations
  3. Basic laws of probability, dependent and independent events, mutually exclusive events
  4. Odds and expected values

4 hours

IV.  Basic Logic and Set Theory

  1. Valid arguments and common fallacies
  2. Set notation and operations

 8 hours

Examinations

Total:

72 Hours

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Planned Instructional Activities:

Lecture, discussion, individual and group work


Entrance Skills and Knowledge:

List the required skills and/or knowledge without which a student would be highly unlikely to receive a grade of A, B, C, or Credit (or for Health and Safety, would endanger self or others) in the Target Course.

  1. Solve linear and literal equations at the Intermediate Algebra level
  2. Graph linear functions at the Intermediate Algebra level
  3. Solve application problems at the Intermediate Algebra level
  4. Perform numerical calculations involving powers and roots

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Source of information: Course Outline of Record dated November, 2001



 Last Updated On: 4/20/06