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Probability & Statistics for K12
This page is reserved for online publications of research data, articles, and other documents, peer-reviewed or not, as well as any constructive criticism, comments and advice, related to the determination of K-12 age-possible topics in statistics and probabilities, as an instrument for the implementation of the ideas explored in the vision paper titled Proposed Model for a Streamlined, Cohesive, and Optimized K-12 STEM Curriculum with a Focus on Engineering.
Research CONCLUSION
A careful analysis of the course content as revealed by the college-level textbooks used in the probability and statistics course has lead to the conclusion that for all practical purposes, the majority of all knowledge content in the selected textbooks could be taught to high school students. Thus, the research on this subject has been completed.
Possible Grade-Level to Introduce this Subject
High school, grade to be determined.
Research Data Tables
Complete Report
edward_k12_probability_statistics_report.pdf | |
File Size: | 348 kb |
File Type: |
Textbooks Used as Sources of Data
Miller & Freund's Probability and Statistics for Engineers, Eighth Edition, and Student Solutions Manual, by Richard A. Johnson, 539 pages long, is one of the most popular textbook used in college engineering programs and has been used recently at East Los Angeles College. After a careful and thorough examination of all pages in this text book, it has been concluded that
(1) For all practical purposes, no pre-requisite knowledge and skills in physics and chemistry is needed to complete the reading of the chapters and the home work assignments; (2) For most of the chapters and sections, the pre-requisite mathematics concepts and skills are minimal and they include [four operations], [absolute value], [summation], [power], [root], [inequality], [infinity], [natural log], [counting] (set), [matrix], [permutation], [combination], [graph], and [charts]; (3) For a few chapters and sections such as Chapter 5 Probability Densities (pages 119-174), Section 6.2 The Sampling Distribution of the Mean (pages 179-186), Section 6.7 Transformation Methods to Obtain Distributions (pages 197-201), Section 14.6 The Kolmogorov-Smirnov and Anderson-Darling Test (pages 458-460), and Section 16.4 The Weibull Model in Life Testing (pages 496-500), beginning calculus skills such as [first integral] and [first derivative] are needed; and for Section 7.3 Maximum Likelihood Estimation (pages 215-221), [first partial derivative] is needed. The above-mentioned calculus skills are very basic and could be treated as special topics in mathematics to be taught before the start of the relevant statistics and probability topics. Therefore, it could be tentatively concluded that with special treatment of a few basic calculus level mathematics skills, namely, [first order integral], [first degree derivative], and [first degree partial derivative], this textbook is age-possible for high school students. A Friendly Remainder ...The subject of statistics and probability does require, beyond pure mathematics skills per se, a high degree of logical thinking ability at the level of abstraction; and the difficult part is how to get abstract stuff into the brain of high school students.
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Probability and Statistics for Engineers and Scientists, 6th Edition, written by Ronald E. Walpole, Raymond H. Myers, and Sharon L. Myers, and published by Prentice Hall, 1998 (ISBN 0-13-840208-6), 736 pages long, is one of the most popular textbook on the subject. After a careful and thorough examination of all pages in this text book, it has been concluded that
(1) For all practical purposes, no pre-requisite knowledge and skills in physics and chemistry is needed to complete the reading of the chapters and the homework assignments; (2) For most of the chapters and sections, the pre-requisite mathematics concepts and skills are minimal and at pre-calculus level; they include [four operations], [power], [root], [counting] (set), [limit], [union], [intersection], [permutation], [combination], [inequality], [infinity], [log], [natural log], [union], [intersection], [absolute value], and [matrix], (3) For a few chapters and sections, calculus skills such as [first integral], [first derivative], [second integral], [second derivative], [third integral], and [third derivative] are involved; and these chapters and sections, as well as the numbers of the pages involving calculus skills are 3.3 Continuous Probability Distribution (page 59 and 60), 3.5 Joint Probability Distribution (page 71-79), 4.1 Mathematical Expression (page 85, 89 and 90), 4.2 Variance and Covariance (pages 97 and 99), 4.3 Means and Variances of Linear Combinations of Random Variables (pages 101-106), 4.4 Chebyshev's Theorem (pages 109 and 110), 6.2 Normal Distribution (pages 147), 6.3 Areas Under the Normal Curve (pages 148 and149), 6.6 Gamma and Exponential Distributions (pages 167 and 169), 6.7 Applications of the Exponential and Gamma Distributions (pages 170-172), 6.10 Weibull Distribution (pages 175 and 176), 7.2 Transformation of Variables (pages 183-188), 7.3 Moments and Moment-Generating Functions (pages 189-193), 9.13 Bayesian Methods of Estimation (pages 276 and 278), and 11.2 Simple Linear Regression (page 362). The above-mentioned calculus skills are could be treated as special topics in mathematics to be taught before the start of the relevant statistics and probability topics, or the chapters or sections involved could be omitted. Therefore, it could be tentatively concluded that most part of this textbook is age-possible for high school students. Making the Abstract more "Visual" ...Unlike some other engineering subjects where most of the topics involve things that are more tangible or hands-on, such as engineering materials, statics, mechanical design or circuit analysis, statistics and probabilities are somehow more "abstract" or "metaphysical;" and this is the difficult part to get the concepts and skills into students' mind. Using colorful illustrations or visual imageries, or analogies might help.
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About Digital Technology ...
Using SPSS for Windows and Macintosh, 5th Edition, written by Samuel B. Green and Neil J, 445 pages long, with 10 Units (45 Lessons), is one of the most popular textbooks on SPSS software. After a careful and thorough examination of all pages in this textbook, it has been concluded that
(1) As expected, beyond the basic understanding of relevant topics of statistics, the mathematics concepts and skills required to complete the reading and homework assignments are all at pre-calculus level, and they include [four operations], [power], [root], [inequality], [table], [chart], [graph], [flow chart], and [Cartesian Coordinate System} (X, Y, Z axes, planes, origin). (2) For all practical purposes, no prior mastery of physics and chemistry concepts and skills is needed for using this textbook. Therefore, this textbook is age-possible for K12 students. |
About SPSS .and Other Statistics Software Programs ..
Many software programs are available for statistics and probabilities. Comparison charts for the features of these programs are available in Wikipedia website. One of the most popular used in business and educational institutions is SPSS. According to Wikipedia, "Long produced by SPSS Inc., it was acquired by IBM in 2009. [...] The software was released in its first version in 1968 as the Statistical Package for the Social Sciences (SPSS) after being developed by Norman H. Nie, Dale H. Bent, and C. Hadlai Hull."
Microsoft Excel program also include tools for statistical analysis,
Microsoft Excel program also include tools for statistical analysis,
The research on this subject has been financed by part of a gift of US$10,000 from Mrs. Xiuyu Li, my mother and resident of the District of Gulangyu, City of Xiamen, Province of Fujian, the People's Republic of China, during my recovery from left arm injury at Athens, Georgia (2009)
本科目的研究成果由我的母亲李秀玉女士(中华人民共和国福建省厦门市鼓浪屿区居民)在我2009年在美国佐治亚州雅典市左手受伤休养期间赠送10000美元中拨款赞助
RESEARCH OUTCOMES Navigator:
(1) Engineering Foundation (Introduction to STEAM for K12, Statics for K12, Dynamics for K12, Strength of Materials for K12, Engineering Materials for K12, Statistics& Probabilities for K12, and Engineering Economics for K12);
(2) Mechanical Engineering (Mechanical Design for K12, Fluid Mechanics for K12, Aerodynamics for K12, Heat Transfer for K12, Thermodynamics for K12);
(3) Engineering Technology (CADD& Product Design for K12, Manufacturing Processes for K12, Engineering Programming for K12);
(4) Civil Engineering (Introduction to Computerized Civil Engineering Design for K12, Introduction to Global Positioning System & Land Surveying for K12, Introduction to Structural Design for K12);
(5) Electrical Engineering (Introduction to Electrical & Electronics Devices for K12, Introduction to Circuit Analysis & Simulation for K12, Introduction to Robotics & Programming for K12);
(6) Capstone Engineering Design and Research;
(7) Available K12 STEAM Learning Resources;
(8) Mathematics Pre-requisites for Undergraduate Engineering Programs;
(9) Recommended Artistic Skills for STEM Professionals.
(1) Engineering Foundation (Introduction to STEAM for K12, Statics for K12, Dynamics for K12, Strength of Materials for K12, Engineering Materials for K12, Statistics& Probabilities for K12, and Engineering Economics for K12);
(2) Mechanical Engineering (Mechanical Design for K12, Fluid Mechanics for K12, Aerodynamics for K12, Heat Transfer for K12, Thermodynamics for K12);
(3) Engineering Technology (CADD& Product Design for K12, Manufacturing Processes for K12, Engineering Programming for K12);
(4) Civil Engineering (Introduction to Computerized Civil Engineering Design for K12, Introduction to Global Positioning System & Land Surveying for K12, Introduction to Structural Design for K12);
(5) Electrical Engineering (Introduction to Electrical & Electronics Devices for K12, Introduction to Circuit Analysis & Simulation for K12, Introduction to Robotics & Programming for K12);
(6) Capstone Engineering Design and Research;
(7) Available K12 STEAM Learning Resources;
(8) Mathematics Pre-requisites for Undergraduate Engineering Programs;
(9) Recommended Artistic Skills for STEM Professionals.
Freedom and opportunities! You will have the right to a high quality K12 science, technology, engineering, arts and mathematics (STEAM) education!
¡Libertad y oportunitades! ¡Usted va a tener el derecho a una K12 educación de alta calidad en ciencia, tecnología, ingenería, artes y matematica (CTIAM)!
自由和机会!你们将拥有接受高质量的、贯穿幼儿园到中小学阶段的科学、技术、工程、艺术和数学教育的权利!
¡Libertad y oportunitades! ¡Usted va a tener el derecho a una K12 educación de alta calidad en ciencia, tecnología, ingenería, artes y matematica (CTIAM)!
自由和机会!你们将拥有接受高质量的、贯穿幼儿园到中小学阶段的科学、技术、工程、艺术和数学教育的权利!