Bemidji State University
Mx067/ DATA INVESTIGATIONS, PROBABILITY, AND STATISTICS FOR MIDDLE SCHOOL TEACHERS (4 credits)
Summer 2016
MTWRF, 12-4:30 pm

Instructor: Dr. Glen Richgels, Mr. Abe Schwarz

Email: -- grichgels@bemidjistate.edu

Office Phone: 755- 2824

Office Hours: see www site

Professional Education Department Mission Statement:

“The Bemidji State University Professional Education program is preparing today's teachers for tomorrow, through effective, inquisitive, and reflective practice. Our students are proficient, self-reliant, and thoughtful practitioners, developed in a viable and growing program, who can teach effectively in various settings with diverse learners."

Course Description: DATA INVESTIGATIONS, PROBABILITY, AND STATISTICS FOR MIDDLE SCHOOL TEACHERS (4 credits)

This course meets the new BOT rule with respect to data investigations and concepts of randomness and uncertainty. The collection, display, analysis, and interpretation of data are studied. Additional topics include randomness, sampling, probability in simple and compound events, the prediction of outcomes using a variety of techniques, discrete and continuous distributions and the comparison of theoretical and empirical results of experiments.

Prerequisites
No Prerequisites

Required Text
No text required – course taught with handouts

Resources:

This course is taught with handouts from a variety of sources and using several computer application / instructional programs. The Practice of Statistics, third edition by Yates, Moore, and Starnes. Mathematics for Elementary Teachers a Contempory Approach, Musser, Burger & Peterson Navigating Through Probability in Grades 6-8, National Council of Teachers of Mathematics Navigating Through Data Analysis in Grades 6-8, National Council of Teachers of Mathematics Webb, D., Richgels, G.W., Rypkema, C. Data and Probability Activities for Teachers, Bemidji State University. Exploring Data by James M. Landwehr and Ann E. Watkins Exploring Probability by Claire M. Newman, Thomas E. Obremski, Richard L. Schaeffer The Art and Techniques of Simulation by Mrudulla Gnanadesikan, Raichard L. Schaeffer, and Jim Swift Exploring Surveys and Information from Samples by James M. Landwehr, Jim Swift, and Ann E. Watkins Mathematics for Elementary Teachers a Contempory Approach, Musser, Burger & Peterson Software: · Microsoft Excel · Microsoft Word · Tinkerplots · Fathom 2 · Minitab Internet Browsers: o Internet Explorer o Mozilla FireFox o Safari

Technology:

A computer or calculator.

Board of Teaching Standards

8710.3320 MIDDLE LEVEL ENDORSEMENT LICENSE FOR TEACHERS OF MATHEMATICS.

Department of Mathematics and Computer Science
8710.3320 MIDDLE LEVEL ENDORSEMENT LICENSE FOR TEACHERS OF MATHEMATICS		In this syllabus you will find the word TEACH. This will mean to: Launch: This is where the teacher sets the context of the problem or activity being worked on this day. This involves making sure the students clearly understand the mathematical context and the mathematical challenge of the day’s activities. Explore: This is the time where the students get to work in pairs, individually, or as a class to solve problems presented by the lesson. Share: This occurs when most of the students have made sufficient progress toward solving the problem presented with today’s lesson. It is during this phase that the students learn how others approached the problem and possible solution routes. Helps students deepen their understanding of the mathematical ideas presented in the day’s lesson. Summarize: During this phase the teacher concludes the lesson by clearly stating what the main idea was in the lesson, being sure to clear up any confusion that may arise during the “share” segment. Helps students focus their understanding of the mathematical ideas presented in the lesson.
Standard	K/A	Activity	Assessment
C.A teacher with a middle level endorsement for teaching mathematics in grades 5 through 8 must demonstrate knowledge of fundamental concepts of mathematics and the connections among them. The teacher must know and apply:
(5) concepts of data investigations:
(a) data and its power as a way to explore questions and issues;	K A	TEACH: Data collection; definition, consistency, reliability, accuracy, precision, data types: qualitative, quantitative discreet, quantitative continuous; data verification; sample vs population; Measures of center: mean, median, mode Measures of variation: min, max, range, standard deviation Assignment: 1, 2, 3, 4, 5, 6, 13, 14, 15	Assessment: - Students will use tools in Tinkerplots to answer questions about a set of data on cats. They will determine how to tell the difference between a cat and a kitten and give an oral report. - Students will examine the data on the space shuttle Challenger disaster to arrive at their own conclusions about launch. Students will give an oral presentation to class. - Students will enter and examine data on battery life to arrive at a decision about the best battery. Students will give an oral presentation to class. -Students will enter and examine data on Yankee homerun hitters to arrive at a conclusion on the greatest Yankee and to order the other Yankees.
(b) investigation through data, including formulating a problem; devising a plan to collect data; and systematically collecting, recording, and organizing data;	K A	TEACH: Students will take part in an activity designed to determine if individuals can tell the difference between Coke and Pepsi. The experiment will include a discussion of problem formulation and hypothesis formulation and hypothesis statement, experimental design, devising a plan for data collection, systematic data collection, recording and organizing data, statistic calculations, data analysis and conclusions. Assignment: 31, 32, 33	Assessment: -Students in teams of two will formulate their own discrimination problem, designed to determine if individuals can differentiate between two products. Their experiment will include problem formulation, hypothesis formulation and hypothesis statement, experimental design, devising a plan for data collection, systematic data collection, recording and organizing data, statistical calculations, data analysis and conclusions. Each team shall present their findings orally to class or in a written report to the instructor.
(c) data representation to describe data distributions, central tendency, and variance through appropriate use of graphs, tables, and summary statistics;	K A	TEACH: Data collection; definition, consistency, reliability, accuracy, precision, data types: qualitative, quantitative discreet, quantitative continuous; data verification; sample vs population; Measures of center: mean, median, mode Measures of variation: min, max, range, standard deviation Assignment: 1, 2, 3, 4, 5, 6, 7, 8, 11, 12	Assessment: -Students will examine the data distribution and using measures of central tendency and measures of variance, determine the height of a typical student; a typical female; a typical male. - Students will give an oral presentation as to their determination of a typical student; a typical female; a typical male; included in their presentation will be their display of data, measures of central tendency, measures of variation, and appropriate graphs and summary statistics.
(d) analysis and interpretation of data, including summarizing data; and making or evaluating arguments, predictions, recommendations, or decisions based on an analysis of the data	K A	TEACH: Data collection; definition, consistency, reliability, accuracy, precision, data types: qualitative, quantitative discreet, quantitative continuous; data verification; sample vs population; Measures of center: mean, median, mode Measures of variation: min, max, range, standard deviation Assignment: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 13, 14, 15, 16	Assessment: - Students will use tools in tinkerplots to answer questions about a set of data on cats. They will summarize data, analyze, and interpret the data to tell the difference between a cat and a kitten and give an oral report. - Students will summarize data, analyze, and interpret the data on the space shuttle Challenger disaster to arrive at their own conclusions about launch. Students will give an oral presentation to class concerning the arguments, predictions, recommendations and decisions based upon the NASA analysis of the data that lead to the Challenger launch. - Students will enter and examine data on battery life to arrive at a decision about the best battery. Students will give an oral presentation to class. -Students will enter and examine data on Yankee homerun hitters to arrive at a conclusion on the greatest Yankee and to order the other Yankees. -Students will examine data on the winning times for the Boston Marathon by men and women; they will predict the winning times for 10 years in the future, 50 years in the future, and when women’s times will be faster than men’s times. Students will give oral presentations to class about their determinations. -Students will examine data on countries, the number of McDonalds in the country and the number of nobel prizes awarded to citizens of the country. Students will examine the data for correlation and for causation. Students will give oral reports about their findings and provide explanations of their hypotheses. -Students organized into teams, will propel a nickel from 3-5 times each, collect, organize, and analyze their data. They will prepare an oral report to influence individuals that their team is the best “nickel flickers” ever and should always be consulted if there is ever a need for “nickel flickers”.
descriptive and inferential statistics, including validity and reliability.	A	TEACH: Data collection; definition, consistency, reliability, validity, accuracy, precision, data types: qualitative, quantitative discreet, quantitative continuous; data verification; sample vs population; Assignment 2, 14 (Battery life activity)	Students will demonstrate university-level competency in descriptive and inferential statistics and this competency will be assessed, in part, on all exams and on the battery life project. Students will further demonstrate the ability to use descriptive and inferential statistics to explore validity and reliability.
(6) concepts of randomness and uncertainty:
(a) inference and the role of randomness and sampling in statistical claims about populations;	K A	TEACH: Examine intuitive language for probability, quantification of probability, numerically equivalent probability numerical values; formal definition of probability, use of the counting principle to determine number of ways that an event can occur and can successfully occur; specification of a sample space with a list, table, and forms of a tree; mutually exclusive events, exhaustive events, complimentary events, independent events, compound events, conditional events; theoretical determination of a probability, experimental estimation of a probability, the law of large numbers, simulation of an event. Assignment: 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30	Assessment: -Students will be asked to determine: 1) How black is a zebra? 2) Does a zebra have black stripes on a white body? 3) Does a zebra have white stripes on a black body? Students will be given a picture of a zebra along with an overlapping grid. Students will take a random sampling of the picture and arrive at a decision. Students will then make an inference about the zebra to answer orally the three questions. -A situation will be presented to the class where there is the possibility of sexual discrimination. Students will carry out a simulation of the event. They will then make appropriate statistical calculations and appropriate data displays. Based upon the statistical calculations and data displays the students will decide if sexual discrimination occurred. Their work and conclusion will be presented orally in class.
(b) probability as a way to describe chance or risk in simple and compound events;	K A	TEACH: Examine intuitive language for probability, quantification of probability, numerically equivalent probability numerical values; formal definition of probability, use of the counting principle to determine number of ways that an event can occur and can successfully occur; specification of a sample space with a list, table, and forms of a tree; mutually exclusive events, exhaustive events, complimentary events, independent events, compound events, conditional events; theoretical determination of a probability, experimental estimation of a probability, the law of large numbers, simulation of an event. Assignment: 17, 18, 19, 20, 21, 22, 23, 34, 35, 36, 37, 38, 39	Assessment: -Students, in teams of two, will construct a game of chance, either simple or a compound event; the students will determine the chance or risk involved in their experiment; determine the theoretical expected value; carry out the experiment a finite number of times; calculate the empirical expected value; compare the theoretical and empirical results. Students will make an oral presentation of their determinations.
(c) predicting outcomes based on exploration of probability through data collection, experiments, and simulations; and	K A	TEACH: Examine intuitive language for probability, quantification of probability, numerically equivalent probability numerical values; formal definition of probability, use of the counting principle to determine number of ways that an event can occur and can successfully occur; specification of a sample space with a list, table, and forms of a tree; mutually exclusive events, exhaustive events, complimentary events, independent events, compound events, conditional events; theoretical determination of a probability, experimental estimation of a probability, the law of large numbers, simulation of an event. Assignment: 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30	Assessment: -Students will be asked to determine: 1) How black is a zebra? 2) Does a zebra have black stripes on a white body? 3) Does a zebra have white stripes on a black body? Students will be given a picture of a zebra along with an overlapping grid. Students will take a random sampling of the picture and arrive at a decision. Students will then make an inference about the zebra to answer orally the three questions. -A situation will be presented to the class where there is the possibility of sexual discrimination. Students will carry out a simulation of the event. They will then make appropriate statistical calculations and appropriate data displays. Based upon the statistical calculations and data displays the students will decide if sexual discrimination occurred. Their work and conclusion will be presented orally in class.
(d) predicting outcomes based on theoretical probabilities and comparing mathematical expectations with experimental results.	K A	TEACH: Examine intuitive language for probability, quantification of probability, numerically equivalent probability numerical values; formal definition of probability, use of the counting principle to determine number of ways that an event can occur and can successfully occur; specification of a sample space with a list, table, and forms of a tree; mutually exclusive events, exhaustive events, complimentary events, independent events, compound events, conditional events; theoretical determination of a probability, experimental estimation of a probability, the law of large numbers, simulation of an event. Assignment: 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39	Assessment: -A situation will be presented to the class where there is the possibility of sexual discrimination. Students will carry out a simulation of the event. They will then make appropriate statistical calculations and appropriate data displays. Based upon the statistical calculations and data displays the students will decide if sexual discrimination occurred. Their work and conclusion will be presented orally in class. -Students, in teams of two, will construct a game of chance, either simple or a compound event; the students will determine the chance or risk involved in their experiment; determine the theoretical expected value; carry out the experiment a finite number of times; calculate the empirical expected value; compare the theoretical and empirical results. Students will make an oral presentation of their determinations.
random variable and the application of random variable to generate and interpret probability distributions;	A	TEACH: Define a random variable, explore probability distributions of a random variable, and calculate expected value. Assignment: 34,35,36,37,38,39

Technology Requirements and Expectations
Students will use internet browsers to access information and answer questions posed in class. Students may use calculators, spreadsheets, and data programs such as Excel, Tinkerplots, Fathom 2, or Minitab to answer problems. Written assignments for class will be composed using a word processor such as Microsoft Word.

Teaching Methodology
Polya’s problem solving steps

1. Understand the problem

2. Devise a plan
3. Carry out the plan
4. Reflect

Lesson Sequencing

Intuitions _ Concrete Û Semi-Concrete Û Abstract

Glen’s Teaching/Learning Principles

1. Teach the way students learn

2. Use group work, heterogeneous, 3-4, change monthly

3. Communication student Û student

4. Communication teacher Û student

5. Multiple solution paths

6. Use contextual settings / problem solving

7. Assessment

1. Grading
2. To inform instruction

University Policies and Procedures
http://www.bemidjistate.edu/students/handbook/policies/

Academic Integrity
BSU students are expected to practice the highest standards of ethics, honesty and integrity in all of their academic work. Any form of academic dishonesty (e.g., plagiarism, cheating and misrepresentation) may result in disciplinary action. Possible disciplinary actions may include failure for part of all of a course as well as suspension from the University.

Students with Special Needs
Upon request this document can be made available in alternate formats. Please contact Kathi Hagen at Disabilities Services at (218) 755-3883 for assistance or the AUC Office at 262-6753 or (800) 369-4970.

Student Rights and Responsibilities

Student Code of Ethics

http://www.bemidjistate.edu/academics/catalog/10catalog/GradCatalog/Frontpages/sectionIV/rights.html

Student Academic Rights and Responsibilities

http://www.bemidjistate.edu/students/handbook/policies/academic_integrity/rights_responsibilities.cfm

Instructor Rights and Responsibilities
- I work with all students and expect success from all students. It is my expectation for those students who attend class regularly and complete assignments that they will earn an A or B.

- I am available for help whenever I am in my office. I encourage students to do homework at a table outside of my office so that I can help them whenever they have difficulties. Help is also available through email and at my home, if prior arrangements have been made.

- I will try to give grade status reports at least every three weeks.

Course Grades
A: 100 – 90% B: 89 – 80% C: 79 – 70% D: 69 – 60%

Course Policies
Attendance: Daily attendance is expected
Participation: Class participation and group work is expected

Tentative Course Calendar

Day 1	Collect class data – question systematic measurement
Day 2	Qual, Quan data, mean media mode measures of center – excel; sample vs population; reliability vs validity; accuracy vs precision
Day 3	Min, max, range, std dev measures of variance – excel
Day 4	Excel, Tinkerplots – collecting data, data verification, data transfer
Day 5	Excel, Tinkerplots – calculation of measures of center and measures of spread or variation; investigate standard deviation
Day 6	Tinkerplots investigation: cat vs kitten determination
Day 7	Scatterplots, histograms, bar charts
Day 8	Scatterplots, line of best fit; correlation coefficient; applets build concepts -- slope, intercept, sampling, and displaying data.
Day 9	Boston Marathon investigation
Day 10	McDonalds vs Nobel prizes investigation
Day 11	Height data- male, female; stem and leaf and then double stem and leaf; line plot, histogram, box and whisker plot, side-by-side box and whisker plot
Day 12	Height data- male, female; stem and leaf and then double stem and leaf; line plot, histogram, box and whisker plot, side-by-side box and whisker plot
Day 13	Challenger space shuttle activity
Day 14	Battery life activity
Day 15	Greatest Yankee activity
Day 16	Flick a nick activity
Day 17	Probability – intuitions, words, quantify, definitions
Day 18	Probability – list, table, trees explicit, abbreviated
Day 19	Probability – mutually exclusive events
Day 20	Probability – independent events
Day 21	Probability – compound events
Day 22	Probability – Conditional events
Day 23	Probability – Conditional events
Day 24	How Black is a zebra? Activity - simulation
Day 25	How Black is a zebra? Activity - simulation
Day 26	Prizes in Cereal boxes activity - simulation
Day 27	Prizes in Cereal boxes activity - simulation
Day 28	Std deviation – create manipulative, 1,2,3 st dev percentages
Day 29	Sexual discrimination activity
Day 30	Sexual discrimination activity
Day 31	Coke vs Pepsi activity
Day 32	Coke vs Pepsi activity – student’s design their own discriminating experiment
Day 33	Discriminating product activity, analysis, reports
Day 34	Random variables and expected value
Day 35	Random variables and expected value; Tom’s card games
Day 36	Fair games
Day 37	Fair game is when expected value = 0
Day 38	Monte Carlo casino day Flip, Bam, and Spin -- experimental and theoretical probability Carnival game design and reports
Day 39	Monte Carlo casino day, analysis, reports