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Open Pedagogy Resource: Active Learning Prompts for Mathematics and Computer Science Faculty: 4.2 Introduction to Statistics and Probability: Math 111

Open Pedagogy Resource: Active Learning Prompts for Mathematics and Computer Science Faculty
4.2 Introduction to Statistics and Probability: Math 111

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table of contents
  1. Title Page
  2. Table of Contents
  3. Preface: About this e-Book
  4. Chapter 1: Open Pedagogy
    1. 1.1 Introduction
    2. 1.2 OER-enabled pedagogy
    3. 1.3 Licensing and sharing Open Educational Resources
    4. 1.4 The OER community
  5. Chapter 2: Active Learning
    1. 2.1 The theories behind active learning
    2. 2.2 What is active learning?
    3. 2.3 Incorporating active learning in your class to get to open pedagogy
    4. 2.4 Where and when to apply active learning activities
    5. 2.5 How to encourage students to create active learning activities
    6. 2.6 Evidence that active learning works
  6. Chapter 3: Creating OER-Enabled Pedagogical Prompts
    1. 3.1 Instructor objectives
    2. 3.2 Student objectives
    3. 3.3 OER-enabled pedagogy prompt planning
  7. Chapter 4: Sample OER Activities and Worked Examples
    1. 4.1 College Algebra: Math 104
    2. 4.2 Introduction to Statistics and Probability: Math 111
    3. 4.3 Quantitative Methods for Decision Making: Math 115
    4. 4.4 Pre-Calculus: Math120
      1. 4.4.1 OER-Enabled Pedagogy: Prompts and Example(s) for Pre-Calculus Course (Math 120)
      2. 4.4.2 OER-Enabled Pedagogy: Prompts and Example(s) for Pre-Calculus Course (Math 120)
    5. 4.5 Computer Science - Programing Courses
  8. Appendices
    1. Appendix A: Links for Open Pedagogy, OER and Active Learning
    2. Appendix B: Video Content on Open Pedagogy, OER and Active Learning
    3. Appendix C: Resources for Open Pedagogy, OER and Active Learning
    4. Appendix D: References
    5. Appendix E: About the Authors

4.2 Introduction to Statistics and Probability: Math 111

Introduction to Statistics and Probability (Math 111) is a course that many students are required to take as part of their major requirements (e.g., the nursing major) at York College, CUNY. The course will introduce students to statistics and probability concepts such as the graphs of data sets, the frequency distributions, the measures of central tendency and the measures of dispersion, the elementary probabilities, the counting principles, i.e., the binomial counting principle, and the normal distributions.  

OER-Enabled Pedagogy: Prompts and Examples for Introduction to Statistics and Probability (Math 111)

In OER Activity Prompt #1, students are asked to create homework questions. In OER Activity Prompt #2, students will be asked to create a study guide. In OER Activity Prompt #3, students will be asked to create a practice test. After completing these activities, students will be able to:

  1. Construct the frequency distribution and their graphs
  2. Graph and interpret quantitative data sets using stem-and-leaf plots and dot plots
  3. Graph and interpret qualitative data sets using pie charts and Pareto charts
  4. Graph and interpret paired data sets using scatter plots and time series charts
  5. Find the measures of central tendency
  6. Find the measures of variation
  7. Find the measures of position

For all these three OER Activity Prompt students will be asked to:

  1. Apply to 4C’s (collaboration, creativity, communication, and critical thinking) during a group activity.
  2. Apply the 5R’s (remix, reuse, retain,  revise, and redistribution).
  3. Create, transform, discuss, analyze, compile, modify  OER material, and classroom material.
  4. Individually create two unique real-life application world problems related to the OER Activity Prompt.
  5. Create any of these: study guides, homework and tests.  
  6. Share their creation among themself and present their work to the class.
  7. Share, post, and license their work to the OER community.

OER Activity Prompt #1: Creating a homework for Test 1

This activity is usually done at the beginning of the first month of the semester after students have the proper prior knowledge and skills to create a homework activity. It will take about 90 minutes. Students will be working in groups of 4 and then present their work in front of the class. This activity can be done by using different active learning techniques. The technique that will be used is think-pair-share.

At the beginning of the class: (10 minutes)

Example: 4:00 PM. Instructors will:

  1. write and introduce the activity.
  2. explain what the students will be doing for the activity.
  3. explain what is in an OER - Active Prompt #1 from line 1 - 4.
  4. give the following two materials to the students:
  1. OER-Activity Prompt #1: Creating Homework for Test 1.
  2. Corrected homework # 1 for Test 1.
  1. Ask students to form groups at 4:10 PM.

Part 1 of OER Activity Prompt #1: Creating a Homework for Test 1                                                                       

York College

Mathematics and Computer Science Department

Introduction to Statistic and Probability

OER- Activity Prompt # 1: Creating a homework                             Math 111  

Instructor: Katuska Campana                                                            Date:________

1.

Prior Knowledge: Students were taught these topics in prior lectures.

Aim: Students will be creating a review homework for Test 1.

Objective: At the end of this activities student will be reviewing

  1. Measures of central tendency
  2. Measures of variation
  3. Measures of positions

Motivation: Students will be watching a YouTube video. ( 5 minutes)

  1. Video: “Constructing a BoxPlot” (KhanAcademy, 2020)  https://www.khanacademy.org/math/probability/data-distributions-a1/bo--whisker-plots-a1/v/constructing-a-box-and-whisker-plot 
  2. OER Book: Introduction to Statistic/OpenStax

2.

Activity Technique: Think-Pair-Share

Think: Instructors will ask a question to the class to engage students in critical thinking. Instructors will ask students to write down their answers.

Pair: Students will be paired in groups to discuss their short answer response.

Share: Instructors will ask students to either:

  1. Pair up with a classmate and share and create at least two problems by remixing or building up from graded homework or other classroom material and or OER materials.
  2. Share their work in front of the class by writing their questions on the board.
  3. Students will license their work.

Technology: students will be encouraged to use graphing calculators, i.e., TI-83 or TI-84.

Accommodations: Students with disability will be accomodated

  1. Students will be accomodated in groups according to their needs.
  2. OER Activity Prompts are designed to integrate students' different learning styles

Environment :This activity can be done in:

  1. In-Class: This activity is going to be executed face to face in a group setting.
  2. Hibrid: This activity can be done hybrid.
  3. Asynchronous Online: This activity can be done Asynchronous.
  4. Synchronous Online: This activity can be done Synchronously.

Materials: Students will be using OER resources and classroom materials: corrected homework.

3.

Task: OER Activity Prompt # 1:Creating homework  for Test 1.

Time:(90 minutes)

Note: This activity will be done at the beginning of the class. Students will form groups after the instructor takes attendance, introduce the activity learning activity, and give students specific guidance about the activity. About the time, for example,  if a class starts at 4:00 PM, the start time from the activity will be 4:10. Remember that time management is crucial in an active learning classroom, so keeping on track of your time is imperative. (This information does not have to be included when you create your activity. This note  is to give instructors more details about this section).

 York College

Mathematics and Computer Science Department

Introduction to Statistic and Probability

Student Name:____________________________Date:__________ Group #____

Working in groups: (15 minutes)During this time students will:

  1. be sitting in groups of two, four or five.
  2. choose a leader or moderator for their group.
  3. work individually first in their groups. They will need to create a word problem that is related to their major and related to the topic that they are working on.
  4. will be compiling, mixing material they got from OER website, and from old homework from another class that were provided by their instructor.
  5. will individually write at least two problems to create homework.

Sharing the Work:(15 minutes)

 After each student works individually in their group and has written at least two world real-life problems and answer most of the questions, students will :

  1. share their work among themself in the group
  2. Share their work to other students  in front of the class

Presenting their work: (50 minutes)

Once students finish working in groups and choosing who is going to present their work. Only 4 groups will present their work. Each group will have 10 minutes to present their work. Each group will be asked to go to the front of the class to present their work. No more than two students per group will be presenting their work to the class. Student might also presenting their work to the class by:

  1. Creating a Video (if time is appropriate) or
  2. Using a video from youtube.
  3. Using technology
  4. showing a PPT or (if time is appropriate)
  5. Presenting their work in front the class
  6. Presenting their work on blackboard, etc.

Note: the group will decide how to present their activity to the class. For the purpose of this activity students will be presenting their work in front of the class and they will be utilizing the board.

Feedback:(5 minutes)

After creating, sharing, and presenting their work, students will be asked to write a feedback paragraph about their classmates’ presentations to be given to the leader of each group. Students must take a picture of their grading to keep a math journal to be cc licensed at the end of the semester to the OER community.

Students will also be asked to write one question from their classmates’ presentation to  include it in their activity.

Reflection: (5 minutes)

Students will be writing a reflective paragraph about what they learn from working in a group, from their activity and from their classmates’ presentations.

Note: As for the feedback and reflection activity, instructors can choose to do only one to spend those extra 10 minutes to allow other groups to present their work. However, it is important that at least one writing activity must be done during any active learning activity as part of keeping students actively involved all the time. If students are not asked to write about their classmates’ presentations, they more likely will not pay attention, and they will be bored during those long 50 minutes.

4.

Homework: (5 minutes) This time is to give homework’s instruction.

  1. Lesson homework & reading homework
  2.  License their work:  students will be asked to license their work at home as part of homework. Students will license their work at:           https://www.creativecommons.org/share-your-wor

Total: 110 minutes

Part 2 of OER Activity Prompt #1: Creating a Homework for Test 1    

         The below group activity is an example of class material that students will use for the OER activity prompt. This group activity also has a video link, an online lesson, and online homework. Students must watch the video, finish the online homework and activity before starting creating  an active prompt.

York College

Mathematics and Computer Science Department

Introduction to Statistic and Probability

Review Homework   Test 1                                                                 Math 111  

Instructor: Katuska Campana                                                            Date: _______

  1. Prior Knowledge: Students were taught these topics in prior lectures
  1. Aim: To prepare students for Test 1
  1. Objective: By the end of this activities, student will be able to
  1. find a measure of central tendency
  2. determine measures of variation
  3. find measures of position
  1. Materials:

Video: Khan Academy-Introduction to mean, media and mode

Online Lesson: Mathisfun-Mean, median and mode

Online homework: Mathisfun-homework

  1. Problem #1. The table below shows ages at a 2019 New York Party at Telemundo.

Age

22

30

36

20

27

45

40

50

55

60

How many people

13

20

15

13

11

20

30

13

10

5

Please form a group of four to discuss the following:

  1. Identify the sample size.                                  
  2. Find the mean, the range, the interquartile range, the median, the mode, and the standard deviation of the sample ages of the data.
  3. Construct the stem-and-leaf plot for the above data.
  4. Interpret the results from (2) and (3), and write about what you have learned.

OER Activity Prompt #2: Creating a Study Guide for Test 1

Part 1 of OER Activity Prompt #2: Creating a study guide for Test 1

This activity is usually done as a follow up from OER Activity Prompt #1. It will take about 30 minutes and can be used for any classroom size using different OER active learning techniques. For OER Activity Prompt #2, students will be using the Think-pair-share technique, and the Test-Teach-Test (TTT) technique.

Time: 60 minutes

Example: Instructors will

  1. introduce the two techniques for activities: Test-Teach-Test and Think-Pair-Share.
  2. explain what students will be doing during  each activity.
  3. give these two materials to the students:
  1. OER-Activity Prompt # 2
  2. Corrected homework #1 for Test 1.
  1. Test:Instructor will give one question quiz (5 minutes)
  2. Teach: a mini lesson (30 minutes)
  3. Test: another one question quiz (5 minutes)
  4. OER Activity Prompt:Think-Pair-Share.

Mathematics and Computer Science Department

OER- Activity Prompt # 2: Creating a Study Guide for Test 1         Math 111  

Instructor: Katuska Campana                                                            Date: ___________

Student Name:____________________________Date:__________ Group #_________

Time: 4:00PM - 5:00PM 

  1. Administrative message: (10 minutes)

2. Prior Knowledge:Students were taught these topics in prior lectures.

3. Aim: Students will create a study guide for Test 1

4. Objective: By the end of this activities, student will be able to

  1. find a measure of central tendency
  2. determine Measures of Variation
  3. find measures of position

5. Test: one question quiz (5 minutes)

Time: 4:15PM - 4:55PM

6. Lecture: mini lesson ( 40 minutes)

 

Note: Read this article if you want to learn more about how to create a lesson.

7. Test: one question quiz (5 minutes)

8. OER Activity Prompt Time: Think-Pair-Share. Students will form groups at 5:00 PM.

Task: Creating a study guide (30minutes)

Time: 5:00PM - 5:40PM 

a. Activity Technique: Think-Pair-Share

b. Materials: Students will be using OER resources and classroom materials.

d. Technology: students will be encouraged to use graphing calculators, such as TI-83 or TI-84

e. Working in groups: (15 minutes)

OER Activity Prompt Technique: Think-Pair-Share.

  1. Think: Students will be individually thinking and creating two real life questions by using OER materials and classroom materials.  
  2. Pair: During this time students will:
  1. be sitting in groups of two, four or five
  2. choose a leader or moderator for their group
  3. be compiling, reusing, mixing material they got from OER websites, and from old homework from another class that was provided by their instructor.
  4. write, at least, two problems per student to create questions for Test 1 study guide.

  1. Share: Students will be then sharing their work (20 minutes)

 After each student works individually in their group and has written at least three world real-life problems and answer most of the questions, students will :

  1. share their work among themself in their group and or
  2. Share their work to their classmates in front of the class. Each group will write their questions on the board to allow other students to copy their questions.

e. Reflection: (5 minutes)

Students will be writing a reflective paragraph about what they learn from working in a group, from their activity and from their classmates’ presentations.

End of the activity at: 5:40 PM

Note:  In this activity students will be writing two reflection paragraphs. These two short response paragraphs will be written in their math journal that students will cc license at the end of the semester as part of a class project.

  1. One after the lesson
  2. One after they finish working in groups

9. Administrative message:  (5 minutes) This time is to give homework’s instruction.

  1. Lesson homework & reading homework
  2.  License their work:  students will be asked to license their work with the Creative Commons as part of their homework.

10. Class dismissed at 5:45 PM  (5 minutes)The last 5 minutes is to speak with students.

OER Activity Prompt #3: Mini Lesson

          In OER Activity Prompt #3, students will also work in group settings for 30 minutes. The group technique students will be doing is Think-pair-share, followed by a short writing response in students’ math journal after each group presents their work. The purpose of this activity is to create a mini lesson that students will be able to use in a peer tutoring activity technique whenever a student misses class or to accommodate students with disabilities who need to be placed in small groups settings of two.

In OER Activity Prompt #3, students will be actively working in group settings for the OER activity, and they will be creating their own questions individually and then sharing them to the group and to the class. Here is an example of how these two-activity-techniques are applied.

OER Activity Prompt time duration: 80 minutes

OER Activity Prompt Technique: Think-Pair-Share

Example: At the beginning of the class, instructors will:

  1. introduce the two activities
  2. Lecture: Test-Teach-Test
  3. OER Activity Prompt: Think-Pair-Share.
  4. Explaining what students will be doing during  the activity.
  5. Introduce and explain OER  - Activity Prompt # 3 sections.
  6. give these two materials to the students:
  1. OER-Activity Prompt # 1 and 2
  2. Corrected homework # 1 and 2

Mathematics and Computer Science Department

Introduction to Statistics and Probability

OER Activity Prompt #3: Mini Lesson                                         Math 111  

Instructor: Katuska Campana                                                      Date: _______________

Prior Knowledge: Students were taught these topics in prior lectures.

Aim: To give students a deep understanding of the measure of center and variation.

Objective:  This activity has two primary goals:

  1. To give students a deep understanding of summarizing and graphing data.
  2. To create a mini lesson about the following topics:
  1. Measures of Central Tendency
  2. Measures of Variation
  3. Measures of Position

Materials: Students will be using OER resources and classroom materials.

Technology: students will be encouraged to use graphing calculators TI-83 or TI-84

Accommodations:

  1. Students will be accomodated in groups according to their needs.
  2. OER Activity Prompts are designed to integrate students' different learning styles.
  3. Students will be accomodated in groups according to their needs.

Task: During this time, students will be working in groups of  five to create a mini Lesson for Test # 1. Students will be:

Think - Pair

  1.  Analyzing, compiling, sharing what they learn from that topic among their groups.
  2. After students Think - Pair, each student will write a unique real-life word problem related to his major and the topic from the activity.

Share

  1. Then students will gather all their problems to create a mini lesson.
  2. Students will decide what problem each person will present in front of the class.
  3. Students will decide if their activity will be cc licensing their work.

Presentations: Four Groups will present their work. Each group will have 10 minutes. Other groups will be taking notes and asking questions to the presenters

Assessment: Instructors can use this time to ask students to write a short response, or feedback  or a one question quiz. For the purpose of this activity students will be writing one paragraph feedback in their math journal.

Total class duration: 110 minutes

By Katuska Campana

Annotate

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4.3 Quantitative Methods for Decision Making: Math 115
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