Course Description and Goals

The overarching goal of this course is to develop knowledge of probability and statistics that will be useful in teaching middle school students. Specifically, we will engage in a variety of activities that will help teachers build procedural fluency and conceptual understanding of probability and statistics. Classes are activity-based, with the activities highlighting both procedural fluency and conceptual understanding of the material. There will be an attempt to alternate between the two types of activities.

Relevance: Probability and data analysis are now taught and tested in elementary school in Michigan and most other states. Furthermore, knowledge of statistical methods is essential for teaching science and social studies, where critical analysis of data is crucial. Future teachers need to be prepared to teach this content. In addition, because of the No Child Left Behind legislation and other accountability efforts, teachers need to be able to interpret statistical measures and graphs to assess the instruction in their schools and to communicate with parents.

Topics: The course will begin with a unit on probability. The statistics portion of the course will include activities to highlight the process of statistical problem solving, first with categorical data and then with quantitative data. Students can expect to learn about graphical representations and data analysis and interpretation as well as solving basic probability problems using multiple representations.

Attendance Policy

Regular on-time attendance and full participation in class are critical to learning. Of course, illness and other emergencies cannot be avoided. If you are unable to attend a class session, you must call or email the instructor in advance.

Due to the extremely compressed time frame for this course, it is important to be present and on time for all course meetings. More than one (1) absence will impact your grade in the course.

Required Texts

All planned course readings are contained in your course pack.

Class Participation

All students are expected to complete in-class assignments and to participate in class discussions and activities in a reflective and professional manner. Average performance includes the following:

• Being prepared for class (including completion of reading and writing assignments in advance, bringing all needed materials to class, etc.)

• Being on time for class

• Listening respectfully to others

• Occasionally contributing to discussions in a professional and thoughtful manner

• Occasionally asking questions of the instructor and fellow students when appropriate

Quality performance in class will surpass these minimum requirements (i.e., participate in discussions and raise questions on a regular basis).

Assignments

You will complete two major written assignments during the course: Thinking Through a Lesson and a Statistical Investigation. In addition, you will complete written reflections daily in class. Each of the three assignments are described on sheets included at the end of the syllabus.

Daily Reflections

At least once per class meeting, you will be given class time to reflect on the day’s activities in writing. On some days, you will be asked just to reflect generally on your experiences; on others, we will provide you with a focus question to consider in writing your reflections. The activities in the course are designed to help you think about middle school mathematical ideas in new and different ways, to discover new mathematical questions that you may wish to investigate, and to consider how the tasks and mathematical ideas you are experiencing relate to your work in the classroom. The reflections are designed to provide you with opportunities to thoughtfully consider those issues and others.

The course instructors will collect and read your daily reflections in order to understand each of your individual thinking and growth, and to make decisions about how to move forward with course activities and discussions.

Grading

Your grade will be calculated as follows:

Thinking Through a Lesson 30 points
Statistical Investigation 30 points
Daily Reflections 20 points
Class Participation 20 points

Other Course Details

Accommodations for Disabilities: Students with disabilities should contact the Resource Center for Persons with Disabilities to establish reasonable accommodations. For an appointment with a counselor, call 353-9642 (voice) or 355-1293 (TTY). Instructors in the course may request a VISA Form (Verified Individual Student Accommodations Form) from a student requesting services.

Observing a Major Religious Holiday. You may make up course work missed to observe a major religious holiday only if you make arrangements in advance with the instructor.

Participation in a Required Activity. To make up course work missed to participate in a required activity for another course or a university-sanctioned event, you must provide the instructor with adequate advanced notice and a written authorization from the faculty member of the other course or from a university administrator.

Attendance. Students whose names do not appear on the official class list for this course may not attend this class.

Disruptive Behavior. Article 2.3.5 of the Academic Freedom Report (AFR) for students at Michigan State University states that “The student's behavior in the classroom shall be conducive to the teaching and learning process for all concerned.” Article 2.3.10 of the AFR states that “The student has a right to scholarly relationships with faculty based on mutual trust and civility.” General Student Regulation 5.02 states that “no student shall . . . interfere with the functions and services of the University (for example, but not limited to, classes . . .) such that the function or service is obstructed or disrupted.” Students whose conduct adversely affects the learning environment in this classroom may be subject to disciplinary action through the Student Faculty Judiciary process.

Academic Honesty and Integrity

We assume that the student is honest and that all course work and examinations represent the student’s own work. Incidents of plagiarism are taken very seriously and will be pursued. Students are strongly cautioned not to copy any text verbatim on any class assignments without using appropriate quotations and source citations. Students are encouraged to discuss the course material, papers, writing assignments, and projects with their peers, both in and out of class. However, it is expected that all course assignments, including oral presentations, will be completed by students individually without assistance from any source unless otherwise noted in the assignment description. Students are encouraged to see the course instructors with any questions or concerns about plagiarism or improper working together.

Violations of the academic integrity policy such as cheating, plagiarism, selling course assignments or academic fraud are grounds for academic action and/or disciplinary sanction as described in the university’s student conduct code. For University regulations on academic dishonesty and plagiarism, refer to www.vps.msu.edu/SpLife/rule32.htm and www.msu.edu/unit/ombud/plagiarism.html. Students who violate MSU rules may receive a penalty grade, including but not limited to a failing grade on the assignment or in the course and/or removal from the program.
Thinking Through a Lesson

(Due 22 June 2009 - 30 points)

The main purpose of the Thinking Through a Lesson assignment is to think deeply about a specific lesson related to probability. The goal here is to move beyond the structural components associated with lesson planning (e.g., listing the materials you will need, describing the way students will be grouped, determining teacher actions during the lesson) to a deeper consideration of how you are going to advance students’ mathematical understanding during the lesson. This is not to say that structural components of a lesson are not important, but rather that a focus on structural components alone is not sufficient to ensure that students learn mathematics.

Part One – Solving the Task as a Learner and as a Teacher

You will select a mathematical task related to probability, either from your own curriculum or from a set of provided tasks related to probability. The task must be high-level (multiple solution paths, representations, rich opportunities for student thinking). You will begin by solving the task as many ways as you can and to anticipate the ways in which you think students will solve the task. This may include considering approaches that are incorrect as well as correct, inefficient as well as efficient, and unsophisticated as well as sophisticated.

After you have solved the task, you will identify the mathematical ideas related to probability that can be learned from the task and your specific goals regarding what you hope your students would learn from engaging in this task.

Part Two – Thinking about How to Promote Student Engagement and Learning

You will continue to work on the lesson, drawing on the work completed in part one. The focus of your independent work will be on thinking through what you as a teacher will do to support your students’ engagement with and learning from this task. The following questions should be used to guide your thinking:

Selecting and Setting up a Mathematical Task

Ø What are your mathematical goals for the lesson (i.e., what is it that you want students to know and understand about probability as a result of this lesson)?

Ø In what ways does the task build on students’ previous knowledge? What definitions, concepts, or ideas do students need to know in order to begin to work on the task? What questions will you ask to help students access their prior knowledge?

Ø What are all the ways the task can be solved?

o Which of these methods do you think your students will use?

o What misconceptions might students have?

o What errors might students make?

Ø What are your expectations for students as they work on and complete this task?

o What resources or tools will students have to use in their work?

o How will the students work -- independently, in small groups, or in pairs -- to explore this task? How long will they work individually or in small groups/pairs? Will students be partnered in a specific way? If so in what way?

o How will students record and report their work?

Ø How will you introduce students to the activity so as not to reduce the demands of the task? What will you hear that lets you know students understand the task?

Supporting Students’ Exploration of the Task

Ø As students are working independently or in small groups:

o What questions will you ask to focus their thinking?

o What will you see or hear that lets you know how students are thinking about the mathematical ideas?

o What questions will you ask to assess students’ understanding of key mathematical ideas, problem solving strategies, or the representations?

o What questions will you ask to advance students’ understanding of the mathematical ideas?

o What questions will you ask to encourage students to share their thinking with others or to assess their understanding of their peer’s ideas?

Ø How will you ensure that students remain engaged in the task?

o What will you do if a student does not know how to begin to solve the task?

o What will you do if a student finishes the task almost immediately and becomes bored or disruptive?

o What will you do if students focus on non-mathematical aspects of the activity (e.g., spend most of their time making a beautiful poster of their work)?

Sharing and Discussing the Task

Ø How will you orchestrate the class discussion so that you accomplish your mathematical goals? Specifically:

o Which solution paths do you want to have shared during the class discussion? In what order will the solutions be presented? Why?

o In what ways will the order in which solutions are presented help develop students’ understanding of the mathematical ideas that are the focus of your lesson?

o What specific questions will you ask so that students will:

§ make sense of the mathematical ideas that you want them to learn?

§ expand on, debate, and question the solutions being shared?

§ make connections between the different strategies that are presented?

§ look for patterns?

§ begin to form generalizations?

Ø What will you see or hear that lets you know that students in the class understand the mathematical ideas that you intended for them to learn?

Ø What will you do tomorrow that will build on this lesson?

Thinking Through a Lesson – Scoring Rubric

A written analysis that includes both parts one and two of the assignment is due at the start of Class 6, Monday 22 June 2009.

Part One – Solving the Task as a Learner and as a Teacher 4 points

Most of the points associated with the project will be earned based on the part 2 of the project. You will, however, include ONE complete solution, with one solution path, to the task in your report. This solution will be scored out of 4 points based on the clarity of the solution to the reader.

Part Two – Thinking about How to Promote Student Engagement and Learning

Mathematical Student Learning Goal 2 Points

2 pts An appropriate goal at a reasonable level taken from either the GLCEs or the GAISE guidelines is well described

1 pt An appropriate goal at a reasonable level taken from either the GLCEs or the GAISE guidelines is given, but the description is lacking.

0 pts The goal is inappropriate or not included

Building on Prior Knowledge 2 Points

2 pts Prior knowledge that students will have is identified and connected to the task and the goal

1 pt Prior knowledge that students will have is identified, but connections to task and the goal are weak or unspecified

0 pts No information about how the task builds on prior knowledge

Classroom Environment and Materials 2 Points

2 pts The classroom environment is described
Materials selected for the task are described and appropriate to the task

1 pt Either classroom environment or materials selected are absent, OR the materials are inappropriate for the task, OR the classroom environment description is overly general or vague.

0 pts No information about classroom environment or materials

Task Selection/Activities 2 Points

2 pts The task is a high-level task and is appropriate for the mathematical goal
Information about how the teacher will launch task is included
Intended task launch does not reduce the cognitive demands of the task

1 pt The task is a high-level task and is appropriate for the mathematical goal
Information about how the teacher will launch task is included
Intended task launch may the cognitive demands of the task, or the task launch information is overly general

0 pts The task is of low cognitive demand

Student Thinking/Expected Student Responses 6 Points

6 pts There is evidence that the student thoroughly considered how students will make sense of the mathematical ideas in the task.
Student solutions or thinking paths are clearly identified and represent a range of approaches to the task, varying by representation or strategy where appropriate
Ideas related to student thinking are fully developed and clear
Solutions include incorrect pathways/note possible student misconceptions

4 pts There is evidence that the student has considered how students will make sense of the mathematical ideas in the task.
Student solutions or thinking paths are identified and represent a range of approaches to the task, with some variation by representation or strategy
Ideas related to student thinking are clear but general
Solutions include incorrect pathways/note possible student misconceptions

2 pt There is weak evidence that the student considered how students will make sense of the mathematical ideas in the task.
Student solutions or thinking paths are very general or unclear OR
Incorrect pathways/note possible student misconceptions are not included OR
Student thinking represents a narrow (or single) range of approaches to the task

0 pts No information about student thinking

Supporting Students Exploration of the Task 6 Points

6 pts There is evidence that the student thoroughly considered how to support the students’ exploration of the task.
Appropriate prompts for students who are having trouble starting the tasks are included and well described.

Appropriate follow up questions to assess students’ understanding are included for a variety of solution paths.

Appropriate extensions to the basic activity are given for the students who finish quickly.

4 pts There is evidence that the student has considered how to support the students’ exploration of the task.

Appropriate prompts for students who are having trouble starting the tasks are included but are unclear

Appropriate follow up questions to assess students’ understanding are included for a single solution path.

The extension to the basic activity given for the students who finish quickly is not appropriate.

2 pt There is weak evidence that the student considered how to support the students’ exploration of the task.

The prompts for students who are having trouble starting the tasks are very general or unclear OR

Appropriate follow up questions to assess student understanding are not included OR

There are no extensions given for students who finish the task quickly.

0 pts No information about how student explorations will be supported.

Sharing and Discussing the Task 6 Points

6 pts There is evidence that the student thoroughly considered how to provide closure for the task

Possible solution paths are well described and presented in an order that makes mathematical sense including those incorrect solutions that are included.

Appropriate responses to incorrect solutions are included and well described.

Appropriate connections between possible solutions are well described.

4 pts There is evidence that the student has considered how to provide closure for the task

Possible solution paths are presented but the order is not appropriate or incorrect solutions have not been included.

Appropriate responses to incorrect solutions are included but are vague or unclear.

Appropriate connections between possible solutions are vague or unclear.

2 pt There is weak evidence that the student considered how to provide closure for the task

The order of presentation of solution paths is not included OR

There are no responses given for incorrect solutions OR

There is no attempt to connect the different solution paths.

0 pts No information about how the task will be discussed.

Statistical Investigation

(Due 5:00pm 29 June 2009 - 30 points)

The purpose of the project is for students to complete a statistical investigation and write the results in scientific format. Students will complete one of the following activities from the course Activities Manual and write the results in scientific report format.

The Birthday Problem

Hog Project

Brain Tosses Project

Linear Regression Project

Enemy Tank Project

Guidelines for Writing a Scientific Paper

Title and Author Panel

The title should be descriptive but short.

Introduction

Here you introduce the topic of the work, briefly summarize any relevant background information, including why the topic is of interest to the research team, and succinctly state the objectives, research question and/or hypothesis.

Design

Here you describe the design of the simulation, survey, experiment, or observational study. There must be sufficient detail to permit the reader to understand what was done and evaluate the appropriateness of the experimental design and technique. A knowledgeable user of statistics should be able to replicate your design from what is written.

Results

This is a summarized report of your observations, not your interpretation, of the results. Present your results in a logical sequence, not the sequence in which they were obtained. This is primarily a visual, rather than verbal, presentation. Graphical representation of data is almost always more effective than tables or text, unless the data can be easily summarized using 2 or 3 numbers. The text should tell the reader the important points to be noted on the graphs or tables, or to call out specific examples from the figure or table to illustrate a point. Raw data should be included only when absolutely necessary; if in doubt, ask your instructor.

Discussion

Here you analyze and discuss your findings. Summaries such as numbered or bulleted items may be used. You should point out the general meaning and importance of your results, and relate them to your research question/hypotheses. You should also include a description of further work that could be done in this area.

Conclusions

This includes a few brief and concise statements summarizing your work.

Statistical Investigation – Scoring Rubric

Title (2 points)

2 pts The title give an accurate preview of what the paper is about

1 pt The title is vague

0 pts There is no title

Introduction (4 points)

4 pts Sufficient background has been provided to understand the nature of the paper that follows AND the final paragraph includes a brief description of the research question/hypothesis/goals and findings of the paper

2 pts Sufficient background has NOT been provided to understand the nature of the paper that follows OR the final paragraph does NOT includes a brief description of the research question/hypothesis/goals and findings of the paper.

0 pts There is no introduction

Design (6 points)

6 pts The description of the design is appropriate AND could be replicated by a knowledgeable statistics reader as written

4 pts The description of the design is appropriate OR not be replicated by a knowledgeable statistics reader as written

2 pts The description of the design is appropriate AND could not be replicated by a knowledgeable statistics reader as written

0 pt No such description exists

Results (6 points)

6 pts The analysis is thorough

All appropriate figures are drawn and labeled correctly including titles and legends and the interpretation of each figure is correct and logical with attention to appropriate features of the data.

4 pts The analysis is missing attributes

The included figures are drawn and labeled correctly including titles and legends and the interpretation of each figure is correct and logical with attention to appropriate features of the data, but some aspects of the analysis have been omitted.

2 pts The analysis is incorrect

Whether or not the analysis is complete, errors have been made in the graphs and/or interpretations of the data.

0 pts No analysis is included

Discussion (6 points)

6 pts The discussion is thorough

The author clearly addresses all of the research questions or hypotheses written in the introduction AND specific data are cited for each claim.

4 pts The discussion is missing attributes

The author addresses some of the research questions or hypotheses written in the introduction AND specific data are cited for each claim mentioned.

2 pts The discussion contains no evidence

The author addresses some or all of the research questions or hypotheses written in the introduction but specific data are not cited for each claim.

0 pts No discussion is included

Conclusion and Writing (6 points)

6 pts The author clearly addresses possible follow up work in the conclusion, the paper is well organized and does not contain spelling, grammar or word usage errors

4 pts The author does not clearly address possible follow up work in the conclusion OR the paper is poorly organized OR contains spelling, grammar or word usage errors

2 pts Two of the three criteria are not met. The author clearly addresses possible follow up work in the conclusion, the paper is well organized, and the paper does not contain spelling, grammar or word usage errors.

0 pts None of the three criteria are met.