ClassFieldTrip.pdf

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B 21st Century Teaching and Learning: Project-based Unit

Snapshot of Unit Content and Student Expectations

Title of Unit: Can You Save The Class Field Trip? Unit Designers:

Andrea Burton Lynette Gallagher Anna Green

Albemarle County Public Schools Context of the Project: Student are surveying and presenting 2 popular choices for their class field

trip. Number of Class

Hours:

15 hours Unit

Design:

x

Project-based Unit Other Subject

Areas/Disciplines Addressed in the Unit:

Music Statistics Graphic Design

Driving Question: What is the most popular and feasible class field trip? Mathematics Content

Addressed:

Graphing Linear Equations, Collecting, Analyzing and Presenting Data

Mathematical Process Goals Addressed

X Problem Solving X Communication X Reasoning X Connections X Representations

Assumption of Prior Knowledge:

Graphing linear equations, conduct survey with or without electronics, working in a group

Courses for Which the Unit is Appropriate

Algebra I, AFDA, Capstone Mathematics Course

College and Career Readiness/21st Century Skills

BIE Page 35-37

T for skills to be taught and expected to use during the unit,

E for skills student are expected to know and be able to use during this unit A for skills that will be assessed during this unit

E Collaboration E Research E/T/A Communication (Oral and/or Written) E Technology E/T/A Critical Thinking/Decision Making

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B Major Student

Products and/or Performances:

Group: Presentation of collected data representing the 2 most popular student choice for field trip

Presentation Audience: Class

X School

Individual: Expert

Community Other:

Engage the students interest and inquiry:

Read students a memorandum written by the superintendent of schools and tell them field trips are eliminated due to cost. Take students on a virtual field trip to amusement park.

Evaluation: Formative Assessments (During the Unit)

Interview Practice Presentations

Mathematicians Journal X Notes X

Preliminary

Plans/Outlines/Prototypes

Checklists

Rough Drafts X Concept maps

Field Tests Other:

Summative Assessment (End of Project)

Written Products, with a rubric X Peer Evaluation, with a rubric

Oral Presentation with a rubric X Self Evaluation Other Product(s) or

Performance(s), with a rubric

X Other: Group

Evaluation, with rubric X

Resources Needed: On-site people, facilities:

Equipment/Technology: Internet, telephone, YouTube, GeoGebra (free download on internet) Materials: Poster board, paper, computers

Community Resources:

Reflection Methods: Individual, Group, and/or Whole Class

Mathematicians Journal X Small/Focus Groups Whole Class Discussions X Fishbowl Discussions

Survey Other: Self Evaluation

with final product

X

Material Adapted From: (Provide credit for any materials or activities adapted from other sources.)

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B Quick Snapshot for the Sequence of Unit Activities

UNIT TITLE: Can You Save The Class Field Trip? MINUTES PER CLASS: 70 – 75 minutes

Day 1 Day 2 Day 3 Day 4 Day 5

Introduction of project - Watch videos - Pass out HO#1

- Discussion of situation

Activity #1:

- Students complete HO#2 (Project Break Down Log) alone and then in groups - Students present their ideas

Groups are formed

Activity #2:

- HO#3 (Music Survey) - Discussion of surveys - Class discussion on conducting surveys. - Students read HO#4 (Article: Bias in Survey Sampling)

- Students do HO#5 (Mathematical Journal) - Discussion of how to conduct surveys

Refocus on Project: Students add any information to HO#2

Activity #3:

- Students research surveys - Students create poster on conducting a survey - Gallery walk of posters - Class discusses and reaches consensus on qualities of a good survey

Groups begin designing survey.

Refocus on Project: Students add any information to HO#2

Teacher introduces and explains HO#6 (Project Rubric) and HO#7 (Calendar)

Students design survey

Checkpoint #1: Groups show teacher their survey and explain how they are collecting data.

Students implement survey, and begin analyzing collected data.

Checkpoint #2: Groups show teacher their data.

Students analyze collected data.

Checkpoint #3: Groups explain how to present their collected data.

Students research field trip options based on

parameters

Students continue to research field trip options

Students compile and finalize field trip options and their rationale for decision

Students begin work on final project

Checkpoint #4: Project Draft Due.

Students continue working on final presentation.

Teacher gives groups initial feedback according to HO#6 (Project Rubric)

Students finalize their presentations.

Due date of Project.

Presentations may begin.

Presentations of projects Presentation of projects

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B

Overview of Student Knowledge and Skills

What do students need to know and be able to do to complete the unit successfully?

Project: Field Trip Decision

KNOWLEDGE AND SKILLS NEEDED Assumed already learned

Students will self-assess

Will be learned and assessed during the unit 1. Graphing Linear Equations x

2. Multiple Representation of Final Product

x x

3. Slope and Rate of Change x

4. Interpreting x and y intercepts x

5. Working in Groups on a long-term project.

x

6.

7.

8.

What project tools are students using to monitor their progress through the unit and especially the project?

X Student developed Know/need to know lists Student developed Daily goal sheet

X Student Mathematician’s Journals Student developed Briefs/Memos Student developed Task lists

Student developed Planning Calendar X Teacher developed Rubrics

Other:

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Unit Title: Can You Save The Class Field Trip?

Driving Question: What is the most popular and feasible class field trip?

Project Description: Students are surveying and presenting popular choices for a class field trip ENGAGE

How are student’s interests being piqued so they want to engage in the inquiry in this project-based unit?

Number of hours .5

Day 1

Virtual Field Trip #1:

Teacher asks, “Who likes to go to the zoo?” Watch webcam of zoo in Houston, Texas.

http://www.houstonzoo.org/meet-the-animals/animal-webcams/

Virtual Field Trip #2:

Teacher asks, “Who likes rollercoasters?”

Watch video of rollercoaster ride (Intimidator at Kings Dominion).

http://www.youtube.com/watch?v=0WpNSImh6Z8

Confidential Memo: Teacher shares HO#1 with class stating all field trips will be taken virtually due to lack of participation and the increase in technology, which makes it possible.

Class Discussion: Teacher leads discussion on pros and cons of decision made by the superintendent.

Mathematician Journal Prompts none EXPLORE Teacher provides guidance for the explorations to prepare students with the

knowledge and skills to engage in the project-based unit. Students are self-assessed on their prior knowledge and skills assumed for the unit

Number of hours: 4

Day 1 continued

Activity #1: Exploration & Planning of Project

Students fill out Project Break Down Log HO#2 individually, then in groups so students sort out what is expected for their proposals. Students present their ideas to the class.

Goal: Students understand what they need to do to accomplish the project goal

Day 2

Activity #2: Survey Discussion & Planning Students complete music survey (HO#3).

Discussion: “How do you make a survey?” “How do you implement the survey?” “Are the results of this survey valid?” “How could we use this information?” “How could we display this information?” “Is this data an accurate picture of the entire population of their grade level?”

Students read: “Bias in Survey Sampling” (HO#4) or electronically at http://stattrek.com/survey-research/survey-bias.aspx

Students complete Mathematical Journal Prompt (HO#5)

Discussion: “What information do we need to plan our field trip?” Goal: Students understand what makes a good survey and what information they will need to gather for project. Groups add to their Project Break Down Log if needed

Mathematician Journal Prompts

HO#5 21st Century Teaching and Learning Inquiry Learning

Project-based Learning Unit

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Day 3

Explore #3: Research Surveys and Survey Techniques

Students read: Information about surveys and creating surveys on Survey Monkey

http://s3.amazonaws.com/SurveyMonkeyFiles/SmartSurvey.pdf

Students summarize information and create a poster on designing and conducting a survey.

Gallery Walk: Posters are hung and students view their classmates Discuss: Class discusses at the end of the walk similarities and additional concerns about the survey they will design and conduct. Goal: Class reaches a consensus about what is a good survey design

Groups begin designing their survey.

EXPLAIN Teacher introduces the project and prepares

students to work independently in small groups

Number of Hours: 1

Day 4

Refocus on Project: Students add any information to Project Break Down Log (HO#2).

Project Rubric: Teacher passes out and explains the rubric (HO #6). Explain how the data collection and the presentation of survey information are assessed separately and the data collection and the presentation of field trip information are assessed

separately.

Refocus on Project: Students add any information to Project Break Down Log (HO#2).

Project Calendar: Teacher passes out the project calendar (HO#7) and students fill in their plan for what they would like to accomplish.

ELABORATE The student groups are working independently with teacher consultations.

Number of Hours: 9

Day 4 continued

Students continue designing their survey. Students may have classmates review it or answer it to test it.

Checkpoint #1: Groups show teacher their survey and explain how they are collecting data.

Day 5 – 10

Students implement their survey both in class and outside of class. Students analyze collected data. Students research field trip options based on parameters. Students compile and finalize field trip options and their rationale for decision. Students create their final products.

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Checkpoints implemented to insure groups are on track and meeting expectations.

Checkpoint #2: Groups show teacher their data.

Checkpoint #3: Groups explain how to present their collected data. Checkpoint #4: Project Draft Due.

Teacher gives groups initial feedback according to HO#6 (Project Rubric)

EVALUATE Working groups submit products or make

presentations

Number of Hours: 4.5

Day 11 – 13

Students finalize their presentations. Presentations may begin.

Teacher assess project using HO#6

Self Evaluation & Debrief using HO#8

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HO #1

Confidential Memo

Desk of the Superintendent

Memo

To:

All District Principal

From:

Superintendent

Cc:

School Board

Date:

[TODAY’S DATE]

Re:

Field Trips

As discussed at our joint School Board & School Principal Meeting last month, the district is considering discontinuing non-curricular field trips. This includes the common grade-wide end of year field trips that have been done in previous years.

Factors considered in the decision: - low attendance of class-wide field trips - low interest in class-wide field trips

- travel time for trip limits time spent at location - cost for those that do attend due to low attendance - cost for those that do attend due to choice of trip

- cost of hiring substitutes for students who do not attend and remain at school - newly developed technology allows for virtual field trips

In conclusion, unless there is support for continuing these field trips by [DUE DATE], the decision will be final.

Any proposals for continuing non-curricular class-wide field trips must include the following: - cost per student for the trip

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B HO #2

Project Break Down Log

Student Name: Project Name:

Facts

(Itemized from Memo)

What is the final product of your work?

What do you need to know to produce your product?

Plan of Action

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HO #3

Survey: Favorite Music Genres

What is your favorite music genre? Circle one.

Pop R & B Heavy Metal

Rap Alternative

Classical Rock

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HO #4

Article: Bias in Survey Sampling

In survey sampling, bias refers to the tendency of a sample statistic to systematically over- or under-estimate a population parameter.

Bias Due to Unrepresentative Samples

A good sample is representative. This means that each sample point represents the attributes of a known number of population elements.

Bias often occurs when the survey sample does not accurately represent the population. The bias that results from an unrepresentative sample is called selection bias. Some common examples of selection bias are described below.

Undercoverage. Undercoverage occurs when some members of the population are inadequately represented in the sample. A classic example of undercoverage is the Literary Digest voter survey, which predicted that Alfred Landon would beat Franklin Roosevelt in the 1936 presidential election. The survey sample suffered from

undercoverage of low-income voters, who tended to be Democrats. How did this happen? The survey relied on a convenience sample, drawn from telephone directories and car registration lists. In 1936, people who owned cars and telephones tended to be more affluent. Undercoverage is often a problem with convenience samples. 

Nonresponse bias. Sometimes, individuals chosen for the sample are unwilling or unable to participate in the survey. Nonresponse bias is the bias that results when respondents differ in meaningful ways from nonrespondents. The Literary Digest survey illustrates this problem. Respondents tended to be Landon supporters; and nonrespondents,

Roosevelt supporters. Since only 25% of the sampled voters actually completed the mail-in survey, survey results overestimated voter support for Alfred Landon.   The Literary Digest experience illustrates a common problem with mail surveys. Response rate is often low, making mail surveys vulnerable to nonresponse bias. 

Voluntary response bias. Voluntary response bias occurs when sample members are self-selected volunteers, as in voluntary samples. An example would be call-in radio shows that solicit audience participation in surveys on controversial topics (abortion, affirmative action, gun control, etc.). The resulting sample tends to overrepresent individuals who have strong opinions.

Random sampling is a procedure for sampling from a population in which (a) the selection of a sample unit is based on chance and (b) every element of the population has a known, non-zero probability of being selected. Random sampling helps produce representative samples by eliminating voluntary response bias and guarding against undercoverage bias. All probability sampling methods rely on random sampling.

Bias Due to Measurement Error

A poor measurement process can also lead to bias. In survey research, the measurement process includes the environment in which the survey is conducted, the way that questions are asked, and the state of the survey respondent. Response bias refers to the bias that results from problems in the measurement process. Some examples of response bias are given below.

Leading questions. The wording of the question may be loaded in some way to unduly favor one response over another. For example, a satisfaction survey may ask the

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response.

Social desirability. Most people like to present themselves in a favorable light, so they will be reluctant to admit to unsavory attitudes or illegal activities in a survey,

particularly if survey results are not confidential. Instead, their responses may be biased toward what they believe is socially desirable.

Sampling Error and Survey Bias

A survey produces a sample statistic, which is used to estimate a population parameter. If you repeated a survey many times, using different samples each time, you might get a different sample statistic with each replication. And each of the different sample statistics would be an estimate for the same population parameter.

If the statistic is unbiased, the average of all the statistics from all possible samples will equal the true population parameter; even though any individual statistic may differ from the population parameter. The variability among statistics from different samples is called sampling error.

Increasing the sample size tends to reduce the sampling error; that is, it makes the sample statistic less variable. However, increasing sample size does not affect survey bias. A large sample size cannot correct for the methodological problems (undercoverage, nonresponse bias, etc.) that produce survey bias. The Literary Digest example discussed above illustrates this point.

The sample size was very large - over 2 million surveys were completed; but the large sample size could not overcome problems with the sample - undercoverage and nonresponse bias.

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HO #5

Mathematical Journal Notes/Questions

Article: Bias in Survey Sampling http://stattrek.com/survey-research/survey-bias.aspx

What is bias? When does it occur?

Selection Bias Response Bias

How you could see each type of bias in your survey (example)? How do you avoid it (tips)?

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HO #6

Project Rubric

Content 4 3 2 1 Group

Score Teacher Score Teacher Comment Survey: Collection

Strategy is effective and efficient

Strategy is effective, but not efficient

Uses a strategy to gather data

No strategy for data collection is used Survey:

Representation of Results

Representation fits data, is easy to interpret, adds to the information

Representation fits data, interpretation of the data is somewhat difficult.

Representation

adequately fits data but interpretation is somewhat difficult

Representation does not fit or distorts data, interpretation is difficult

Survey: Rationale of Most Popular Uses complex mathematical reasoning. Uses effective mathematical reasoning

Some evidence of mathematical reasoning.

Little evidence of mathematical reasoning.

Trip Options: Representation of Choices

Representation fits data, is easy to interpret, adds to the information

Representation fits data; interpretation of the data is somewhat difficult.

Representation

adequately fits data but interpretation is somewhat difficult

Representation does not fit or distorts data, interpretation is difficult

Trip 1: Trip 1: Trip 2: Trip 2: Trip 3: Trip 3: Trip Options:

Mathematical Justification

Complex mathematical reasoning used.

Explanation is detailed and clear.

Effective mathematical reasoning used.

Explanation is clear.

Mathematical reasoning used.

Explanation is slightly difficult to understand.

Little evidence of mathematical reasoning. Explanation is difficult to understand.

Trip 1: Trip 1: Trip 2: Trip 2: Trip 3: Trip 3: Rationale:

Trip

Comparison

Detailed, clear, and shows complete understanding of the mathematical concepts used to solve the problem(s).

Clear, shows substantial understanding of the mathematical concepts used to solve the problem(s).

A little difficult to understand, but includes critical components, shows some

understanding of the mathematical concepts needed to solve the problem.

Difficult to understand, missing several

components, shows limited understanding of the concepts needed to solve the problem OR is not written.

Rationale: Best Option

Uses complex and refined mathematical reasoning.

Uses effective

mathematical reasoning

Some evidence of mathematical reasoning.

Little evidence of mathematical reasoning.

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Presentation 4 3 2 1 Group

Score

Teacher Score

Teacher Comment Survey Results The work is presented

in a neat, clear,

organized fashion that is easy to read.

Data is well organized, accurate, and easy to read.

The work is presented in a neat and organized fashion that is usually easy to read.

Data is organized, accurate, and easy to read.

The work is presented in an organized fashion but may be hard to read at times.

Data is accurate and easy to read.

The work appears sloppy and unorganized. It is hard to know what information goes together.

Data is accurate.

Trips The work is presented in a neat, clear,

organized fashion that is easy to read.

Data is well organized, accurate, and easy to read.

The work is presented in a neat and organized fashion that is usually easy to read.

Data is organized, accurate, and easy to read.

The work is presented in an organized fashion but may be hard to read at times.

Data is accurate and easy to read.

The work appears sloppy and unorganized. It is hard to know what information goes together.

Data is accurate.

Overall Source information collected for all graphics, facts and quotes. All documented in desired format.

Source information collected for all graphics, facts and quotes. Most

documented in desired format.

Source information collected for graphics, facts and quotes, but not documented in desired format.

Very little or no source information was collected.

Content is well organized using headings or bulleted lists to group related material.

Uses headings or bulleted lists to

organize, but the overall organization of topics appears flawed.

Content is logically organized for the most part.

There was no clear or logical organizational structure, just lots of facts.

Presentation Score /16 /16

Final Teacher Comments Final Score:

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HO #7

Project Calendar

Student Name: Project Name:

What we accomplished: What we accomplished: What we accomplished: What we accomplished: Due: Survey and explain data collection What we accomplished:

Due: Data Due: Presentation Method Due: Project Draft What we accomplished: Due: Project

What we accomplished: What we accomplished: What we accomplished: What we accomplished:

Day 11

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HO #8

Self Evaluation

SELF REFLECTION ON PROJECT WORK

Think about what you did in this project, and how well the project went. Student Name:

Project Name: Driving Question:

List the major steps of the project:

About Yourself: What is the most important thing you learned in this project:

What do you wish you had spent more time on or done differently: What part of the project did you do your best work on:

About the Project: What was the most enjoyable part of this project:

What was the least enjoyable part of this project: