math i function families: interceptslrieber.coe.uga.edu/edit6170/resources/teams/summer2… ·...

Math I Function Families: Intercepts

Tami Echard and Twila Masaschi (T2)

EDIT 6170

Summer 2010

Table of Contents

EXECUTIVE SUMMARY 3

NEEDS ANALYSIS 3

BACKGROUND OF THE PROBLEM 3PROBLEM STATEMENT 5NEEDS ANALYSIS 5RATIONALE FOR THE NEED FOR INSTRUCTION 6GOAL STATEMENT 6

LEARNER ANALYSIS 6

ENTRY BEHAVIORS 6PRIOR KNOWLEDGE OF THE TOPIC 7MOTIVATION 7EDUCATION AND ABILITY LEVELS 7GENERAL LEARNING PREFERENCES 7

CONTEXT ANALYSIS 8

COURSE AND UNIT DESIGN 8

LESSON DESIGN 9

FORMATIVE EVALUATION PLAN 10

FORMATIVE EVALUATION 10

REFERENCES 13

APPENDIX A 14

APPENDIX B 27

APPENDIX C 30

APPENDIX D 31

APPENDIX E 32

APPENDIX F 35

APPENDIX G 37

APPENDIX H 38

APPENDIX I 41

APPENDIX J 43

APPENDIX K 45

2

Executive Summary

Needs analysis, done through teacher surveys and gathering data on assignments, quizzes, and tests

from our Math I Students, shows a need for improvement, correction, and addition of content in the

Math I Course offered by Georgia Virtual School. Once the issues with content as well as gaps in

content were identified, correction to content was made, Jing videos with added content and

written examples were added to enhance the written lectures that already existed, self assessments

such as matching, labeling, multiple choice, flash cards, sorting, and other activities were added

with practice problems in order for the students to have self-guided, ungraded activities that would

illustrate their knowledge, and finally more resources of online learning objects, brain pops,

presentations, and other interactive activities was added to enhance the course content. Once this

was completed, and evaluation was completed through teacher review, department chair review,

and data collected on assignments, quizzes, and tests from the Math I Students in the “new” course.

Results from this data was used to show where the improvement occurred as well as where a need

for improvement in content might still be OR explained why there was no improvement due to a

summer course, repeat students, or other reasons. Our data can be seen in the attached appendices.

Needs Assessment

Background of the Problem:

The context or the system of interest that we will be dealing with is within Georgia Virtual

School’s Math I Course. The Math I Course is offered to Georgia Virtual School students who

are located across the state of Georgia, which therefore technically is part of many public,

private, and home school sectors across the state of Georgia. So this course can ultimately

affect and involve employees at the Department of Education, Parents, Students, Teachers,

Administration Team, and Support Staff.

3

After reviewing our Math I course, we have concluded that students within the Math I course

were unable to succeed in Math I without greater assistant from the teacher. From the way

in which the courses are designed, we aim to have the teacher be an additional resource to

the student. The material should be delivered to the student through a series of videos,

activities, and practice.

The goal of the revised Georgia Performance Standards is to increase the students’

understanding. We cannot continue to teach the way we have before and expect the

students to perform at this new level. In the Georgia Performance Standards High School

Mathematics Research and Resource Manual, the “traditional” methods are addressed.

“Teachers need not fear that they will be made obsolete. They will, however, feel increasing pressure to bring their methods--along with the curriculum--into line with the way the modern world works. That means putting a greater emphasis on teaching kids to collaborate and solve problems in small groups and apply what they've learned in the real world. Besides, research shows that kids learn better that way than with the old chalk-and-talk approach.” (Georgia Performance Standards, 2007)

Although we have used the newer delivery method of virtual model, the original Math I

course was close to a traditional classroom. There were “lectures” delivered via a written

document. In our eyes this was far worse than a teacher standing in front of you delivering

material. Few students are using these written lectures to attempt to master material.

In remarks by Secretary Arne Duncan he discussed how technology can transform education.

One specific goal he addressed deals directly with our Math I course. Here is the first goal he

mentioned:

“The first goal is learning--creating more effective and engaging learning experiences for all students. The content and skills students need to learn--as well as what we know about how, when and where they learn best--have changed. With technology, we can personalize learning, increasing relevance and the opportunity to achieve. Technology can help disadvantaged learners or learners with special needs to excel--

4

from low-income early learners, to English Learners, to learners with disabilities.” (Duncan, 2010)

We can use technology to personalize learning and increase the student’s opportunity to

achieve. By providing students a variety of ways to receive the same information, they can

learn from what best works for them.

According to the student survey administered to all students participating with Georgia

Virtual School, only 53% of the math students responded agree or strongly agree with the

statement “The assignments in my online course adequately prepared me for the

assessments given.” From the student’s perspective, the assignments, and likely the

instruction delivered prior to the assignments we’re not addressing what was being

assessed. (See appendix A) This makes us think we may want to look at the instruction,

assignments, and assessments to see that they are all aligned to the objectives for lessons.

Problem Statement:

Students participating in the Georgia Virtual School Math I course are not adequately

mastering the Georgia Performance Standards set forth by the State of Georgia with regards

to Interpretation of Functions.

Needs Analysis:

We are in a unique situation with regards to this project. We had an established course that

we can use to pull student data. This course has specific student data by assignment, quiz,

and tests. We evaluated the data for the first module of the Georgia Virtual School Math I

course. The reason we focused on this first course of the overall Georgia Virtual Math I

curriculum was a timing issue. We knew we would want these students to participate in our

small group evaluation and they would be at this point during our summer term. The data,

5

which is located in Appendix B, shows the individual students performance in three units in

the first course. The first unit – Interpretation of Functions – was the lowest.

Rationale for the Need for Instruction:

The data showed a deficiency in the third lesson on Intercepts. This will be our focus lesson.

We selected this specifically because the concept of intercepts will be revisited in other Math

I lessons as well as Math II and Math III. It is important that the students understand the x-

intercepts as zeros and roots of a function as well as solutions of equations. This concept of

intercepts will be significant in graphing linear equations and writing equations of linear

functions.

Goal Statement:

After correcting content, enhancing instruction by adding media and additional external

online resources, and creating self-assessment activities students will be able to master the

Georgia Performance Standards for Interpretation of Functions, specifically Intercepts of a

Function.

Appendix A: Student Survey ResultsAppendix B: SY 2009-2010 Math I Assessment Data

Learner Analysis

Entry Behaviors

Upon entering the Math I Course, students should have successfully completed and mastered

all performance standards provided by the state of Georgia within Math 8. Specific

performance standards dealing with the lessons covered in Interpretation of Functions can

be viewed in Appendix D.

6

Prior Knowledge of the Topic Area

The students who were selected to participate in our small group evaluation were those

students who registered with Georgia Virtual School for the summer 2010 term. These

students are in need for credit for the course because it is required by the state of Georgia.

These students could be first time Georgia Virtual School students or former Georgia Virtual

School students who have failed the Math I course or they could be students who are former

Georgia Virtual School students or first time Georgia Virtual School students who are trying

to graduate early. We are unaware of their situation because it is not something that

Georgia Virtual School asks of their students.

Motivation

These students were motivated to participate because they needed course credit for Math I

in order to meet the state of Georgia requirements and advanced to Math II.

Education and Ability Levels

All students who participated in this study were Math I students who had met the

performance standards for Math 8 provided by the state of Georgia and because of their

mastery of these skills should be at the level to attain the performance standards by the state

of Georgia set for Math I.

General Learning Preference

Georgia Virtual School courses are developed with all learning preference, visual,

kinesthetic, and oral learners in mind.

7

Context Analysis

Instruction will take place in the online classroom of Georgia Virtual School located at

gavirtualschool.org. Lessons from this course will prepare students to master the performance

standards set forth by the state of Georgia for the Math I Course. Georgia Virtual School courses are

self-paced with all assignments due on a weekly basis by Friday at 5p.m. according to the suggested

pacing guide.

Course and Unit Design

The course for this study is based on the needs identified in the needs assessment. The goal for this

instruction is that after receiving corrected content, enhanced content through media and external

resources, and self-assessment activities, the students will be able to demonstrate and interpret the

characteristics of functions using graphs, tables, and simple algebraic techniques as well as use the

language of mathematical argument and justification. This Function Families course provides

students the opportunity to master Georgia Performance Standards for the Math I curriculum.

The three units that will make up this course are Interpretations of Functions, Mathematical

Argument and Proof, and Graphs and Transformations. After completing Interpretations of

functions the student should be able to demonstrate how to interpret functions through domain

and range, rates of change, intercepts, maximum and minimum, increase and decrease, end

behavior, and compare rates of change. After completing Mathematical Argument and Proof, the

student should be able to demonstrate how to use the language of mathematical argument and

justification through conjecture, inductive reasoning, deductive reasoning, counterexamples,

indirect proof as appropriate, and understand and use the relationships among a statement and its

converse, inverse, and contrapositive. Finally, after completing Graphs and Transformation the

8

student should be able to generate graphs of transformations of basic functions including vertical

shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

Appendix C: Macro Instructional ICM

Lesson Design

Team T2 chose to focus on the Intercepts lesson because it had the lowest assessment scores for

Interpretation of Functions unit. After completing this lesson, students will be able to state, list, and

identify points as x- and y-intercepts and state whether a point is an x-intercept, y-intercept, or

neither by completing the self-assessment activity and ten question assignment.

First, we will engage our students through Essential Questions to inspire further learning. Next,

students will read some brief introductory material about intercepts. After the introduction, they

will watch a five-minute Jing video created by team T2 to further explain intercepts and walk

through examples. More resource material will be offered from www.brightstorm.com,

www.purplemath.com, and www.mathexpression.com dealing with x- and y-intercepts. This

material in the virtual class is available to students at all times to provide varied instruction.

After the students have read the lecture, viewed the video, and explored any additional resources,

the students are invited to complete five self-assessed practice problems. These self-assessed

practice problems have been entered directly into the learning environment by our team.

If the students are confident in their knowledge of the content material, they will proceed to a ten-

question assignment. However, if the student does not feel he can successfully complete the

assignment, he may revisit any of the material presented.

Appendix D: Micro Instructional ICM9

http://www.mathexpression.com/

http://www.purplemath.com/

http://www.brightstorm.com/

Appendix E: Course, Unit, and Lesson Design OutlineAppendix F: Instructional Strategy Planning Sheet

Formative Evaluation Plan:

Because this is a shortened semester, the requirement for the project formative evaluation was

limited to a small-group evaluation. Our small group evaluation will consist of students enrolled in

the GAVS Math I course for the Summer 2010 term.

Since the improvements we made in this course will be implemented into our Georgia Virtual

School (GAVS), we are required by GAVS to complete an external review as well as expert review.

Content specialists will complete both these reviews.

Appendix G: Formative Evaluation Planning WorksheetAppendix H: GAVS Accessibility ReviewAppendix I: GAVS Copyright ReviewAppendix J: GAVS Content Review

Formative Evaluation:

The small-group instruction was performed with five Math I students enrolled in the Summer 2010

course with GAVS. These students had successfully completed their Math 8 course requirements.

Students completed this lesson at their own pace. If they completed the lecture, video, external

resource activities, self-assessment and assignment, we anticipate the minimal time requirement to

be 60 minutes.

Students in this small group completed an assignment, took a quiz, and a test containing

information on the intercepts lesson within Interpretation of Functions.

10

The assignment consisted of 10 questions with a time limit of 45 minutes. The quiz consisted of 15

questions with a time limit of 45 minutes. Finally, the test consisted of 20 questions with a time

limit of 60 minutes. Each assessment received grade that was recorded as a percent. The results

were averaged by assessment type as well as a unit average.

The unit average was calculated using Assignment Average 15%, Quiz Average 20%, and the Test

Average was 35%. (This is a total of 70% of the students’ grade. The resulting unit average was

adjusted accordingly.)

Looking at the original data from the SY 2009-10, the intercepts assignment average was a 71.3%.

The Quiz average was a 63.4%. The test average was a 68.8%. The overall unit average was a

56.0%.

Using the data collected from our small group of Summer 2010, the intercepts assignment average

was a 77.5%. The Quiz average was a 72.5%. The test average was an 83.7%. The overall unit

average was a 74.8%.

The results of our small group evaluation were impressive. The individual lesson average increased

by 6.2%. The quiz and test average increases were more notable at 9.1% and 14.9% respectively.

The overall unit average went up 18.8%.

While we know that the added instructional material contributed to the improvement in these

scores, we are aware that these results based on five students (although, we only included data of

four students because the fifth student did not complete the course orientation and was not

11

participating) are not an adequate sample. We will continue to monitor the achievement of

students in subsequent terms.

Appendix K: Summer 2010 Assessment Data

12

References

Duncan, Arne. "Using Technology to Transform Schools." United States Department of Education News. 03 Mar 2010: n.p. SIRS Government Reporter. Web. 28 Jun 2010.

Georgia Performance Standards High School Mathematics Research and Resource Manual, Spring 2007. Retrieved June 25, 2010, from https://extranet.georgiastandards.org/standards/GPS%20Support%20Docs/Math-GPS-High-School-Research-and-Resource-Manual.pdf.

13

https://extranet.georgiastandards.org/standards/GPS%20Support%20Docs/Math-GPS-High-School-Research-and-Resource-Manual.pdf

https://extranet.georgiastandards.org/standards/GPS%20Support%20Docs/Math-GPS-High-School-Research-and-Resource-Manual.pdf

Appendices

Appendix AStudent Survey Results – Georgia Virtual School SY 2009-2010

Student Survey Results

Fall 09

Spring 10

Summer 10

Number of students who completed the survey 2238 2312

How did you learn about Georgia Virtual School? Fall

09Spring

10Summer

10From a counselor or teacher at my school 78% 80% Georgia Virtual School Website 6% 6% Georgia Virtual School Employee 1% 1% News Story 1% 1% Other 14% 12%

What is your experience with online courses? Fall

09Spring

10Summer

10This is my first online course 72% 56% I have taken 1 course previously with GA Virtual School 11% 24% I have taken 2 or more online courses previously with GA Virtual School

10% 15%

I have taken online courses from another online program 6% 5%

14

Why did you decide to take this course online? (choose all that apply) Fall

09Spring

10Summer

10I wanted to get ahead for early graduation 7% 7% I wanted to make room for an elective course 5% 6% I wanted to try online learning 17% 16% I needed to retake a course that I was unsuccessful in before

4% 8%

There was a scheduling conflict in my regular school schedule19% 20%

This course is not offered at my school 29% 26% I just moved to Georgia and this course was not required by my previous school system 1% 2%

I am home schooled 7% 8% Other 11% 8%

Which of the following best describes you?

Fall 09

Spring 10

Summer 10

I am taking this class as part of my regular school day. 75% 70% I am taking this class in addition to my regular school day. 15% 19% I am home schooled. 10% 11%

How would you describe your online learning experience compared to your learning experience in a traditional classroom setting? Fall

09Spring

10Summer

10My online learning was more than in a traditional classroom 20% 21% My online learning was comparable to my learning in a traditional classroom

38% 38%

My online learning was less than in a traditional classroom 34% 32% I am home schooled 8% 9%

15

Which of the following best describes you? Fall

09Spring

10Summer

10My technology skills have improved as a result of taking an online class

52% 49%

My technology skills have not changed as a result of taking an online class.48% 51%

What type of diploma are you pursuing? Fall

09Spring

10Summer

10Colege Preparatory 31% 32% College Preparatory with Distinction (GPA Above 3.0) 56% 55% Technology/Career Preparatory 7% 7% Technology/Career Preparatory with Distinction (GPA Above 3.0)

5% 5%

Special Education 1% 1%

What are your plans after high school? Fall

09Spring

10Summer

10I plan to attend a 4 year college. 82% 83% I plan to attend a 2 year college. 5% 6% I plan to attend a trade school or technical college 3% 2% I plan to join the military. 2% 3% I plan to get a job. 2% 2% Other 6% 4%

16

With your most recent online class in mind, please indicate your level of agreement with each statement. (1 = Strongly Agree, 5 = Strongly Disagree)

Comment Average Score Fall

09Spring

10Summer

10The online registration process is convenient. 1.84 1.80 The online registration process is user friendly. 1.80 1.78 The Georgia virtual school staff is accessible and responsive.

1.74 1.72

My facilitator is knowledgeable about Georgia Virtual School 1.69 1.66 My facilitator was accessible and responsive. 1.65 1.62 The Desire 2 Learn helpdesk was helpful in solving my technical problems and answering questions. 2.00 1.95

The online learning environment is a convenient way to learn 2.01 1.96 Overall, I am satisfied with my online learning experience 2.00 1.95 I would take another online course 2.14 2.13

Respondents were asked whether they Strongly Agree, Agree, Neutral, Disagree, Strongly Disagree with the comments below

Comment

% of Respondents who Agree or Strongly Agree

Fall 09

Spring 10

Summer 10

The online registration process is convenient. 90% 89% The online registration process is user friendly. 89% 90% The Georgia virtual school administration and staff are accessible and responsive

90% 91%

My facilitator is knowledgeable about Georgia Virtual School 93% 92% My facilitator was accessible and responsive 92% 93% The Desire 2 Learn helpdesk was helpful in solving technical problems and answering questions. 82% 83%

The online learning environment is a convenient way to learn.76% 79%

Overall, I am satisfied with my online learning experience. 76% 78%

17

I would take another online course. 70% 69%

In which of the following subject areas are you currently taking an online course? (Choose all that apply) Fall

09Spring

10Summer

10AP Course 12% 10% Business 4% 4% World Languages 29% 24% Language Arts 10% 10% Mathematics 11% 14% Science 9% 13% Social Studies 15% 18% Elective 10% 7%

Content Area Information

The assignments in my online course adequately prepared me for the assessments given.

Content Area

% of respondents who agree or strongly agree

Fall 09

Spring 10

Summer 10

Business/Electives 87% 57% Language Arts 86% 54% Math 86% 53% Science 78% 75% Social Studies 82% 86% World Languages 89% 91%

18

My online teacher was accessible and responsive.

Content Area


Fall 09

Spring 10

Summer 10


My online teacher provides feedback that is helpful to my learning.

Content Area


Fall 09

Spring 10

Summer 10


19

Elluminate chat sessions are offered by my teacher.

Content Area


Fall 09

Spring 10

Summer 10


Elluminate chat sessions are helpful to my learning.

Content Area


Fall 09

Spring 10

Summer 10


20

Assignments were graded in a timely manner by my teacher.

Content Area


Fall 09

Spring 10

Summer 10


Overall, my online teacher was effective.

Content Area


Fall 09

Spring 10

Summer 10


21

I would take another online course in the same content area.

Content Area


Fall 09

Spring 10

Summer 10


How many hours per week do you spend working ONLINE on your course?0-2 hours 2-4 hours 4-6 hours 6-8 hours More than 8 hours

Fall 09Spring

10Summe

r 10Fall 09

Spring 10

Summer 10

Fall 09Spring

10Summe

r 10Fall 09

Spring 10

Summer 09

Fall 09Spring

10Summe

r 10

Business/Electives 21% 24% 24% 28% 33% 25% 17% 16% 5% 7%

Language Arts 22% 18% 14% 19% 27% 26% 21% 22% 16% 15%

Math 17% 13% 25% 23% 33% 29% 13% 17% 12% 18%

Science 13% 15% 18% 24% 37% 29% 19% 23% 13% 9%

Social Studies 10% 11% 17% 23% 35% 34% 25% 21% 13% 11%

World Languages 12% 10% 20% 20% 33% 38% 23% 22% 12% 10%

22

How many hours per week do you spend working OFFLINE on your course?

0-2 hours 2-4 hours 4-6 hours 6-8 hours More than 8 hours Fall 09

Spring 10

Summer 10

Fall 09Spring

10Summe

r 10Fall 09

Spring 10

Summer 10

Fall 09Spring

10Summe

r 10Fall 09

Spring 10

Summer 10


Language Arts 48% 42% 25% 26% 11% 15% 7% 6% 9% 0%

Math 46% 46% 28% 25% 14% 18% 6% 4% 6% 7%

Science 53% 55% 29% 23% 8% 12% 4% 4% 6% 6%

Social Studies 53% 58% 26% 22% 11% 10% 6% 4% 4% 6%

World Languages 58% 58% 26% 22% 8% 12% 3% 3% 5% 5%

My teacher responded to my emails or phone calls:

Within 24 hours Within 2-3 daysIn a time period greater

than 3 days Never

Fall 09Spring

10Summer

10Fall 09

Spring 10

Summer 10

Fall 09Spring

10Summer

10Fall 09

Spring 10

Summer 10

Business/Electives 70% 70% 23% 25% 5% 3% 2% 2%

Language Arts 72% 74% 19% 16% 3% 3% 6% 7%

Math 83% 78% 13% 17% 2% 3% 2% 2%

Science 72% 72% 20% 21% 4% 3% 4% 4%

Social Studies 74% 77% 21% 20% 3% 2% 2% 1%

World Languages 81% 79% 16% 16% 2% 4% 1% 1%

23

Most questions related to course content or assignments are/were resolved by my teacher:

Within 24 hours Within 2-3 days In a time period greater than 3 days

Never

Fall 09Spring

10Summe

r 10Fall 09

Spring 10

Summer 10

Fall 09Spring

10Summe

r 10Fall 09

Spring 10

Summer 10

Business/Electives 65% 70% 27% 24% 5% 4% 3% 2%

Language Arts 72% 71% 19% 18% 3% 4% 6% 7%

Math 78% 76% 17% 18% 2% 3% 3% 3%

Science 71% 69% 23% 22% 3% 5% 3% 4%

Social Studies 73% 79% 22% 17% 3% 3% 2% 1%

World Languages 78% 78% 18% 17% 3% 3% 1% 2%

How would you describe the grading system for your online course?

The grading system for my online course is more

rigorous than my traditional classes.

The grading system for my online course is about the

same as my traditional classes.

The grading system for my online course is less

rigorous than my traditional classes.

Fall 09Spring

10Summer

10Fall 09

Spring 10

Summer 10

Fall 09Spring

10Summer

10

Business/Electives 29% 33% 59% 57% 12% 10%

Language Arts 40% 44% 49% 48% 11% 8%

Math 33% 33% 57% 58% 10% 9%

Science 34% 35% 58% 58% 8% 7%

Social Studies 33% 30% 59% 59% 8% 11%

World Languages 31% 30% 58% 61% 11% 9%

24

What is your expected grade in your course?90-100 80-89 70-79 60-69 Below 60

Fall 09Spring

10Summe

r 10Fall 09

Spring 10

Summer 10

Fall 09Spring

10Summe

r 10Fall 09

Spring 10

Summer 10

Fall 09Spring

10Summe

r 10


Language Arts 44% 40% 33% 36% 16% 17% 3% 2% 4% 5%

Math 41% 39% 28% 28% 24% 25% 3% 3% 4% 5%

Science 43% 40% 32% 40% 19% 16% 4% 2% 2% 2%

Social Studies 56% 52% 32% 32% 10% 13% 1% 1% 1% 2%

World Languages 53% 56% 29% 28% 13% 12% 3% 2% 2% 2%

Business

Fall 09 Spring 10 Summer 10

% of respondents agree or strongly agree that the process of receiving and returning software, textbooks, or equipment is efficient. 61% 64%

% of respondents agree or strongly agree that the software, textbooks, or equipment that I received was essential in completing my course. 66% 67%

% of respondents agree or strongly agree that online tutorials and websites helped make the course material easier to understand 79% 78%

Language Arts

Reading Requirements: Fall 09 Spring 10 Summer 10

% of respondents indicated there are MORE required readings than their traditional class. 41% 47% % of respondents indicated the required readings are the SAME as their traditional class. 47% 15% % of respondents indicated there are LESS required readings than their traditional class. 12% 8%

25

Reading Requirements: Fall 09 Spring 10 Summer 10

% of respondents indicated there is MORE required writing than their traditional class. 44% 50% % of respondents indicated the required writing is the SAME as their traditional class. 43% 40% % of respondents indicated there is LESS required writing than their traditional class. 13% 10%

Science


% of respondents agree or strongly agree that virtual labs are helpful to their learning. 73% 76% % of respondents agree or strongly agree that kitchen labs are helpful to their learning. 56% 56%

World Languages


% of respondents agree or strongly agree that there is enough speaking and listening practice in their online World Language course. 83% 84%

26

Appendix BSY 2009-2010 Math I Assessment Data

Assignments Quizzes

Student ID 1 2 3 4 5 6 7Assignment

Average 1 2Quiz

Average Test

Unit 1 Average

#43813 75.0 80.0 70.0 50.0 50.0 30.0 40.0 56.4 60.0 33.3 46.7 56.3 45.9#42124 100.0 85.0 100.0 100.0 90.0 90.0 97.5 94.6 93.3 96.7 95.0 96.9 81.6#42350 65.0 75.0 90.0 75.0 70.0 70.0 50.0 70.7 83.3 86.7 85.0 68.8 62.0#132599 80.0 90.0 77.5 85.0 75.0 100.0 60.0 81.1 75.0 93.0 84.0 100.0 79.0#138915 70.0 80.0 100.0 55.0 65.0 80.0 90.0 77.1 90.0 98.3 94.2 81.3 71.0#33827 80.0 80.0 85.0 77.5 70.0 90.0 80.0 80.4 76.7 66.7 71.7 93.8 73.3#43308 37.5 30.0 50.0 5.0 10.0 10.0 30.0 24.6 0.0 16.7 8.3 12.5 11.6#44154 90.0 50.0 65.0 37.5 65.0 65.0 65.0 62.5 56.7 83.3 70.0 90.6 68.7#132020 35.0 30.0 60.0 10.0 15.0 10.0 50.0 30.0 36.7 3.3 20.0 9.4 13.2#132021 22.5 55.0 50.0 0.0 55.0 50.0 20.0 36.1 76.0 20.0 48.0 34.4 32.2#132128 60.0 60.0 85.0 42.5 20.0 67.5 70.0 57.9 100.0 83.3 91.7 65.6 59.8#132272 90.0 65.0 85.0 45.0 87.5 70.0 70.0 73.2 56.7 50.0 53.3 87.5 65.4#132290 40.0 40.0 10.0 65.0 70.0 100.0 75.0 57.1 20.0 51.7 35.8 96.9 64.2

65.0 63.1 71.3 49.8 57.1 64.0 61.3 61.7 63.4 60.2 61.8 68.8 56.0

Unit 1 Average: 56.0%

27

Unit 2 - Mathematical Argument and ProofAssignments Quizzes

Student ID 1 2 3 4 5 6 7 8 9 10 A

ssig

nm

ent A

vera

ge

1 2 3

Qu

iz

Ave

rage

Test

Un

it 2

A

vera

ge

#43813 50.0 50.0 50.0 30.0 75.0 50.0 20.0 45.0 30.0 0.0 40.0 60.0 26.726.7 37.8 50.0 44.4

#42124 90.0100.

0100.

0 80.0 70.0 70.0 90.0 85.5 59.5 72.0 81.7 93.3 86.765.3 81.8 90.0 85.9

#42350 95.0100.

0 95.0 100.0 90.0 50.0 80.0 80.0 50.0 60.0 80.0 73.3 73.346.7 64.4 70.0 70.6

#132599 85.0100.

0 95.0 100.0 100.0 60.0 65.0 65.0 90.0 90.0 85.0 93.3 66.783.3 81.1 80.0 81.4

#138915 90.0100.

0100.

0 85.0 90.0 65.0 50.0 65.0 95.0 75.0 81.5 90.0 56.763.3 70.0 87.5 81.2

#33827 80.0100.

0100.

0 100.0 100.0 90.0 45.0 70.0 65.0 60.0 81.0 93.3 75.040.0 69.4 90.0 82.2

#43308 10.0 40.0 20.0 60.0 70.0 30.0 10.0 20.0 25.0 30.0 31.5 30.0 30.0 6.7 22.2 35.0 30.6

#44154 90.0100.

0100.

0 60.0 60.0 60.0 70.0 80.0 10.0 65.0 69.5 80.0 80.050.0 70.0 86.7 78.2

#132020 30.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.0 0.0 0.0 0.0 0.0 0.0 0.6 *

#132021 50.0 10.0 60.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 12.0 0.0 0.0 0.0 0.0 0.0 2.6 *

#132128 90.0 90.0100.

0 60.0 60.0 70.0 60.0 40.0 10.0 40.0 62.0 66.7 60.033.3 53.3 62.5 59.8

#132272 70.0 95.0100.

0 100.0 70.0 70.0 65.0 60.0 75.0 70.0 77.5 93.3 60.046.7 66.7 75.0 73.2

#132290 80.0 70.0 85.0 90.0 70.0 80.0 75.0 40.0 70.0 60.0 72.0 80.0 66.756.7 67.8 82.5 76.0

70.0 73.5 77.3 66.5 65.8

53.5 48.5 50.0 44.6 47.8 59.7

65.6

52.4

39.9 52.7 62.2 59.0

*These two students were removed from this unit's data due to non-participation. Unit 2 Average: 59.0%

28

Unit 3 - Graphs and TransformationsAssignments Quizzes

Student ID 1 2 3 4 A

ssig

nm

ent A

vera

ge

1 2

Qu

iz

Ave

rage

Test Unit 3 Average#43813 85.0 40.0 60.0 30.0 53.8 53.3 21.4 37.4 40.0 42.2#42124 85.0 95.0 95.0 95.0 92.5 93.3 92.9 93.1 92.5 92.7#42350 90.0 50.0 80.0 40.0 65.0 83.3 57.1 70.2 72.0 70.0#132599 80.0 70.0 70.0 60.0 70.0 80.0 86.7 83.3 87.5 82.6

#138915100.

0 50.0 60.0 62.5 68.1 73.3 64.3 68.8 80.0 74.3#33827 90.0 90.0 70.0 85.0 83.8 66.7 85.7 76.2 95.0 87.2#43308 10.0 20.0 30.0 40.0 25.0 26.7 57.1 41.9 15.0 24.8#44154 70.0 50.0 60.0 90.0 67.5 70.0 71.4 70.7 77.5 73.4#132020 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 *

#132021 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 *

#132128 60.0 30.0 80.0 85.0 63.8 63.3 89.3 76.3 77.5 74.2#132272 65.0 60.0 70.0 85.0 70.0 66.7 85.7 76.2 85.0 79.3

#132290100.

0 80.0 70.0100.

0 87.5 100.0100.

0100.

0 90.0 92.3

64.248.8

57.3 59.4 57.5 59.7 62.4 61.1 62.5 61.0

Unit 3 Average: 61.0%

*These two students were removed from this unit's data due to non-participation.

30

Appendix C: Macro Instructional ICM

31

Appendix D: Micro Instructional ICM

Prerequisiteso Recognize a relation as a correspondence between varying quantities. o Recognize a function as a correspondence between inputs and outputs

where the output for each input must be unique.

o Distinguish between relations that are functions and those that are not functions.

o Recognize functions in a variety of representations and a variety of contexts.

o Use tables to describe sequences recursively and with a formula in closed form.

o Identify relations and functions as linear or nonlinear. o Solve problems involving linear relationships

o Translate among verbal, tabular, graphic, and algebraic representations of functions.

o Interpret slope as a rate of change. o Determine the meaning of the slope and y-intercept in a given situation. o Graph equations of the form y = mx + b. o Graph equations of the form ax + by = c. o Graph the solution set of a linear inequality, identifying whether the

solution set is an open or a closed half-plane.

o Determine the equation of a line given a graph, numerical information that defines the line or a context involving a linear relationship.

32

Appendix E: Course, Unit, and Lesson Design OutlineCourse and Unit Design (Macro-Instructional) and Lesson Design (Micro-instructional Design):A. Title: Function FamiliesGoal: Students will demonstrate and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques as well as use the language of mathematical argument and justification by completing a culminating activity.

Unit 1 ObjectiveTitle: Interpretation of FunctionsObjective: Students will demonstrate how to interpret functions through domain and range, rates of change, intercepts, maximum and minimum, increase and decrease, end behavior, and compare rates of change by completing a twenty question test.

Lesson 1:Title: Domain and RangeObjective: Students will be able to identify, list, and interpret domain and range from graphing, coordinate sets, and the vertical line test. by completing a self assessment activity and a ten question assignment.

Lesson 2:Title: Rates of ChangeObjective: Students will be able to define, interpret, and discover rates of change by using graphs, the slope formula, and understanding rise over run by completing a self assessment activity and a ten question assignment.

Support Objective 1: Students will be able to summarize how the change in y over the change of x identifies the "rise" of a graph and therefore is a interpretation of the slope by completing a self assessment activity and a ten question assignment.

Lesson 3:Title: InterceptsObjective: Students will be able to state, list, and identify points as x- and y- intercepts by completing a self assessment activity and a ten question assignment.

Support Objective 1: Students will be able to state whether a point is an x-intercept, y-intercept, or neither by completing a self assessment activity and a ten question assignment.

Lesson 4:Title: Maximum and MinimumObjective: Students will be able to state, list, and identify extrema as maximum and minimum values through locating these values on graphs by completing a self assessment activity and a ten question assignment.

34

Lesson 5:Title: Recognizing Increasing and Decreasing FunctionsObjective: Students will be able to identify and interpret increasing and decreasing graphs of functions and explain the significance in a change in x and/or y values by completing a self assessment activity and a ten question assignment.

Supporting Objective: Students will be able to state whether a function is increasing or decreasing by completing a self assessment activity and a ten question assignment.Supporting Objective: Students will be able to summerize how a change in x would affet the y-value in an increasing function by completing a self assessment activity and a ten question assignment.

Lesson 6:Title: Investigating end behavior of a functionObjective: Students will be able to define, identify, and explain the end behavior of a given function by completing a self assessment activity and a ten question assignment.

Lesson7:Title: Comparing rates of changeObjective: Students will be able to define, interpret, and compare linear and quadratic rates of change by completing a self assessment activity and a ten question assignment.

Unit 2 ObjectiveTitle: Mathematical Argument and ProofObjective: Students will demonstrate how to use the language of mathematical argument and justification through conjecture, inductive reasoning, deductive reasoning, counterexamples, indirect proof as appropriate, and understand and use the relationships among a statement and its converse, inverse, and contrapositive by completing a twenty question test.

Unit 3 ObjectiveTitle: Graphs and TransformationsObjective: Students will demonstrate how to use the language of mathematical argument and justification through conjecture, inductive reasoning, deductive reasoning, counterexamples, indirect proof as appropriate, and understand and use the relationships among a statement and its converse, inverse, and contrapositive by completing a twenty question test.

Pre-Requisite Skills: o Recognize a relation as a correspondence between varying quantities. o Recognize a function as a correspondence between inputs and outputs where

35

the output for each input must be unique. o Distinguish between relations that are functions and those that are not functions. o Recognize functions in a variety of representations and a variety of contexts. o Use tables to describe sequences recursively and with a formula in closed form. o Identify relations and functions as linear or nonlinear. o Translate among verbal, tabular, graphic, and algebraic representations of functions.o Interpret slope as a rate of change. o Determine the meaning of the slope and y-intercept in a given situation. o Graph equations of the form y = mx + b. o Graph equations of the form ax + by = c. o Graph the solution set of a linear inequality, identifying whether the solution set is an

open or a closed half-plane. o Determine the equation of a line given a graph, numerical information that defines the

line or a context involving a linear relationship. o Solve problems involving linear relationships.

36

Appendix F: Instructional Strategy Planning SheetInstructional Component Instructional Plan Media Choice1. Pre-instructional activitiesa) Pre-Assessment testb) Motivating the learners/gaining

their attention through essential questions

c) Informing the learners of the lesson standards

1a. Students take a pre-assessment test to show the teacher what areas of content need to be more heavily stressed as well as allow the students to have a preview of upcoming material.

1b. At the beginning of the lesson, students are presented with essential questions that will direct them toward what will be covered in the lesson..

1c.All lessons include a link to the Georgia Performance Standards.

1a. Student; self-paced guide

1b. Student; self-paced guide

1c. Student; self-paced guide

2. Content presentationa) Presenting the content to be learned

(i.e. stimulus material)b) Guiding the learners as they are

presented with the content.

2a & b. Students are presented with written lecture, Jing Video, and external online resources. Students also attend a one hour Elluminate during the week of the lesson. During this Elluminate the students can interact directly with the teacher.

Self-paced guide; computer; teacher

3. Learner participationa) Giving the learner opportunities for

practice (i.e. self-assessment activities)

b) Giving the learner feedback during practice

3a & b. Students will complete a brief self-assessment activity. These activities include feedback to direct the learner. The teacher also provides feedback during the Elluminate session.

Self-paced guide; computer, teacher

37

4. Assessmenta) Assignments, Quizzes, and Tests to

see if anything has been learned as a result of this lesson

4a. After completing the assignments, teacher feedback is provided before the student proceeds to the quiz. Quiz feedback is provided before the student proceeds to the test.

Teacher; computer

5. Follow-through activitiesa) Culminating project at the

conclusion of the Function Families Course

5a. Students will complete a project containing activities that cover all Georgia Performance Standards within Function Families.

Teacher; computer

38

Appendix G: Formative Evaluation Planning Worksheet

Formative Evaluation Planning WorksheetLesson Objectives: Students will be able to state, list, and identify points as x- and y-intercepts. Students will also be able to state whether a point is an x-intercept, y-intercept, or neither.

Who What When HowExperts Will have the experts review over the

following areas:1. Accuracy of Content2. Accessibility3. Copyright

It is important that all GAVS content follow the Georgia Performance Standards. The expert reviewers will focus on the lesson content as it applies to the standards. It is also important that all examples and practice problems are accurate and mathematically correct.

The GAVS expert reviews also include accessibility and copyright evaluations.

Expert reviewers are given 48 hours to complete their review and provide feedback regarding necessary corrections or modifications.

The review will be conducted through the attached spreadsheets.

See Appendices G, H, I

Learners: small group

The small-group evaluation will consist of 5 students enrolled through Georgia Virtual School in the Math I course for the Summer 2010 term.

The small group session will occur during the Summer 2010 term.

Assignments, quizzes and tests will be the assessments used to evaluate the effectiveness of the content revisions.

39

Appendix HAccessibility Review

Georgia Virtual School Course Accessibility Review Form

Submit completed for to [email protected]

Course Name:

Instructions:

Using the 1-5 scale below, indicate the degree to which the standard on the left is met in each module. The spreadsheet will automatially calculate the averages for you. If course standards are not available in the modules, they can been seen at www.georgiastandards.org

Function Families

Standard

Inte

rpre

tati

ons

of F

Mat

hem

atic

al A

rgu

men

t an

d P

roof

Gra

ph

s an

d T

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mat

ion

s

Rad

ical

Exp

ress

ion

s

Op

erat

ion

s w

ith

Pol

ynom

ials

Pro

per

ties

of P

olyg

ons

Tri

angl

e Co

ngr

uen

cies

Spec

ial S

egm

ents

in T

rian

gles

Pro

per

ties

of Q

uad

rila

tera

ls

Pro

bab

ilit

y

Sum

mar

y St

atis

tics

an

d D

ata

Des

crip

tion

s A

sses

smen

ts

Rev

isit

ing

Fun

ctio

ns

Fact

orin

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Solv

ing

Equ

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Rat

ion

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Ave

rage

CommentsAll course documents are in pdf or rtf format

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Flashing or scrolling images or text are not used

4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 54.93

8

Vocabulary turns black when scrolling and appears as if it could be linked. The "Finish" link doesn't take the student anywhere.

Captions are provided for 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Every word is not

40

videos or presentations if general text is not available in the presentation

written in mathematical explanation, but all important content is expressed. HOWEVER, I am considering this from a hearing teacher of mathematics perspective. I don’t know how clear it would be to a hearing impaired student. Closed captioning is not available on some of the links. The teacherchalkLOR is not linked.

Foreground and background color combinations provide sufficient contrast

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

Some of the instruction PowerPoint videos use yellow ink in distribution, which is a little difficult to see, but it is not the main color. There are also several videos which write in red. I can't remember if that was an okay color or not. It is very easy to read, but I think it was mentioned to not use this color.

Link descriptions should clearly identify the general target site

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

The extra links for additional resources are named for the section and then 1,2,3 etc…. I think that they could be named more specifically, but it wouldn't carry the consistency.

Do all links in the module work (no page not found errors)

3 3 4 5 4 5 5 5 5 4 5 5 5 5 5 54.56

3

The Monteray Institute Links are a little slow & often need to be tried a few times or refreshed.

Data tables include row and column headings 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

41

Tables are not used for layout purposes or to align content on the page

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Headings and subheading conform to the GAVS course template

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Presentation style is consistent throughout the module

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

Within the modules the presentation styles are consistent. However, on the self-checks, some modules when checking will tell the correct answer if incorrect, some will say zero points awarded and others will just say incorrect.

The module is easy to navigate. 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

p.9. of Properties of Geometric Figures is not consistent with the rest of the course.

Does the module work in multiple browsers 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

"alt" tags are available for all descriptive images

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

Login information is provided to students if a GAVS subscription site is being referenced 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

Average 4.8 4.9 4.9 5 4.9 5 5 5 5 4.9 5 5 5 5 5 54.9

Several school systems do not allow YouTube. We might consider downloading these videos (KeepVid). Also, when you open a module, the second video will usually load up before the first & I almost missed the first one several times by scrolling down to the video that had the arrow to begin first. On some of the self checks that have multiple answers, if you don't answer at all, it will give you partial credit which is incorrectly graded. There is just basic inconsistency on the self checks throughout the course, but not within the modules. On the "Click Show" type practice activities, the screen is too large to not have to scroll back and forth to see answers. If you click next slide, you then have to scroll up to see the answer.

42

Appendix I:Copyright Review

Georgia Virtual School Course Copyright Review Form Submit completed for to [email protected]

Course Name:Instructions: Using the 1-5 scale below, indicate the degree to which the standard on the left is met in each module. The spreadsheet will

automatially calculate the averages for you. If course standards are not available in the modules, they can been seen at www.georgiastandards.org. It is assumed for GAVS reviews that all content is accessed through the GAVS learning management system and is accessible by password only.

Standard Inte

rpre

tati

ons

of F

un

ctio

ns

Mat

hem

atic

al A

rgu

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t an

d

Pro

of

Gra

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d T

ran

sfor

mat

ion

s

Rad

ical

Exp

ress

ion

s

Op

erat

ion

s w

ith

Pol

ynom

ials

Pro

per

ties

of P

olyg

ons

Tri

angl

e Co

ngr

uen

cies

Spec

ial S

egm

ents

in T

rian

gles

Pro

per

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of Q

uad

rila

tera

ls

Pro

bab

ilit

y

Sum

mar

y St

atis

tics

an

d D

ata

Des

crip

tion

s A

sses

smen

ts

Rev

isit

ing

Fun

ctio

ns

Fact

orin

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Solv

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Equ

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Rat

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xpre

ssio

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Pro

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of G

eom

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Ave

rage

CommentsSources are cited for descriptive images within the module

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Printed documents in a course are teacher created or used under copyrights published at the source site

5 2 5 5 5 5 3 5 5 5 5 4 5 5 5 54.625

The Chance of Winning Intro Vocabulary really looks like it has been cut and pasted from a textbook.

Any sound or music files are for educational purposes not entertainment

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

43

Content, images, or presentations used are not commercially produced for online distribution unless subscribed to by GAVS

5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Links to content outside of GAVS open in a new browser window. 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

Average 5 4.4 5 5 5 5 4.6 5 5 5 5 4.8 5 5 5 5

Additional Comments: On the resources from the GADOE, do we have the right to publish the teacher resources of frameworks…..it says copyright, but just checking? p.9. more resources pdf. of Properties of Geometric Figures is not consistent with the rest of the course and I don't know about copyright.

44

Appendix J:Content Review

Name of Softchalk (Module)

Page Number of Where Content is Incorrect

Description of what needs to be changed

Interpretation of Functions

2 (GPS standard missing/not covered) More time needs to be spent on function notation, this is part of GPS DONE

2 (paragraph 2 and 3 of domain and range lecture)

State the same thing can be combined ELIMINATE 3RD PARAGRAPH IN DOMAIN AND RANGE LECTURE DONE

2 Include examples with ordered pairs, graphs, for determining functions, also show how to use vertical line test DONE

2 first self check Indicate that axes labeled by 1 COMPLETED

3 Show how to calculate slow with 2 points and with graph using rise over run DONE

Note /pg 5 quiz review

Instead of all the assignments it would be better to have homework and homework checks. This also gives them more practice. At this level students think anything under the quiz tab is a quiz. I would do 18 to 20 problems of homework for the first 3 sections then have them do the homework quiz, check answers, and then the quiz review and a quiz in lieu of 3 individual assignments. NOT CHANGING IN THE REVISION

4 Intercept football analogy discuss how 2nd player crosses line of ball of 1st player to get ball COMPLETED

4 Emphasize standard form A pos and no fractions, include examples of finding intercepts with standard form as well as significance of y=0 or x=0 to concept of "being on an axis". DONE

6 Discuss using a calculator. Show x=-b/2a is x coordinate of vertex and significance to axis of symmetry (line thru vertex)DONE

45

7 Give examples contrasting what looks like when you graph versus what appears in the table.DONE

7 (2nd self check/answer wrong) There is a point of inflection at (-.33,-.26) this graph is steadily increasing from left to right. Answer should be "B"Same problem also on page 9. COMPLETED

7 (3rd self check, reword problem)

Function is misspelled. Question should be reworded to state"Which statement below accurately represents the periods of increase and

decrease of the graph" or "Determine which statement best describes the graph below" COMPLETED

8

Include pictures and examples of 4 types of end behavior, should we discussion notations with "infinity" ? Since domain and range was already discussed. Also discuss leading coefficient and even versus odd degree (this would help with #3 self check)DONE

8 (#2 self check/remove problem) This is more for polynomial functions and not in the end behavior section, this should be removed. COMPLETED

9 (GPS standard missing/not covered) GPS indicates should mention sq root and other functions. Definitely mention quadratic, none in self check. DONE

Interpretation of Functions Assessments

Rubric will need to be added. NOT ON TASK...JUST PROJECT

46

Appendix K:Summer 2010 Assessment Data

Unit 1 - Interpretation of FunctionsAssignments Quizzes

Student ID 1 2 3 4 5 6 7

Assignment Average 1 2

Quiz Average Test

Unit 1 Average

#150503 75.0 75.0 95.0 30.0 70.0 30.0 60.0 62.1 66.7 46.7 62.2 91.3 76.7#153209 80.0 75.0 75.0 30.0 80.0 40.0 45.0 60.7 66.7 53.3 53.3 69.6 63.0#155093 75.0 70.0 90.0 90.0 60.0 100.0 45.0 75.7 96.7 90.0 86.4 93.5 87.6#156241 20.0 65.0 50.0 25.0 75.0 60.0 85.0 54.3 60.0 73.3 70.0 80.4 71.9

62.5 71.3 77.5 43.8 71.3 57.5 58.8 63.2 72.5 65.8 68.0 83.7

Unit 1 Average:71.9%

47

math i function families: interceptslrieber.coe.uga.edu/edit6170/resources/teams/summer2… ·...

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