using the graphing calculatoryourspace.minotstateu.edu/laurie.geller/capstone examples... · web...

Implementation of the TI-NspireTM in College Algebra to Enhance Student Learning

Investigator: John E. Dolleslager Jr.

Introduction

Since the introduction of the calculator in the 1970s, mathematics classrooms have

changed, or have they? Many students don’t find mathematics classes interesting; some may

even say that mathematics concepts are difficult. I want to incorporate the TI-NspireTM calculator

into College Algebra lessons to determine whether it enhances student achievement.

Statement of Purpose

The purpose of this project is two-fold. First, I want to determine if the use the TI-

NspireTM enhances student achievement in College Algebra. Second, I want to determine if the

TI-NspireTM calculator increases student confidence in mathematics.

Research Question

Will the use of the TI-NspireTM and/or TI-NspireTM computer emulator software in

instruction and learning of mathematics enhance student learning of the mathematics concepts in

College Algebra to an 85% proficiency level, based on test scores for each individual student and

will using the TI-NspireTM enhance the students’ confidence in their mathematical abilities?

Literature Review

The graphing calculator is a device that is relatively new to the teaching of mathematics.

How could using a graphing calculator affect student learning? Do non-graphing calculator

students learn less than students that use graphing calculators? (Burrill, 2003). “Graphing

calculators are really inexpensive hand-held computers with built-in numerical solvers and

graphing software” (Waits & Demana, 1998, p. 1). Rich’s findings in 1991 show that students

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that use the graphing calculators had a more positive understanding of graphs and Burrill (2003)

points out that the graphing calculator has several ways to present information.

Since the graphing calculator can perform some of the routine operations faster than what

pencil and paper manipulations would have been able to do, the graphing calculator can provide

more classroom time for the development of better understanding of mathematical concepts

(Waits & Demana, 1998). “Evidence shows that the mathematics and the technology must work

together for the outcomes to be most beneficial” (Burrill, 2002, p. v). Pomerantz (1997) made the

comment that graphing calculators provide students tools that assist but do not replace the pencil

and paper manipulations; instead the two work together to enhance the students’ ability to solve

problems with various techniques.

The graphing calculator “has a positive effect on students’ understanding of graphs and

their connection to algebraic representation” (Leng, Chuen & Nancy, 2009, p. 2). Meanwhile,

Pomerantz (2007) discussed several myths about the use of technology and the calculator in the

mathematics classroom. She pointed out that calculators can facilitate the mathematics learning

process by eliminating some of the mundane or tedious calculations.

According to the Curriculum and Evaluation Standards for School Mathematics (NCTM,

1989), all students in grades 9-12 should have access to graphing calculators. This document

went on to say that every mathematics classroom should have a computer for demonstrations and

students will be able to use computers in their mathematics classes (NCTM, 1989). Some

teachers feel the use of the calculator will have some downfalls. Pomerantz (1997) said that some

teachers view the use of calculators as a crutch; some also think that it will replace some basic

math skills (Pomerantz, 1997). The teachers against the use of technology in the mathematics

classroom have a couple of arguments (Wenglinksy, 1998). The first argument for teachers not

wanting to incorporate technology into the mathematics classroom is their own lack of

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knowledge with the technology (Wenglinsky, 1998). Wenglinsky goes on to say that these

teachers are “intimidated by technology” and they dislike those teachers who can integrate

technology into their classroom easily. Adding technology into the classroom doesn’t necessarily

mean students will benefit. “Mathematics and the technology must work together for the

outcomes to be most beneficial” (Burrill, 2003, p. v).

“A positive classroom environment creates a positive foundation for direct instruction to

occur” (Idirs, 2006, p. 2). Students need to feel wanted and valued in the mathematics classroom.

According to Roschelle and Gallagher (2005), “Learning with a calculator contributes broadly to

student achievement as measured on tests that allow calculator use” (p. 4). According to the

Center for Teaching in Learning (2007a), research has found appropriate classroom use of

graphing calculators increases students’ ability to understand concepts and solve problems.

Using the graphing calculator and its ability to display data using multiple representations is

similar to the way that manipulatives like the GeoboardsTM and UnifixTM cubes, are used in

elementary schools. In the middle and high school setting, students need more advanced tools.

These advanced tools allow for a connection between abstract ideas to something more tangible

(Center for Technology in Learning, 2007b).

Research Methods

Sample/Technique

This study will take place in a small public high school in a town of about 1,000 in a

Midwestern state. The population of the school is about 220 student in grades 7-12. The

population of the study is approximately 26 students in the 12th grade. The purpose of this project

is to determine if the use of the TI-NspireTM calculator enhances student achievement in College

Algebra. During this study, College Algebra students will use the TI-NspireTM graphing

calculator to explore linear functions, quadratics functions (including completing the square),

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function transformations, and polynomial functions. There will be approximately 25 students in

the College Algebra class. I chose this particular class because it was the one mathematics class I

would be teaching. My mathematics classes that I teach changes every year, except for College

Algebra. Some years, College Algebra is the only mathematics course I teach. Permission to

conduct the study has been granted from the school principal (see Appendix A). A parental

consent form and student assent from will be sent home and collected prior to the study (see

Appendix B and Appendix C).

Data Collection Instruments

The study will begin in January 2012 at the beginning of the third quarter with pre-

surveys given to the students before the study to determine their level of comfort using the

graphing calculator and their confidence in mathematical knowledge attained from the students’

previous mathematics classes. The survey will also assess their comfort level of using that

graphing calculator (see Appendix D). The information about the students’ level of comfort for

using the TI-NspireTM calculator will give me some background of previous knowledge they have

using the TI-NspireTM calculator.

The students will be given a test after each chapter to determine if each student meets an

85% proficiency level. The 85% proficiency level will be based on both parts of the tests: a

calculator part (where the students will be required to use the calculator and explain what

functions/menus/buttons they used and why they used them) and a traditional paper pencil test

where they will not be required to write their keystrokes/reason. Also this test will allow for

more questions to be asked and get a sense of their knowledge of the material.

Throughout the study, I will observe the students using the TI-NspireTM, record my

observations, and analyze the results. The study will end in March 2012 at the end of the third

quarter at which time a post-survey will be administered to determine whether the use of the TI-

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NspireTM helped the students feel more confident in their mathematical abilities. In addition, I

will determine if they achieved an 85% level of proficiency based on their test scores. Also, at

the end of the study, I will interview a select number of students to find their views on how the

project went, what they felt went well, what they think didn’t go well.

For each assignment the students complete that requires the use of the calculator, they

will be asked to describe in detail what functions/menus/buttons they used to answer the

questions, as well as why they those to answer them that way. This information will be included

on their homework assignments as a means to practice answering this type of question on other

assessments, like tests. These types of questions are different than any other they have seen on

mathematics tests they have taken before. The chapter one tests are included in Appendix G and

Appendix H. After each test I will grade the tests to determine if each student met an 85%

proficiency level.

Human Protection Issues

Informed Consent

A parent/guardian consent form will be used to obtain permission to use student survey

responses in the analysis for this study. A student assent form will also be used to inform the

students of the survey. See parent/guardian consent and student assent forms in Appendix B and

Appendix C, respectively.

The pre-study survey (see Appendix D) includes student names for the purpose of

matching pre-study and post-study responses. Once data have been collected from the surveys,

the documents will be kept in a locked cabinet or on a password-protected computer. Upon

completion and defense of the research project, all surveys will be destroyed. When analyzed,

survey data will be aggregated so individual students are not revealed.

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The unit tests (see each unit test in Appendices G and Appendix H) are requirements of

the course and will include student names. These documents will be scored, recorded, and

reviewed by the students. When analyzed, test score data will be aggregated so individual

students are not revealed. These documents will be kept in a locked cabinet and data analysis

results will be kept on a password-protected computer. Upon completion and defense of the

research project, all reflections related to the unit tests will be destroyed.

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References

Alfonso, Z., Long, V. (2005). Graphing calculators and learning styles in rural and non-rural

high schools. Working paper No. 23. Athens, OH: Appalachian Collaborative Center for

Learning, Assessment, and Instruction in Mathematics

Burrill, G., J. Allison, G.Breaux, S. Kastberg, K. Leatham, & W. Sanchez. (2002). Handheld

graphing technology in secondary school mathematics: Research findings and

implications for classroom practice. Dallas, TX: Texas Instruments. Retrieved August

28, 2011 from http//education.ti.com/sites/US/downloads/pdf/CL2872.pdf

Burrill, G. (2003). Teaching and learning mathematics using handheld graphing technology.

Retrieved October 18, 2010 from http://www.icme-organisers.dk/tsg15/Burrill.pdf

Burrill, G. (2008). The role of handheld technology in teaching and learning secondary school

mathematics. Retrieved October 18, 2010 from http://tsg.icme11.org/ document/get/218

Burrill, G., Allison, J., Breaux, G., Kastberg, S., Leatham, K., & Sanchez, W. (2002). Handheld

graphing technology in secondary school mathematics: Research findings and

implications for classroom practice. Dallas, TX: Texas Instruments.

Browning, C., & Garza-Kling, G. (2010). Graphing calculators as tools. Mathematics Teaching

in the Middle School, 15(8), 480-485.

Center for Technology in Learning, SRI International. (2006, November 8). TI-Nspire math and

science learning handhelds: What research says and what educators can do. (SRI Project

P17094.200).

Center for Technology in Learning. (2007a). The pedagogical potential of TI-Nspire: TI EdTech

Research Notes. Dallas, TX, SRI International.

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Center for Technology in Learning. (2007b). Why should a teacher use technology in his or her

mathematics classroom: TI EdTech Research Notes. Dallas, TX, SRI International.

DePeau, E., & Kalder, R. (2010, November). Using dynamic technology to present concepts

through multiple representations. Mathematics Teacher, 104(4), 268-273.

Fernandes, L. (2007). The abacus: A brief history. Retrieved October 18, 2010 from

http://www.ee.ryerson.ca:8080/~elf/abacus/history.html

Forster, P., & Mueller, U. (2002). What effect does the introduction of graphics calculators have

on the performance of boys and girls in assessment in tertiary entrance calculus?

International Journal of Mathematical Education in Science and Technology, 33(6), 801-

18. doi: 10.1080/00207390210130903

Hubbard, D. (1998, May 1). Improving Student Knowledge of the Graphing Calculator’s

Capabilities. Retrieved from EBSCOhost.

Idris, N. (2006). Usage of graphing calculator TI-83 plus: Motivation and achievement.

Retrieved October 19, 2010 from http://pkukmweb.ukm.my/~penerbit

/jurnal_pdf/jpend31_10.pdf

Kennedy, D. (1995). Climbing around the tree of mathematics. Mathematics Teacher,

September, 460-465

Leng, N., Chuen, T., & Nancy, N. (2009). Teaching and learning calculus with the TI-Nspire: A

design experiment. Retrieved October 10, 2010 from

http://atcm.mathandtech.org/EP2009/papers_full/2812009_17308.pdf

Lubinsky, J. (2010). It all adds up! Using technology in the math classroom. High-tech teaching

success! A step-by-step guide to using innovative technology in your classroom (pp. 20-

69). Waco, TX: Prufrock Press.

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National Council of Teachers of Mathematics (NCTM). (1989). Commission on Standards for

School Mathematics. Curriculum and Evaluation Standards for School Mathematics.

Reston VA.

Patten, S. (2001). School: The Story of American Public Education. Stone Lantern Films and

PBS. 2001. Retrieved from http://www.pbs.org/kcet/publicschool/

about_the_series/index.html.

Pomerantz, H. (1997). The role of calculators in mathematics education. Retrieved from

http://education.ti.com/sites/US/downloads/pdf/ therole.pdf.

Rich, B. (1991). The effect of the use of graphing calculators on the learning of function

concepts in precalculus mathematics. Doctoral Dissertation, The University of Iowa,

1990.

Roschelle, J. & L. Gallagher (2005). A Research Perspective on Using Graphing Calculator

Interventions to Improve Mathematics Achievement. Palo Alto, CA: SRI International:

12.

SRI (2006). TI-Nspire™ math and science learning handhelds: what research says and what

educators can do. Menlo Park, CA.

United States Department of Education. (2008). Foundations for success: The final report of the

National Mathematics Advisory Panel. Retrieved from http://

www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf.

Waits, B., & Demana, F. (1998). The role of graphing calculators in mathematics reform.

Waits, B., & Demana, F. (2001). Calculators in mathematics teaching and learning: Past,

present, and future. Part 2: Technology and the mathematics classroom. Reston, VA:

National Council of Teachers of Mathematics.

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Wenglinksy, H. (1998). Does it compute? The relationship between educational technology and

student achievement in mathematics. Princeton, NJ: The Educational Testing

Service.Retrieved from http://www.ets.org/Media/ Research/pdf/PICTECHNOLOG.pdf

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Appendix A

School Principal Consent Form

Dear Mr. Schwabe:

I am completing work toward the Master of Arts in Teaching: Mathematics degree through Minot State University. As a degree requirement, I am to conduct a research project in my classroom during the third quarter this year. I am planning to implement pre- and post-project surveys, chapter tests and interviews with students for TI-NspireTM usage in the college algebra classroom.

During this time, students will take a pre- and post-study surveys regarding their usage of graphing calculators in previous math classes and their previous comfort level of learning the mathematics concepts. Classroom and student confidentiality will be observed regarding all data collected and no individual will be identified by name.

Before the study begins, I will send home consent forms for parents/guardians to notify them of this project and request their permission allowing their student to participate in the research study. A copy of this letter is attached for your inspection.

I am requesting that you permit me to carry out this research in my classroom. Please contact me if you have any questions. Thank you for your consideration.

___________ I grant permission for John E. Dolleslager Jr. to conduct the above mentioned research in his classroom.

___________ I DO NOT grant permission for John E. Dolleslager Jr. to conduct the above mentioned research in his classroom.

________________________________________________________Signature of Mr. Jason Schwabe, Principal at Thompson High School

__________________________________Date

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Appendix BParental/Guardian Consent Form

A Research Project by John E. Dolleslager Jr.


John E. Dolleslager Jr.

Invitation to ParticipateYour child is invited to participate in a study of the use of the TI-NspireTM graphing calculator in the College Algebra classroom. The study is being conducted by College Algebra instructor, Mr. John E. Dolleslager Jr., a graduate student a Minot State University.

Basis for Subject SelectionYour child has been selected because the College Algebra class is a very convenient sample due to the fact that I am your child’s instructor, and with approximately 25 students, the class will allow the researcher to gather an appropriate amount of data to analyze.

Purpose of the ResearchI am currently completing work towards my Masters of Arts of Teaching: Mathematics degree through Minot State University. For my final degree requirement, I am conducting an action research project during quarter 3, January 19th through March 23rd, to determine if student use of the TI-NspireTM graphing calculator will enhance student achievement in a College Algebra classroom and confidence in mathematics using the TI-NspireTM. Specific ProceduresStudents in this College Algebra class will cover the normal College Algebra curriculum. At the beginning of the study, your student will complete a survey to assess his/her current level of comfort with using the TI-NspireTM. Throughout the quarter, students will complete guided inquiry lessons using the TI-NspireTM graphing calculator. At the end of the quarter, students will complete a post-project survey to determine if their level of comfort with the graphing calculator increased. Survey responses, statistical analysis of chapter tests, interviews with selected students, and my observations will be analyzed to determine whether the use of the TI-NspireTM graphing calculator through guided inquiry improved the students’ achievement and confidence in the mathematics using the graphing calculator in College Algebra. My results will be summarized and included in my research paper. None of the students in my class will be identified in my results. Mr. Schwabe, principle of Thompson High School has approved this research study.

Duration of ParticipationThe study will last from January 19th to March 23, 2012, the entire third quarter.

Benefits to the IndividualThere are no direct benefits in participating in this study, but participation will give your student additional tools to help him/her prepare for math tests. The study may show the benefits of using the TI-NspireTM graphing calculator.

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Risks to the IndividualThe risks to your student are no more than he/she would encounter in a regular classroom setting.

Alternatives to ParticipationIf you do not wish for your child to participate in this study, your child will still be required to complete the assigned homework, complete the assigned tests since it will be part of the normal class. However, your child will not be required to complete the surveys.

ConfidentialityThe researcher will treat all data confidentially. Names of participants and their data sets will kept in a locked filing cabinet or password-protected computer in the researcher’s room and will be destroyed once the paper has been defended and approved. The researcher agrees to maintain strict confidentiality, which means your student’s name will not be discussed or divulged with anyone outside of this research project. The researcher will also make sure confidential information will not be discussed in an area that can be overheard that would allow an unauthorized person to associate or identify the student with such information.

Voluntary Nature of ParticipationDuring this study, the survey responses and scores from and the chapter tests from your student do not have to be included. However, I hope you approve of your student being involved in this study because a larger sample size improves the accuracy of the results of my study. If you decide to participate, you are free to withdraw your consent at any time. If you do not consent or withdraw your consent, your student’s data will not be included in my results and your student will not complete the surveys, but your student will still be asked to complete guided inquiry lessons since these are a regular part of my course.

Human Subject StatementThe Institutional Review Board of Minot State University has given me permission to conduct this research. If you have questions regarding the right of research subjects, please contact the Chairperson of the MSU Institutional Review Board (IRB), Dr. Vicki Michels at 701-858-3594 or [email protected].

Offer to Answer QuestionsIf you have any questions or concerns now or during the study, feel free to contact me at 701-599-2765 or email me at [email protected]. Thank you for your consideration.

Consent StatementYou are voluntarily making a decision whether or not to participate in this study. With your signature below, you are indicating that upon reading and understanding the above information, you agree to allow your student’s surveys and chapter tests scores to be used in this study. You will be given a copy of the consent form to keep.

___________________________________ Participant (Please Print Student’s Name)

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___________________________________ ________________ Signature of Parent or Guardian Date

___________________________________ ________________Signature of Researcher Date

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Appendix C

Student Participant Assent FormA Research Project by John E. Dolleslager Jr.


John E. Dolleslager Jr.

Invitation to ParticipateYou are invited to participate in a study of the use of the TI-NspireTM graphing calculator in the College Algebra classroom. The study is being conducted by College Algebra instructor, Mr. John E. Dolleslager Jr., a graduate student a Minot State University.

Basis for Subject SelectionYou have been selected because the College Algebra class is a very convenient sample due to the fact that I am your instructor, and with approximately 25 students, the class will allow the researcher to gather an appropriate amount of data to analyze.

Purpose of the ResearchI am currently completing work towards my Masters of Arts of Teaching: Mathematics degree through Minot State University. For my final degree requirement, I am conducting an action research project during quarter 3, January 19th through March 23rd, to determine if student use of the TI-NspireTM graphing calculator will enhance student achievement in a College Algebra classroom. Specific ProceduresIn this College Algebra class we will cover the normal College Algebra curriculum. At the beginning of the study, you will complete a survey to assess your current level of comfort with using the TI-NspireTM. Throughout the quarter you will complete guided inquiry lessons using the TI-NspireTM graphing calculator. At the end of the quarter, you will complete a post-study survey to see if your level of comfort with the graphing calculator increased. Survey responses, statistical analysis of chapter tests, interviews with selected students and my observations will be analyzed to determine whether the use of the TI-NspireTM graphing calculator through guided inquiry improved the students’ achievement in College Algebra. My results will be summarized and included in my research paper. None of the students in our class will be identified in my results. Mr. Schwabe, principle of Thompson High School has approved this research study.

Duration of ParticipationThe study will last from January 19th to March 23, 2012, the entire third quarter.

Benefits to the IndividualThere are no direct benefits in participating in this study, but your participation will give you additional tools to help you prepare for math tests. The study may show the benefits of using the TI-NspireTM graphing calculator.

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Risks to the IndividualThe risks to you are no more than you would encounter in a regular classroom setting.

Alternatives to ParticipationIf you do not wish to participate in this study, you will still be required to complete the assigned homework, complete the assigned tests since it will be part of the normal class. However, you will not be required to complete the surveys.

ConfidentialityThe researcher will treat all data confidentially. Names of participants and their data sets will kept in a locked filing cabinet or password-protected computer in the researcher’s room and will be destroyed once the paper has been defended and approved. The researcher agrees to maintain strict confidentiality, which means your name will not be discussed or divulged with anyone outside of this research project. The researcher will also make sure confidential information will not be discussed in an area that can be overheard that would allow an unauthorized person to associate or identify the student with such information.

Voluntary Nature of ParticipationDuring this study, your survey responses and scores from the chapter tests do not have to be included. However, I hope will participate in this study because a larger sample size improves the accuracy of the results of my study. If you decide to participate, you are free to withdraw your consent at any time. If you do not consent or withdraw your consent, your data will not be included in my results and you will not complete the surveys, but you will still be asked to complete guided inquiry lessons since these are a regular part of the course.

Human Subject StatementThe Institutional Review Board of Minot State University has given me permission to conduct this research. If you have questions regarding the right of research subjects, please contact the Chairperson of the MSU Institutional Review Board (IRB), Dr. Vicki Michels at 701-858-3594 or [email protected].

Offer to Answer QuestionsIf you have any questions or concerns now or during the study, feel free to contact me at 701-599-2765 or email me at [email protected]. Thank you for your consideration.

Consent StatementYou are voluntarily making a decision whether or not to participate in this study. With your signature below, you are indicating that upon reading and understanding the above information, you agree to allow your surveys and chapter test scores to be used in this study. You will be given a copy of the consent form to keep.

___________________________________ Participant (Please Print Student’s Name)

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___________________________________ ________________ Signature of Participant Date

___________________________________ ________________Signature of Researcher Date

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Appendix DStudent Pre-Survey of Calculator Use

USING THE GRAPHING CALCULATORA STUDENT SURVEY

How familiar are you with how to do each of the following with a graphing calculator?

StatementRating of familiarity

Not familiar Somewhat familiar Familiar Very

Familiar

Graph a function 1 2 3 4

Graph more than one function on the same screen 1 2 3 4

Graph an inequality 1 2 3 4

Evaluate an expression 1 2 3 4

Evaluate a function at a particular point 1 2 3 4

Use the TRACE feature 1 2 3 4

Show a table of values for a function 1 2 3 4

Use the ZOOM feature 1 2 3 4

Use the WINDOW feature 1 2 3 4

Use the INTERSECT feature 1 2 3 4

Use the MAXIMUM and MINIMUM feature 1 2 3 4

Plot points into the calculator 1 2 3 4

Use the calculator to find the distance between two points 1 2 3 4

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PREVIOUS MATH EXPERIENCEA STUDENT SURVEY

Please answer the following questions regarding your previous math classes.

Statement Did not take the

classVery

rarely Rarely Most of the time

All of the time

I was able to use a calculator in Algebra I 0 1 2 3 4

I was able to use a calculator in geometry 0 1 2 3 4

I was able to use a calculator in Algebra II 0 1 2 3 4

I was able to use a calculator in pre-calculus 0 1 2 3 4

I was able to use a calculator in probability and statistics 0 1 2 3 4

I was able to use a calculator in senior math 0 1 2 3 4

I was able to use a calculator in consumer/applied math 0 1 2 3 4

Name:___________________________

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Please answer the following questions regarding level of understanding after completing this course.

I did not take this course

Not at all confident

Not confident about most

topics

Confident about most

topics

Confident about all

topics

Algebra I N/A 0 1 2 3

Geometry N/A 0 1 2 3

Algebra II N/A 0 1 2 3

Pre-calculus N/A 0 1 2 3

Probability and statistics N/A 0 1 2 3

Senior math N/A 0 1 2 3

Consumer/Applied math N/A 0 1 2 3

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Appendix EStudent Post-Survey of Calculator Use

USING THE GRAPHING CALCULATORA STUDENT SURVEY

How familiar are you with how to do each of the following with a graphing calculator?

StatementRating of familiarity

Not familiar Somewhat familiar Familiar Very

Familiar

Graph a function 1 2 3 4

Graph more than one function on the same screen 1 2 3 4

Graph an inequality 1 2 3 4

Evaluate an expression 1 2 3 4

Evaluate a function at a particular point 1 2 3 4

Use the TRACE feature 1 2 3 4

Show a table of values for a function 1 2 3 4

Use the ZOOM feature 1 2 3 4

Use the WINDOW feature 1 2 3 4

Use the INTERSECT feature 1 2 3 4

Use the MAXIMUM and MINIMUM feature 1 2 3 4

Plot points into the calculator 1 2 3 4

Use the calculator to find the distance between two points 1 2 3 4

Not at all confident

Not confident about most

topics

Confident about most

topicsConfident about

all topics

How confident are you in mathematics after completing this study? 0 1 2 3

Name:____________________________

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Appendix FSample lesson – for guided inquiry

College algebra

Introduction to transformations Name:______________________

Graph the following on the same graph below. Be sure to label the x- & y-intercepts & vertex.

a)

b)

c)

1) How are the above similar, use proper mathematical terms?

2) How are the above different, use proper mathematical terms?

3) Make a generalization for what the number in front does to the parent function.

22


d)

e)

f)



6) Make a generalization for what the number that is added to or subtracted from the original do to the parent function.

23


g)

h)

i)



9) Make a generalization for what the number in parentheses do to the parent function.

24


j)

k)



12) Make a generalization for what the negative sign does to the parent function.

25

13) If , what do the values of a, b & c do to the function?

Graph the following by using only the rules you just set. Be sure to label the x- & y-intercepts & vertex. Confirm each one using the graphing calculator.

l)

26

m)

n)

27

o)

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Appendix GChapter 1 Calculator Test

Chapter 1 College Algebra TestCalculator Version

Name:______________________

Find all solutions to each equation; state any restrictions on the domain (State your answers to 3 decimal places):

1) x=______________________

Restrictions on domain______________________

State HOW you used the calculator to solve this problem, specify which menus you used & why you chose to solve it this way:

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2) x=______________________

Restrictions on domain______________________


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3) Find the distance between the points (0.89, 0.23) & (-1.34, -2.88)

Distance:____________________


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4) Sketch the graph of . Be sure to label the intercepts and x- & y-axis.


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Appendix HChapter 1 Test – Pencil and Paper Version

Chapter 1 College Algebra TestPencil/Paper Test

Name: _________________________

Find all real or imaginary solutions to each equation.

1)

Solution _________________________2)

Solution _________________________3)

Solution _________________________4)

Solution _________________________Sketch the graph of each equation. Label all the intercepts.

5)

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6)

7)

8)

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Solve each problem.

9) Find the slope of the line .

Slope _________________________

10) Find the slope of the line through the points (3, -2) & (5, -4).

Slope _________________________

11) Find the equation of the line that contains the points (3, -2) & (5, -4) in slope-intercept and standard forms.

Slope-intercept _________________________

Standard _________________________

12) Find the exact distance and midpoint between the points (3, -2) & (5, -4).

Distance _________________________

Midpoint _________________________

13) Solve, graph and report your answer in interval notation:

Solution _________________________

14) Terry had a square patio. After expanding the length by 20 ft and the width by 10 ft the area was 999 ft2. What was the original area? Draw a picture to represent this problem and then solve.

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