csegraves.weebly.comcsegraves.weebly.com/.../5/6/5/25650794/final_research_paper_se… · web...

Running head: WEBQUESTS & FALS 1

WebQuests and Formative Assessment Lessons and Students Who Struggle in Mathematics

Cindy Segraves

Kennesaw State University

Dr. Nicole Harp

Research Quantitative/Qualitative – EDRS 8900

April 30, 2015

WEBQUESTS & FALS 2

Introduction

Orientation

WebQuests were first introduced by Bernie Dodge, a San Diego State University

professor, in 1995 to promote the use of the Internet in schools (Castek & Mangelson, 2008).

WebQuests are frequently presented in professional development classes and education programs

as an ideal example of effective integration of technology in the classroom (Abbit & Ophus,

2008). More recently, in 2010, formative assessment lessons have emerged as a non-technology

classroom activity through an initiative of the Gates Foundation called Math Design

Collaborative. States adopting the Common Core Standards have embraced the use of formative

assessment lessons for improving students’ depths of knowledge in mathematics (Christman,

Duffy, Lawrence, & Sanders, 2011). The Georgia Department of Education has recently

integrated formative assessment lessons into the frameworks of tasks.

Both WebQuests and formative assessment lessons use scaffolding approaches and

require higher-order processing skills and the ability to apply and synthesize knowledge to solve

a problem; WebQuests via tasks on the Internet, and formative assessment lessons using hands-

on activities with tables, charts, and manipulatives. However it is not clear if WebQuests and

formative assessment lessons help students who struggle in mathematics and have difficulty with

calculating solutions and applying and transferring knowledge to develop a solution to a more

complex problem (Montague, Warger, & Morgan, 2000).

Purpose

The purpose of this study was to examine and compare the effect of WebQuests and

formative assessment lessons on student learning and engagement for students who struggle in

WEBQUESTS & FALS 3

high school mathematics class. The intent of this study is to fill the gap that exists in the current

literature regarding how and if WebQuests and formative assessment lessons improve the

mathematics achievement of underperforming students.

Research Questions

1) How does a WebQuest relate to student learning for students who struggle in high

school mathematics class?

2) How does a formative assessment relate to student learning for students who struggle

in high school mathematics class?

Importance of the Study

With each implementation of new standards, high school mathematics becomes more

rigorous and challenging. Students who have underperformed in mathematics as they progressed

through school, enter a high school mathematics class lacking the skills, confidence, and interest

needed to master the advanced mathematics topics included in the curriculum. Students who

struggle in mathematics, become easily discouraged and frustrated when encountering more

advanced mathematics concepts, and they do not see the relevance to their lives. Mathematics

instruction is most effective when students are exposed to multiple methods for building content

knowledge and solving challenging problems within authentic everyday circumstances. It is

important to identify instructional practices and student-centered activities that will provide

authentic and challenging problem-solving opportunities while keeping students engaged.

Definition of Terms

Common Core State Standards: A framework of standards for mathematical practice and

mathematical content for what teachers are expected to teach. The standards are grouped by

WEBQUESTS & FALS 4

domain according to grade level. By the school year beginning in 2012, all but 5 states had

adopted the standards (Fuchs, D., Fuchs, L., & Powell, 2013).

Formative assessment lesson: A formative assessment lesson (FAL) is designed to enrich

teachers’ instruction skills and ability to incorporate the Common Core Standards, increase

student engagement, and increase students’ depth of knowledge. Each lesson includes a pretest,

collaborative activity, whole class discussion, and a posttest. The FALs are developed by

mathematics experts at the Shell Centre; part of the Math Design Collaborative, MDC.

(Lawrence & Sanders, 2011).

Webb’s Depth of Knowledge Model: Webb’s Depth of Knowledge Model (DOK) describes the

depth of content understanding and scope, demonstrated by the skills required to complete a task

or problem; planning, researching, and making conclusions (Carlock, D., Hess, K.K., Jones,

B.S., & Walkup, J.R., 2009).

WebQuest: A structured, online instructional tool designed around a research task (Boone, T.,

Higgins, K., & Skylar, A.A., 2007). A WebQuest is divided into five sections; the Introduction

creates interest in the WebQuest; the Task gives a short explanation of the activity and each role;

the Process states the detailed steps, expectations, and the list of Internet links; the Evaluation

provides a scoring guide or rubric; and the Conclusion reviews what students should have

learned and accomplished after completing the WebQuest (Kossow & Schweizer, 2007).

Literature Review

In 1995, WebQuests were introduced to encourage the use of the Internet in schools

(Castek & Mangelson, 2008). WebQuests are frequently presented in professional development

WEBQUESTS & FALS 5

classes and education programs as an ideal example of effective integration of technology in the

classroom (Abbit & Ophus, 2008).

More recently, 2010, FALs have emerged as a non-technology strategy for improving

higher-order, problem-solving skills through an initiative of the Gates Foundation called Math

Design Collaborative. States adopting the Common Core Standards have embraced the use of

FALs for improving students’ depths of knowledge in mathematics (Christman, Duffy,

Lawrence, & Sanders, 2011).

Both WebQuests and formative assessment lessons use scaffolding approaches and

require higher-order processing skills and the ability to apply and synthesize knowledge to solve

a problem. This literature review will explore the literature available about the use of

WebQuests and formative assessment lessons and their effect on student learning and student

achievement.

WebQuests

WebQuests are authentic activities that require students to work collaboratively to use the

Internet within a given framework to solve an authentic, real-world problem. The purpose of the

WebQuest is to deepen student understanding of recently learned knowledge and increase

student engagement (Ausband & Polly, 2009). A WebQuest is divided into five sections; the

Introduction creates interest in the WebQuest; the Task gives a short explanation of the activity

and each role; the Process states the detailed steps, expectations, and the list of Internet links; the

Evaluation provides a scoring guide or rubric; and the Conclusion reviews what students should

have learned and accomplished after completing the WebQuest (Kossow & Schweizer, 2007).

WEBQUESTS & FALS 6

A study by Ausband and Polly (2009), was conducted to find the extent teacher-designed

WebQuests develop students’ thinking skills as defined by Marzano’s Higher-Order Thinking

Skills (HOTS), the level of authenticity and technology integration according to the Levels of

Teaching Innovation Framework (LoTi), and teachers’ perceptions of the effectiveness of their

WebQuests. The research found that the majority of the WebQuests were not as challenging, as

infused with technology, or as authentic as teachers perceived. These findings were supported

by Bell, Dodge, Mason, and Molebash (2002), when they reviewed WebQuests on the

WebQuest.org website, and found the bulk of WebQuests did not require higher levels of

analysis.

In another study, the effects of using WebQuests by students learning the proportion

concept in mathematics was measured with achievement tests and student questionnaires. The

study indicated that the students who used WebQuests performed higher than the students who

used other technology tools while learning proportions, but the students’ attitudes towards

mathematics in general were not significantly different (Yang, 2013).

Formative Assessment Lessons

A FAL is designed to enrich teachers’ instruction skills and ability to incorporate the

Common Core Standards, increase student engagement, and increase students’ depth of

knowledge. Each lesson includes a pretest, collaborative activity, whole class discussion, and a

posttest. The FALs are developed by mathematics experts at the Shell Centre; part of the Math

Design Collaborative (MDC) initiated by the Bill and Melinda Gates Foundation (Lawrence &

Sanders, 2011).

WEBQUESTS & FALS 7

Lawrence and Sanders (2011) surveyed and observed teachers who participated in the

pilot year of implementing the use of FALs. The majority of teachers thought their students’

reasoning abilities had improved as a result of using FALs, but were not sure of the direct effect

on student achievement. They found teachers liked taking the role of facilitator, the support

provided by the teaching guide and other resources, and the increased awareness of student

weaknesses and misconceptions. Some of the concerns teachers expressed were the level of

engagement for students who struggle in mathematics, and the length of time each lesson needs

for preparation and implementation; requiring at least two class periods.

In a study of middle school mathematics classrooms using formative assessment

strategies similar to FALs, the results indicated the researcher-designed tasks that included brief

formative assessments were more effective in increasing student understanding and ability to

transfer knowledge for those students who performed higher on the pretest (Baker, Choi,

Herman, Phelan, & Vendlinski, 2011).

Students Who Struggle in Mathematics

Fuchs et al. (2013) state that “95% of students identified with a mathematics learning

disability before fifth grade continue to struggle with mathematics in high school. Many more

students struggle with low mathematics performance without a formal diagnosis of a

mathematics learning disability” (p. 40).

Most states have adopted the Common Core Standards in mathematics, which require all

students, regardless of any disabilities, to meet the same mathematics standards. Teachers must

now find ways beyond traditional approaches for instructing students who struggle in

mathematics, whether because of a learning disability or other reason, so they may succeed in the

WEBQUESTS & FALS 8

increasingly rigorous, conceptually-concept based mathematics classroom (Deshler,

Scheuermann, & Schumaker, 2009).

One argument for using activities such as WebQuests and Fals, is they will increase

student engagement, which will then lead to improved student learning. According to Furrer,

Kindermann, Marchand, and Skinner (2008), students’ motivation and enthusiasm for

participating in a learning activity is a strong indicator of their level of achievement. Students

who struggle in mathematics class often react to frustration, discouragement and apathy by

avoiding work; displaying such behaviors inattention, appearing to work but simply going

through the motions, or disruptive behavior. Further study is necessary to determine if

WebQuests and FALs can be student-centered and contribute to student learning, while keeping

students who struggle in mathematics engaged and challenged without contributing to their

discouragement and frustration.

In a study conducted for exploring methods for improving problem-solving skills of

students with mathematics disabilities, students were divided into four groups to measure their

growth in solving word problems, transferring knowledge to word problems, and solving real-

world problems. The four groups were a control group, a group receiving direct problem-solving

and transferring tutoring, a group receiving computer-based tutoring on solving real-world

problems, and a fourth group receiving both the direct tutoring and practice for solving real-

world problems on the computer. The study indicated that students with mathematical

disabilities who received computer-based real-world problem solving assistance showed a slight

advantage in increased problem-solving skills above the control group, but the most

improvement in problem-solving skills occurred with those students who received direct and

explicit instruction (Appleton, Fuchs, D., Fuchs, L., & Hamlett, 2002).

WEBQUESTS & FALS 9

Library Search

Research terms used to locate relevant literature for the research proposal included:

WebQuest + mathematics, formative assessment lesson, students struggle + mathematics,

technology + mathematics instruction, student motivation, student engagement, Mathematics

Common Core Standards + students struggle, mathematics instruction, mathematics learning

disabilities

The following secondary resources were used in finding the relevant research literature:

1. Eric

2. Ebsco

3. Galileo

The following primary sources were used in finding the relevant research literature:

1. Appleton, A., Fuchs, D., Fuchs, L., & Hamlett, C. (2002). Explicitly teaching for transfer:

Effects on the mathematical problem-solving performance of students with mathematics

disabilities. Learning Disabilities Research & Practice, 17(2), 90-106.

This article described a study of the effectiveness of direct instruction in improving students’

with mathematical disabilities problem-solving abilities.

2. Ausband, L., & Polly, P. (2009). Developing higher-order thinking skills through webquests.

Journal of Computing in Teacher Education, 26(1), 29-34

This article explored the effectiveness of WebQuests in developing higher-order thinking

skills.

WEBQUESTS & FALS 10

3. Fuchs, D., Fuchs, L., & Powell, S. (2013). Reaching the mountaintop: Addressing the

common core standards in mathematics for students with mathematics difficulties.

Learning Disabilities Research & Practice, 28(1), 38-48.

This article provided statistical data about students who struggle in mathematics.

4. Furrer, C., Kindermann, T., Marchand, G., & Skinner, E. (2008). Engagement and

disaffection in the classroom: Part of a larger motivational dynamic? Journal of

Educational Psychology, 100(4), 765-781.

This article discusses student motivation and engagement, and their effect on student

achievement.

5. Research for Action. (2011). A view from the inside: Teacher’s perceptions of the mdc

initiative and their use of the formative assessment lessons. Philadelphia, PA: Lawrence,

N., & Sanders, F.

This Research for Action Report relays observations made during the first implementation of

FALs.

6. Montague, M., Morgan, T.H., & Warger, C. (2000). Solve it! Strategy instruction to improve

mathematical problem solving. Learning Disabilities Research & Practice, 15, 110-116.

This article described common characteristics and behaviors of students who struggle in

mathematics.

7. Yang, K. (2013). The webquest model effects on mathematics curriculum learning in

elementary school students. Computers & Education, (72), 158-166.

This article described a study about how WebQuests affect student engagement and learning.

WEBQUESTS & FALS 11

Conclusion

The literature regarding WebQuests shared a common finding that the effectiveness of

the WebQuest depends on its design. An effective WebQuest goes beyond merely having

students use the Internet, but instead requires students to apply their previous knowledge and

skills to accomplish a challenging and authentic task. Further research is needed to evaluate

WebQuests’ effect on student learning; specifically for students who struggle in mathematics

class. Will WebQuests improve their depth of knowledge or prove to be too abstract and

difficult for those students?

Because of its newness, research on FALs is very limited, but just as with the

WebQuests, the design of the lesson seems to be a key factor in its potential effectiveness. More

research is needed as more FALs are integrated and aligned with the Common Core Georgia

Performance Standards (CCGPS). Too often educational trends are quickly accepted and just as

quickly dropped when immediate results are not achieved. As Abbitt and Ophus (2008) stated

new ideas are “. . . highly praised initially, widely implemented without support of research and

evaluation, and then abandoned when they fail to live up to their initial promise” (p. 42).

Methodology

Overview of Research Design

The research took place in two classrooms at Clinch County High School, and one

classroom at Valdosta High School during the lessons for multiplying and dividing polynomial

expressions, and again within the multiplying and dividing rational expressions unit. Valdosta

High School’s mathematics department strictly follows a mathematics framework developed by

Atlanta Public Schools that is an adaptation of Georgia’s mathematics frameworks. Because of

WEBQUESTS & FALS 12

those restrictions, the students at Valdosta High School were the control group. One classroom

at Clinch County High School performed a WebQuest and the other a FAL during the

polynomial expressions lessons. The Clinch County classrooms then switched the type of

activity they performed during the rational expressions lessons.

For each quasi experiment, one with polynomial expressions and one with rational

expressions, all teachers provided direct instruction for the initial introduction of the concept,

and all students had the same skills practice opportunities prior to the activity. The lessons in

each area were designed to take 8 days. During the first five days, the students took the pretest,

received content instruction, and engaged in individual practice. The classes at Clinch County

High School spent the final three days performing the WebQuest and FAL activities and taking

the posttest. The control group spent the last three days of the lessons receiving additional

instruction and practice as outlined by the Atlanta Public Schools frameworks.

Participants

The participants were 60 students in 3 high school mathematics class. Two classes were

at Clinch County High School, and one class at Valdosta High School. All students in the

classes were at least one year behind their grade level classmates, and demonstrate a diverse set

of skills, abilities, disabilities, and motivation levels. Twelve of the students were served by the

Special Education Department, two were English Language Learners, and fourteen students had

reading and processing learning disabilities. The three classes had similar student demographics;

in all, there were 43 male students and 24 female; 23 students were White, 41 students were

African-American, and 3 were Hispanic. All but 4 students qualified for free or reduced lunch.

WEBQUESTS & FALS 13

Data Sources/Instruments/Procedures

The effect on student learning was measured with pretests and posttests that given before

and after the polynomial expressions lessons and the rational expressions lessons. The teacher at

Valdosta High School obtained permission from the Mathematics Department Head to

administer the pretests and posttests. Each test consisted of ten content specific questions for

multiplying and dividing polynomial and rational expressions, taken from the polynomial and

rational unit tests. Nine questions were multiple choice and one question was constructed

response. The Clinch County High mathematics department developed the unit tests to align

with the Common Core Georgia Performance Standards rigor and content standards, and each

question was assigned a DOK level. The sources of the questions were the mathematics

textbook, Common Core Georgia Performance Standards end of course test study guide, and

released questions from previous Georgia Common Core state assessments.

Reliability/Validity

This study is easily replicated. All teachers used the same initial instruction, SmartBoard

presentation, individual white board practice questions, and practice sheets; following the

Atlanta Public Schools frameworks. The students in the control group received instruction

consistent with peers at their school. The students in the treatment groups performed a

WebQuest with one of the lessons, and a FAL with the other to avoid any possible advantages

afforded from having already performed a WebQuest or FAL that would affect the reliability of

the results.

The questions from the unit tests used on the pretest and posttest were from the Holt

McDougal Analytic Geometry textbook, CCGPS study guide, and released questions from

WEBQUESTS & FALS 14

previous CCGPS end of course tests. These questions were constructed by mathematics

education professionals and have been proven to be a valid and reliable measure of the depth of

student knowledge with multiplying and dividing polynomial and rational expressions. The

pretests and posttests were graded by a mathematics teacher who was not a participant in the

study. The names of the students were marked out.

Data Presentation

The average polynomial expressions pre-test scores (M) were 34.5 for the WebQuest

students, 33 for the FAL group, and 27.5 for students in the control group. The groups’ standard

deviations (SD) were13.95, 13.42, and 13.33 respectively; demonstrating a wide variability in

pre-test scores. The median pre-test scores were 35 for the students performing WebQuests, and

30 for students completing the FAL and the students in the control group. The most frequent

(mode) pre-test scores were 30 for the WebQuest and FAL groups, and 20 for the control group.

The minimum and maximum scores for the WebQuest group was 0 and 60, the FAL groups

minimum and maximum was 10 and 60, and the control group’s was 0 and 50.

The post-test mean score was 71.5 for the WebQuest group, 74 for the FAL group, and

the control group’s mean score was 71. The post-test SD for the WebQuest group was 12.68,

11.58 for the FAL group, and 15.18 for the control group; again showing a significant variability

in scores for all three groups. The post-test median scores for the WebQuest, FAL, and control

group students was 70, and the mode was also 70 for all three groups. The minimum and

maximum post-test scores for the WebQuest group was 30 and 90, the FAL groups minimum

and maximum was 50 and 90, and the control group’s was 50 and 100.

WEBQUESTS & FALS 15

WebQuest Group

Polynomials Post-Test

Mean 71.50Median 70.00Mode 70.00Standard Deviation 12.68

The average rational expressions pre-test scores were 27.5 for the WebQuest students, 28

for the FAL group, and 28.5 for students in the control group. The groups’ standard deviations

(SD) were13.72, 11.05, and 12.26 respectively; demonstrating a wide variability in the students’

knowledge of rational expressions prior to instruction. Both the median pre-test scores and the

mode for all three groups was 30. The minimum and maximum scores for the WebQuest group

was 0 and 50, the FAL groups minimum and maximum was 10 and 50, and the control group’s

was 10 and 60.

The post-test mean score for the WebQuest group was 67.5, 72 for the FAL group, and

the control group’s mean score was 71.5. The post-test SD for the WebQuest group was 15.17,

11.96 for the FAL group, and 13.09 for the control group; again showing a significant variability

in scores for all three groups. The post-test median scores for the WebQuest, FAL, and control

group students was 70, and the mode was also 70 for all three groups. The minimum and

maximum scores for the WebQuest group was 30 and 90, the FAL groups minimum and

maximum was 50 and 90, and the control group’s was 50 and 100.

FAL Group

PolynomialsPost-Test

Control Group

Polynomials

Post-Test Mean 74.00 Mean 71.00Median 70.00 Median 70.00Mode 70.00 Mode 70.00Standard Deviation 11.88

Standard Deviation 15.18

WEBQUESTS & FALS 16

WebQuest Group

RationalPost-Test

Mean 67.50Standard Error 3.39Median 70.00Mode 70.00Standard Deviation 15.17

Data Analysis

In comparing the effects of a WebQuest activity on treatment class 1

students’ achievement with polynomial expressions to their achievement using a

FAL activity with rational expressions, the mean score with the WebQuest (mean =

71.5) was lower than the mean score achieved with the FAL (mean = 72). A

paired-t-test, however, showed the difference in means was statistically

insignificant (t = -0.16, df = 19, p < .44, one-tailed).

The effects of a WebQuest activity on treatment class 2 students’ student

achievement with rational expressions compared to their achievement using a FAL

activity with polynomial expressions showed the mean score with the WebQuest

(mean = 67.5) was lower than the mean score achieved with the FAL (mean = 74).

A paired-t-test again indicated the difference in means was not statistically

significant (t = -1.45, df = 19, p < .08, one-tailed).

FAL Group

Rational Post-Test


Control Group

Rational Post-Test


WEBQUESTS & FALS 17

In comparing the polynomial expressions unit’s post-test mean scores of students who

participated in a WebQuest activity to the scores of those who did not complete the WebQuest,

the mean score for those who did the WebQuest (mean = 71.5) was slightly higher than the mean

score of the students who did not complete the WebQuest (mean = 71). As expected for such a

minimal difference, the paired-t-test showed there is no significant difference at the p < .91 level

to reject the null hypothesis (t = .11, df = 38).

The post-test mean score for the students who participated in a FAL activity during the

polynomials unit (mean = 74) was 3 points higher than the mean score of those who did not

complete the FAL (mean = 71). As with the comparison between the WebQuest treatment group

and the control group, the paired-t-test showed there is not a significant difference at the p < .49

level to reject the null hypothesis (t = .70, df = 38).

Comparing post-test mean scores from the rational unit had similar results. Even though

the mean score of students who participated in a WebQuest (mean = 67.5) was 4 points lower

than the mean score of the students who did not the WebQuest (mean = 71.5), a paired t-test

showed that there is not a significant enough difference at the p < .38 level to reject the null

hypothesis (t = -.89, df = 38). The mean score for those who participated in the FAL (mean =

72) was slightly higher as compared to the mean score of the students who did not participate in

the FAL (mean = 71.5), and the paired-t-test showed there is no significant difference at the p

< .49 level to reject the null hypothesis (t = .13, df =38).

Summary statistics of the polynomial expressions’ post-test scores suggests math

proficiency with polynomial expressions does not improve significantly from one particular

activity. A single factor ANOVA was computed to examine the effect of different activities on

students’ proficiency with polynomial expressions. There was no significant effect with any of

WEBQUESTS & FALS 18

the activities on math proficiency with polynomial expressions for the three conditions [F (2, 57)

= 0.29, p>0.05].

Summary statistics of the rational expressions’ post-test scores also suggests math

proficiency with rational expressions does not improve significantly from one particular activity.

The mean post-test score for the WebQuest group was 67.5, FAL group was 72, and the control

group mean was 71.5. A single factor ANOVA was computed to examine the effect of different

activities on home s students’ proficiency with polynomial expressions. There was no significant

effect with any of the activities on math proficiency with rational expressions for the three

conditions [F (2, 57) = 0.67, p>0.05].

Findings

Data analysis of the post-test scores shows that no one type of learning activity had a

significance impact on student achievement when compared to the performance by the group of

students who followed the state recommended frameworks. The scores of the students who

participated in a FAL, in both the polynomial and rational unit, were slightly higher. The

teachers in the study had participated in a collaborative initiative over the prior two years that

focused on using FAL’s in the classroom, and the extra training may account for the higher mean

scores. In the same vein, none of the participating teachers had used a WebQuest in their

classroom before this study, which could explain the lower mean scores for the students

performing WebQuests in the polynomial and rational unit.

One of the participating teachers was out for several days during the rational unit, and her

students experienced a larger gap in time between the instruction and practice and performing the

WebQuest than the students participating in a FAL or traditional practice; a possible explanation

WEBQUESTS & FALS 19

for why the rational WebQuest students had the lowest mean score among all the post-test

means. In addition, the WebQuests were developed by a first time designer, possibly influencing

their quality and effectiveness, as compared to the FAL’s and frameworks that were developed

by experienced educators.

Conclusion

This study highlights the need for more research on not only the effects of WebQuests

and FAL’s on student achievement, but also the effectiveness of other instructional practices for

improving the understanding of mathematics for students who struggle in mathematics. Neither

this study nor the limited amount of research available offer a consistent or definitive answer to

the question of how WebQuests and formative assessment lessons relate to student learning.

Identifying ways for improving student learning for students who struggle in mathematics will

contribute to closing the achievement gap among different student groups.

WEBQUESTS & FALS 20

References

Abbit, J., & Ophis. J. (2008). What we know about the impacts of webquests: A review of

research. AACE Journal, 16(4), 441-456.

Appleton, A., Fuchs, D., Fuchs, L., & Hamlett, C. (2002). Explicitly teaching for transfer:

Effects on the mathematical problem-solving performance of students with mathematics

disabilities. Learning Disabilities Research & Practice, 17(2), 90-106.

Ausband, L., & Polly, P. (2009). Developing higher-order thinking skills through webquests.

Journal of Computing in Teacher Education, 26(1), 29-34.

Baker, E., Choi, K., Herman, J., Phelan, J., & Vendlinski, T. (2011). Differential improvement in

student understanding of mathematical principles following formative assessment

intervention. The Journal of Educational Research, (104), 330-339.

Doi:10.1080/00220671.2010.484030

Bell, R., Dodge, B., Mason, C., & Molebash, P. (2002). Promoting student inquiry: WebQuests

to web inquiry projects (WIPs). Paper presented at the Society for Information

Technology and Teacher Education International Conference 2002, Nashville, TN.

Boone, R., Higgins, K., & Skylar, A.A. (2007). Strategies for adapting webquests for students

with learning disabilities. Intervention in School and Clinic, 43(1), 20-26.

WEBQUESTS & FALS 21

Institute of Education Sciences. (2009). Cognitive rigor: Blending the strengths of

bloom's taxonomy and webb's depth of knowledge to enhance classroom-level processes.

Washington, D.C.: Carlock, D., Hess, K.K., Jones, B.S., Walkup, J.R.

Castek, J., & Mangelson, J. (2008). Thinking outside the book: Engaging students with

webquests. Retrieved from

http://www.ala.org/offices/resources/thinking_outside_the_book.

Deshler, D., Scheuermann, A., & Schumaker, J. (2009). The effects of the explicit inquiry

routine on the performance of students with learning disabilities on one-variable

equations. Learning Disability Quarterly, 32, 103-120.

Fuchs, D., Fuchs, L., & Powell, S. (2013). Reaching the mountaintop: Addressing the common

core standards in mathematics for students with mathematics difficulties. Learning

Disabilities Research & Practice, 28(1), 38-48.

Furrer, C., Kindermann, T., Marchand, G., & Skinner, E. (2008). Engagement and disaffection in

the classroom: Part of a larger motivational dynamic? Journal of Educational

Psychology, 100(4), 765-781.

Kossow, B., & Schweizer, H. (2007). Webquests: Tools for differentiation. Gifted Child Today,

30(1). 29-35.

Montague, M., Morgan, T.H., & Warger, C. (2000). Solve it! Strategy instruction to improve

mathematical problem solving. Learning Disabilities Research & Practice, 15, 110-116.

http://www.ala.org/offices/resources/thinking_outside_the_book

WEBQUESTS & FALS 22

Research for Action. (2011). Establishing a strong foundation: District and school supports for

classroom implementation of the mdc framework. Philadelphia, PA: Christman, J.B.,

Duffy, M., Lawrence, N., Sanders, F.

Research for Action. (2011). A view from the inside: Teacher’s perceptions of the mdc initiative

and their use of the formative assessment lessons. Philadelphia, PA: Lawrence, N., &

Sanders, F.

Yang, K. (2013). The webquest model effects on mathematics curriculum learning in elementary

school students. Computers & Education, (72), 158-166.

WEBQUESTS & FALS 23

Appendix A

Multiplying and Dividing Polynomial Expressions Pretest and Posttest Questions

1. Which of the following is equal to (x2 2x 3)(3x2 4x 1)?F 3x4 2x3 18x2 10x 3G 3x4 2x3 16x2 10x 3H 3x4 x3 18x2 10x 3J 3x4 x3 16x2 10x 3

2. A 9 in. by 18 in. sheet of cardboard is being made into a box for a class project. As shown below, squares with side length x are cut from each corner of the sheet, and then the sides are folded up to form the box. One expression for the volume of the box is (18 2x)(9 2x)x. Interpret the first factor, 18 2x, in the context of the problem.

The factor 18 2x represents the height of the box.The factor 18 2x represents the length of the box.The factor 18 2x represents the width of the box.The factor 18 2x represents the volume of the box.

3. When x3 125 is written as a product of a binomial and a trinomial, what is the trinomial factor?

x2 5x 25 x2 5x 25 x2 10x 25 x2 10x 25

WEBQUESTS & FALS 24

4.For p(x) 4x3 28x 24, the value of p(3) is 0. Which of the following must therefore be true?

3 is a factor of p(x) 4x3 28x 24.3x is a factor of p(x) 4x3 28x 24.x 3 is a factor of p(x) 4x3 28x 24.x 3 is a factor of p(x) 4x3 28x 24.

5.Use the remainder theorem to find the remainder when the polynomial p(x) x3 3x2 5x 7 is divided by x 5.

182 732 168

6.Which variable term in the expanded form of (3x 1)4 has the greatest coefficient? The x-termThe x2-termThe x3-termThe x4-term

7.Use the remainder theorem to find the remainder when the polynomial p(x) x3 3x2 5x 7 is divided by x 5.

182 732 168

8.The quotient when the polynomial p(x) x3 3x2 16x 12 is divided by

x 1 is Which of the following is not necessarily true?

p(1) 01 is not a zero of p(x).x 1 is not a factor of p(x).

WEBQUESTS & FALS 25

Substituting 1 for x in p(x) results in 30.

9.Which of the following best describes the product of ax2 bx c and mx2 nx p, where x is a variable and a, b, c, m, n, and p are nonzero real numbers?

A quadratic polynomialAn exponential expressionA third-degree polynomialA fourth-degree polynomial

CONSTRUCTED RESPONSE10. A coin is randomly tossed onto the rectangular mat shown. The probability that the coin

lands in square region A is given by the expression Interpret the expressions x 2, x 22, and (2x 5)(3x 2) in the context of the problem.

__________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

WEBQUESTS & FALS 26

Appendix B

Multiplying and Dividing Rational Expressions Pretest and Posttest Questions

1. Which of the following expressions are equivalent to

2. When you divide to simplify the expression what is the fractional part of the quotient?5

3x2 2x 4

3. Simplify .

A C

B D

WEBQUESTS & FALS 27

4. Simplify .

A

B

5. Simplify .

A x 1 C

B (x 1) D

6. Simplify

F H

G J

7. Identify all asymptotes of .

F vertical asymptote: ; horizontal asymptote:

G vertical asymptote: ; horizontal asymptotes: and y = 3

H vertical asymptotes: and x 2; horizontal asymptote:

J vertical asymptotes: and x 3; horizontal asymptotes: and y 3

8. Which function is continuous?

A C

B D

WEBQUESTS & FALS 28

9. P varies directly with Q and inversely with R, and P 3 when Q 8 and R 6. Find Q when P 0.5 and R 4.

F H

G J

10. Claire was asked to evaluate when x 0, x 2, and x 4. To avoid having to evaluate four quadratic polynomials multiple times, Claire decided to simplify the expression before evaluating it for the first value of x. Her work is shown below.

Now substitute for x in the simplified expression .

Describe Claire’s mistake.

__________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

_________________________________________________________________________________________

WEBQUESTS & FALS 29

Appendix C

Pre-test and Post-test Scores

WebQuest Treatment Group Pre-Test

WebQuest Treatment Post-Test

FAL Group Pre-Test

FAL Group Post-Test

Control Group Pre-Test

Control Group Post-Test

20 70 40 100 50 70

30 60 50 70 20 50

40 80 30 60 20 60

40 70 30 80 20 70

30 70 10 50 40 80

50 70 60 70 30 80

30 80 40 80 30 70

40 90 30 70 50 100

40 80 10 70 40 100

60 80 30 60 20 50

30 60 50 90 10 80

30 80 40 80 10 60

40 70 40 70 0 40

10 50 20 80 40 70

0 60 50 90 30 80

WEBQUESTS & FALS 30

50 100 30 70 30 80

30 50 20 70 20 70

30 60 20 60 20 70

50 80 30 80 30 60

40 70 30 80 40 80

WEBQUESTS & FALS 31

Appendix D

Pre- and Post-test Descriptive Statistics

WebQuest Group Polynomials Pre-Test

WebQuest GroupPolynomials Post-Test

Mean 34.50 Mean 71.50Standard Error 3.12 Standard Error 2.84Median 35.00 Median 70.00Mode 30.00 Mode 70.00Standard Deviation 13.95 Standard Deviation 12.68Sample Variance 194.47 Sample Variance 160.79Range 60.00 Range 50.00Minimum 0.00 Minimum 50.00Maximum 60.00 Maximum 100.00

FAL Group Polynomials Pre-Test

FAL Group Polynomials Post-Test


Control Group Polynomials Pre-Test

Control Group Polynomials Post-Test

Mean 27.50 Mean 71.00Standard Error 2.98 Standard Error 3.40Median 30.00 Median 70.00

WEBQUESTS & FALS 32

Mode 20.00 Mode 70.00Standard Deviation 13.33 Standard Deviation 15.18Sample Variance 177.63 Sample Variance 230.53Range 50.00 Range 60.00Minimum 0.00 Minimum 40.00Maximum 50.00 Maximum 100.00

WebQuest Group Rational Pre-Test

WebQuest Group Rational Post-Test


FAL Group Rational Pre-Test

FAL Group Rational Post-Test


Control Group Rational Pre-Test

Control Group Rational Post-Test

Mean 28.50 Mean 71.50Standard Error 2.74 Standard Error 2.93

WEBQUESTS & FALS 33

Median 30.00 Median 70.00Mode 30.00 Mode 70.00Standard Deviation 12.26 Standard Deviation 13.09Sample Variance 150.26 Sample Variance 171.32Range 50.00 Range 50.00Minimum 10.00 Minimum 50.00Maximum 60.00 Maximum 100.00

Appendix E

Treatment Groups t-Test: Paired Two Sample for Means

Treatment Class 1: t-Test: Paired Two Sample for Means

WebQuest Post-Test

FAL Post-Test

Mean 71.50 72.00Variance 160.79 143.16Observations 20.00 20.00Pearson Correlation 0.33Hypothesized Mean Difference 0.00Df 19.00t Stat -0.16P(T<=t) one-tail 0.44t Critical one-tail 1.73P(T<=t) two-tail 0.88t Critical two-tail 2.09

Treatment Class 2: t-Test: Paired Two Sample for Means

WebQuest Post-Test

FAL Post-Test

Mean 67.50 74.00Variance 230.26 141.05Observations 20.00 20.00Pearson Correlation -0.09Hypothesized Mean Difference 0.00Df 19.00t Stat -1.45P(T<=t) one-tail 0.08t Critical one-tail 1.73P(T<=t) two-tail 0.16

WEBQUESTS & FALS 34

t Critical two-tail 2.09

Appendix F

t-Test: Two-Sample Assuming Equal Variances

WebQuest/ Control Group Polynomials Unit t-Test: Two-Sample Assuming EqualVariances

WebQuest Post-Test

Control Post-Test

Mean 71.50 71.00Variance 160.79 230.53Observations 20.00 20.00Pooled Variance 195.66Hypothesized Mean Difference 0.00Df 38.00t Stat 0.11P(T<=t) one-tail 0.46t Critical one-tail 1.69P(T<=t) two-tail 0.91t Critical two-tail 2.02

FAL/ Control Group Polynomials t-Test: Two-Sample Assuming Equal Variances

FAL Post-Test

ControlPost-Test

Mean 74.00 71.00Variance 141.05 230.53Observations 20.00 20.00Pooled Variance 185.79Hypothesized Mean Difference 0.00Df 38.00t Stat 0.70P(T<=t) one-tail 0.25

WEBQUESTS & FALS 35

t Critical one-tail 1.69P(T<=t) two-tail 0.49t Critical two-tail 2.02

WebQuest/Control Group Rational t-Test: Two-Sample Assuming Equal Variances

WebQuest Post-Test

Control PostTest

Mean 67.50 71.50Variance 230.26 171.32Observations 20 20Pooled Variance 200.79Hypothesized Mean Difference 0.00df 38.00t Stat -0.89P(T<=t) one-tail 0.19t Critical one-tail 1.69P(T<=t) two-tail 0.38t Critical two-tail 2.02

FAL/ Control Group Rational t-Test: Two-Sample Assuming Equal Variances

FAL

PostTestControl

Post-TestMean 72.00 71.50Variance 143.16 171.32Observations 20.00 20.00Pooled Variance 157.24Hypothesized Mean Difference 0.00df 38.00t Stat 0.13P(T<=t) one-tail 0.45t Critical one-tail 1.69P(T<=t) two-tail 0.90t Critical two-tail 2.02

WEBQUESTS & FALS 36

Appendix G

ANOVA

Polynomials Unit Anova: Single Factor

SUMMARY

Groups Count SumAverag

eVarianc

eWebQuest Treatment Post-Test 20 1430 71.5 160.79FAL Group Post-Test 20 1480 74 141.05Control Group Post-Test 20 1420 71 230.53

ANOVA

Source of Variation SS df MS FP-

value F critBetween Groups 103.33 2 51.67 0.29 0.75 3.16Within Groups 10115 57 177.46

Total10218.3

3 59

Rational Unit Anova: Single Factor

SUMMARYGroups Count Sum Average Variance

WebQuest Group Post-Test 20 1350 67.5 230.26FAL Group Post-Test 20 1440 72 143.16Control Group Post-Test 20 1430 71.5 171.32

WEBQUESTS & FALS 37

ANOVASource of Variation SS df MS F P-value F crit

Between Groups 243.33 2 121.67 0.67 0.52 3.16Within Groups 10350 57 181.58

Total 10593.33 59

Appendix H

Histograms

10 20 30 40 50 60 70 80 90100

More0

2

4

6

0.00%20.00%40.00%60.00%80.00%100.00%120.00%

WebQuest Polynomials Histogram

FrequencyCumulative %

Scores

Freq

uenc

y

10 20 30 40 50 60 70 80 90100

More0

2

4

6

8

0.00%20.00%40.00%60.00%80.00%100.00%120.00%

FAL Polynomials Histogram


Scores

Freq

uenc

y

WEBQUESTS & FALS 38

10 20 30 40 50 60 70 80 90100

More0

2

4

6

0.00%20.00%40.00%60.00%80.00%100.00%120.00%

Control Group Polynomials Histogram


Scores

Freq

uenc

y

10 20 30 40 50 60 70 80 90100

More0

2

4

6

8

0.00%20.00%40.00%60.00%80.00%100.00%120.00%

WebQuest Rationals Histogram


Scores

Freq

uenc

y

10 20 30 40 50 60 70 80 90100

More0

2

4

6

8

0.00%20.00%40.00%60.00%80.00%100.00%120.00%

FAL Rationals Histogram


Scores

Freq

uenc

y

WEBQUESTS & FALS 39

10 20 30 40 50 60 70 80 90100

More0

2

4

6

8

0.00%20.00%40.00%60.00%80.00%100.00%120.00%

Control Group Rationals Histogram


Scores

Freq

uenc

y

csegraves.weebly.comcsegraves.weebly.com/.../5/6/5/25650794/final_research_paper_se… · web...

Documents