THE DIVISION SKILLS OF 3RD GRADE STUDENTS · “The diverse nature of mathematical knowledge demands different strategies from the teachers in the classroom” (Afzal, Gondal, & Fatima,

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Running Header: THE IMPACT OF A TARGETED TECHNOLOGY INTERVENTION ON

THE DIVISION SKILLS OF 3RD GRADE STUDENTS

The Impact of a Targeted Technology Intervention on the Division Skills of 3rd Grade Students

Amanda Burk

California State University, San Bernardino

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THE IMPACT OF A TARGETED TECHNOLOGY INTERVENTION ON THE DIVISION

SKILLS OF 3RD GRADE STUDENTS

Abstract

Keywords:

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The Impact of a Targeted Technology Intervention on the

Division Skills of 3rd Grade Students

Math plays an important role in a student’s life, as well as their lives when they have left

school. As students’ progress through their school lives the mathematical concepts become more

and more difficult. This difficulty can be compounded if students are missing key skills from

their early elementary days. “Students who have not mastered basic computational fluency by

the end of elementary school are at risk for future difficulties with mathematics and problems

solving” (Kanive, Nelson, Burns, & Ysseldyke, 2014, p. 84). Bryant, Hartman, and Kim (2003)

state that “skill deficits can impede student’s ability to comprehend and master a variety of

mathematical concepts” (p. 162). In fact, as students struggle with math concepts, their attitude

towards math becomes more negative as they climb grade levels (Swetman, 1995).

Mathematics instruction traditionally was a teacher at the chalkboard, and students at

their desk copying down fact tables and solving problems. Today, it can look very different.

Explicit, systematic, and direct instruction using visual representations appears to be the best

method for math instruction today (Baker, Gersten, & Lee, 2002; Ketterlin-Geller, Chard, &

Fine, 2008). “Mathematical proficiency is directly linked to the quality of instruction students

receive during elementary grades” (Burns, Kanive, & DeGrande, 2010, p. 184). Quality

mathematics instruction needs to be a mix of understanding the concepts provided, being fluent

in the ability to perform the operations, and problem solving (Grams, 2018). “The diverse nature

of mathematical knowledge demands different strategies from the teachers in the classroom”

(Afzal, Gondal, & Fatima, 2014, p. 48). However, this can be difficult in a classroom with many

different ability levels and challenges. Afzal et al (2014) also state that a “mathematics learner

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should be allowed to construct knowledge in their own cultural and social context” (p. 48). The

problem with this knowledge construction is that math is traditionally taught in the same basic

pattern, one skill building on the next. “Teachers do not have sufficient time to provide students

with the instructional scaffolding they need to master mathematical concepts or develop fluency”

(Ketterlin-Geller et al, 2008, p. 36). This lack of time, and need for additional interactions with

mathematics is where the intervention, and specifically the technology intervention comes in.

There is a need for early intervention that help develop skills that deal with numbers and

computations (Fuchs et al, 2006; Cheung & Slavin, 2013). For math interventions to be effective

for students, they must be correctly targeted to specific skills (Burns et al, 2011). This study

focused on using a technology intervention that targeted division fact fluency for 3rd grade

students.

Literature Review

Interventions

Interventions are an important part of education that can help bridge the gap between the

teacher’s instruction and the student being able to use that information on their own.

“Interventions that focused on mathematical fact fluency improved recall of mathematics facts,

computational fluency, and performance on different types of mathematic problems” (Kanive et

al, 2014, p. 84). Many studies have found a link between mathematical fact fluency and the

further application of other math concepts (Burns et al, 2010; Fuchs et al, 2006). The more

practice in repetition, especially in fact fluency, the better the recall and usability of the skill

(Burns et al, 2010). “Fluent computation is an important math goal, and frequent difficulty for

students who struggle in math” (Burns et al, 2010, p. 188). Ketterlin-Geller et al (2008) state

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that “Mathematics interventions designed to reteach fundamental mathematical concepts and

procedures and provide extended time… may improve students achievement” (p. 42).

Technology

The National Council of Teachers of Mathematics (2011) state that “technology is

essential in teaching and learning math; it influences the math taught and enhances student

learning.” Technology today is an ever-expanding landscape, and it is important to use

technology in the mathematics classroom. “Instructional technology often improves teaching

programs in mathematics” (Kulik, 2003, p.X). Previous uses of technology might have used skill

and drill games, tutorials, or even simulations (Kulik, 2003). Today’s technology use is much

different. “Technology based instruction and interventions provide students with individualized

practice that can be implemented with a larger group of students. Computer-based practice

intervention was more effective for increasing fact fluency among struggling learners than

classroom instruction alone” (Kanive et al, 2014, p.87). By using the technology that is

available, it allows one teacher to enhance students’ learning even when there are many students

with different needs (Afzal et all, 2014).

Prodigy

Prodigy is a game-based mathematics intervention. It has a Role-Playing Game (RPG)

format where students move around a world and interact with other characters. Students create

an avatar of a wizard, that then travels through the land and battles monsters and other characters

with their pets. In order to be successful in these battles, students must answer math questions

(www.prodigygame.com). Why Prodigy? “Using technology for basic skills and factual

learning has been beneficial and using a proprietary software as an intervention has proven

http://www.prodigygame.com/

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successful” (Grams, 2018, p. 42). Prodigy also has a variety of reports that teachers can access

that helps keep them informed of students progress and growth in skills

(www.prodigygame.com). By providing both teachers and students with this specific

information, it helps to enhance math achievement (Baker et al, 2002). Teachers can access the

student data and assign specific skills to be worked on that they may need more help with or all

grade level appropriate skills. “Students demonstrate higher academic achievement when

instruction and independent practice are provided at each student’s appropriate level” (Kanive et

al, 2014, p. 87). It is up to the teacher how they want to use this intervention.

Research Questions

RQ₁: What will the effect be on division skills for 3rd grade students who receive both instruction

for their classroom teacher and the targeted technology intervention?

RQ₂: Do student’s attitudes about division and math in general change over the course of the

study? How?

Ho1: There is no significant difference between the post-test mean scores of students who

received the targeted intervention and those who did not receive it.

Research Methodology

The research design is a Mixed Methods Convergent Design, primarily quantitative to

answer the research questions (McMillian, 2016).

Participants

Participants were 3rd graders, 7-9 years old both male and female, from a Title 1 school

located in Northern Arizona. The composition of the school is 100% Native American. The

http://www.prodigygame.com/

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students are a convenience sample chosen from one teacher’s classroom. Students were then

randomly selected for one of the two groups.

Research Design

The research study had two co-currently happening pieces. The first piece was a quasi-

experimental design that studied the impact of the technology intervention. There were two

groups participating. Group A consisted of 8 students (5 boys and 3 girls) who received both

explicit, direct instruction in Division from the classroom teacher, and the Prodigy intervention.

Group A’s intervention however dealt with all the 3rd grade mathematic standards. Group B

consisted of 9 students (8 girls and 1 boy) who received both explicit, direct instruction in

Division from the classroom teacher and the Prodigy intervention. Group B’s intervention was

for specific division fact fluency skills. Both groups took pre-tests, mid-tests, and post-tests to

determine their growth in their division fact fluency (Appendix A). These tests had 15 questions

on division facts from 1-9, and students had 20 minutes to complete the test. The second piece

was a survey that took place with each student after each of the tests. (Appendix B) Due to the

age of the students, the survey was completed in one on one interviews of about 5 minutes each.

The survey was developed for this study using a Likert-type scale with a 5-point response scale

for students to answer 5 questions. There were also two open ended questions. These answers

were categorized and recorded.

Validity and Reliability

The tests were created by the classroom teacher and I using question types that were

consistent with the AzMERITS tests that students take towards the end of the year. These

quizzes were then reviewed by the other 3rd grade teacher and the principal at the school site.

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Survey questions were also created by the classroom teacher and I and again reviewed by the

other 3rd grade teacher and the principal at the school site.

Students had their math instruction at the same time every day, after lunch. The quizzes

were given to students at the beginning of the math period on the Monday of 3 out of 4 weeks.

Any make up tests were given later in the afternoon on Tuesday. Math intervention time took

place the last 40 minutes of the instructional day. Student fatigue was not really an issue during

this study. Due to the fact they were coming in from recess, it was more necessary to calm

students down a bit before the tests could be taken. There were no instances of a student

refusing to take the test. All students looked forward to Prodigy during the intervention time, so

there was no extra encouragement needed. Student surveys took place during the morning group

time on Tuesdays after the quizzes had been taken.

Data Analysis

Results from the tests were compiled on a spreadsheet and analyzed using the qualitative

techniques of the measures of central tendency (mean, median, mode) and standard deviation. A

t-test was also performed on the data to compare the mean test results. Results from the Likert-

type survey questions were compiled using a spreadsheet and then counted and tallied. The

open-ended questions were categorized according to themes and then tallied on a spreadsheet.

Results

RQ₁: The effect for students who had both classroom instruction and targeted

intervention skills?

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Group B, the targeted division skills group’s scores (M=8.67, SD=5.52) were slightly higher on

the post test than Group A’s scores (M=6.5, SD=5.01, p=0.20). The null hypothesis was

confirmed because there was not a statistically significant difference (p >0.05) between the post

tests of Group A and B.

RQ₂ Student Attitudes

0 0

4.5

8.5

6.5

8.67

0

2

4

6

8

10

Group A Mean Group B Mean

Quiz Means

Pre-Quiz Mid Quiz Post- Quiz

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

1 2 3

Question 4: I ________ Math

Group A Scores Group B Scores

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Student Attitudes changed slightly over the course of the unit on Division. Overall, for the

students’ feelings about Math, Group A stayed the same at 87.5% across the three surveys.

Group B changed from 75% at the first survey to 88.9% at the third.

Discussion

The results of this study suggest that using targeted skills for student’s intervention may

help with their retention and ability to use these targeted skills. Current studies suggest that

students show higher academic achievement when their instruction and intervention are tailored

to their specific levels (Kanive et al, 2014). Students’ attitudes about math changed slightly

during the study, predominately in Group B. It was not determined whether this was due to their

increased confidence in their math skills because of the targeted intervention, or if it was just

from time passing. However, due to the small sample size (17 students) and the short time frame

(4 weeks) further study is needed to determine if the results continue in the same vein.

Conclusion

“Division is a complex skill to teach because it requires prerequisite knowledge related to

other mathematical skills” (Bryant et al, 2003, p. 154). Previous studies have shown that

explicit, systematic, and direct instruction using visual representations is the best method for

math instruction today (Baker, Gersten, & Lee, 2002; Ketterlin-Geller, Chard, & Fine, 2008). It

has also shown that “Interventions that focused on mathematical fact fluency improved recall of

mathematics facts, computational fluency, and performance on different types of mathematic

problems. Student’s demonstrate higher academic achievement when instruction and

independent practice are provided at each student’s appropriate level” (Kanive et al, 2014, p. 84).

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For students to be successful they need a combination of both explicit instruction and targeted

intervention skills.

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References

Afzal, M.T., Gondal, B. & Fatima, N. (2014). The effect of computer based instructional

technique for the learning of elementary level mathematics among high, average, and low

achievers. International Journal of Education and Development using Information and

Communication Technology (IJEDICT), 10(4), 47-59 Retrieved from

http://libproxy.lib.csusb.edu/login?url=http://search.ebscohost.com/login.aspx?direct=tru

e&db=eric&AN=EJ1059055&site=ehost-live

Baker, S., Gersten, R., & Lee, D.S. (2002). A synthesis of empirical research on teaching

mathematics to low-achieving students. Elementary School Journal, 103(1), 51-73.

Retrieved from



Bryant, D.P., Hartman, P., & Kim, S.A. (2003). Using explicit and strategic instruction to teach

division skills to students with learning disabilities. Exceptionality, 11(3), 151-164.

Retrieved from



Burns, M.K, Kanive, R., & DeGrande, M. (2010). Effect of a computer-delivered math fact

intervention as a supplemental intervention for math in third and fourth grades. Remedial

and Special Education, 33(3), 184-191. https://doi.org/10.1177/0741932510381652

Cheung, A.C.K., & Slavin, R.E. (2013). The effectiveness of educational technology applications

for enhancing mathematics achievement in K-12 classrooms: A meta-analysis.

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Educational Research Review, 9, 88-113.

http://dx.doi.org.libproxy.lib.csusb.edu/10.1016/j.edurev.2013.01.001

Fuchs, L.S., Fuchs, D., Compton, D.L, Powell, S.R., Seethaler, P.M., Capizzi, A.M.,

Schatschneider, C., & Fletcher, J.M. (2006). The cognitive correlates of third-grade skill

in arithmetic, algorithmic computation, and arithmetic word problems. Journal of

Educational Psychology, 89(1), 29-43. Retrieved from



Grams, D. (2018). A quantitative study of the use of DreamBox Learning and its effectiveness in

improving math achievement of elementary students with math difficulties (Doctoral

Dissertation). Retrieved from ProQuest. (10744570)

National Council of Teachers of Mathematics (2011, April 23). Executive summary: Principles

and standards for mathematics education. Reston, VA: NCTM

Kanive, R., Nelson, P.M., Burns, M.K., & Ysseldyke, J. (2014). Comparison of the effects of

computer-based practice and conceptual understanding interventions on mathematics fact

retention and generalization. Journal of Educational Research, 107(2), 83-89.

http://dx.doi.org.libproxy.lib.csusb.edu/10.1080/00220671.2012.759405

Ketterlin-Geller, L.R., Chard, D.J., & Fine, H. (2008). Making connections in mathematics:

Conceptual mathematics intervention for low-performing students. Remedial and Special

Education, 29(1), 33-45.

http://dx.doi.org.libproxy.lib.csusb.edu/10.1177/0741932507309711

McMillan, J.H. (2016) Fundamentals of Educational Research. Boston, MA. Pearson

http://dx.doi.org.libproxy.lib.csusb.edu/10.1080/00220671.2012.759405

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SRI International. (2003). Effects of using instructional technology in elementary and secondary

schools: What controlled evaluation studies say. Arlington, VA: James Kulik

Swetman, D.L. (1995). Rural elementary students’ attitudes toward mathematics. Rural

Educator,16, 20-22. Retrieved from



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Appendix A

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Appendix B

Student Interview Document: (this will be conducted one on one with students)

I know this very well------------------------I think I know it-------------------------I don’t know it yet

5-----------------------4------------------------------3------------------------2---------------------------1

1: I feel ________________about my multiplication facts.

2.I feel ________________ about my ability to do division.

3.I feel ________________ about my math ability.

Love It -------------------------Like it------------------------It’s Ok--------------------------Don’t Like It

5-----------------------4------------------------------3------------------------2---------------------------1

4. I __________________ Math.

5. I __________________ Prodigy.

6. My favorite thing about Math is: ________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

7. My favorite thing about Prodigy is: ______________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

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Appendix C

Pre-Quiz Time Left Mid Quiz TimeLeft Growth Post- Quiz Time Left Growth

Group A

1 0 12:10 0 5:47 0 0 0:00 0

2 0 0:24 4 6:04 4 3 0:00 -1

3 13 0:03 8 7:48 -5 14 10:43 6

4 0 16:36 11 11:56 11 13 10:25 2

5 0 16:34 5 0:00 5 6 0:00 1

6 0 11:04 0 2:19 0 8 0:00 8

7 0 9:40 0 0:00 0 2 0:00 2

8 0 14:20 9 0 9 6 0:00 -3

Group A Mean 0 4.5 4.5 6.5 1.875

Group A Median 0 4.5 6

Group A Mode 0 0 6

Group A S.D. 4.596194 4.405759 5.0142654

Group B

9 0 9:55 4 6:54 4 6 0:00 2

10 13 0:00 13 10:05 0 15 14:20 2

11 0 13:37 11 3:25 11 7 8:50 -4

12 0 0:00 7 0:00 7 6 0:00 -1

13 0 9:23 0 12:51 0 3 0:00 3

14 0 17:58 14 2:32 14 14 1:20 0

17 0 8:24 8 0:00 8 12 0:00 4

16 DNT DNT 0 0:00 0 0 0:00 0

15 0 6:16 13 0:00 13 15 0:00 2

Group B Mean 0 8.5 8.5 8.6666667 0.888889

Group B Median 0 8 7

Group B Mode 0 13 6

Group B S.D. 4.333333 5.164247 5.2068331

Division Quiz Scores

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Appendix D


Group A

1 0 0 0

2 0 4 3

3 13 8 14

4 0 11 13

5 0 5 6

6 0 0 8

7 0 0 2

8 0 9 6

Group A Mean 0 4.5 6.5

Group A Median 0 4.5 6

Group A Mode 0 0 6

Group A S.D. 4.596194 4.405759 5.0142654

Group B

9 0 4 6

10 13 13 15

11 0 11 7

12 0 7 6

13 0 0 3

14 0 14 14

17 0 8 12

16 DNT 0 0

15 0 13 15

Group B Mean 0 8.5 8.67

Group B Median 0 8 7

Group B Mode 0 13 6

Group B S.D. 4.333333 5.164247 5.2068331

Division Quiz Scores

0 0

4.5

8.5

6.5

8.67

0

1

2

3

4

5

6

7

8

9

10

Group A Mean Group B Mean

Quiz Means


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Appendix E

ID

Pretest

Group A

Pretest

Group B

Post Test

Group A

Post Test

Group B

1 0 0

2 0 3

3 13 14

4 0 13

5 0 6

6 0 8

7 0 2

8 0 6

9 0 6

10 13 15

11 0 7

12 0 6

13 0 3

14 0 14

15 0 15

16 0 0

17 0 12

Mean 1.625 1.444444 6.5 8.666667Standard

Deviation 4.596194 4.333333 5.014265 5.522681

Independent t-Test

Null Hypothesis:

There is no significant difference

between the post test mean scores

of students who received the

targetted intervention and those

who did not

t-Test: Two-Sample Assuming Unequal Variances

Post Test Group A Post Test Group B

Mean 6.5 8.666666667

Variance 25.14285714 30.5

Observations 8 9

Hypothesized Mean Difference 0

df 15

t Stat -0.847768854

P(T<=t) one-tail 0.204945407

t Critical one-tail 1.753050356

P(T<=t) two-tail 0.409890815

t Critical two-tail 2.131449546

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Appendix F

Participant 1.1 1.2 1.3 1.4 1.5 2.1 2.2 2.3 2.4 2.5 3.1 3.2 3.3 3.4 3.5

1 3 4 5 5 5 5 5 5 5 5 5 5 5 5 5

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

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

4 5 4 5 5 3 5 4 5 5 3 5 5 5 5 4

5 5 5 4 5 5 5 5 3 5 5 5 5 4 5 5

6 3 3 5 5 5 3 3 5 5 5 5 4 5 5 5

7 4 5 5 4 5 5 5 5 5 5 5 5 5 5 5

8 4 4 4 5 5 4 3 4 5 5 5 4 5 5 5

9 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

10 5 3 3 3 5 5 5 5 5 5 5 5 5 5 5

11 5 3 5 4 5 5 3 5 4 5 5 4 5 4 5

12 4 5 5 5 5 4 4 4 5 5 4 4 5 5 5

13 5 1 5 5 5 5 3 5 5 5 5 4 5 5 5

14 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

15 5 2 5 5 5 5 3 5 5 5 5 5 5 5 5

16 5 5 5 5 5 5 5 5 5 5

17 5 5 5 5 5 5 5 3 5 5 5 5 5 5 5

n= 16 16 16 16 16 17 17 17 17 17 17 17 17 17 17

blank= 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0

total= 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17

5 9 6 13 13 14 13 8 11 15 15 16 11 15 15 16

4 4 4 2 2 0 3 3 3 2 1 1 6 2 2 1

3 3 4 1 1 2 1 5 3 0 1 0 0 0 0 0

2 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0

1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

Total: 16 16 16 16 16 17 17 17 17 17 17 17 17 17 17

Valid Percent

5 56.3% 37.5% 81.3% 81.3% 87.5% 76.5% 47.1% 64.7% 88.2% 88.2% 94.1% 64.7% 88.2% 88.2% 94.1%

4 25.0% 25.0% 12.5% 12.5% 0.0% 17.6% 17.6% 17.6% 11.8% 5.9% 5.9% 35.3% 11.8% 11.8% 5.9%

3 18.8% 25.0% 6.3% 6.3% 12.5% 5.9% 29.4% 17.6% 0.0% 5.9% 0.0% 0.0% 0.0% 0.0% 0.0%

2 0.0% 6.3% 0.0% 0.0% 0.0% 0.0% 5.9% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

1 0.0% 6.3% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

Group A Scores

n= 8

5 2 2 6 7 5 3 3 4 7 6 8 5 6 7 7

4 3 4 2 1 2 2 2 2 1 1 0 3 2 1 1

3 3 2 0 0 1 2 2 2 0 1 0 0 0 0 0

2 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Total: 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8

Valid Percent A

5 25.0% 25.0% 75.0% 87.5% 62.5% 37.5% 37.5% 50.0% 87.5% 75.0% 100.0% 62.5% 75.0% 87.5% 87.5%

4 37.5% 50.0% 25.0% 12.5% 25.0% 25.0% 25.0% 25.0% 12.5% 12.5% 0.0% 37.5% 25.0% 12.5% 12.5%

3 37.5% 25.0% 0.0% 0.0% 12.5% 25.0% 25.0% 25.0% 0.0% 12.5% 0.0% 0.0% 0.0% 0.0% 0.0%

2 0.0% 0.0% 0.0% 0.0% 0.0% 12.5% 12.5% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

1 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

Group B Scores

n= 9

5 7 4 7 6 8 8 5 7 8 9 8 6 9 8 9

4 1 0 0 1 0 1 1 1 1 0 1 3 0 1 0

3 0 2 1 1 0 0 3 1 0 0 0 0 0 0 0

2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

Total: 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9

Valid Percent B

5 87.5% 50.0% 87.5% 75.0% 100.0% 88.9% 55.6% 77.8% 88.9% 100.0% 88.9% 66.7% 100.0% 88.9% 100.0%

4 12.5% 0.0% 0.0% 12.5% 0.0% 11.1% 11.1% 11.1% 11.1% 0.0% 11.1% 33.3% 0.0% 11.1% 0.0%

3 0.0% 25.0% 12.5% 12.5% 0.0% 0.0% 33.3% 11.1% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

2 0.0% 12.5% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

1 0.0% 12.5% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0%

21



Appendix G

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

1 2 3

Question 1: I feel _____ about my multiplication facts


0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

1 2 3

Question 2: I feel _____ about my ability to do division


0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

1 2 3

Question 3: I feel ______ about my math ability


0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

1 2 3

Question 4: I ________ Math


0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

1 2 3

Question 5: I _________ Prodigy


22



Appendix H

Question 5:

Division 5 21%

Multiplication 4 17%

Manipulatives 3 13%

Numbers 4 17%

Addition 2 8%

Learning 4 17%

Prodigy 2 8%

24 100%

Question 6:

Math 7 29%

Pets 6 25%

Battle 5 21%

Buy Stuff 1 4%

Play 1 4%

Create own Person 1 4%

See Friends 2 8%

Fun 1 4%

24 100%

Student Survey Results - Categories

Division21%

Multiplication17%

Manipulatives12%

Numbers17%

Addition8%

Learning17%

Prodigy8%

STUDENT ANSWERS TO QUESTION 5: FEELINGS

ABOUT MATH

Math29%

Pets25%

Battle21%

Buy Stuff4%

Play4%

Create own Person

4%

See Friends9%

Fun4%

STUDENT ANSWERS TO QUESTION 6: FEELINGS ABOUT PRODIGY

THE DIVISION SKILLS OF 3RD GRADE STUDENTS · “The diverse nature of mathematical knowledge demands different strategies from the teachers in the classroom” (Afzal, Gondal, & Fatima,

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