Multiplication Fact Fluency and Multiple Intelligences in a Third Grade Classroom

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Multiplication Fact Fluency and Multiple Intelligences in a Third Multiplication Fact Fluency and Multiple Intelligences in a Third

Grade Classroom Grade Classroom

Julie A. Nugent

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MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Multiplication Fact Fluency and Multiple Intelligences in a Third Grade Classroom

Julie A. Nugent

University of Maine at Farmington

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MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Abstract

The purpose of this quasi-experimental study was to examine if teaching students their

multiplication facts in a way that utilized their multiple intelligence strength would be a more

effective way of teaching students their multiplication facts than having students learn their

multiplication facts through rote memorization only. All four groups who received a teaching of

multiplication facts intervention made gains in learning their multiplication facts. The three

multiple intelligence groups did make more gains in learning more facts, than the one group who

only learned their facts through rote memorization. However, the rote memorization group was

able to give more facts automatically in the post assessment when compared with the other three

multiple intelligence groups.

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Review of Literature

How Do Children Best Learn Math Facts ?: A Literature Review

Math fact fluency in the elementary years is extremely important. Students need to be

fluent in knowing their addition, subtraction, multiplication, and division facts. Fluent means

they can accurately and automatically recall the answers to all their math facts. Burns et al.

(2015) found that students who were fluent in their math facts, had more time and energy to

spend on the demands of problem solving. If students are unable to master their math facts, they

have to work much harder and longer on more complex math problems. This can cause

frustration and makes more complex math problems more difficult to solve. It can even lead to

children developing a dislike for math (Boaler 2015).

Review of Literature

Teaching Children Math Facts Through the Use of Technology

Musti-Rao and Plait (2015) found that in order to improve learning for all students and

increase instructional efficiency, teachers need interventions that can be applied class wide or to

large groups of students, but at the same time differentiate instruction by providing an

appropriate level of challenge for each student. If a school has computer devices for each

student, that computer device may be used to give students that individualized instruction.

Multiple studies involved children learning their facts using technology. Researchers found that

children really enjoyed using technology, such as an iPad or laptop, to learn their math facts.

(Berrett & Carter, 2018; Caviola, Gerotto, & Mammarella, 2015; Musti-Rao, & Plati, 2015;

Nelson, Burnes, Kanive, & Ysseldyke, 2013) In multiple studies, children were asked to take a

pre-test to see how many math facts they knew, they practiced their math facts using a computer

app for a certain period of time, and then took a post test to see how many more math facts they

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MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

knew after using the app. Berrett and Carter (2018) found that using technology, many of the

recommended and effective practices intended to improve math fact fluency such as modeling,

drill and practice, immediate and regular feedback, and adaptive individualized presentation

were able to be accomplished by the technology device.

Teachers have reported they liked using technology because it could be differentiated for

each student, it was easy to use, and the children enjoyed the practice time. Nelson, Burns,

Kanieve, and Ysseldyke (2013) found that the inherent flexibility of technology-based practice

interventions allows for individuals, small group, or classroom application- something that

stands in contrast to similar interventions that may require more time and personnel as the

number of students increase. Students were able to make more responses using the technology

involved with iPads or desktops and students assigned to the iPad practice-base intervention

groups tended to produce higher fluency scores relative to students assigned to the control group.

Shobana and Plati (2015) found that students showed a steady increase in the number of

math facts they practiced during each of the intervention sessions, making twice as many

responses in the iPad intervention when compared to a Detect, Probe, Repeat, (DPR) practice

worksheet. Students liked being able to tap a screen or click an answer more than writing out

their facts on a paper with a pencil. Because of these factors, students who learned their math

facts using technology were able to learn more math facts.

Teaching Children Math Facts Rote Method

Another way children can learn math facts is through repeated practice using a paper and

pencil procedure. Several studies reviewed involved children learning their math facts through

rote memorization of some kind. There seem to be many paper and pencil methods of teaching

math facts. A pretest is given before the intervention begins, the paper pencil intervention is

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MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

given, and then a post test is given to track student progress. All the paper pencil methods

involve the child writing out the math facts as a way of learning them. Researchers in these

studies have shown that repeated practice using paper and pencil practice, writing out math facts

repeatedly, helps students achieve fluency, and the ability to retain what they have learned. Some

math facts require more repetition to learn than do others, and students at younger grades or with

math difficulties may require more repetition that students in older graders or with higher math

skills. (Burns, Nelson, Ysseldyke, and Kanive, 2015; Schutte, et al., 2015)

Teaching Children Math Facts by Playing Games

Another way to teach children math facts is by having them repeatedly play math games

involving math facts. In this way, children are learning their math facts in a way that is not timed

and is not done by having students memorize facts by either repeatedly writing them or typing

them on a computer screen like the previous two methods. Boaler (2015) found that

mathematics facts are important, but the memorization of math facts through times table

repetition practice and timed testing is unnecessary and causes math anxiety. By having children

play math fact games, they develop number sense. According to Boaler (2015), number sense is

a person’s ability to use and understand numbers. The researchers of these studies provided

various games that focused on understanding the mathematical operations rather than just

memorizing the facts. The games often included hands on materials and discussions. Godfrey

and Stone (2013) found when students played math fact fluency games, students focused on

higher-level thinking strategies and by discussing them with a partner, this caused their fluency

and number sense to increase.

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Conclusion

Poncy, Fontenelle, and Skinner (2013) found that many students in our country do not

know their math facts, addition, subtraction, multiplication, and division. This lack of math fact

mastery has led to students struggling with more complex math problems and math frustration.

The goal of this literature review was to research what is the best way for students to learn their

math facts. Through this literature review, three main ways of teaching math facts have become

clear. The first and second ways are by repeated practice whether it is on a computer or by paper

and pencil. The third way is by playing math fact math games that involve students developing a

strong number sense through discussion and hands on materials. All three ways work in the

research. The repeated practice using computer technology seems to be the easiest for teachers to

use, the most differentiated, and the favorite among students. The repeated rote practice also

worked, was very popular, and can be done in various ways. The way of playing math games

seems to focus more on students understanding the math facts, retention of math facts and not on

just memorization of facts.

These methods were all shown to work, but none of them looked into the fact that

children are all individuals with individual multiple intelligence strengths that could be used to

help them learn. Multiple Intelligence is way of looking at human intelligence. In this view of

intelligence, Gardner (2011) found that humans are intelligent in many different ways, and each

type of intelligence is correlated to a specific area of the brain and corresponds with certain

personal skills and preferences. Teachers have always known from their own teaching

experiences, that students learn in different ways, and Gardner’s Multiple Intelligence (MI)

Theory supports their own classroom experiences. Traditionally, schools have been designed for

students who are mathematical and linguistic, not for students who are artistic, musical or

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kinesthetic learners. If educators can recognize that students learn in different ways, they can

design learning activities that involve student strengths. The result of this will be more

engagement and, therefore, more learning for students.

Research Purpose/Question

The purpose of this study was to examine if teaching students their multiplication facts in

a way that utilized their multiple intelligence strength would be a more effective way of teaching

students their multiplication facts. Does this method of teaching students by utilizing their

multiple intelligence strength, improve a student’s ability to learn their multiplication facts more

effectively than a more traditional rote memorization method?

Methods

This was a quasi-experimental design study. Specifically, a group of eight and nine-year-

old children in a third-grade classroom were surveyed to find each student’s multiple

intelligence strength. The survey was found and shown to the students’ third-grade classroom

teacher to make sure it was age appropriate or if she thought they would have any trouble

reading it. It was reviewed and edited to remove formal language, so the students were better

able to understand it (See appendix A). Help was given to any students who needed help reading

any of it when the survey was given. Each of the statements on the survey were read aloud to the

students one at a time so that they could ask any clarifying questions they had. The students

wrote in their numbers for each statement on the survey. They filled in each number for each

statement one at a time. Their classroom teacher had reported that they do a zero-five scale each

day for their daily behavior goal, so they were very familiar with the zero-five system of rating

things that was used in the survey.

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From that survey, three multi-intelligence-based groups were formed. The multiple

intelligence strength groups were: musical-rhythmic(five students), visual-spatial(four students),

and body-kinesthetic group(four students). All eight multi-intelligence groups were not formed

because not all of them fit with teaching multiplication facts. A fourth group was also formed

that would learn their math facts only through rote memorization (See appendix C for an

example of the rote memorization worksheets).

A math running record was given to each of the students in the class before the

intervention was started, to determine how many multiplication facts they already knew and how

many they didn’t know. See appendix B for the multiplication running record sheet. The students

were then separated into the four groups(three multi-intelligence groups and one rote

memorization group). Each group received the math intervention for ten minutes per day during

their math block period, Monday-Friday. Learning multiplication facts is a required standard for

third grade in this school, so learning multiplication facts was something the class would

normally be doing even if this intervention were not being done.

During the first two weeks of his experiment, all four groups of students started learning

their multiplication facts in a very traditional manner, rote memorization. Specifically, all four

groups were given multiplication fact practice worksheets for them to complete and the students

practiced their multiplication facts by writing out their multiplication facts repeatedly. See

appendix C for multiplication worksheet example. How many math facts each student learned

was tracked by giving them a formative, untimed, mixed, biweekly, multiplication facts quiz.

The biweekly assessment was one the classroom teacher routinely used and took less than 3

minutes to complete. The results of this biweekly quiz were used to form instruction for the next

week and to see if there was a difference in the amount of facts learned between the multiple

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intelligence groups and the rote memorization group. This was done throughout the experiment.

See appendix D for the math facts quiz.

After two weeks of having all students do the repeated rote learning of multiplication

facts, three of the four groups started learning their multiplication facts through the multiple

intelligence strength math interventions. The study was started in this way so that students in the

three multiple intelligence groups could see how different it was to learn their facts from just

writing them out to the activities they were doing in the multiple intelligence groups. Examples

of how students were taught their multiplication facts utilizing the students’ multiple intelligence

strength are shown in Table 1.

Table 1

Multiple Intelligence Group Activities

Visual-Spatial

Drew and created arrays, drew groups of objects, made area models, and

wrote out repeated addition for each multiplication fact in all of the times

tables to get a good visual for each fact.

Musical-Rhythmic

Watched multiplication rap videos for each times table and the group was

given a multiplication song sheet that went with a well know song. Each

day the group watched the multiplication rap video and also sang the

multiplication fact song together multiple times.

Body-Kinesthetic

Built each fact with hands on manipulatives such as Legos and adding

groups of marbles into egg carton containers.

Wrote out their facts on pieces of card stock which they laid out in the

hallway like a hopscotch game. They then hopped from fact to fact saying

the fact as they went. They also put their multiplication fact cards in a line

next to each other and hopped next to each other saying their facts as they

hopped on their cards as a race to see who could say their facts first.

Rote Memorization Filled in one multiplication fact practice sheet each day in class.

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MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Then after the six-week intervention period, a multiplication running record was again

given to each student in the class to see what growth each student had made in learning their

multiplication facts as a result of this intervention.

The results of the students who were taught their math facts in a way that utilized their

multiple intelligence strength was compared to the students who continued to learn their

multiplication facts through rote multiplication only. This was done to see if the multiple

intelligence groups had more growth than the group that learned their multiplication facts by just

writing out their multiplication facts. Comparisons were made to see how many multiplication

facts each student learned individually, and then each group learned, before and after the math

intervention was done. How many multiplication facts each individual student, and then each

group learned to automaticity, was also completed.

Site

This study took place in York County in Southern Maine at Waterboro Elementary

School which is located in Waterboro, Maine. This elementary school is one of five elementary

schools in RSU 57. The school has a total population of 557 students in grades PreK-grade five.

The school has 42% of its students receiving free or reduced school lunch. Waterboro

Elementary School has 22.8% of its students receiving special education services. The school

does receive Title I funding. It has two reading specialists and two math specialists who

implement tier three interventions, and four education technicians who teach push in support of

Tier two plans in the classrooms.

The participants of this study were one of the four, third grade classrooms at Waterboro

Elementary School. Seventeen students in the class participated in the study. The students were

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all either eight or nine years old. One student joined the study eleven days after the study began

because she had just move into the school district and had just joined the class.

Informed consent letters explaining the study, participate requirements, risks, benefits,

and confidentiality were sent to parents (Appendix F). Written consent forms were also read to

and obtained from each student who participated in this study (Appendix E).

Instruments

Multiplication Running Record Assessment by Newton (2016; Appendix B) was used as

my pre and post assessment. The biweekly informal multiplication fact quizzes and rote

memorization group practice worksheets were worksheets that the teacher has had and used for

many years (See appendix D). After reading about the characteristics of each multiple

intelligence groups strengths, I found activities that corresponded with each strength by

searching the internet and my teacher files.

The Musical-Rhythmic multiple intelligence group used multiplication raps that came

from the website Focabulary ( https://www.flocabulary.com/topics/multiplication-division/)

and the multiplication songs were from the Teacher’s Pay Teachers website (See appendix G).

The Visual Group used the Multiplication Fact Box worksheets (See appendix H). I also had my

visual group use manipulatives such as math tiles to make arrays so they could visually see the

math facts they were learning. The Kinetic-Body Group used Legos, marbles, egg cartons,

cardstock, and markers to learn their facts.

Procedure

This study began in December 2019. It began by giving each child a multiplication

running record as a pre-assessment. The running records were scored for each child and stored

to be able to compared with my post assessment data. Before each multiplication running record

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was given, the project and consent form was read and explained to each student. Each student

was asked to sign the consent form if they wanted to, and all the students consented to being in

the study and signed the forms. A parent consent form was given to each student to bring home,

ask their parent to sign, and bring back to school the next day. Seventeen out of eighteen

students brought back their consent forms signed. One student did not bring back her parent

consent form, and therefore could not participate in the study because parent consent was not

given.

In December, the Multiple Intelligence Survey was presented to the class. Each

statement was read aloud to the class and students filled in how they rated themselves. The

surveys were tabulated and collected to that students could be assigned into multiple intelligence

groups.

On the following Monday, each student was given a multiplication practice worksheet to

fill out each day as part of their morning work. No instruction was given with the worksheet

other than to complete it, and the answers to the multiplication problems were listed at the top in

case the student did not know the answer and wanted to look up at the answer. Each day these

were collected as the student finished them, and on Friday they were given the multiplication test

for that times tables quiz. The percentage of correct responses were recorded.

At the beginning of week three of the intervention, the class was separated into four

groups based on how the students answered their multiple intelligence surveys. They were

separated into a Rote Memorization Group, a Visual Group, a Body-Kinesthetic Group, and a

Musical-Rhythmic Group. An area with a table and chairs was set up outside the classroom so

that groups could be pulled out for the math intervention. The rote memorization group

continued to work on their worksheets in the classroom as part of their morning work. For the

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other three groups, they were called out one at a time for approximately ten minutes per day for

the math intervention. For each of the groups, activities were ready that utilized their multiple

intelligence strength. Each group was presented with what multiplication table we were working

on that week and what the multiplication strategy that went with that table was. This was

repeated each day Monday-Thursday for six weeks. At the end of each week, the formative

multiplication quiz was given.

At the end of the intervention, each student was again given the multiplication running

record, so that their pre and post multiplication running record assessments could be compared to

see what effect the intervention had on how many math facts they had learned.

Data Analysis

The data collected from this quasi-experimental study was used to determine if students

would learn more multiplication facts if they were taught their multiplication facts in a way that

utilized their multiple intelligence strength, than if they were taught through rote memorization

only. Multiplication running records were used as a pre and then post assessment to determine if

students in the multiple intelligence groups learned more facts than the group that learned their

facts by rote memorization only. The multiplication running record has twelve specifically

chosen multiplication facts for students to answer in the first part, a second part which focuses in

on their learning of their multiplication strategies, and then a short math survey. The individual

scores of each individual student were reported with the group they were in, and finally a percent

was found for each group to show the amount of growth each group had in learning their math

facts.

The amount of multiplication facts each student knew automatically out of the twelve

facts on the assessment was also totaled as when you give the multiplication running record, the

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recorder scores the student on whether they could give them math fact automatically, within five

seconds (5s), or with prolonged thinking (pth). This was done to see the multiplication fluency of

each student before and after the intervention. This data was also done for each group and the

percent of growth for each group is shown. The students were not taught that they had to be

automatic in their math interventions so being automatic was not stressed in the math

intervention lessons, however, this data was collected to see if there was any difference in the

automaticity of the students between their pre and post assessments.

Results

The following tables and graphs show the details of how many facts each student learned

individually pre and post assessment. Then the results of how many math facts each group

learned by percent is shown. The results are then presented again in the same way for how many

facts each student, and then each group, learned to automaticity.

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Table 2

The Amount of Multiplication Facts Each Student Learned From the Intervention

Student Number

Pre-Intervention

Post Intervention

Difference

Number of facts

Between Pre and

answered

Post Interventions

correctly

Visual-Spatial Group

1

0

4

3

10

11

1

7

4

7

3

10

1

8

7

Musical-Rhythmic Group

6

9

12

3

9

5

0

14

1

12

11

17

5

12

7

18

11

12

1

Body-Kinesthetic Group

2

7

11

4

5

12

7

15

10

9

-1

16

5

10

5

Rote Memorization Group

8

6

9

3

11

2

9

7

12

11

12

1

13

7

6

-1

Table 2 shows the individual student scores for the amount of multiplication facts each

student learned from the math intervention. Two students actually knew one less multiplication

fact after the intervention than before the intervention, but overall most students improved in the

amount of facts they knew after the intervention. Each of the groups had one student learn seven

more facts after the intervention then before. The Musical-Rhythmic group had the students with

the most growth. One student in that group went from knowing one fact on the pre running

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record to knowing all twelve facts on the post running record. This table shows that the math

intervention appeared to make a difference in the students learning their math facts. This

becomes even more clear by looking at the percent of growth for each of the intervention groups

shown in figure 1 below.

Figure 1

Percentage of Growth from Intervention for Each Group

100%

90%

80%

70%

60%

50%

40%

32% 32%

36%

30%

21%

20%

10%

0%

Rote Memorization Visual-Spatial Body Kinesthetic Muscial-Rhythmic

Figure 1 shows that students in the multiple intelligence groups did learn more

multiplication facts than the students in the rote memorization group. The most facts were

learned by the Musical-Rhythmic Group. They had a 36% growth in learning new facts, and the

rote memorization group had the least amount of growth of new facts at 21% growth. So, the

percent of growth between the Musical-Rhythmic group, which had the highest percentage of

growth, and the Rote Memorization group, which had the lowest percentage of growth was 15%.

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The mean of the three multiple intelligence groups was 32% growth while the rote

memorization group had 21% growth. The difference between these two percentages shows the

students in the multiple intelligence groups had 11% more growth than the students in the rote

memorization group. This indicates that when students are taught in a way that utilizes their

multiple intelligence strengths, they may learn more effectively.

Data was also collected in this study on the amount of multiplication facts each student

learned to automaticity. Learned to automaticity means that a student could look at a

multiplication fact written on a paper and give the answer to that fact within five seconds. If the

student got the answer correct after five seconds, it was recorded as correct, but not done to

automaticity. Table 4 shows each the amount of multiplication facts each student knew to

automaticity before and after the math intervention was done.

MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

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Table 3

The Amount of Multiplication Facts Each Student Learned to Automaticity

Student Number

Pre-Intervention

Number correctly

answered

Visual-Spatial Group

1

0

1

3

0

7

1

2

1

10

0

2

Musical-Rhythmic Group

6

4

7

3

9

1

2

14

1

6

5

17

5

0

18

6

5

-1

Body-Kinesthetic Group

2

5

3

5

0

15

3

7

4

16

3

5

2

Rote Memorization Group

8

2

4

2

11

1

6

5

12

6

10

4

13

4

5

1

Table 3 shows the amount of facts each student learned to automaticity compared to how

many facts the students learned, the amount of facts learned to automaticity was much less. One

student learned one less multiplication fact after the intervention than before and three students

learned did not learn any more multiplication facts after the intervention than before the

intervention. This shows that this type of math intervention may not be as effective if teaching

students to learn their multiplication facts to automaticity.

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Figure 4

Percent of Growth by Group for the Amount of Multiplication Facts Learned and for the Amount

of Multiplication Facts Learned to Automaticity

100%

90%

80%

70%

60%

50%

40%

36%

32% 32%

25%

30%

21%

19%

20%

14%

9%

10%

0%

Musical-Rhythmic Body-Kinesthetic Visual-Spatial Rote Memorization

Total Amount of Facts Learned Facts Learned to Automaticity

In looking at the percentage of growth by groups learning their facts to automaticity, the

results were that the rote memorization group actually had the most growth at 25% and the

visual-spatial group had the least amount of growth at 9%, with a 14% difference between the

highest and lowest groups.

The mean of the multiple intelligence group growth for automaticity was 14% growth

while the rote memorization group was 25%, with a 9% difference between the two groups. This

shows that the students in the rote memorization group learned more facts to automaticity than

the students in the multiple intelligence groups so if students want to be learn their multiplication

facts to automaticity, rote learning will produce the most learning of facts.

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MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

In summary, the results of this study show that the students in the multiple intelligence

groups learned more facts than the rote memorization group, however, the students in the rote

memorization group learned more facts to automaticity than the multiple intelligence groups did.

Discussion

In this study, the effect of teaching third grade children their multiplication facts in four

different ways was explored to determine if teaching students their multiplication facts in a way

that utilized their multiple intelligence strength would be a more effective way to have students

learn their multiplication facts than through rote memorization. A multiple intelligence survey

was given to the class to determine which group each student should be placed into. The students

were then placed into three different multiple intelligence groups (a visual-special group, a

musical-rhythmic group, a body-kinesthetic group), and a rote memorization group. Specific

activities were designed and taught to each group for a six-week math intervention. A pre and

post intervention multiplication running record assessment was given to collect data on how

many multiplication facts each student learned and how many multiplication facts each student

learned to automaticity. The data was then compiled and is shown in the tables and figures of this

study.

Limitations

One limitation of this study was students all had different background knowledge of

multiplication. The students were not assigned by any other factors other than their multiple

intelligence strengths. Some students in each group knew how to multiply, and some students

had very little exposure to multiplication. For example, the background of each student or what

students were doing with their parents at home could not be controlled. One student in the rote

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MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

memorization group was practicing her multiplication tables with flash cards with her parents at

home, and some students had no practice going on at home.

Another limitation of this study was the amount of time that the study was able to be

done in. The math intervention had to be done in the six-week time period. The results may have

been different if the intervention time could have been longer.

The final limitation was that the participants were not randomly selected; they were

selected based on their ability to participate in the study. The sample was convenient to the

researcher and may not be a representative of the total population of third graders.

Implications for Practice

Given the study results, there are several implications for practice. When giving the post

assessment for this study, the students were still using the strategies they were taught while

taking their post assessment. For example, the musical-rhythmic group was singing the songs

they had learned, the visual-spatial group was drawing arrays, pictures and sets, the body-

kinesthetic group was in motion as they gave their answers. All of the multiple intelligence

activities were not taught with speed in mind. So, it was not unexpected that those students did

not have the most growth in automaticity but did have the most learning of facts. The group who

had only practiced rote memorization was used to just knowing a fact and writing it down. They

learned in a way that was pure memorizing from writing and seeing the facts, so that was very

similar to the multiplication fact assessment they were given. Therefore, it was not unexpected to

see that they had the learned the most multiplication facts to automatically.

From the data collected and displayed in the tables and graphs of this study, it can be

concluded that the math intervention of teaching students to their multi-intelligence strengths

appeared to make a difference in the amount of multiplication facts the students were able to

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MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

learn. In comparing the group of students who only learned their multiplication facts through rote

memorization with the groups that learned their multiplication facts through a multiple

intelligence strength, the data showed the students in the multiple intelligence groups learned

more facts. The results showed the students in the rote memorization group actually improved

the most in the number of facts known to automaticity. This may be because the assessment was

most similar to the way they were learning their facts.

These results show that students should be taught what multiple intelligence is and be

able to explore what their multiple intelligence strengths are, so they have the opportunity to

strengthen ones they are weaker in, and utilize the ones they are stronger in. This could also be a

reason that providing students choice is so important when they are learning. By providing

students a choice as to how they want to learn and present their findings, they are allowed to

utilize their multiple intelligence strengths in effective ways.

Implications for research

This study had to end because the intervention time had ended, but important information

could be learned by doing a follow up assessment another six weeks or more after the post

assessment to see if there is a difference in the amount of multiplication facts that each group

retained. It would be interesting to see if the multiple intelligence groups were still using the

strategies they were taught and had retained their facts, or had they forgotten them. Did one

group have more retention of facts than the others? Have they become more automatic with their

facts because they now have had time to practice them and become more proficient at them? It

would be interesting to see if the rote memorization group still remembered the facts they had

memorized, or did they forget them because they were no longer writing them out.

23

MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

A result not shown in the data because it was unexpected, and so data was not collected

on it, was the motivation and excitement to learn multiplication facts that was seen from the

multiple intelligence groups compared with the rote memorization group. The multiple

intelligence group students were waiting at the door for their math intervention time, while the

rote memorization group would ask if they really had to finish the worksheets they were given.

Four students who complete daily behavior charts because they routinely have a hard time

following class rules, did not have even one problem with following class rules the entire six-

week time of the intervention. This showed that allowing students to learn new material in a way

that utilized their multiple intelligence strength was motivating to students. Since such positive

behavior responses were noticed when teaching these groups, it would be an interesting study to

track the behavior of students who are being taught in a way that utilizes their multiple

intelligence strength versus those same students being taught in a way that makes using their

multiple intelligence strength hard to use.

Conclusion

According to Berrett and Carter (2017) math fact fluency is foundational for later

mathematics education. Students need to learn their math facts to help them be able to solve

more difficult problems. The results of this study support the idea of teaching students using their

multiple intelligences as often as possible. This study provides strong evidence that students do

learn more multiplication facts when they are given the opportunity to learn them in a way that

utilizes their multiple intelligence strength. It is recommended that more research be conducted

to determine if teaching multiplication facts in a way that utilizes multiple intelligence strengths

will help students to retain more multiplication facts, if teaching in this way could be applied to

teaching many other subjects, or if it makes a difference in student behavior in class.

24

MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Reference List

Adams, F. (2013). The multiplication songs. Teachers Pay Teachers.

https://www.teacherspayteachers.com/FreeDownload/The-Multiplication-Songs-523630

Bay-Williams, J. M., & Kling, G. (2014). Enriching addition and subtraction fact mastery

through games. Teaching Children Mathematics, 21(4), 238. https://doi.org/

10.5951/teacchilmath.21.4.0238

Berrett, A. N. & Carter, N. J. (2018). Imagine math facts improves multiplication fact fluency in

third-grade students. Journal of Behavioral Education, 27 (2), 223-239.

https://doi:10.1007/s10864-017-9288-1

Bliss, S. L., Saecker, L., Sager, K. E., Mccallum, E., Rowland, E., & Skinner, C. H. (2006).

Increasing multiplication fluency using a taped-problems time-delay

intervention. PsycEXTRA Dataset, 35(3), 419–434. https://doi: 10.1037/e513792007-001

Boaler, J. (2015, January 28). Fluency without fear: Research Evidence on the best ways to learn

math facts. youcubed. https://www.youcubed.org/evidence/fluency-without-fear/

Burns, M. K., Ysseldyke, J., Nelson, P. M., & Kanive, R. (2015). Number of repetitions required

to retain single-digit multiplication math facts for elementary students. School

Psychology Quarterly,30(3), 398-405. https://doi:10.1037/spq0000097

Carr, M., Taasoobshirazi, G., Stroud, R., & Royer, J. M. (2011). Combined fluency and

cognitive strategies instruction improves mathematics achievement in early elementary

school. Contemporary Educational Psychology, 36(4), 323-333.

https://doi:10.1016/j.cedpsych.2011.04.002

Caviola, S., Gerotto, G., & Mammarella, I. C. (2016). Computer-based training for improving

mental calculation in third- and fifth-graders. Acta Psychologica, 171, 118-127.

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MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

https://doi:10.1016/j.actpsy.2016.10.005

Creswell, J. W., & Guetterman, T. C. (2019). Educational research: planning, conducting, and

evaluating quantitative and qualitative research. New York, NY: Pearson.

Candler, L. (2015) Multiple intelligence theory for kids. Teachers Pay Teachers.

https://www.teacherspayteachers.com/Product/Multiple-Intelligences-Survey

-for-Kids-Free-200841

Gardner, H. (2011). The Unschooled Mind: How Children Think and How Schools Should Teach

Basic Books.

Godfrey, C. J., & Stone, J. (2013). Mastering fact fluency: Are they game? Teaching

Children Mathematics, 20(2), 96. https://doi:10.5951/teacchilmath.20.2.0096

Greene, I., Tiernan, A. M., & Holloway, J. (2018). Cross-age peer tutoring and

fluency-based instruction to achieve fluency with mathematics computation

skills: A randomized controlled trial. Journal of Behavioral Education, 27(2),

145-171. https://doi:10.1007/s10864-018-9291-1

Math Multiplication and Division.(n.d). Flocabulary by Nearpod. Retrieved February 21, 2020

from https://www.flocabulary.com/topics/multiplication-division/

Miller, K. C., Skinner, C. H., Gibby, L., Galyon, C. E., & Meadows-Allen, S. (2011). Evaluating

generalization of addition-fact fluency using the taped-problems procedure in a

second-grade classroom. Journal of Behavioral Education, 20(3), 203–220. https://doi:

10.1007/s10864-011-9126-9

Musti-Rao, S., & Plati, E. (2015). Comparing two class wide interventions: Implications of

using technology for increasing multiplication fact fluency. Journal of Behavioral

Education, 24(4), 418–437. https://doi: 10.1007/s10864-015-9228-x

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Nelson, P. M., Burns, M. K., Kanive, R., & Ysseldyke, J. E. (2013). Comparison of a math fact

rehearsal and a mnemonic strategy approach for improving math fact fluency. Journal of

School Psychology, 51(6), 659-667. https://doi:10.1016/j.jsp.2013.08.00

Newton, N. (2016). Math Running Records in Action. Eye on Education Books.

Newton, N. (2016). Math Running Records. Math Running Records.

https://www.mathrunningrecords.com

O’Connell, S. & SanGiovanni, J. (2014). Mastering the Basic Math Facts in Multiplication and

Division: Strategies, Activities & Interventions to Move Students Beyond Memorization.

Heinemann.

Poncy, B. C., Fontenelle, S. F., & Skinner, C. H. (2013). Using detect, practice, and repair (DPR)

to differentiate and individualize math fact instruction in a class-wide setting. Journal of

Behavioral Education, 22(3), 211–228. https://doi: 10.1007/s10864-013-9171-7

Schutte, G.M., Duhon, G.J., Solomon, B. G., Poncy B. C., Morre, K., & Story, B. (2015). A

comparative analysis of massed vs. distributed practice on basic math fact fluency

growth rates. Journal of School Psychology, 53(2), 149-159. https://doi:

101016/j.jsp.2014.12.003

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MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Appendices

Appendix A

Multiple Intelligence Survey for Children

!

! ! !

!

! ! ! !

!

28

MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Appendix B

Multiplication Running Record

MULTIPLICATION RUNNING!

RECORD

Student!Page

0! x 4 4! x 8

1! x 2 6! x 7

5! x 3 4! x 4

10! x 7 7! x 8

2! x 6 8! x 5

3! x 9 9! x 6

Math !Running! Records!by!Dr.!Nicki!Newton!2016 © Routledge!!

!

! ! !

!

29

MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Part 1:

Multiplication Running Record Recording Sheet

Strategy Levels and Accuracy

0 x 4

a ca sc asc

fco/skf coh pth dk

M0

0 1 2 3 4

1 x 2

a ca sc asc

fco/skf coh pth dk

M1

0 1 2 3 4

5 x 3

a ca sc asc

fco/skf coh pth dk

M5

0 1 2 3 4

10 x 7

a ca sc asc

fco/skf coh pth dk

M10

0 1 2 3 4

2 x 6

a ca sc asc

fco/skf coh pth dk

M2

0 1 2 3 4

3 x 9

a ca sc asc

fco/skf coh pth dk

M3

0 1 2 3 4

4 x 8

a ca sc asc

fco/skf coh pth dk

M4

0 1 2 3 4

6 x 7

a ca sc asc

fco/skf coh pth dk

M6

0 1 2 3 4

4 x 4

a ca sc asc

fco/skf coh pth dk

MD

0 1 2 3 4

7 x 8

a ca sc asc

fco/skf coh pth dk

MHN/M7

0 1 2 3 4

8 x 5

a ca sc asc

fco/skf coh pth dk

MHN/M8

0 1 2 3 4

9 x 6

a ca sc asc

fco/skf coh pth dk

MHN/M9

0 1 2 3 4

Codes:

a- automatic

sc- self corrected

asc- attempted self-correction

ca – counted all on fingers

skf – skip counted on fingers

coh- counted on in head

pth – prolonged thinking time

dk – didn’t know

Codes:

M0 – multiplying by 0

M1 – multiplying by 1

M10 – multiplying by 10

M5 – multiplying by 5

M2– multiplying by 2

M3 – multiplying by 3

M4

- multiplying by 4

M6 – multiplying by 6

M7– multiplying by 6

M8– multiplying by 6

M9– multiplying by 6

MD – multiplying doubles

MHN- multiplying higher

numbers

Codes:

0 – doesn’t know

1 – counting strategies

by ones or skip

counting using fingers

or drawings

2 - mental math/solving

in head (usually skip

counting)

3- using known facts

and strategies

4- automatic recall

Comments:

!

! ! !

!

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MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Part 2:

Multiplication Flexibility Assessment

Teacher: We are now going to administer Part II of the Running Record. In this part of the Running Record we are going to talk

about what strategies you use when you are solving basic multiplication facts. I am going to tell you a problem and then ask you to

tell me how you think about it. I am also going to ask you about some different types of facts. Take your time as you answer and

tell me what you are thinking as you see and do the math. I am going to take notes so I can remember everything that happened

during this Running Record.

Multiplying by 0

What do you do when

you are multiplying by

zero?

For example:

1 x 0

5 x 0

Multiplying by 1

What do you do when

you are multiplying by

1?

For example:

3 x 1

12 x 1

Multiplying by 10

What do you do when you

are multiplying by 10?

For example:

8 x 10

10 x 10

Multiplying by 5

What do you do when you

are multiplying by 5?

For example:

7 x 5

4 x 5

M0 M1 M10 M5

Multiplying by 2

What do you do when

you are multiplying by

2?

For example:

2 x 4

2 x 9

M2

Multiplying by 4

What do you think and

do when you are

multiplying by 4?

For example:

4 x 2

4 x 9

M4

Multiplying by 8

If I didn’t know 8 x 3 what

is a way that I could solve

this problem?

How about 8 x 9?

M8/MHN

Multiplying by 3

What strategies do you use

when you are multiplying

by 3?

For example:

3 x 3

3 x 6

M3

Multiplying by 6

What do you think and

do when you are

multiplying a number by

6?

For example:

6 x 5

6 x 9

Multiplying by 9

If I didn’t know 9 x 4,

what is a way I could

think about and solve

this problem?

Multiplying by 7

If I were stuck on 7 x 9,

what would you tell me to

do?

How about:

7 x 2 or 7 x 3?

Multiplying by doubles

What do you do think and

do when you are

multiplying a number by

itself?

For example:

5 x 5

8 x 8

M6/MHN M9/MHN M7/MHN MD

Comments/Notes about gestures, behaviors,

remarks:

Question Prompts:

That’s interesting/fascinating: tell me what you did.

That’s interesting/fascinating: tell me how you solved it.

That’s interesting/fascinating: tell me what you were thinking.

How did you solve this problem?

Can you tell me more about how you solve these types of

problems?

What do you mean when you say ________? (i.e. ten

friends/neighbor numbers etc.)

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MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Appendix C

Example of Rote Memorization worksheet for students to use when practicing their math

facts.

32

MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Appendix D

Example of untimed multiplication facts quiz

33

MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Appendix E

Student Consent Form

Hello,

My name is Mrs. Nugent, and I am a student at the University of Maine at Farmington. I am

interested in learning about how students learn their multiplication facts so I came up with a

project/study where I will teach students their multiplication facts in different ways to see if one

way works better than another way.

If you agree to be in my study/project, I am going to meet with you in a small group during your

math class for 10 minutes each day to work on learning your multiplication facts.

You can ask questions about this study/project at any time. If you decide at any time not to

finish, you can tell me you want to stop. This does not count for a grade in class, but your teacher

will see how many multiplication facts you have learned during the time I have been working

with you. When I present my project/study, I will not tell anyone’s name so no one will know

how you did.

If you sign this paper, it means that you have read/listened to this and that you want to be a part

of my project/study. If you don’t want to be in the project/study, don’t sign this paper. Being in

the project/study is up to you, and no one will be upset if you don’t sign this paper or if you

change your mind later.

Contact Information: If you have any questions about this study, please contact me, Julie

Nugent, at [email protected], 207-247-6126. You may also reach the faculty advisor, Brian

Cavanaugh on this study at [email protected] or 1-207-778-7385.

You may also contact the Chair of the IRB Karol Maybury at [email protected]

Your signature: _______________________________________________ Date _____________

Your printed name: ____________________________________________ Date _____________

Signature of person obtaining consent: ____________________________ Date _____________

Printed name of person obtaining consent: _________________________ Date _____________

__________________________________

_____________________________________ ________________

12-9-19

Dear Parents,

I, Julie Nugent, am inviting your child to participate in a research project. I am currently a math specialist at Waterboro Elementary School, and

I am also a student at the University of Maine at Farmington. I am researching how students best learn their multiplication facts.

What Will Your Child Be Asked to Do?

If you consent for your child to participate, your child will

• Be given a multiple intelligence survey to see what their multiple intelligence strength is. (Everyone has one)

• Be taught their multiplication facts in a small group for 10 minutes per day as part of their math class for 6 weeks.

• Students will be grouped according to their multiple intelligence strength. Students will then be taught their multiplication facts in

ways that utilizes their multiple intelligence strength or by a rote multiplication method.

• Be monitored during that 6-week period to see how many multiplication facts they have learned.

Risks

There is the slight possibility that your child may not like the other students they have been grouped with.

Your child may find they don’t like being pulled out of class to be working in a small group

Benefits: Your child may learn more about what their multiple intelligence strength is and how they can use that strength to help themselves

when learning new material. They may learn many of their multiplication facts which is a 3

rd

grade standard for our school and which will

benefit them as they continue to have to solve more complex math problems. Additionally, this study may help future students at school and in

other classrooms, as I hope to learn more about how students best learn their multiplication facts and share that information with other teachers.

Confidentiality: I will be assigning each child a number and information will be recorded only with that number attached to it. No data will be

collected using your child’s name. The list of what child goes with what number will be kept confidential on a password protected computer.

Your child’s name will not be on any of the notes or documents. Data and any paperwork will be kept in in a locked file cabinet. Your child’s

name or other identifying information will not be

reported in any publications. I will review this information with your child’s classroom teacher. She will know which student is which number

so she can use this information in her classroom instruction. This information will be shared as my capstone project at the University of Maine at

Farmington without any names attached to it. The information from this study will be destroyed at the end of the 2019/2020 school year.

Voluntary: Participation is voluntary. If you choose to have your child take part in this study, s/he may stop at any time. Whether or not your

child participates will not impact your child’s relationship with the school, his classroom teacher or any other teachers. Your child may skip any

questions he does not wish to answer or withdraw from the research project at any time.

Contact Information: If you have any questions about this study, please contact me, Julie Nugent, at [email protected] or 207-247-

6126. You may also reach the faculty advisor, Brian Cavanaugh on this study at [email protected] or 1-207-778-7385. You may also

contact the Chair of the IRB, Karol Maybury at [email protected]

Your signature below indicates that you have read and give consent for your child to participate in this project. You will receive a copy of this

form.

Please print your child’s name

Signature Date

34

MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Appendix F

Parental Consent Form

35

MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Appendix G

Multiplication Songs

The Multiplication Songs

Two Times Tables

(Tune: Happy Birthday)

Two, Four, Six, Eight, Ten, Twelve...

Fourteen, Sixteen, and Eighteen...

Twenty, Twenty-Two, Twenty-Four-r-r...

These are the two's up to Twelve...

But there are more....

Three Times Tables

(Tune: Yankee Doodle)

Three, Six, Nine, Twelve, Fifteen, Eighteen,

Twenty-One, Twenty-Four-r,

Twenty-Seven, Thirty, Thirty-Three, and

Thirty-Six,

The End!

Four Times Tables

(Tune: Row, Row, Row Your Boat)

Four, Eight, Twelve, Sixteen,

Twenty...Twenty-Four

Twenty-Eight, Thirty-Two, Thirty-Six, Forty,

Forty-Four and Forty-Eight (Clap, clap)

Five Times Tables:

(Normal sing-song-chant everyone uses)

5, 10, 15, 20, 25, 30,

35, 40, 45, 50, 55, 60,

Hint: Notice, each number ends

in either a 5 or 0.

2

3

4

5

The Multiplication Songs

Six Times Tables:

(Twinkle, Twinkle Little Star)

Six, Twelve, Eighteen, Twenty-Four,

Thirty, Thirty-Six, Forty-Two,

Forty-Eight and Fifty-Four,

Sixty, Sixty-Six, Seventy-Two,

Sixes are not hard to count,

We're all done,

So take a bow.

Seven Times Tables:

(Tune: The Ants Go Marching)

Seven, Fourteen, Twenty-One,

Twenty-Eighty,Thirty-Five,

Forty-Two and Forty-Nine,

Fifty-Six, Sixty-Three,

Seventy and Seventy-Seven,

Eighty-Four will end the song...

Of our seven times tables,

So!

All our ants!

Can sleep well for the night!

Do, Do, Do, Do,

Do, Do, Do, Do, Zzzzzz!!!!

Eight Times Tables:

(Tune: B-I-N-G-O)

Eight, Sixteen, and Twenty-Four,

Thirty-Two and Forty,

Forty-Eight, Fifty-Six,

Sixty-Four, Seventy-Two,

Eighty and Eighty-Eight,

And Ninety-Six will end this song!

Ole!!!

(

For added fun, run through the real song one time

before each new round of the math version until you

are just humming the letters for "B-I-N-G-O" during

the last round.)

6

7

8

4

5

Array Picture of Sets

Multiplication

Fact

Area Model Repeated Addition Equation

36

MULTIPLICATION FACT FLUENCY AND MULTIPLE INTELLEGENCES

Appendix H

Multiplication Fact Box