significantly more positive in computer-mapping condition

compared to no-mapping and hand-mapping conditions. Baki

and Mandacı-Şahin (2004) carried out a study to determine the

pre-service elementary teachers’ misconceptions about the sub-

ject “set” through CSCM. It was suggested that the students’

concept mapping process using the Inspiration® package pro-

gramme could be used as an effective assessment technique.

Royer and Royer (2004) investigated the difference between

hand drawn and computer generated concept mapping with 9th

and 10th graders. They found that the group using the com-

puters created more complex maps than the others did. Also,

they theorised that computers enabled students to communicate

more clearly, to add and revise concept maps more easily, and

to discover relationships between sub-concepts more readily.

Yavuz (2005) examined the effectiveness of conceptual change

instruction accompanied with demonstration and computer

assisted concept mapping on seventh grade students’ under-

standing matter concepts. The results indicated that this teach-

ing process provided a better acquisition of scientific concep-

tions related to matter concepts and produced more positive

attitudes toward science as a school subject than traditionally

designed science instructions. Kwon and Cifuentes (2009) in-

vestigated the comparative effects of individually-constructed

and collaboratively-constructed computer-based concept map-

ping on middle school science concept learning. They found

that computer-based concept mapping facilitated knowledge

construction and the students had a deeper understanding by

working collaboratively rather than by working individually.

Chiu and Hsiao (2010) studied how elementary school students

generated concept maps in computer-supported collaborative

learning. They found that almost 70% of the collaborative

groups were classified as passive or reticent and frequently off-

task. These student groups were poorly functioning collabora-

tive groups and produced poor quality discourses and products.

Also, it was concluded that there was a great need for methods

such as training or intervening approaches that could enhance

the interaction and improve the quality of the discourse in the

computer-mediated collaboration for elementary school stu-

dents. Huang et al., (2012) explored the effect of multidimen-

sional concept mapping instruction on students’ learning per-

formance in a web-based computer course. The 103 fourth

graders were divided into three groups: multidimensional con-

cept map (MCM) instruction group, Novak concept map (NCM)

instruction group, and traditional textbook (TT) instruction

group. The experimental results suggested that subjects in the

MCM group performed significantly better than those in the

NCM group which in turn performed significantly better than

those in the TT group.

As understood from the reviewed literature, CSCM ensure

learners perform more effective learnings especially when com-

pared to no-mapping and/or hand-mapping conditions. There-

fore, in the current study, we examined the effect of teaching

mathematics performed with the help of CSCM on the con-

ceptual learning.

Methodology

Participants

Within true-experimental research method, this study was

conducted with a total of 39 seventh-grade students from an

elementary school in Turkey. These students studying in the

same class were divided into two groups according to whether

their school numbers were even or odd (experimental group (E)

= 20 and control group (C) = 19). Students in experimental

group were organized as 2-student cooperative groups (see

Figure 1(b)).

Computer-Supported Concept Maps (CSCM)

Material

The CSCM material was developed by NetBeans’ editor by

using the Java language. While constructing CSCM material,

extra attention was paid to ensure that it included all concepts

on probability subject taught at 7th grade level and that rela-

tionships between these concepts were given in a concise way.

For example, the relationship between “Experiment” and “Re-

sult” is stated as “what is gathered from experiment is a result”.

However, all these concepts and relationships were not given

directly; rather, users were given some cues in the system to

find them by themselves. For instance, some cues such as “it

takes values ranging from 0 to 1” and “it is a concept related to

chance” were given for the space in which “probability” con-

cept was to be placed. If the user puts a wrong concept, link or

Copyright © 2012 SciRes.

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R. GÜRBÜZ ET AL.

(a)

(b)

Figure 1.

Reflections from experimental group.

formula into the system, “you have entered wrong info” feed-

back is shown on the screen and, thus, the first cue that will

lead the user to correct answer is provided. If the user enters

wrong info despite this cue, system gives another cue with a

more explanatory feedback. For example, when the user writes

“Not-Mutually Exclusive Event” upon seeing the cue “the

probability of a randomly selected geometric shape from the

screen to be red or hexagon, is related to … concept”, system

gives the feedback “Congratulations! Correct Answer”. If the

user writes “Mutually Exclusive Event” upon seeing the same

cue, system presents another cue (Cue 2) such as “do these two

incidents have common units or not?” When, however, the user

who cannot find the correct answer despite all these cues, clicks

on the Cue 2 in Figure 2, the system will give another more

detailed explanation to the user such as: “Let us calculate the

probability of a geometric shape selected randomly from the

screen in Figure 2 to be red or square together. After analyzing

the screen, it is possible to see that when the geometric shape is

both red and square, we call this ‘Not-Mutually Exclusive

Event’. Therefore, the probability of these two incidents can be

calculated by this formula: P(RUS) = P(R) + P(S) − P(R∩S).

The reason why we subtract P(R∩S) is that we use red squares

both when calculating red shapes and squares”. This material

improves students’ self-confidence both because it motivates

them and also because it helps create a learning environment in

which they can construct information by themselves. Moreover,

since this material creates an environment in which students

discover the relationships between concepts by themselves, it

gives users opportunity to build new relationships they do not

anticipate.

This material was pilot-studied with 18 seventh-grade stu-

dents who did not participate in the real study and were divided

into nine groups each consisting of two students. By using the

pilot study, the probable deficiencies of the material and the

problems, which could be encountered during the application

process, were determined and necessary corrections were made.

A sample interface from the designed material is illustrated

in Figure 3.

Instrument

The instrument used (Conceptual Learning Test-CLT) was

composed of 12 questions (some of them were given in Appen-

dix) which were in open-ended format. Some of the questions

were developed by the researchers, and some were developed

with the help of related literature (Fast, 1997; Pratt, 2000;

Baker & Chick, 2007; Nilsson, 2007, 2009; Gürbüz, 2006b;

2010).

The validity of the instrument was confirmed by two mathe-

matics educators and two mathematics teachers. Furthermore,

the pilot test was performed with 34 seventh-grade students

who did not participate in the real study. The pilot study re-

vealed that questions on the subject of probability were under-

standable and clear for seventh-grade students. In this study, the

Kuder-Richardson formula 20 (KR-20) reliability coefficient of

the instrument was found to be 0.88.

Procedure

The CLT was administered to both groups as a pretest before

instructions. Both groups were encouraged to answer all the

questions. A researcher managed the experimental group, while

the maths teacher in the study managed the control group by

conducting the application process simultaneously. The remain-

ing two researchers participated in the study as observers for

experimental and control groups by rotating. Each group was

taught three times/week, 40 min/session, for 4 weeks. After the

instructions, CLT was re-administered to both groups as a post-

test.

In experimental group, some questions related to daily life

such as “what does scoring a goal through a penalty shoot de-

Figure 2.

A sample cue and explanation given to users by the system.

Copyright © 2012 SciRes. 1233

R. GÜRBÜZ ET AL.

Copyright © 2012 SciRes.

1234

Figure 3.

An interface from CSCM material

pend on?”, “the probability of having rain in Adiyaman is 1/4.

How do you think I got it?” were asked to students. After these

questions had been discussed with students for a while, teach-

ing of probability concepts were performed with materials

(spinners, dice, dart, board etc. (see Figure 1(a)) by an experi-

enced researcher. Then, CSCM was employed in teaching pro-

cess after students had been informed about CM and CSCM. In

this process, the students were requested to run the computer

animations, and they were asked to share their thoughts with

their partners. Moreover, the student groups asked questions to

each other such as “why are you doing that?” and “how did you

get that?” or made statements such as “oh no, that is not right,

because…” and “…but that is wrong, because…” during the

implementations. This process was ensured by devoting con-

siderable class time to solving problems, proposing and justi-

fying alternative solutions, critically evaluating alternative cour-

ses of action, leading to different methods of solving problems.

Students are expected and encouraged to make conjectures,

explain their reasoning, validate their assertions, discuss and

question their own thinking and the thinking of others, and

argue what is mathematically true. Also during this process, the

researcher acted as a counselor, cooperator, and supervisor. As

a result, students became more active, improved their know-

ledge, questioned the knowledge they received, and were able

to explain what they had just learned instead of behaving as

merely passive receivers. In other words, it could be stated that

students in this group learnt subjects the way they wanted. For

instance, they reached solution of any given question by con-

ducting limitless experiments, by using tree diagrams and by

discussing among themselves as they wished.

In the control group, the instructions were performed on a

teacher-centered basis and delivered verbally, according to the

book. The teacher (usual teacher) would note down the ne-

cessary points on the chalkboard (talk-and-chalk type instruc-

tion). While writing on the board, the teacher framed the

important parts using colored chalk. During the process the

students sat in their seats silently and listened to the teacher.

Then, the teacher gave them some time to take notes from the

board. The teacher also asked if they had any questions about

the subject. Meanwhile, he walked around the class and ans-

wered their questions. In brief, 70% - 75% of the probability

subject was composed of only the teacher’s talk. At the end of

the lesson, the teacher asked the students to answer the ques-

tions at the end of the unit. In the control group, questions such

as “suppose that there are some balls numbered from 1 to 8 in a

glass jar. When you close your eyes, mix the balls and choose a

ball in the jar, what is the probability of getting a ball num-

bered with an odd number?” were generated and solved. To

sum up, the experiments were done and the results were

obtained by imagination without using any other materials or

animations. Students in this group learnt based on rules esta-

blished by the teacher. When a student asked teacher a question

while solving a question, the teacher solved it by reminding

students of rules he showed before. For example, when a stu-

dent asked a question such as: “Teacher! Why are we adding

the scores? Should not we multiply them instead?” the teacher

responded: “Let us remember our rule, if two events are

discrete, probability of them are added”.

R. GÜRBÜZ ET AL.

During the study, most of the students in the control group

wondered how their peers in the experimental group were doing.

Therefore, they frequently checked the computer laboratory to

figure out what was going on there. After hearing from their

friends in the experimental group about the applications there,

they asked researchers/teachers to add them to this group, as

well.

Data Analysis

The effect of teaching with the help of CSCM and of tradi-

tional teaching was investigated by the CLT. Students’ answers

have been classified according to the levels in a Rubric (see

Table 1) developed by Gürbüz (2007, 2010). According to the

scores presented in Table 1, statistical comparisons of concep-

tual learning levels of groups were made. To achieve this end,

the mean scores gathered from the questions in CLT were cal-

culated. Scores gathered were analyzed through SPSS statistical

package program. Data were analyzed using independent sam-

ples t-test, and analysis of covariance (ANCOVA). In fact,

covariance analysis was applied in order to observe any poten-

tial difference between the means of the post-test scores of the

groups. A Bonferroni pairwise comparisons test was used to

determine the direction of differentiation.

Results and Discussion

Descriptive statistical results of the pretest and posttest for

the experimental and control groups are given in Table 2. In

this study, the independent samples t-test was performed to

compare the pretest scores of the groups. The results of the

independent samples t-test showed that no significant differ-

ence was found among the pretest scores of the groups [t(37)

= .487, p = .629]. Therefore, it can be said that both groups had

the same level prior to the instructional process.

In order to compare the effects of the instructional strategies

Table 1.

Criteria used in order to assess CLT.

Levels Score Content Students’ sample responses

Level A

Completely

Correct Answer

5

The explanations which are

accepted as scientifically true

are included in this group

Q1 The area of red section is 9π, of the green section π(52 – 42) = 9π and yellow

section π(4 2 – 32) = 7π. So the probability of hitting yellow section is the lowest

because P(R) = 9/25; P(Y) = 7/25 and P(G) = 9/25

Q3 The sixth baby may be boy or girl. Because, for each child, the proba

b

ility o

f

being boy or girl is equal and is 1/2.

Q6

Spinner 2

12 3 4 5

1SD D D D

2DS D D D

3DD S D D

4DD D S D

Spinner 1

5D D D D S

There are 5 cases of having the same numbers and 20 cases of having different

numbers. Thus, the probability of having different numbers is higher (D:

Different, S: Same).

Level B

Partially

Correct Answer

4

Explanations are true but com-

pared to the correct answers;

some parts are missing, so it

is included in this group.

Q1 π(32) = 9π Red area

π(52 – 42) = 9π Green area

π(42 – 32) = 7π Yellow area

Q2 The probability of choosing a blue shape is 10/30 and of choosing a rectangle

is 6/30. Thus, the probability of a randomly chosen geometric shape to be blue o

r

rectangle is 10/30 + 6/30 = 16/30.

Level C

Wrong Answer Type

(1)

3

The explanations, which con-

tain partially correct statements

but are connected to the right

reasons or don’t give reasons

are included in this group.

Q1 3. 32 = 27 Red section

3. 12 = 3 Yellow section

3. 12 = 3 Green section

The probability of stopping at red section is the highest

Q2 The probability of chosing a blue shape is 10/30 and of chosing a rectangle is

6/30.

Level D

Wrong Answer Type

(2)

2

Expressions that contain whol-

ly wrong or irrelevant expla-

nations are in this group.

Q2 Small geometric shapes have higher chance to be chosen

Q3 The sixth baby would more likely be girl, because the first five are all boys.

Q4 Game is a chance. The one in his luck day wins the game

Level E

Uncodeable 1

Incomprehensible explanations

or explanations that have no

connection to the question are

in this group.

Q1 It depends on the ability of the shooter.

Q4 Whoever turns the spinner first, has the highest chance

Q5 Blue because blue balls are placed on the upper part of the basket.

Level F

Unanswered 0

Those that made no expla-

nations and those who wrote

the question itself in the expla-

nation part are in this group.

Q2 What is the probability of a randomly chosen geometric shape to be blue o

r

rectangl e?

Q3 Their first five children are males

Q6 (123 45) (123 45)

Note: Qa: Some question items used in CLT.

Copyright © 2012 SciRes. 1235

R. GÜRBÜZ ET AL.

implemented on the groups in the post-test scores using AN-

COVA, the tests of homogeneity within the group regression

slopes were conducted. As a result of the analysis the slopes

were found to be homogenous, as in Group*Pre-test [F(1 - 35)

= .609, p = .440], within the groups. Therefore, a covariance

analysis was applied in order to observe any potential differ-

ence between the means of the posttest scores of the groups.

The result of the one-way ANCOVA is given in Table 3.

As shown in Table 3, the analysis of the posttest score data

indicates significant overall intervention effects, controlling the

pretest [F(1, 36) = 35.946, Partial η = .500, p < .01]. Regarding

the posttest scores, the students in the experimental group bene-

fitted significantly more than those in the control group (Mean

difference = 1.031, p < .01). From the results of the pair-wise

test, it can be stated that the CSCM strategy was more effective

than the traditional teaching methods in terms of improving

conceptual learning. In this study, the effect sizes (partial eta

sequared) were calculated to be .500. It can be stated that the

CSCM strategy had a high effect on the conceptual learning

according to Cohen (1988). These outcomes corroborate the

results of Anderson-Inman & Zeitz (1993), Anderson-Inman et

al., (1998), Simone et al., (2001), Chang et al., (2002), Stoyanova

& Kommers (2002), Brown (2003), Baki & Mandacı-Şahin

(2004), Kwon & Cifuentes (2009) and Huang et al., (2012).

It could be asserted that researcher teacher factor has also

affected this process along with CSCM, because, teacher sel-

dom invited students to present their work to other students and

never discussed or allowed students to share unsuccessful at-

tempts. In the contrast, researcher encouraged students to solve

problems in any way they desired and to discuss with the whole

class their methods as well as their unsuccessful attempts. He

also encouraged solution of problems in alternative ways.

Clearly, teacher and researcher’s students were offered prob-

ability theory of different natures. The nature of probability

theory made available to learn in teacher’s classes was charac-

terized by a domain that deals with final results only, where

ways employed to reach these results are not important, and

problems are solved by simply following rules developed by

experts. In contrast, by participating in the researcher’s classes,

students were exposed to a different nature of probability the-

ory. The nature of probability theory made available to learn in

researcher classes was characterized by a domain that deals

Table 2.

Pretest and posttest scores of the groups.

Pre-test Post-test Estimated post-test*

Group n

M SD M SD M* SE

Experimental 20 1.57 .66 3.12 .73 3.092.120

Control 19 1.47 .59 2.02 .63 2.060.123

Table 3.

Results of the covariance analysis on post-test scores of the groups.

Measure

(Post-test) F df p Partial η2Direction

Overall 35.946 1-36 .000 .500

(Bonferroni) Mean Difference

(I-J)

Experimental (I)

versus Control (J) 1.031 .000 I > J

with final results as well as with ways of reaching these results;

a domain in which examining mistakes is important and con-

structive and could help in achieving correct solutions and un-

derstanding. In parallel with this, Boaler (1997), Even and

Kvatinskt (2010) and Gürbüz, Birgin and Çatlioğlu (2012) also

focused on the fact that teachers and different teaching ap-

proaches adopted by teachers had a significant influence on

students’ learning. The researcher referred to the role of prob-

ability theory on mathematics and in other domain. Also, he put

emphasis on probability theory depending on predictor’s know-

ledge. But, teacher didn’t mention any of these cases. What the

teacher did not address in class was basically not required ex-

plicitly for the examinations and was not included in the text-

books they used, which were closely connected to the examina-

tions. Some related research on teacher anxiety (Black & Wil-

lam, 1998; Ayres, Sawyer, & Dinham, 2004) also showed that

central exams had an effect on learning environments and that

these exams encouraged test-based teaching.

It is thought that providing students’ pre-test and post-test

answers will more clearly show the effect of this intervention.

For this reason, explanations related to some questions in CLT

made by some of the students of experimental group in the pre-

and post-test were examined carefully.

It was found that the students who had mistakes regarding

question Q1 had different justifications for their wrong answers

in pretest. For example, “Green because green is on the narrow

side of dart”, “Red has the highest probability since it is on

center”, “The probability of targeting on yellow and green col-

ored sections is the lowest because they have smaller radii”. As

stated by Kahneman (2003), Gürbüz (2007), Gürbüz, Çatlıoğlu,

Birgin and Erdem (2010) and Gürbüz and Birgin (2012), these

students gave their answers based on their visual intuitions

rather than on their logical reasoning. Some of the students

were found to give non-mathematical answers such as “It de-

pends on the ability of the shooter” or “It depends on chance,

so, no comment can be made”. Such approaches of students

who gave wrong answers to question Q1 are in line with the

student approaches in the studies of Jones, Langrall, Thornton

and Mogill (1997), Gürbüz (2007, 2010), Gürbüz et al., (2010),

Erdem (2011) and Gürbüz and Birgin (2012). In posttest, when

comparing to pretest, the students had more true justifications

regarding question Q1. For example, “The area of red section is

9π, of the green section π(52 − 42) = 9π and yellow section π(42 –

32) = 7π. So the probability of hitting yellow section is the low-

est because P(R) = 9/25; P(Y) = 7/25 and P(G) = 9/25”, “You

need to find the area each section covers. π(32) = 9π Red area;

π(52 – 42) = 9π Green area and π(42 – 32) = 7π Yellow area”.

It was observed that, in Q2, students’ knowledge related to

mutually exclusive and not-mutually exclusive events were not

sufficient in pretest and thus they gave wrong or incomplete

answers for different reasons. For example, responses such as

“The probability of getting blue is 10/30 while getting rectan-

gle is 2/30”, “The probability of getting blue and rectangle is

the same because there is blue color, too, in rectangular

shapes” The probability of getting blue and rectangle is 2/10”

were given by the students. On the other hand in posttest, it was

found out that students grasped the difference between discrete

and indiscrete events. However, it cannot be said that all stu-

dents understood that there was an intersection set in indiscrete

events. For example, “P(AUB) = P(A) + P(B) – P(A∩B), the

probability of getting blue is 10/30, the probability of getting

rectangle is 6/30 and the probability of getting both blue and

Copyright © 2012 SciRes.

1236

R. GÜRBÜZ ET AL.

rectangle is 2/30, so, P(AUB)= 10/30 + 6/30 – 2/30 = 14/30”,

“the probability of getting blue is 10/30, the probability of get-

ting rectangle is 6/30”, “P(AUB)= 10/30 + 6/30 = 16/30”.

It was also found out that the students, who made mistake in

Q3 in pretest, also gave different justifications for their wrong

answers. For example, The sixth baby would more likely be boy

because the first five are all boys”, “The sixth baby would more

likely be girl because the first five are all boys”. Kahneman and

Tversky (1972) stated that for a family with 6 children, it’s

believed that the order of genders will more likely be MFF-

MFM (M: Male; F: Female) instead of MMMMMM or MMM-

FFF. It’s possible to find similar results in the studies by Fast

(1997) and Gürbüz and Birgin (2012). However, it can be sug-

gested that these mistakes disappeared considerably in the post-

test. Students gave more correct answers in post-test such as

“the probability of a baby being boy or girl is equal and it is

1/2”, “The fact that the first five children are boys does not

affect whether the sixth baby will be a boy or a girl”, “The fact

that the first five children are boys does not necessitate the

sixth baby to be a boy, so they are equal”.

In Q4, students either gave wrong answers or did not give

answers at all as they confronted different dice. They gave re-

sponses such as “I am not answering that question as this dice

is different from the dice we are familiar with”, “Ali will win as

there are more even numbers”, “Veli will win because the

probability of total score to be 7 or 9 is higher”. Students’ such

kind of misconceptional answers can be argued to have stem-

med from students’ lack of sufficient knowledge in sample

space concept. Within the same context, Baker and Chick

(2007), Bezzina (2004), Chernoff (2009), Fischbein, Nello and

Marino (1991), Gürbüz (2007, 2010), Keren (1984), Nilsson

(2007), Polaki (2002) and Gürbüz and Birgin (2012) showed in

their studies that students’ knowledge about sample space con-

cept played an important role in their answers to questions re-

lated to probability subject. Some students, on the other hand,

gave illogical answers without any mathematical thinking and

gave responses such as “Whoever starts earliest will win”, “Ali

will win because 10 steps they have to take is also an even

number”, “Whoever is on his/her luck day will win”. Polaki

(2002) names this type of thinking as subjective probabilistic

thinking. However, in posttest, most students corrected the

mistakes they made in pretest and gave more logical answers

such as “Ali and Veli has equal chance because cases of getting

even numbers are (2,4) or (2,6); cases of getting odd numbers

are (3,4) or (3,6)”, “we can show this on a table (see Figure

4(a)). There are equal numbers of even and odd numbers,

therefore, the chances of winning are equal for both of them”.

Question Q5 is the question that most students answered cor-

rectly. Though there were a few wrong answers given, in pre-

test, students showed overall a good performance in answering

it. Explanations related with Q5 given by some of the students

in pretest are as follows: “It is green because green ones are on

the top of the basket”, “since the number of green balls in the

basket is higher than others, the probability of getting green is

the highest”. Here, since the students focused on the location of

the balls in question Q5, they made some mistakes. This finding

is in line with the findings gathered from studies carried out by

Jones et al., (1997), Gürbüz (2007), Gürbüz et al., (2010), Er-

dem (2011) and Fırat (2011). However, it was seen that stu-

dents gave correct answers to this question in post-test such as

“it is green because the number of green balls is the highest”,

“Since the number of green balls in the basket is higher than

others, the probability of getting green is the highest.

Numerically, P(G) = 4/9”.

Question Q6 can be argued to be one of the questions for

which the students revealed the highest number of mistakes.

For example, there were responses such as “since there are 2

spinners and 5 numbers, probability is 2/5”, “because location

of numbers are different in 1st and 2nd spinner, the probability

of getting different numbers is higher”, “the probability of

getting different numbers is high because it is generally impos-

sible to get even numbers”. These mistakes stem from the fact

that students perceive these cases as independent, they lack

sufficient knowledge about the concept of sample space. Fis-

chbein et al., (1991), Lecoutre (1992), Batanero and Serrano

(1999), Baker and Chick (2007), Nilsson (2007, 2009), Gürbüz

(2010), Erdem (2011), Fırat (2011) and Gürbüz and Birgin

(2012) reported similar conclusions in parallel with this in their

studies. It was observed that students gave correct answers to

Q6 in posttest. Explanations related with Q6 provided by some

of the students in posttest are as follows: “the probability of

getting different numbers is higher because there are fewer

cases of getting the same numbers [(1,1) or (2,2), (3,3), (4,4),

(5,5)]”, “the probability of getting the same numbers is P(S) =

5/25 and the probability of getting different numbers is P(D) =

20/25, so, the probability of getting different numbers is higher

(S: Same, D: Different)”, “as can be observed on Figure 4(b),

there are 5 cases of getting the same numbers and 20 cases of

getting different numbers. Thus, the probability of getting

different numbers is higher”.

These findings can be summarized that the teaching per-

formed with the help of CSCM showed a positive impact on

conceptual learning of probability. This positive effect is thought

to be provided by CSCM accompanied by a student-centered

learning environment. The findings of the present study suggest

that different teaching approaches and different teachers are

also effective in students’ level of learning the subject.

+4 44 6 6 6

2

6 6 6 8 8 8

2

6 6 6 8 8 8

2

6 6 6 8 8 8

3

7 7 7 9 9 9

3

7 7 7 9 9 9

3

7 7 7 9 9 9

(a)

Spinner 2

12 3 4 5

1SD D D D

2DS D D D

3DD S D D

4DD D S D

Spinner 1

5D D D D S

Note: D: Different, S: Same.

(b)

Figure 4.

Some examples of students’ answers.

Copyright © 2012 SciRes. 1237

R. GÜRBÜZ ET AL.

General Discussion, Conclusion and Proposals

In this research, we determined the effect of teaching mathe-

matics performed with the help of CSCM on 7th graders’ con-

ceptual learning of probability. From the findings, it may be

suggested that the posttest scores of both groups show a sig-

nificant increase when compared to the pretest results. Thus,

both instructional methods can be argued to improve the stu-

dents. Yet, when the improvements in the groups are compared

it can be said that the intervention in the experimental group

was more effective in terms of conceptual learning. When

monitoring the students in the experimental group, it was ob-

served that they enjoyed the process, were interactive, and had

the opportunity to construct knowledge visually. These effects

of CSCM on learning corresponded with the results of a great

deal of studies (Anderson-Inman & Zeitz, 1993; Anderson-

Inman et al., 1998; Simone et al., 2001; Chang et al., 2002;

Stoyanova & Kommers, 2002; Brown, 2003; Baki & Mandaci-

Şahin, 2004; Kwon & Cifuentes, 2009; Huang et al., 2012).

Contributions of groups’ members to each other indicated

that one of the other factors ensuring this process to be effective

is cooperative learning strategy, because almost all positive

effects of cooperative learning were effectively used during this

process. During the instructions, it was seen that especially

students whose learning motivations were low benefitted more

from the process, through their partners. This result was in ac-

cordance with previous studies (Stoyanova & Kommers, 2002;

Brown, 2003; Kwon & Cifuentes, 2009) that discussed the

positive effects of working with the CSCM in cooperative

groups. Moreover, feedbacks given in the system depending on

students’ answers enhanced the effectiveness of CSCM. In their

study, Chang et al. (2001) referred to similar effect of feed-

backs in CSCM environment.

Furthermore, it could be claimed the fact that different

teachers conducted the instructions in each group was also ef-

fective in groups’ different level of learning probability subject.

That teachers decided on which approach to employ during the

process and that they used it effectively influenced students’

learning. Effective guidance by teacher (researcher) in experi-

mental group, opportunities to talk and correct feedback given

by researcher as much as possible, having students use CSCM

effectively in cooperative groups and using dice, spinners and

darts made the process effective. That the researcher followed

the process in order to teach effectively could be explained by

his/her professional competence. From this point of view, it can

be stated that educatories’ professional competence is one of

the other important factors affecting this process. In this sense,

many previous academic studies (Shulman, 1986, 1987; Ball,

1988, 1990; Hill, Rowan, & Ball, 2005; Davis & Simmt, 2006;

Tchoshanov, 2011) highlighted the importance of this compe-

tence in order for performing effective instructions.

Regarding suggestions for further research, it is advisable to

look into what should be done for the students’ adaptation to

work in CSCM. The effect of the CSCM on determining and

remedying misconceptions should be investigated. These types

of CSCM can be used as assessment tools besides teaching

materials. By observing probability teaching process of differ-

ent teachers (both through video-camera and participative ob-

servation), approaches employed by them and their effects on

learning could be compared.

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Appendix: Some Question Items in CLT

Q1

Dartboard

1

gg

r

rr

g

g

gg

g

g

r

r

13

yy

y

y

y

y

y

In the dartboard, whose radii lengths are shown above, “r”

represents red, “g” represents green and “y” represents yellow.

As each shot targets at any yellow, green or blue color, the

probability of targeting at which color is the lowest when a

random shot occurs? Why? Could you use numerical expres-

sions to support your ideas?

Q2

RRRRR

BBBBB

RRRR

BB BBB

YY YYY

YYYYY

R

In the board shown above, “R” represents red, “B” represents

blue and “Y” represents yellow. What is theprobability of a

randomlychosengeometricshapeto be blueorrectangle? Could

you express your ideas numerically?

Q3

Family Gül areexpectingtheirsixthbaby. Their first five chil-

dren are males. Having a male or female baby is more probable

in this case? Why?

Q4

Ali and Veli will play a game by using toy cars on a 10 step

long road. Each player will roll the two dice designed such as

(222 333) and (444 666) at the same time. If the sum of the

outcomes is even, Ali will move his toy car one step further. If

the sum of the outcomes is odd, then Veli will do the same. The

one who completes the 10-step long road earlier will win. In

your opinion, who wins the game? Why?

Q5

R

R

R

B

G

G

On the balls,

“R” r epres ents re d

;

“B” repr esents bl u

e

and “G” re pr esents

g

reen res

p

ectivel

y

G

G

B

There are 4 green, 3 red and 2 blue balls, in total 9 balls in

this basket. When you close your eyes, mix the balls and

choose a ball in the basket, the probability of getting which

colored ball is the highest? Why? Could you use numerical

expressions to support your ideas?

Q6

12

3

4

5

Spinner 1Spinner 2

4

1

2

3

5

Do you think the probability of getting the same numbers or

different numbers is higher when spinners above are turned

together? Why? Could you express your ideas numerically?

Copyright © 2012 SciRes.

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