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Liu, T.-C. (2010). Developing Simulation-based Computer Assisted Learning to Correct Students' Statistical Misconceptionsbased on Cognitive Conflict Theory, using "Correlation" as an Example.Educational Technology & Society, 13 (2), 180192.

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Developing Simulation-based Computer Assisted Learning to CorrectStudents Statistical Misconceptions based on Cognitive Conflict Theory, using

Correlation as an Example

Tzu-Chien Liu

Graduate Institute of Learning & Instruction and Center for Teacher Education, National Central University, Taiwan// [email protected]

ABSTRACTUnderstanding and applying statistical concepts is essential in modern life. However, common statistical

misconceptions limit the ability of students to understand statistical concepts. Although simulation-basedcomputer assisted learning (CAL) is promising for use in students learning statistics, substantial improvement isstill needed. For example, few simulation-based CALs have been developed to address statistical

misconceptions, most of the studies about simulation-based CAL for statistics learning lacked theoreticalbackgrounds, and design principles for enhancing the effectiveness of dynamically linked multiplerepresentations (DLMRs), which is the main mechanism of simulation-based CAL, are needed. Therefore, thiswork develops a simulation-based CAL prototype, Simulation Assisted Learning Statistics (SALS), to correct

misconceptions about the statistical concept of correlation. The proposed SALS has two novel elements. One isthe use of the design principles based on cognitive load and the other is application of the learning model basedon cognitive conflict theory. Further, a formative evaluation is conducted by using a case study to explore the

effects and limitations of SALS. Evaluation results indicate that despite the need for further improvement, SALSis effective for correcting statistical misconceptions. Finally, recommendations for future research are proposed.

KeywordsSimulation-based CAL, Misconception, Cognitive conflict theory, Learning model, Cognitive load, Dynamically

linked multiple representations

Introduction

Understanding and applying statistical concepts is now essential for citizens in information-intensive societies (Gal,

2002; Garfield & Ben-Zvi, 2007; Shaughnessy, 2007). In accordance with this trend, statistics is considered an

important learning topic in most educational levels in many countries (Shaughnessy, 2007).

However, helping students to develop statistical literacy is difficult (Gal, 2002; Garfield & Ben-Zvi, 2007).Statistical misconceptions are common in students at all levels from elementary to graduate as well as in adults and

even researchers. These misconceptions conflict with scientifically accepted statistical concepts and seriously hinderthe comprehension and application of statistics (Castro Sotos et al., 2007; Cohen, Smith, Chechile, Burns, & Tsai,

1996; Garfield & Ben-Zvi, 2007; Liu, Lin, & Tsai, 2009; Morris, 2001; Shaughnessy, 2007).

Statistical misconceptions are systematic patterns of error in interpreting, understanding or applying statistical

concepts, which may result from language, daily experience, existing knowledge and learning materials (CastroSotos et al., 2007; Cohen et al., 1996; Liu et al., 2009). The literature reveals three characteristics of statistical

misconceptions (Cohen et al., 1996; Cumming & Thomason, 1995; Garfield & Ben-Zvi, 2007; Liu et al., 2009;Morris, 2001): (1) they are difficult to detect; (2) they are difficult to correct; and (3) they impede further learning of

statistics. Therefore, statistical misconceptions are extremely challenging to educators who seek to enhance the

statistical literacy of their students. Given these considerations, helping students to redress their statistical

misconceptions is an important research issue.

Recent studies have proposed simulation-based computer assisted learning (CAL) for helping students learn statistics

(e.g. Cumming & Thomason, 1995; Morris, 2001). Simulation-based CAL is a learning environment that combines

learning guides and Dynamically Linked Multiple Representations (DLMRs). Using DLMRs to learn statistical

concepts (e.g., correlation) enables students to interact with one representation (e.g., changing the value of acorrelation coefficient) and receiving instant feedback from other representations (e.g., the corresponding change in a

scatter plot and a table with x and yvalue). Scholars suggest that such linking of abstract ideas (e.g., correlation

coefficient) with concrete representations (e.g., scatter plot) can help students understand statistical concepts (e.g.,correlation) (Meletiou-Mavrotheris, 2004; Mills, 2002).


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Design principles for simulation-based learning environment

The main mechanism of simulation-based CAL is DLMRs, which has potential benefits for statistics instruction

(Cumming & Thomason, 1995; Morris, 2001). Despite the advantages of DLMRs, however, scholars in other fieldshave noted major disadvantages of DLMRs, which include passive learning and cognitive overload (Ainsworth,

1999; 2006; Lowe, 1999). This section describes how the simulation learning environment was designed based on

cognitive load-related literature (e.g., Sweller, van Merrienboer, & Paas, 1998; Wouters, Paas, & van Merrienboer,2008) regarding inciting germane cognitive load (the load that can enhance students to engage in learning),

decreasing intrinsic cognitive load (the difficulty or complexity of the learning material itself) and preventing

extraneous cognitive load(the unnecessary load that hinders learning).

Inciting germane cognitive load by expectancy-driven methods:When learning with DLMRs, students manipulateone representation, and corresponding representations are changed automatically and immediately. Learning by

this overly automated method may be excessively passive and may limit the ability of students to reflect on

relationships between representations, which then results in inability to construct the required understanding(Ainsworth, 1999; 2006). Germane cognitive load is the load for facilitating student engagement in learning. A

literature review of Wouters et al. (2008) found that using expectancy-driven methods (such as presenting a question

to the students before their learning) is effective for inciting germane cognitive load. Therefore, the current study

applied expectancy-driven methods to promote active learning with DLMRs.

Decreasing intrinsic cognitive load by appropriately structuring the presentation of learning content:Cognitiveoverload is a common problem in learning with DLMRs (Lowe, 1999). Cognitive overload is caused by a cognitive

task that exceeds the capacity of working memory (Sweller et al., 1998; Wouters et al., 2008). When learning with

DLMRs, students must observe different representations, pay attention to the relate changes that occursimultaneously in the representations, and identify the relationships between different representations based on their

manipulation results. Mayer (2005) and Wouters et al. (2008) pointed out that segmenting the learning content or

activity in an appropriately structured way could reduce intrinsic cognitive load when processing complex learningtasks. Therefore, a simulation learning environment should be designed to provide explicit hints in a highly

structured manner and to guide students in manipulating DLMRs and observing progressively complex relevant

relations within each representation.

Applying contiguity principle to reduce extraneous cognitive load:Extraneous cognitive load is another cause of

cognitive overload in DLMRs learning. When learning with DLMRs,students must observe and relate changes that

occur simultaneously in different representations, which may result in cognitive overload (Lowe, 1999). Therefore,reducing extraneous load imposed by inappropriate instructional design and freeing cognitive resources for learningare key design objectives. Applying the contiguity principle that representations place near corresponding parts of

other representations to reduce visual scanning is viewed as an effective means of reducing extraneous cognitive

load, which should be of priority concern when designing simulation-based CAL (Mayer & Moreno, 2003).

Introduction to SALS

The simulation-based learning environment

The SALS was written in Flash Action Script. The major learning environment of SALS (used in Reflection andConstruction phase) was the simulation-based learning environment (Fig. 1), which included the DLMRs area on the

right and learning guide area on the left. The major purpose of the simulation-based learning environment was tosupport hands-on exploration activities in controlled settings. The components in DLMR area included the data

points of the scatter plot, sample size (N), correlation coefficient (r), and the values of variables xandyin the table.

Students could manipulate each component and observe the corresponding changes in other components. For

example, after adding, deleting, moving, or re-sampling the data points, students could observe changes in samplesize, correlation coefficient, or the values of variablexandy.


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Figure 1:SALS learning environment

Figure 2: Applying design principles of SALS

To enhance the effectiveness of the DLMRs, the simulation-based learning environment reflected the three designprinciples (Fig. 2). First, topromote active learning with DLMRs, learning guide was provided in problem situations

to prompt students to perform exploratory activities in which they were encouraged to find answers by manipulating

DLMRs (Fig. 2, point A). To decrease intrinsic cognitive load,the learning guide area provided a highly structured


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series of prompts to guide students to manipulate and observe specific representations and to lead them toprogressively explore the relationships among the representations (Fig. 2, point B).

Finally,to reduce extraneous cognitive load, the DLMRs in SALS contained various special functions. For example,the multiple windows function enabled students to display four windows simultaneously in the DLMR area (Fig. 2,

point C), to systematically manipulate the representations in all four windows, and to compare the results. For

another example, passing the cursor over a data point automatically displayed the values forx andy(point D in Fig.2). Therefore, students could easily determine the values of xand yfor each data point without consulting a table.

Because these functions did not require students to keep the intermediate results in their working memory, their

extraneous cognitive load was reduced, which enabled them to focus on the relationships among different

representations.

Learning model

The cognitive conflict approach was used to develop a learning model with four phases (Externalization, Reflection,

Construction, and Application) (Fig. 3). The DLMRs was the main learning tool in the Reflection and Construction

phases and in part of the Application phase. The aim of each phase and the progression between each phase are

described below.

Figure 3: The SALS learning model

Externalization phase: Making students aware of their preconceptions before instructional intervention is the first

step of the cognitive conflict approach. Thus, the objective of this phase is to enable students be aware of their own

ideas about the statistics concepts they are learning. This phase achieves this by posing a question in the context of

daily life so as to make it meaningful to the students. The question is also presented as a role-play: an animated

anchorwoman reports background information related to the question before interviewing the students (Fig. 4). Thestudents then play the role of interviewees and answer the question (Fig. 5). By involving the students in the situation

underlying the question and by helping them to externalize their views, the role-play motivates students to learn the

target concepts in the following phases.

Figure 4: Externalization phase: an animation is used to give background information before presenting the question.


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Figure 5: Externalization phase: The students answer the question

Reflection phase: This phase prompts students to reflect on their own ideas that were externalized in theExternalization phase. To achieve this, the simulation-based learning environment displays a series of questions

related to the concepts raised in the Externalization phase in order to guide them to manipulate the DLMRs and toobserve the results progressively. After completing this task, the learning guide then prompts students to compare

their ideas that were externalized in the Externalization phase with the exploration results obtained in this phase and

to reflect on their differences.

Construction phase: This phase introduces exploratory activities to help students construct their concepts about

correlation. In this phase, clear learning guides (including definitions of the target concept and clear manipulating

procedures) are used to prompt students to manipulate the DLMRs, to observe and identify the relationships among

different representations and, then, to construct their own concepts about correlation. Students who do not

understand the concept at the end of this process are asked to repeat the entire Construction phase.

Application phase:This phase provided students with two problem situations in different contexts and with different

solution paths. When solving the problems, the students were given minimal support. One objective was to allowstudents to elaborate on their newly constructed concepts by applying them to solve novel problems. The second was

to evaluate the ability of the students to transfer these concepts. One problem was presented as a hands-on activity

that required the students to solve a problem by applying their concepts to manipulate DLMRs. Another problem was

presented as a multiple-choice item to test the same correlation concept raised by the question in the Externalizationphase, but in a different context. Students who correctly solved both problems were assumed to have understood the

correlation concept and could select the next activity to learn another one. Otherwise, they were guided back to the

Construction phase to relearn the concepts.

Learning activities

Ten learning activities were designed for SALS based on the above learning model and earlier studies about

correlation misconceptions. Each learning activity was associated with a learning topic about correlation and was

designed to correct a corresponding misconception (Table 1). These misconceptions were selected for the following

reasons. First, holding these misconceptions could obstruct their learning of concepts related to correlation. Second,the misconceptions have been confirmed by earlier studies (e.g., Liu & Lin, in press; Liu et al., 2009; Morris, 2001).Third, these misconceptions are widely held by students (Liu & Lin, in press). Fourth, as reported by Yu, Behrens

and Anthony (1995), these misconceptions should be easily represented by multiple representations. Fifth, earlier

studies (Liu et al., 2009; Liu & Lin, in press) have suggested possible reasons why students hold these

misconceptions, and these reasons should be considered when designing SALS learning activities.


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Procedure

The two students were individually instructed to perform the think-aloud method (average training time, 32 minutes)and to manipulate SALS (average training time, 25 minutes). The two students then used SALS to learn correlation

concepts individually and without a time limit (average time to complete each of the ten learning activities, 8.4

minutes). The students used the think-aloud method to present their learning processes while working with SALS,

and the researchers took notes and video recorded the utterances and manipulation behaviors of the students. Aftercompleting the learning activities, the students immediately took the TDICM (post-test). The researchers then

showed the students video recordings of their learning processes and interviewed them to determine the reasons for

their specific behaviors and expressions. The researchers then interviewed the students to assess their perceptions of

SALS. Finally, all data, including manipulation behaviors, the results of think-aloud, and the interviews were

transcribed into digital protocols for triangulation to enhance validity.

Evaluation results and discussion

The current study utilizes a case study to formatively evaluate whether SALS can correct statistical misconceptions

and how such a system can be optimized. A comparison of pre-test and post-test scores on the TDICM showed that

SALS learning could reduce misconceptions about correlation concepts in both students. All nine misconceptionsheld by Student A were corrected while six of the eight held by Student B were corrected. To further explore how

SALS benefited the students and the possible shortcomings of SALS, the following sections display the results anddiscussions about the effects of learning model, the contributions of design principles of simulation-based learning

environments, and limitations of SALS.

The effects of learning model based on cognitive conflict approach

The learning model including four phases (Externalization, Reflection, Construction, and Application) was

developed in this study according to cognitive conflict approach. Each phase was designed to achieve specific aim to

make students have successful cognitive conflict for conceptual change. This section describes the learning processesobserved in the fifth learning activity and the subsequent interview results to show how the learning model can

benefit the students. The fifth activity is designed for addressing the misconception that a positive correlation is

stronger than a negative one, which is among the most common misconceptions (e.g., Liu & Lin, in press; Liu et al.,

2009; Morris, 2001). For brevity, the following discussion focuses on student A in the last two phases (Constructionand Application) since the two students demonstrated similar learning processes in these two phases of the fifth

activity.

Externalization phase: The SALS used role-play (i.e., interview by the animated anchor) in this phase to present a

question in the context of the daily life experiences of the students to make them to externalize their existing ideas

and to motivate them to continue exploring possible answers by manipulating DLMRs in next two phases. For

example, in the Externalization phase of the fifth learning activity, the animated news anchor described a study of the

relationship between two variables, rate of attendance and statistical achievement. This broadcast displayed fourcorrelation coefficients (r= -0.9, -0.5, 0, and 0.6) for the two variables in four different high schools. The students

were then asked to select one of four options to indicate the strength of the four correlation coefficients ( r) from

highest to lowest as follows: (A) -0.9, -0.5, 0, 0.6; (B) 0, -0.9, -0.5, 0.6; (C) 0, -0.5, 0.6, -0.9; (D) None of the above.

When asked this question, Student A selected answer A (-0.9, -0.5, 0.0, 0.6). After finding that her answer was

wrong, she said, The value of a correlation coefficient is similar to a numerical value, isnt it? Why is my answer

wrong? Student B also selected answer A, and her think-aloud utterances indicated that she thought all the otheranswers were nonsense. When her SALS feedback indicated that her answer was wrong, she felt confused and said,

What? Is that wrong? Let me think for a while. Yeah! I think my answer is correct! Is it wrong? The student

then turned around and looked at the researchers. The answers from both students and their responses to the

corresponding items in the TDICM pre-test results showed that they had probably analogized the concept of

numerical value to the concept of correlation coefficient and had applied the misconception that a positivecorrelation is stronger than a negative correlation. The learning processes of the two students demonstrates that this


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learning phase can help students to become aware of their existing ideas, particularly their misconceptions, which isthe first and most important step in facilitating cognitive conflict.

The interview results also indicated that the context and presentation of the questions were important for cognitivelyengaging the students to answer the questions and then to externalize them so that they became aware of their own

concepts or misconceptions. Further, since the students were cognitively engaged in the question situation, once they

discovered that their existing concept (e.g., numerical value) were wrong or unsuitable for explaining the newconcept (e.g., correlation coefficient), they eagerly sought more information. For example, Student A indicated that

the questions were related to situations she had encountered daily life. Therefore, when she found that her response

was wrong, she was puzzled. She also stated, In fact, I cannot believe that my answer is wrong of course, I want

to know why my response is wrong.

Reflection phase:The purpose of this phase was to guide students to answer questions about concepts raised in the

Externalization phase through simulation-based exploratory activities and also to demonstrate how the answers

differed from their own ideas, which were externalized in Externalization phase. For example, in the Reflectionphase of the fifth learning activity, the learning guide instructed the student to use the multiple windows function to

manipulate and compare scatter plots with different correlation coefficients (r = -0.9, -0.5, 0, and 0.6) and then to

explore the possible relationships among correlation coefficients(r) and corresponding scatter plots. During the

manipulation and comparison, Student A said, Let me see! In the figure (scatter plot) whereris -0.9, all data pointsfall almost on a line.In contrast, in the figure (scatter plot) where ris 0, the data points are so scattered. Is there a

rule? She then clicked the re-sampling buttons in the four windows and murmured to herself, It looks likethat...so I think my previous answer (in Externalization phase) may be wrong.

The learning process for Student B was more difficult. Although she also understood how the scatter plot with r= -0.9 differed from the scatter plot with r= 0, she did not realize that the positive and negative correlation coefficients

had different correlation directions. She said with a pointing finger, This (the scatter plot with r= -0.5) looks like

that (the scatter plot withr= 0.6). Because she was unable to answer the question sets correctly, the SALS askedher to compare the variations between the four scatter plots, which she again manipulated with different correlation

coefficients. After carefully comparing the four scatter plots, she said, Okay! Ive got it. According to the think-

aloud protocol, she thought that the direction of the scatter plot with r= -0.9 is like that with r= -0.6 but is incontrast with the one with r = 0.5. These observations of the student learning processes suggest that the guided

exploratory activities in this learning phase help students to reflect on their existing concepts.

Construction phase:In this phase of the simulation, the SALS learning guide clearly described the target concept andthe manipulation procedures so that the simulation could lead students to construct the correct correlation concepts.For instance, after reading the definition of correlation strength, Student A referred to the SALS learning guide and

slowly moved the bar of the correlation coefficient from r= 1 to r= -1 while observing the corresponding change in

the scatter plot and inferring the degree of correlation. After repeatedly moving the bar, she finally discovered thetrend of the change. She found that the scatter plots for the same correlation coefficient may have different patterns

but similar trends. She said in thinking aloud that when the value of ris changed to 1 or -1, the pattern of data points

in the plot would be more like an oblique line.

Next, Student A was asked by the learning guide to think about the characteristics of the scatter plots with r= 1 or r

= -1 based on her earlier observation. She answered correctly. Her think-aloud protocol revealed that she thought that

the scatter plot is like a line when r= 1 or r = -1, and the more that the scatter plot resembles an oblique line implies

a stronger correlation. Therefore, she thought that the correlation degree is the strongest when r = 1 and r = -1.

Besides, during the interview, Student A said that the definition of the target concepts provided by learning guide isuseful for her to interpret her manipulation results and to understand the concepts. These student learning processes

and interview results demonstrate that this learning phase can help students to understand statistical concepts by

giving them sufficient knowledge of the target concepts as well as exploratory activities.

Application phase:In this phase, the students engaged in two problem situations to enhance their understanding of

concepts and to examine the degree of conceptual change. In the first problem situation, students were shown a

scatter plot with r= 0.6 and asked to change it into a scatter plot with a stronger correlation degree and a negativedirection by removing the data points within it. Solving this problem required an understanding of the concept of

correlation degree and the conceptual relationship between a correlation coefficient and a scatter plot. Only relying


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on a textual definition would have been insufficient. For example, although Student A indicated that she understoodthe meaning of correlation degree, she was still confused when she first undertook this task. She murmured,

Uhwhat should I do? Uhthe more the figure (scatter plot) is like an oblique line, the stronger the correlation

degree it has. And when the correlation coefficient is negative, the figure (scatter plot) tends to be a line from thehigher left to the lower right. So, I should move the data points first, and thenAfter moving several data points

and rearranging the plot, she successfully completed the activity. These observations demonstrate that, although

Student A initially had no clear idea how to complete the task, she could gradually integrate and apply the statisticalconcepts she had learned. Therefore, this task not only confirmed her understanding, it also helped her to construct a

more elaborate conceptual structure. Moreover, the scatter plot presented in this task differed from those in the

earlier learning activities, which showed that Student A could apply her constructed correlation concepts to solve an

unfamiliar problem. Therefore, her successful completion of this activity demonstrated her conceptual understanding

of correlation degree and direction. The second task was a situation-based multiple-choice test. Because the situationwas unfamiliar to the students, they were required to elaborate on their constructed statistical concepts. Both students

A and B correctly answered the question by applying the concepts they had learned.

Examining and elaborating students conceptions was the last step of SALS. Unlike the guided learning in previous

phases, this phase focused on enabling students to apply the correlation concepts in different situations and in

different ways but with minimal support, thus requiring them to construct more complete concepts. Depending on

their performance in this phase, SALS could also determine whether the students understood the target concept byexamining whether they could apply the constructed concepts to other novel problems. Students who were unable to

do so were instructed by the SALS to return to the Construction phase to relearn the concept. The interviewsindicated that this design increased the confidence of the students in learning and using statistics. For example, after

completing the Application phase activity, Student A said that the statistical concepts had many daily life

applications while Student B mentioned that statistics was not as daunting as she had expected.

The contributions of the simulation-based learning environment

Three methods (problem situations, appropriately structured guided learning, and contiguity principle) were used in

SALS to promote active learning, to reduce intrinsic cognitive load, and to reduce extraneous cognitive load whenlearning with DLMRs during the Reflection and Construction phases. While earlier sections on students learning

processes during the two phases showed how these methods work and their effectiveness, this section describes

students perceptions about these methods.

First, the interview data revealed that presenting questions before the exploration activities enhanced DLMRslearning. For example, Student B stated in the interview, The questions (presented before the manipulation)

stimulate me to pay attention because I want to know the answers. Additionally, guiding students to explore

DLMRs systematically reduced the intrinsic cognitive load of DLMRs learning. For example, Student A said, Theillustration of the second phase (Reflection) is very clear. Even though my knowledge of these symbols and figures is

not sufficient, I can learn what I should according to this (learning guide). Finally, the application of contiguity

principle in the design of DLMR functions was effective in reducing extraneous cognitive load. For example,

Student A said in the interview, Learning with simulations is very complex. I must pay attention to the figures(scatter plots), which have many numbers (the values of r, x, y, and N) and relationships. Comparing different

manipulations is even more difficult. it (multiple windows function) is very useful since I dont need to remember

these figures and numbers.

Limitations of SALS

Although the evaluation results showed that the two students corrected their most correlation misconceptions and the

designs of the simulation-based learning environment could achieve their objectives, some limitations of SALS were

revealed by the think-aloud protocols, interview data and learning behaviors. For example, the students indicated that

some of the texts in the learning guide were difficult to understand and that the SALS response time was sometimes

slow. The two faults may reduce learning interest. For instance, student B complained when she manipulatedDLMRs, Why didnt the values of r change? I moved the bar (of r)quick, quick I hope that I can finish the

learning activity more quickly. Further, although the learning guide in the Reflection phase provided clear hints for


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helping students learn statistical concepts by manipulating and observing DLMRs, the researcher found that, in thethird and seventh learning activities, Student B could not understand how representations from her manipulation

results are related and, thereafter, continued directly to the next phase. This may have affected her subsequent

learning, and she thus failed to correct two of her misconceptions. These problems should be considered in futureversions of SALS.

Conclusions and recommended future works

Although understanding and applying statistical concepts are essential abilities (Gal, 2002; Garfield & Ben-Zvi,

2007; Mills, 2002), students often have statistical misconceptions (Castro Sotos et al., 2007; Shaughnessy, 2007).This study designed and developed Simulation Assisted Learning Statistics (SALS), a simulation-based CAL for

eliminating misconceptions about the statistical concept of correlation. Two important elements were considered in

the design and development of the SALS. One is the learning model based on cognitive conflict theory that includes

four learning phases,Externalization (making students aware of their implicit concepts),Reflection(guiding students

to find contradictory information and assisting them in reflecting on their existing concepts and misconceptions),Construction (supporting students in constructing correct statistical concepts), and Application (examining the

change in misconceptions and helping students to transfer and apply the newly learned concepts). Another is the

design principles of a simulation-based learning environment based on cognitive load literature, including Inciting

germane cognitive load by expectancy-driven methods, Decreasing intrinsic cognitive load by presenting the

learning content in a structure way and Reducing students extraneous cognitive load with contiguity principle.

The results of the formative evaluation indicated that students substantially reduced their correlation misconceptions

after learning with SALS. Closely examining student learning processes and interview results also revealed that the

learning model of SALS and the design principles of simulation-based learning environment could achieve their own

objectives.

Based on the results of this study, the following areas for future research are recommended. First, given the

limitations of the SALS prototype, such as the difficult language used in the learning guide and the slow response

rate of SALS, further work is necessary to revise the language in the learning guide area of some activities and to

improve the SALS software. Further, to emphasize the manipulation results, a further question (e.g., What are thefeatures of your manipulation results?) should be included in future versions of SALS to remind students to

carefully observe and reflect on their manipulation results in the Reflection phase. Third, while simulation tools have

been widely applied in statistics education (Garfield & Ben-Zvi, 2007; Mills, 2002; Morris, 2001; Morris et al.,2002), studies by Morris et al. (2002) and Mills (2002) suggest that further empirical studies are warranted to

evaluate the effectiveness of such tools for learning. This study only selected two undergraduate students who had

more misconceptions to be the study cases and conducted a formative evaluation to explore the merits and limitations

of SALS (prototype version). Based on the results of this study, Liu, Lin, & Kinshuk (in press) further conducted a

mixed method (embedded experiment model) with a larger number of samples to verify the effectives of SALS (therevised version) and to investigate whether SALS can achieve the objectives that have been set for it. Further details

in that study can be found in Liu et al. (in press).

Fourth, although the formative evaluation demonstrated the potential of the three design principles of simulation-

based learning environment for learning statistics, further experiments should examine the effects of each of these

design principles. Finally, whereas the learning focus in this study was correlation, future works could test otherstatistical concepts to confirm the positive effects of both the Learning Model and SALS.

Acknowledgements

The authors would like to thank the National Science Council of the Republic of China, Taiwan, for financially

supporting this research under Contract No. NSC 94-2520-S-008-002. The author would also like to thank the

students who participated in this study. Finally, the author would like to thank the editor of ET&S and the

anonymous reviewers of this paper for their kind assistance and helpful suggestions.


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