Developing Simulation-Based Computer Assisted Learning to Correct Students' Statistical Misconceptions Based on Cognitive Conflict Theory, Using "Correlation" as an Example

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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 hinder the 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 (Castro Sotos 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 a correlation coefficient) and receiving instant feedback from other representations (e.g., the corresponding change in a scatter plot and a table with x and y value). 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).

Despite the recognized potential of simulation-based CAL for helping students to understand statistics, the design and development of simulation-based CAL for learning statistics still warrant further study (Kadijevich, KokolVoljc, & Lavicza, 2008; Mills, 2002; Morris, 2001; Morris et al., 2002). For instance, Shaughnessy (2007) and Castro Sotos et al. (2007) concluded in literature reviews that holding statistical misconceptions is a major obstruction to comprehending statistics. However, only few simulation-based CALs (e.g., Cumming & Thomason, 1995; Morris, 2001) have been designed to correct statistical misconceptions.

Besides, an effective learning technology requires learning models based on appropriate theory. However, earlier studies (e.g., Mills, 2002; Morris et al., 2002) have noted the lack of theoretical background for designing and developing simulation-based CAL to enhance statistical understanding.

Finally, DLMRs is a core mechanism of simulation-based CAL. Applications of DLMRs for learning in other fields reveal limitations such as passive learning (e.g., Ainsworth, 1999) and cognitive overload (e.g., Lowe, 1999). Therefore, the design of simulation-based CALs for correcting statistical misconceptions should maximize the advantages of DLMRs and minimize its disadvantages. …