Sequential Pattern Analysis: Method and Application in Exploring How Students Develop Concept Maps

Concept mapping is a technique that represents knowledge in graphs. It has been widely adopted in science education and cognitive psychology to aid learning and assessment. To realize the sequential manner in which students develop concept maps, most research relies upon human-dependent, qualitative approaches. This article proposes a method for sequential pattern analysis, inspired by sequential pattern mining algorithms generally applied to commercial forecast and decision supports. The method can be programmed for automatic execution and thus reasonably fast, yielding reproducible results. To validate the proposed method, 187 college students were recruited to create respective concept maps on a computerized concept mapping system. While the concept mapping data was analyzed by the sequential pattern analysis method, it was found that the mapping sequences used by students that created superior concept maps were similar and had a pattern in which propositions were formed in a temporal order from more inclusive to less inclusive. Conversely, no similarity was found in the concept mapping sequences by those who created inferior concept maps. The findings support theoretical expectations about concept mapping and are consistent with qualitative evidence based on student self-reports. INTRODUCTION Concept mapping is a technique developed by Prof. Joseph D. Novak at Cornell University in the 1960s to visually represent an individual's knowledge structure about a particular topic. The generated concept map is composed of nodes and links. The nodes represent concepts, while the links represent the relationships between the concepts. The concepts and propositions should be hierarchically structured. More inclusive, more general concepts and propositions are positioned at the top of the map (Novak & Gowin, 1984). Concept mapping is based on Ausubel's theory of meaningful learning. In the concept mapping process the learner is required to make a conscious effort to identify the key concepts in new information and relate them to concepts in his/her existing knowledge structure. Concept mapping has frequently been used as an instructional aid to promote learning and retention of new information. The map produced during the instruction would reflect the structure of the students' ideas and display the interrelationships among these ideas. Concept mapping, thus, could also be used to assess the varying degrees of student understanding (e.g., Hay, 2007; Markham, Mintzes, & Jones, 1994; Moreira, 1979, 1985; Schmid & Telaro, 1990). Many studies showed that the concept maps of divergent learner groups exhibited different representational structures. Fraser and Edwards (1985), Novak (1988), and Winitzky, Kauchak, and Kelly (1994, p. 127) found that experts’ concept maps presented more thorough, elaborate, complex, interconnected and hierarchical ordering. Novices' concept maps were less complex, less structured and organized in isolated bits or small chunks. Kinchin, Hay, and Adams et al. (2000) found that student concept maps could be categorized into three major patterns, including spoke, chain and net structures. The “spoke” structure is a radial structure in which all related concepts are linked directly to the core concept, but not linked directly to each other. The “chain” is a linear sequence of concepts in which each concept is linked to those immediately above and below. A logical sequence exists from beginning to end, but the hierarchical relation of many links is invalid. The “net” is a highly integrated and hierarchical network. To quantitatively assess such difference between concept maps, Novak and Gowin’s (1984) scoring scheme has been often adopted. Experts would be expected to score higher on their concept maps than novices. This scheme scores the structural features of a concept map involving propositions, hierarchy, cross links and examples. The construct validity can be established because these features represent different aspects of meaningful learning, specifically concept differentiation and integration (Shaka & Bitner, 1996). Although subsequent researchers have made minor modifications (e.g. such as adding a branch count), all tended toward an aggregate score for the structural elements (e.g., Dorough & Rye, 1997). While most studies emphasize measuring the produced concept map, some (e.g., Deguchi, Yamaguchi, Funaoi, & Inagaki, 2004; Karvonen, Rautama, Tarhio, & Turkia, 2001; McAleese, 1998; Rautama, Sutinen, & Tarhio, 1997; Wong, 1998) take notice of the importance of probing the manner in which a student proceeded to generate his/her respective concept map. It was suggested that examining the concept mapping process would help determine the mental activity and knowledge processing that led to the given results. Wong (1998) thus TOJET: The Turkish Online Journal of Educational Technology – January 2012, volume 11 Issue 1 Copyright © The Turkish Online Journal of Educational Technology 146 asked students to recall and provide their actions in generating a concept map. The student responses showed that both high achievers (scored at high levels on achievement tests) and low achievers knew what the components of a concept map should be, the need to consider how the concepts were related and that concepts should be positioned hierarchically. However, their thoughts and actions during generating a concept map seemed inconsistent. When asked how they went about organizing concepts and deciding on the links between concepts, high achievers emphasized the importance of understanding the concepts and forming meaningful relationships between the concepts. High achievers made an effort to identify the meanings and distinguish the concept features, organize the concepts into clusters of related concepts, form correct links between concepts in a cluster and between concepts in different clusters, and organize the concepts in the map hierarchically. Low achievers did not put in as much effort as the high achievers in identifying the meanings of concepts and forming meaningful relationships between concepts. Their responses showed a lack of understanding the concepts and their links, and a lack of effort at in-depth knowledge processing. This probably explains why the concept maps produced by low achievers were incomplete and had more inappropriate concepts, inappropriate links and incorrect hierarchical structure. Karvonen et al. (2001) and Rautama et al. (1997) also considered a concept map as a process rather than an image. They suggested implementing computing techniques to present this concept mapping process. A computer-aided design was proposed in 1997 and implemented in 2001 to trace, record, preserve and visualize a continuous set of mapping actions. The mapping process information was presented as a script that consisted of operations, like adding a new concept to the map and linking it to other concepts. Biswas and Sulcer (2010) and Deguchi, Yamaguchi, Funaoi, and Inagaki (2004) further developed computer programs that allowed playback of the mapping process. They expected that learners would study their own knowledge construction approaches and the teachers could inspect the students’ learning problems through reviewing the mapping sequences. It is laborious and difficult for teachers and students to examine or realize concept mapping details. This paper therefore proposes an approach that could efficiently, reliably and validly disclose the pattern and useful information concerning student concept mapping sequences. A METHOD FOR ANALYZING CONCEPT MAPPING SEQUENCES Inspired by sequential pattern mining techniques in a large customer transactions database, an approach for exploring student sequential patterns in constructing concept maps is proposed. The sequential pattern is a temporal ordered list of elements that appear together in the concept mapping sequences produced by the involved or concerned students. The Direct Sequential pattern Generation (DSG), a graph-based algorithm proposed by Yen and Chen (1996) is borrowed and transformed in this work. Other discovering data sequences techniques (e.g., Agrawal & Srikant, 1995; Gomathi, Moorthi, & Duraiswamy, 2008; Tsai & Shieh, 2009) may also be suitable for use. This method is composed of the following stages. Stage 1. Build temporal sequences consisting of theoretically meaningful actions. Because the proposition (i.e. concept-relationship-concept triple) is the basic unit of meaning in a concept map (Dochy, 1996), a proposition is taken as the essential element for processing mapping-sequence analysis. Therefore, at the first stage the log data by each student during concept mapping, consisting of low level events (e.g., forming concepts or relationlinks), is organized into a sequence of propositions ordered by increasing proposition-generating-time. As shown in Figure 1, Vi, Vj and Vk are created concept nodes, eij and ejk are created relation-links, and {Vi, eij, Vj} and {Vj, ejk, Vk} are the formed propositions. These two propositions could be converted into two connected proposition nodes Pij and Pjk. There is a common joint concept Vj between the propositions Pij and Pjk. The direction of the link between Pij and Pjk is determined by the proposition formation time. Figure 1: Build proposition-based sequences Stage 2. Generate large 1-sequences and transform student-sequences. The following definitions are derived from Agrawal and Srikant (1995). It is defined that a student supports a sequence s if s is contained in his/her mapping sequence. The support for a sequence is the fraction of the total number of students that support this sequence. Each sequence that satisfies a certain minimum support threshold is a large sequence. A sequence of TOJET: The Turkish Online Journal of Educational Technology – January 2012, volume 11 Issue 1 Copyright © The Turkish Online Journal of Educational Technology 147 length k is called a k-sequence and a large sequence of length k a large k-sequence. To discover the sequential patterns is to find the maximal large sequence(s) among all large sequences. The stage involves finding all large 1-sequences. Afterward, each student-sequence is converted into a transformed student-sequence that is an ordered list of large 1-sequences. Table 1 presents an example of students’ (No. 1-5) mapping sequences and illustrates how the original student-sequences are transformed to large 1-sequences with the support set to 100%. Table 1: Concept mapping sequences of five exemplary students Student No. 1 No. 2 No. 3 No. 4 No. 5 Mapping sequence ABCDE BFACDE ACGFBD BGACD GAECBD Transformed mapping sequence A, B, C, D B, A, C, D A, C, B, D B, A, C, D A, C, B, D Note. A, B, C, D, E, F and G stand for proposition nodes Stage 3. Construct association graph. This stage combines two large-1 sequences to generate a 2-sequence and scans all of the transformed student-sequences. When the support for a 2-sequence achieves the minimum support threshold, it is viewed as a large 2-sequence. A directed edge is then created from the first large 1sequence to the second large 1-sequecne. If the support is set at 100%, the 2-sequence appeared in all transformed student-sequences. The algorithm can be simplified as follows: LS1 = { large 1-sequences }