Spiral teaching sequence and concept maps for facilitating conceptual reasoning of acceleration

In this study, the performances of the experimental groups (Groups 1 & 2) in Test I and Test II were found to be better than those of the control group (Group 3). Meanwhile, the performance of Groups 1 and 2 in Test II surpassed that of Test I (see Table 3). The results indicate the learning outcomes obtained by the spiral teaching intervention. The students’ self-report opinions also pointed out that the conceptual question testing and the spiral teaching intervention of explaining and addressing prevalent difficulties was helpful for constructing concepts, reflecting the assertion of formative assessment (Beatty et al., 2006). Besides, the improvement in the experimental groups’ performance from Test I to Test II was obvious, which may reflect the pedagogical demand of providing a sophisticated review of the solutions of Test I and pointing out prevalent pitfalls.

However, from a comparison of Test I (in Table 5) of the experimental groups and the control group, it was found that for those students with a strong knowledge background (Team A) or with low motivation (Group 2 of Team C), providing them with a concept map seemed not to be beneficial, since they may either have confidence in their own background of the topic or be unwilling to learn. The influential factors of metacognition and motivation on learning outcomes is consistent with the literature (e.g., Amadieu et al., 2009; Selçuk, 2010; Sağlam, 2010).

With respect to the complexity of the questions, those involving one route are easier to solve than those involving two. If the basic concepts are appropriately applied, many problems can be easily solved. Physics requires both analysis and synthesis abilities (Tobias & Hake, 1988). For the analysis, we found that conceptual questions which involved one concept were mostly easier to solve than those involving two (see Table 6). The students’ ability to understand and apply the formulas, as well as the amount of cognitive load created for the students, all influenced the outcomes. As shown in Table 6, the correct ratio of almost all groups for Test I and Test II showed improvement, showing the demand of sophisticated review and spiral teaching sequence in order to help clarify the concepts.

From the students’ questionnaire survey, the teaching intervention results are discussed as follows: (1) detailed review of the solutions provided the most obvious help to the students, as shown in Table 4. The students felt interested in the conceptual questions, which differed from those they usually see in school, thus stimulating their thinking; (2) however, preview of the concepts regarding acceleration was of limited help to the students (see Table 5); and (3) the concept map also failed to provide the anticipated teaching effect (based on Table 5). It is possible that the students were not familiar with the pedagogical tool of the concept map.

Several suggestions are provided based on the students’ responses. When introducing the novel tool of concept maps, teachers need to provide more guidance in order to allow the students to comprehend the meanings and purposes. This is consistent with the arguments put forward by Novak (1998) and Roth and Roychoudhury (1993). In their questionnaire responses, the students said that they could understand the concept map, but they still could not use it to solve the problems. This also shows the importance of the spirally repeated practice to help the students gradually comprehend and be able to use concept maps, echoing the plea of Langbeheim et al. (2013). Most of the students may remember the acceleration formulas very well, but they encounter difficulty adopting them effectively to solve problems. Moreover, based on cognitive load theory, the initiation of the concept map intended to reduce the students’ cognitive load and to help them integrate and link the associated concepts (Lindstrøm & Sharma, 2009). However, if a concept map is a novel representation for the students, they may not be able to understand its meaning or utilize it as a reasoning tool (Seufert, 2003). It is also possible to raise the cognitive load, leading to a decrease in student acceptance and satisfaction (Hwang, Kuo, Chen, & Ho, 2014). Using representations to reduce cognitive load may not always be effective for students (Sweller et al., 1998).