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

Student performance on the conceptual questions

Table 3. The correct ratio of Test Ⅰ and Test Ⅱ for the three groups of each team

	Group 1				Group 2				Group 3
	A	B	C	avg	A	B	C	avg	A	B	C	avg
Test Ⅰ	42%	37%	38%	39%	41%	41%	24%	35%	42%	30%	24%	32%
Test Ⅰ	47%	47%	39%	44%	58%	54%	39%	50%	41%	32%	22%	32%

In Table 3, the average correct ratios of Group 3 (without any form of instructional intervention) for Test Ⅰ and Test Ⅱ were found to be very close, indicating that the degree of difficulty of Tests Ⅰ and Ⅱ was similar. In contrast, improvement from Test Ⅰ to Test Ⅱ was observed for both Group 1 and Group 2, which implies the benefit of reviewing the solutions and principles of Test Ⅰ. Meanwhile, the improvement from Test Ⅰ to Test Ⅱ of Group 2 appeared to be larger than that of Group 1 for all teams, which suggests that providing the concept map may have been unhelpful, or even redundant.

In order to evaluate the extent of the students’ improvement due to receiving the different types of scaffolding, such as preview and review, we adopted the effect size tool. The results are listed in Table 4.

Table 4. Effect size between Test Ⅰ and Test Ⅱ

	Team A	Team B	Team C
Group 1	0.21*	0.59**	0.05
Group 2	0.78**	0.76**	0.93***
Group 3	-0.02	0.16	-0.13

d>0.2 small*，>0.5 medium**，>0.8 large effect***

Table 4 shows the effect size of the improvement between Test Ⅰ and Test Ⅱ for each group in all teams. The effect size for Group 1 and Group 2 ranges from 0.21 (small effect) to 0.93 (large effect) except for Group 1 of Team C. However, with no preview or review, Group 3 of the three teams had no effect between Test Ⅰ and Test Ⅱ. Therefore, providing spiral instructional guidance was found to be essential to facilitating improvement in learning acceleration.

Table 5. The effect sizes of different teams in Test Ⅰ

	Team A	Team B	Team C
Groups 1→3	0.01	0.41*	0.77**
Groups 2→3	-0.02	0.7**	-0.02

*small effect，**medium effect

When evaluating the outcomes of providing a preview, we compared how students in Groups 1 and 2 performed on Test Ⅰ compared to Group 3, which received no preview. Table 5 shows that in Team B, students who received the preview (Groups 1 & 2) outperformed those who did not (Group 3). However, no difference on Test Ⅰ was found among the three groups in Team A. The students of Team A (PR=95%) had a strong academic background. Therefore, preview of the acceleration concepts may not have been beneficial for these students.

The situation of Team C appears to be complicated. With the teaching strategy of the preview, Group 1 appeared to outperform Group 3, whereas Group 2 did not show any advantage from the preview. The discrepancy between Group 1 and Group 2 may be due to the students’ attitudes toward the task. According to the teacher's response, in Team C, Group 1 may have been more motivated to take part in the activity than Group 2; this motivation difference may have led to the discrepant performance in Test Ⅰ. In sum, we found that three out of the six groups did not benefit from the teaching strategy of the preview. Possible reasons may be that (1) it was unnecessary due to the students’ strong background (i.e., Team A) or (2) the students were indifferent due to their low motivation (i.e., Group 2 of Team C). Therefore, the expected outcomes of the preview may not have been achieved if the students were not willing to learn or if they did not perceive the instructional guidance as necessary.

Since the only difference in the instructional design provided for Group 1 and Group 2 was the concept map before Test I, comparison of the two groups’ performance in Test I was undertaken in order to examine the benefit of the concept map. Table 5 shows that the benefits of the concept map appeared only for Team C, because the effect size of Groups 1→3 is greater than that for Groups 2→3, and they are significantly effective. However, the scaffolding of the concept map seemed not to be beneficial for Teams A and B.

According to the concept map (Figure 1), reasoning the questions of acceleration may involve the five possible routes. We classified the required routes corresponding to the concept map for each question, and the correct ratios (%) of questions in Tests Ⅰ and Ⅱ involving a single route and those involving multiple routes are shown in Table 6.

Table 6. Correct percentages for single-route and multiple-route questions

Reasoning routes	Group 1		Group 2		Group 3
	Test Ⅰ	Test Ⅱ	Test Ⅰ	Test Ⅱ	Test Ⅰ	Test Ⅱ	average
Single route	43%	51%	38%	57%	39%	42%	45%
Multiple routes	34%	48%	39%	55%	33%	35%	41%

Comparing the three groups’ performance on the two tests, five out of the six data showed that those problems requiring multiple routes were more difficult than those involving a single route. Since problems requiring multiple routes are more complex than those requiring a single route, it is possible that this complexity increases the difficulty. In addition, for students, the questions of multiple routes appearing to be more difficult may be not only due to the complexity, but also to their awareness of and ability to connect different concepts from different topics.

Students’ evaluation of the teaching design

The students of groups 1 & 2 of team C filled in a questionnaire survey, and the results of the closed questions are shown in Table 7. Among the five levels of agreement, the percentages of highly agree and those of agree were summed to give the agree percentage; meanwhile the disagree percentage is the sum of the disagree and highly disagree percentages, as shown in Table 7.

Table 7. The Students’ evaluation of the outcome of the intervention teaching

	Satisfied with achievement	Enhanced learning interest	Stimulated thinking	Understood solving skills	Promoted confidence	Enhanced conceptual comprehension	Can apply in the future	Informative
Agree	71%(3)	43%	64%	55%	29%	75%(1)	72%(2)	59%
Disagree	0%	4%	2%	2%	20%	2%	0%	4%

Table 7 shows that the two groups’ evaluation of the learning unit appears to be fairly consistent. The top three that received the highest agreement among the eight items were exactly the same for the two groups, namely 1) enhanced conceptual comprehension, 2) can apply to problem solving in the future, and 3) satisfied with learning achievement. Meanwhile, the aspect of promoted confidence in learning physics was found to receive the least agreement in both groups, implying that promoting confidence may not be an easy task to fulfill with such a short-term learning experience.

Taken together, the results of the open form questionnaire survey also showed the students' appraisal that the intervention left a deep impression on them. Many students noted that the question design stimulated their thinking and enhanced their conceptual comprehension. However, a few students expressed their feeling of frustration when participating in the learning. For example, “Although the questions appear to be simple, they can easily identify our misunderstanding and prevalent pitfalls.” “The questions are very different from what we have usually practiced. They are very interesting and provoke thinking. I feel [they are] informative.” “Physics is truly tough; the ideas are just like what the aliens invented.”

The last quotation actually reflects the key notion of social constructivism, highlighting the essential role of providing instructional scaffolding for students to comprehend physics conceptions, which are initiated and gradually formulated by the scientific community (Driver, 1994).

In addition, the questionnaire survey asked the students to rate the most beneficial among the four instructional scaffoldings, that is, the preview, concept map, conceptual questions, and review, the results of which are listed in Table 8.

Table 8. The selection of the most beneficial instructional strategies

	Preview	Concept map	Conceptual test questions	Review
Most beneficial	17%(3)	23%(2)	17%(3)	43%(1)

More than 40% of the students rated the review of the tests as the most effective scaffolding. One merit of the review was that it provided not only the correct solutions, but also the prevalent pitfalls that the students may have encountered. Even the way of understanding a given problem (e.g., by identifying the key features) and the way to reason through the problem (e.g., by performing a component analysis) were explicitly and thoroughly elaborated in the review. The concept map was only ranked as the second most effective scaffolding. Since concept maps are not commonly adopted in physics classes in Taiwan, the scaffolding may require more guidance from the instructor in order to fulfill its expected benefits.

In short, the analysis of the qualitative data showed that the teaching interventions which were effective for student learning acceleration and the students' preferences for intervention scaffoldings were not exactly the same.