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

Students’ initial knowledge may influence their learning of physics concepts (Reiner et al., 2000), but teachers can teach and guide students to change their initial knowledge into expert subject knowledge (Leach & Scott, 1995). The concept of “acceleration” is fundamental to Newtonian Mechanics; however, the literature has reported numerous difficulties that students may encounter in understanding the meaning of “acceleration” (e.g., Rosenblatt & Heckler, 2011). With respect to students’ difficulties grasping the details of scientific conceptions, the adoption of conceptual maps and a spiral teaching sequence is perceived as promising instructional scaffolding (Langbeheim et al., 2013, Lindstrøm & Sharma, 2009).

With the goal of helping students to learn the concepts of “acceleration,” including instantaneous acceleration and average acceleration, this study adopted a spiral teaching sequence and a conceptual map to help students understand the meanings and various routes of reasoning the different terminologies of acceleration. The spiral teaching sequence consisted of four instructional strategies, i.e., 1) preview of the core concepts of acceleration, 2) depiction of a concept map, 3) practice of conceptual questions, and 4) instructional review of the solutions utilizing the concept map. The purposes of this study were to 1) evaluate the learning outcomes of the teaching intervention, 2) examine the pedagogical effect of the four instructional strategies, and 3) compare the difficulties of the concepts of acceleration regarding the complexity of derivation routes.

Learning difficulties related to Acceleration

Acceleration may be regarded as a basic concept in mechanics, but it is excessively abstract because the phenomena of acceleration may not always seem sensible (Singh, 2009). The source of the difficulties students face in learning the concept of acceleration may be misguided by their everyday life experience (Rosenblatt & Heckler, 2011). For example, they may feel that when an object is at rest, there is no force exerted on it (Sequeira & Leite, 1991), and may think that an object’s natural state is to remain resting; therefore, for an object to move, it needs some force to keep acting on it. And the heavier an object that is falling, the greater the acceleration (Bayraktar, 2009); or, they may think that when an object moves, it has a force parallel to its velocity (Martin-Blas et al., 2010).

On the other hand, from the perspective of social constructivism, the language, symbols, models, and rules of science are constructed by the scientific community, and learning science is a process of exchanging knowledge between the individual and the scientific community (Driver, 1994). The difficulty that many students encounter when learning physics is due to the confusion caused by the difference in the meaning of the language as it is used in physics and in daily life (Williams, 1999; Taibu, Rudge, & Schuster, 2015). Moreover, if students misunderstand a scientific concept, they may choose the inferencing method based on their beliefs (Gardner, 1984). For example, they may treat constant speed circular motion as constant velocity rectilinear motion, and ignore centripetal force because they tend to believe that constant speed means the state of equilibrium (Reif & Allen, 1992). Besides, students may consider the role of “acceleration” as always “speeding up,” ignoring the effect of “slowing down” (Champagne, Gunstone, & Klopfer, 1983).

Formulas can illustrate the meanings of the physics concepts and the quantitative relations among related terminologies (Hewitt, 2001). However, physics formulas may not be able to express the causality and limitations of the associated conceptions. For example, students often ignore the fact that Newton’s Second Law ( ) is limited to being observed from an inertial reference frame (Lehavi & Galili, 2009). On the other hand, the community of scientists will choose to apply appropriate scientific knowledge in different situations (Leach & Scott, 2002); for example, students mistakenly think that when an object is in circular motion, its acceleration will always orient towards the center (Shaffer & McDermott, 2005), as they ignore the fact that, under the vertical circular motion, acceleration is actually a combination of tangential and centripetal components ( ) (Reif & Allen, 1992). Therefore, the difficulty of conceptual reasoning does not always come from misconceptions; it may come from a lack of understanding of the scientific discourse or the failure to identify the key features of the context of the questions.

Concept maps and cognitive load theory

In order to help students to construct a robust scientific conceptual framework, drawing concept maps is highly recommended in the literature (Lindstrøm & Sharma, 2009; Marée et al., 2013). It is suggested that teachers should explicitly draw concept maps for their students, which can help their conceptual comprehension and enhance their learning interest (Roth & Roychoudhury, 1993). Concept maps consisting of both terminology and formulas may offer comprehensive teaching scaffolding to help students understand and clarify the concepts and their related formulas (Chang, 2011).

Concept map design adheres to Sweller’s (1988) cognitive load theory (Lindstrøm & Sharma, 2009). Because working memory is limited, using an effective representation and teaching process design can reduce extraneous cognitive load and increase germane cognitive load, thus improving students’ learning effect (Paas & van Merrienboer, 1993). Because visual and verbal working memories are independent, using visual and aural learning modes to design teaching is preferable to relying on a single mode (Paivio, 1991). Visual representations can also strengthen the retention of the meaning of the written text (Peeck, 1993), improve problem solving ability, and promote the integration of new knowledge. However, there is a prerequisite that students have to have the ability to integrate multiple representations (Sweller et al., 1998).

Instructional Design

Bruner (1978) suggests that scientific concepts, such as acceleration, should be introduced as completely and early as possible to students, who should be allowed repeated practice in order to develop and redevelop their understanding as they become more intellectually mature and can grasp its substance. Bruner argues that the repeated exposure of the student to the specific topic may enhance a deep and more intuitive understanding of the concepts. The essence of a “spiral curriculum” is that the basic concepts are first introduced briefly, then the core concepts are reintroduced with increasing sophistication. The adoption of a spiral curriculum has been found to benefit students’ conceptual evolution, both in terms of their conceptual comprehension and epistemological framing (Langbeheim et al., 2013). Besides, a spiral instructional sequence allows students to repeatedly revisit the ideas in different contexts in order to distinguish the differences among related scientific concepts, such as acceleration and velocity, force and impulse (Arons, 1991; Rosenblatt & Heckler, 2011).

Based on the formative assessment theory, Beatty et al. (2006) argued that conceptual questions can help students to explore, organize, integrate, and extend their conceptual understanding. Conceptual questions usually surpass calculating questions in terms of promoting understanding of concepts, allowing the students to better learn to probe the concepts. They are different from the summary assessment questions in traditional courses (Beatty et al., 2008). Contextualized questions will evoke students’ dissatisfaction, leading to a change in their concepts (Scott, Asoko, & Leach, 2007). The literature has found a close link between the level of learning motivation and the learners’ commitment to learning strategies, such as organization or rehearsal, which have been found to significantly influence their academic performance (e.g., Selçuk, 2010). If students are confident in their incorrect conceptions of physics, formative assessment is required to improve their cognitive and metacognitive learning strategies (Sağlam, 2010).