Knowledge Evidence Paper

Metacognition in Physics Problem Solving

From a constructivist perspective, students do not come to their first physics lesson as an empty vase waiting to be filled with new knowledge (O'Donnell, 2012). New knowledge is built from prior experiences and existing knowledge (Hewson, 1992), and students arrive to physics class with a wealth of experiences with everyday phenomena that can be related to and used to explain physics concepts (Disessa, 1996; Gunstone, Gray, & Searle, 1992; von Aufschnaiter & Rogge, 2010; Vosniadou, 1994). Students also come to a physics class with exposure to physics vocabulary, such as velocity, acceleration, energy, and work, without a full understanding of the physics definition of those words (Wade-Jaimes, Demir, & Qureshi, 2018). These experiences impart a combination of beliefs, observations, and mental models which help shape the students’ preexisting knowledge of physics (von Aufschnaiter & Rogge, 2010; Vosniadou, 1994). In the literature on physics education, this preexisting knowledge is referred to using a range of terminology such as: (a) prior knowledge, (b) prior conceptions, (c) misconceptions, (d) missing conceptions, (e) alternate conceptions, (f) alternative frameworks, (g) intuitive knowledge, (h) folk knowledge, (i) prior experiences, and (j) preconceptions (Disessa, 1996; Eryilmaz, 2002; Gunstone et al., 1992; Posner, Strike, Hewson, & Gertzog, 1982; Sherin, 2006; Taasoobshirazi & Sinatra, 2011; von Aufschnaiter & Rogge, 2010; Vosniadou & Mason, 2012). As many of those terms suggest, the prior conceptions a student brings to class may not fully align with the scientifically accepted physics concepts.

Students tend to initially rely on previous interactions with everyday phenomena to understand the new physics concepts being taught. While the beliefs and mental models formed from the experiences can help students make connections to new concepts or ideas, the connections the students make are sometimes misleading or incomplete (von Aufschnaiter & Rogge, 2010). A misalignment between the student’s prior conception and the physics concept being taught blocks progress towards an understanding aligned with the scientifically accepted understanding of that concept (Hammer, Elby, Scherr, & Redish, 2005) and can result in a misconnection (von Aufschnaiter & Rogge, 2010). A misconception is an erroneous interpretation of a scientific concept (Vosniadou & Mason, 2012). A misconception may cause a student to think they understand the concept because they have made a connection, but it is a partial understanding or misunderstanding. These misaligned prior conceptions make physics more difficult for students to understand (von Aufschnaiter & Rogge, 2010). Students with misconceptions may need more support to fully understand the scientifically accepted physics concept.

Some students may need to experience the physics concept multiple times from various viewpoints to be confident in their understanding (Wade-Jaimes et al., 2018). The process of shifting from a prior understanding that does not properly align with the scientifically accepted conception to a more complete conceptual understand is a gradual process that may take multiple iterations (Vosniadou & Mason, 2012) When teachers expose students to physics concepts through multiple experiences and exposures, students have more time to check their own mental models and work towards an alignment with the scientifically accepted physics concept (Wade-Jaimes et al., 2018). Unfortunately, most students lack opportunities to experience physics during their K-12 education.

Many students do not have significant time to learn physics in an academic setting and start to address their prior knowledge before their first stand-alone physics class in high school. Elementary students average only 20 minutes of science a day. This science instruction is split between life science, earth/space science, and physical sciences, which includes both chemistry and physics (Plumley, 2019). While roughly 40% of students have the opportunity to take a single-discipline science course in middle school, physics tends to again be combined with chemistry in a physical science class (Havekost, 2019). This amounts to very little time budgeted for physics instruction in elementary and middle schools, creating a space where many students do not have formal school exposure to physics concepts until high school.

Although there are few opportunities before high school to engage in physics, high school physics teachers can help students grapple with their prior knowledge. A majority of high school physics teachers believe the pre-existing knowledge students bring to class is an important part of their physics education. Sixty-five percent of the physics teachers who participated in the 2018 National Survey of Science and Mathematics Education agreed that students’ prior knowledge and skills promote effective instruction (Banilower, 2019). Unfortunately, only 45% of physics teachers reported that they actively work to understand students’ prior knowledge (Banilower, 2019). It is important for teachers to understand their students’ prior experiences relating to a concept so they can teach in a way to help facilitate a change in students’ conceptual understanding (Hewson, 1992).

Students misconceptions can develop in multiple ways. Some students come to class with a misconception already formed from repeated experiences with the physics phenomena in everyday life (von Aufschnaiter & Rogge, 2010). Some misconceptions are formed in class and are a result of students connecting new concepts learned in class in real time to the first association that comes to mind (Rowlands, Graham, Berry, & McWilliam, 2007). When a student is learning a new concept, they try to relate it to something they are familiar with or have experienced. If they do not have an appropriate experience to connect to the new concept, a misconception can be spontaneously formed (Rowlands et al., 2007). Additionally, if a student has a correct, but weak, understanding of a concept, they can be convinced by a peer that the peer’s incorrect understanding of the concept offers a better explanation of the concept than their own correct conception (Wade-Jaimes et al., 2018). This creates a situation where a student’s correct conception shifts to become a misconception.

Knowing that students come to class with a wide variety of prior knowledge, a physics teacher can provide all students with a common experience in the classroom that better aligns with the new concept. These experiences are an attempt to bridge the gap between the students’ real-world experiences and the physics concepts (Redish & Hammer, 2009; Sherin, 2006; von Aufschnaiter & Rogge, 2010). By engaging students in experiences that more appropriately align with the scientific understanding of the new concept, students are able to create immediate, correct connections to the concept rather than choosing a prior experience that may not be an appropriate connection.

Not only is it helpful for teachers engage with students’ prior conceptions, teachers can provide students with opportunities to engage with and reflect upon their prior knowledge. Reflecting on one’s own understanding is a type of metacognitive experience that can provide students opportunities to add to, revise, or delete from their knowledge base (Flavell, 1979). Students can be provided the time and space to evaluate the usefulness of their prior conceptions and gauge if those prior conceptions help or hinder learning. In a typical high school physics classroom this is not a common practice. “It is somewhat striking that, in contrast to what is known from learning theory about the importance of reflection, only 24 percent of physics classes have students write reflections on what they are learning” (Banilower, 2019, p. 19). Without metacognitively engaging with and reflecting on their prior knowledge students may struggle to shift their prior conception to be better aligned with the scientifically accepted conception.

The purpose of this paper is to analyze the literature on how metacognition is used in physics, specifically while problem solving. Gaining a better understanding of how students think while problem solving can help show how students use problem solving to address misconceptions and shift their prior knowledge towards an understanding that better aligns with the scientifically accepted concept. This paper begins by defining problem solving, specifically what constitutes problem solving in physics. Next, the theoretical framework of conceptual change is discussed, starting with foundational studies and building to the findings of current research. Finally, metacognition is defined with an explanation of the two parts of metacognition, knowledge of cognition and regulation of cognition. Discussion follows about how metacognition has been studied within the context of physics education and how metacognition can be used to investigate conceptual change in physics problem solving. Finally, implications for future research will be discussed.

Methods

The goal of this literature review is to understand how students shift their understanding of physics concepts from an incorrect or partially correct understanding towards the scientifically accepted conception. The Education Research Complete, PsycINFO ProQuest Education Databases, and Social Sciences Citation Index data bases were used to search for articles that were (a) published in peer-reviewed journals, (b) available in full text, (c) published in English, and (d) focused on student understanding rather than teacher understanding. To accomplish this, two separate searches were performed within data bases.

The first search used the key words “conceptual change” and “physics”. The total number of articles resulting from the initial search is shown in Table 1. This search was further limited to articles that were published after the Posner, Strike, Hewson, and Gertzog (1982) article. This was the first article on conceptual change in science education. Because of the large number of articles that resulted in this search, articles included in this study met the previously explained criteria as well as were articles that that focused on the conceptual change process rather than articles that measured the conceptual change that resulted from specific treatment. Additional articles were found in the reference sections of the articles found in the data base searches.

A second search was completed using the keywords “metacognition” and “physics”. The total number of articles resulting from the initial search is shown in Table 1. In addition to the inclusion requirements stated earlier, articles in this search were limited to those that followed the Flavell (1979) article which formally defined metacognition. Additional articles were found in the reference sections of the articles found in the data base searches.

Table 1.

Results of the two initial literature searches on four separate databases.

Problem Solving

From a psychology lens, problem solving applied generally is a cyclical process that involves seven steps: (a) identifying the problem, (b) defining and representing the problem, (c) developing a solution strategy, (d) organizing knowledge about the problem, (e) allocate resources, (f) monitor progress, and (g) evaluate the solution for accuracy (Pretz, Naples, & Sternberg, 2003). Problems can be categorized into two classes: well-defined and ill-defined problems. Well-defined problems are those whose goal is distinct, and solutions tends to be straightforward. An ill-defined problem is one that the goal is not clearly outlined, making identifying and representing the problem difficult (Pretz et al., 2003). Ill-defined problems tend to have multiple solutions while a well-defined problem may only have one.

For the purpose of this literature review, physics problem solving is defined as a well-defined word problem that has one or more unknown quantities for which student is expected to calculate or solve. Solving a physics problem is a multistep process that involves both physics conceptual understanding and mathematical skills, specifically algebraic manipulation (Kuo, Hull, Gupta, & Elby, 2013). The process of solving a typical physics problem involves picking the appropriate concept or equation, using algebra to manipulate and solve the equation, and then using conceptual reasoning to check the validity of the answer (Kuo et al., 2013). Physics problem solving requires both physics content knowledge and problem-solving strategies (Nandagopal & Ericsson, 2012). Even though there are aspects of solving physics problems that potentially use conceptual understanding, students do not necessarily gain conceptual understanding from learning to solve problems (Fink & Mankey, 2010; Mulhall & Gunstone, 2012). A student that can correctly mathematically solve a problem may not fully understand the underlying physics concepts involved in the problem (Nandagopal & Ericsson, 2012). In doing so, students are not engaging in understanding the concept or addressing misconceptions while solving the physics problem.

Most physics textbooks suggest similar steps to the ones explained above when solving a physics problem (Etkina, Gentile, & Van Heuvelen, 2014; Knight, 2013). First, students are encouraged represent the problem by creating a diagram or sketch. Next, students are asked to organize their knowledge of the physics problem when they list their known quantities for the problem as well as what unknown quantity they are asked to solve for. Students then choose the appropriate concept or equation needed to solve the problem. After choosing the equation or concept, students should solve for their unknown variable using algebra manipulation. Once the equation is solved for the unknown, the students plug in their known numbers with appropriate units. Finally, the students calculate their answer with correct units (Etkina et al., 2014; Knight, 2013).

When approaching a problem, students tend to identify, define, and represent the problem in terms of what they already know (Pretz et al., 2003). This causes a problem when their prior knowledge and experiences do not properly align with the scientific concept addressed in the problem (von Aufschnaiter & Rogge, 2010). A misalignment between the student’s prior knowledge and the knowledge needed to solve the problem could cause the student to evaluate their own understanding. If this evaluation leads the student to be dissatisfied with their existing knowledge, the students will start the process of conceptual change (Dole & Sinatra, 1998; Posner et al., 1982).

Conceptual Change

Students come to class with a “great deal of experience that is relevant to the study of physics” (Sherin, 2006, p. 535), but not all those experiences align with physics concepts as they are taught in physics classes (Sherin, 2006). Students can build from, restructure, and/or shift their previous conception of physics to better align with scientists’ conceptions of physics as a result of their experiences in the classroom. This process is known as conceptual change. Conceptual change refers to both the resulting change in understanding and the learning process that leads to that change (Chi, Slotta, & de Leeuw, 1994; Dole & Sinatra, 1998; Slotta, Chi, & Joram, 1995).

When a student finds a discrepancy between their own conception and the scientific conception, there are three choices a student can make: assimilate their knowledge, accommodate their knowledge, or keep their current conception. Assimilation, or extension (Hewson, 1992), occurs when a student uses the new conception to build upon their prior conception. The new knowledge merges with the students’ old knowledge to enrich or add to their ideas (Posner et al., 1982; Vosniadou, 1994). Accommodation, also referred to as an exchange (Hewson, 1992), happens when a student replaces, revises, or reorganizes their prior conception based on the new conception (Posner et al., 1982; Vosniadou, 1994). While assimilation and accommodation can both involve blending prior knowledge with new knowledge, in assimilation, the resulting conception tends to look more like the prior conception while accommodation is a more radical change where the resulting conception is more similar to the new conception (Posner et al., 1982; Vosniadou, 1994).

The basic understanding of the conceptual change process is a student will typically first try to assimilate their prior conception with the new concept, allowing old ideas to adjust and meet the needs of the new concept. If the process of assimilating is unsuccessful, the student will then attempt to accommodate and replace the prior conception with the new concept (Posner et al., 1982). If the student is not satisfied with the results of assimilation or accommodation, the students will keep their existing conception, resulting in no conceptual change (Posner et al., 1982; Vosniadou, 1994). While the ideas of assimilation and accommodation explain how students are shifting their prior conceptions, it does not address why students decide to change their conception. Perhaps most importantly, the student must be dissatisfied with their current understanding of the concept for the process of conceptual change to even begin. This understanding has led to attempts to better explain and model conceptual change.

Conceptual Change Model

Posner et al.’s (1982) Conceptual Change Model (CCM) was the first to build from the definition of conception change to show the process a student undergoes when deciding whether or not to accommodate their prior conception. As shown in Figure 1, four conditions must be met for a student to decide to accommodate: (a) the student must have dissatisfaction with their prior conceptions and the student must find the new conception to be (b) intelligible, (c) plausible and (d) extendable (Posner et al., 1982). If any of the four conditions are not met, the student will keep their prior conception. Intelligibility means the student understands the terms, symbols and syntax used in the new conception, allowing them to create a representation of the concept. A conception is plausible if it (a) aligns with the student’s fundamental assumptions, (b) is consistent with other knowledge and past experiences, (c) can be used to create an image of the conception, and (d) can be used to solve problems. An intelligible concept allows for the student to further use and apply it. To be considered extendable, the student needs to be able to use the new conception to interpret new experiences and see future, fruitful potential (Posner et al., 1982).

Figure 1. Conceptual Change Model showing necessary steps for a learner to accommodate and accept a new conception (Posner et al., 1982).

In order to accept the new conception, the student must first be dissatisfied with their prior conception. The student must feel that their current conception does not help them to understand and apply the new information. Commonly, this happens after the student attempts to assimilate their prior conception but cannot due so due to an anomaly. Anomalies occur when a student struggles to make sense of something while attempting to adapt the new conception to their prior conception. This anomaly creates dissatisfaction with the prior conception, creating the possibility the student will adopt the new conception. Once the student finds their prior conception dissatisfying, the student must find the new conception intelligible, plausible, and extendable. If the student finds the new concept intelligible, plausible, and extendable, the anomalies causing the initial issues with their prior conceptions should have been resolved (Posner et al., 1982).

While the CCM builds from the basic understanding of conceptual change to explain the necessary steps for a change to occur, it leaves some questions about the process that students undertake when they are in the process of conceptual change. The CCM only allows for two options, conceptual change or no conceptual change, and does not account for the range of possible shifts in conceptual understanding that a student may experience. Conceptual change is a gradual process and may take many interactions with a phenomenon to fully occur, if a student does fully align their understanding of a concept with that of the scientifically accepted conception (Vosniadou & Mason, 2012; Wade-Jaimes et al., 2018). Additionally, the CCM starts with a student being dissatisfied with their prior knowledge, but it does not explain what leads the students to be dissatisfied. Understanding how students evaluate their prior conceptions could lead to better understanding of how students decided to engage in conceptual change.

Cognitive Reconstruction of Knowledge Model

The Cognitive Reconstruction of Knowledge Model (CRKM), developed by Dole and Sinatra (1998), builds from the CCM to show a more comprehensive model of conceptual change, expressing more of the complexities involved in the conceptual change process. As shown in Figure 2, the CRKM reorganizes the components of the CCM and adds the following constructs: (a) strength of the existing conception, (b) motivation, (c) peripheral cues and (d) engagement (Dole & Sinatra, 1998).

Figure 2. Dole and Sinatra’s (1998) Cognitive Reconstruction of Knowledge Model of conceptual change.

The CRKM considers five major factors into a students’ decision to engage in conceptual change: (a) learners existing conception, (b) motivation, (c) message, (d) engagement, and (e) peripheral cue. Learner’s existing conception refers to the coherence of the students’ prior conception. This takes into consideration whether the prior conception is detailed and well-structured or fragmented and lacking information. Learner’s existing conception also makes allowances for how committed the student is to their prior concept. Students who are very committed to their conceptions are less likely to engage in conceptual change (Dole & Sinatra, 1998).

The first step towards conceptual change occurs when a student is dissatisfied with their prior conception. The CRKM puts dissatisfaction along with other factors that may encourage or discourage a student to change their conception under the heading of motivation. The other factors within motivation include if the conception is personally relevant to the student, if their peers are interested in the new concept, and finally if the student is willing to engage in the learning of the new concept (Dole & Sinatra, 1998). If a student is not motivated to change their conception for any of those reasons, conceptual change will not occur.

When a teacher is presenting new materials, some students choose to engage in conceptual change because of the strength of the teacher’s argument or message (Dole & Sinatra, 1998). The teacher’s message includes whether the student finds the new conception comprehensible, coherent, plausible, and rhetorically compelling. Some students are not motivated by the argument itself, but by the peripheral cues provided in the message. Peripheral cues are how attractive, trustworthy, credible, or easily understandable the students find the source of the information (Dole & Sinatra, 1998). When a student is not convinced by the message, peripheral cues provided by the teacher can convince students to engage in conceptual change.

When involved in a lesson, different students engage in the lesson at various levels. Engagement is the level at which students participate in processing, exercise reflection, and utilize strategies for learning (Dole & Sinatra, 1998). Low engagement tends to result in weak, or more likely no conceptual change. High engagement can result in strong conceptual change, but like low engagement, can also result in no conceptual change (Dole & Sinatra, 1998).

The CRKM model does not treat the resulting conceptual change as an all or nothing occurrence, instead it recognizes that in addition to no conceptual change occurring, conceptual change happens on a spectrum from a weak conceptual change to a strong conceptual change. The CRKM also accounts for the fact that a strong conceptual change requires higher engagement from the student and weak conceptual change can be a result of low engagement (Dole & Sinatra, 1998).

The CRKM creates a more complete model of conceptual change, building from the original CCM. The CRKM model allows for a wider range of conceptual changes. Where the CCM only allowed for a change or no change (Posner et al., 1982), the CRKM characterizes the final change on a spectrum from a weak conceptual change to a strong conceptual change (Dole & Sinatra, 1998). The CRKM model also sets the groundwork for a larger discussion as to what factors play into a student deciding to change their current understanding of a concept. While both models emphasize that a student must be dissatisfied with their conception (Dole & Sinatra, 1998; Posner et al., 1982), the CRKM model uses aspects of the student’s prior conception and their student’s motivation to explain why a they decide to engage in a change (Dole & Sinatra, 1998). A final strength of the CRKM model over the CCM is that is accounts for the socio-cultural aspects of the classroom by including the social context, messaging, and peripheral cues (Dole & Sinatra, 1998). Social interactions are an important aspect of conceptual change (Vosniadou, & Mason, 2012). These factors combine to create a more detailed theoretical framework of conceptual change.

Current Research: Building from the CRKM in Physics

Following the development of the CRKM, researchers used quantitative measures to further investigate the relationships between variables proposed in the original CRKM model as well as recommend other factors important to the conceptual change process in a physics classroom (Taasoobshirazi, Heddy, Bailey, & Farley, 2016; Taasoobshirazi & Sinatra, 2011). As shown in Figure 3, the first study to empirically model the CRKM focused on how need for cognition and approach goal orientation influenced physics motivation which in turn influenced both conceptual change scores and course grade. Each of the constructs were evaluated using separate measures and structural equation modeling was used to test the proposed relationships (Taasoobshirazi & Sinatra, 2011).

Figure 3. Taasoobshirazi and Sinatra’s (2011) model of factors leading to conceptual change in physics.

For the purpose of Taasoobshirazi and Sinatra’s (2011) study, need for cognition was defined as how often a student engaged in and enjoyed cognitive activities such as seeking out information or thinking about big ideas. Approach goal orientation was evaluated by whether a student was focused on understanding and learning with a mastery goal or if the student was focused on performance and apparent competence with a performance goal. Motivation was a multidimensional construct that included intrinsic motivation, extrinsic motivation, task relevancy, self-determination, self-efficacy and assessment anxiety. The results of the analysis showed that need for cognition and approach goal orientation correlated highly with physics motivation. Despite finding high correlations, researchers felt there were variables missing from the model (Taasoobshirazi & Sinatra, 2011).

Based from the recommendations of that study, a second study was conducted to include achievement emotions such as enjoyment, boredom and anxiety as well as deep cognitive engagement in the previous model of conceptual change in physics (see Figure 4). Enjoyment is a positive emotion that had been shown to have a positive link with mastery goals and motivation. Boredom and anxiety are negative emotions that tend to deter focus from the task at hand (Taasoobshirazi et al., 2016). Just as it is defined in the CRKM, engagement is how the students involve processing, reflection, and strategies in their learning (Dole & Sinatra, 1998; Taasoobshirazi et al., 2016).

Figure 4. The original conceptual change model tested by Taasoobshirazi et al. (2016).

An initial analysis found that boredom, anxiety and need for cognition did not play a significant role in the CRKM model. Once those constructs were removed, a new model (see Figure 5) was developed that included (a) enjoyment, (b) approach goal orientation, (c) motivation, (d) deep cognitive engagement, (e) course grade and (f) conceptual change. This updated version showed a strong relationship between the variables (Taasoobshirazi et al., 2016). Again, researchers recommend that new variables, such as learner and contextual variables, should be tested with the CRKM to better understand which variables are most important in creating conceptual change in physics.

Figure 5. Taasoobshirazi et al.’s (2016) revised conceptual change model.

A separate study considered how different levels of student engagement and goal orientation effects the conceptual change process (Ranellucci et al., 2013). Deep processing involves extension, elaboration and critical thinking while shallow processing is memorization and reproducing content. Deep processing, rather than shallow, resulted in larger conceptual change. Deep processing was also tied to students with mastery-approach goals. Mastery approach goals are goals focused on understanding and learning, as opposed to performance-approach goals which are goals focused on ability and competence. The study also found that students with higher levels of prior knowledge that align with the scientifically accepted knowledge are more likely to experience conceptual change (Ranellucci et al., 2013). This reinforced the CRKM approach and the importance of student engagement in conceptual change.

Regardless of the context of a student’s prior knowledge and their level of engagement in the lesson, for a student to start the process of conceptual change, the student must first and foremost be dissatisfied with their prior conception (Dole & Sinatra, 1998; Posner et al., 1982). To do so, a student must be aware with their own beliefs, understandings, and other cognitive enterprises, also known as metacognition (Flavell, 1979). If a student reaches an anomaly in their cognition, a metacognitive experience should flag the need to critically analyze their conception (Flavell, 1987). Metacognitive experiences encourage conceptual change in that they “can affect your metacognitive knowledge base by adding to it, deleting from it, or revising it” (Flavell, 1979, p. 908).

Some research has started to look at metacognition as part of the conceptual change process. As part of measuring depth of processing, Ranellucci et al. (2013) coded for metacognitive comments made by the students during a think aloud. A think aloud is a data collection technique where researchers ask participants to talk out their thought processes while completing a task, such as solving a physics problem (van Someren, Barnard, & Sandberg, 1994). The use of metacognitive comments was used to judge the level of engagement a student had with the new material, not necessarily how a student was using metacognition to address their prior conceptions. Their recommendations were that future research clearly define and separate depth of processing and cognitive engagement when investigating conceptual change (Ranellucci et al., 2013).

The different models of conceptual change help to explain the process a student undergoes when shifting their conception of a physics concept once the students decides they are dissatisfied with their current understanding (Dole & Sinatra, 1998; Posner et al., 1982; Ranellucci et al., 2013; Taasoobshirazi et al., 2016; Taasoobshirazi & Sinatra, 2011). The models do not explain how a student evaluates their prior conception to decide if they are dissatisfied. Metacognition, particularly comprehension monitoring, is part of the conceptual change process (Hewson, 1992) and assessing students’ judgements of their understandings through metacognitive insights may provide a better measure of conceptual change than knowledge tests (Gunstone et al., 1992). Stronger conceptual change can happen when a student engages in metacognitive awareness (Gunstone et al., 1992). This missing part of the conceptual change models creates to a desire to better understand how students engage with and assess their own cognition during the process of conceptual change. In other words, how do students engage in metacognition in order to initiate the conceptual change process.

Metacognition

Flavell defined metacognition as “knowledge and cognition about cognitive phenomena” (1979, p. 906). Metacognition is different from cognition. “Metacognitions are second-order cognitions: thoughts about thoughts, knowledge about knowledge, or reflections about actions” (Weinert, 1987, p. 8). Cognition is the skills and knowledge that are needed to perform a task while metacognition is the understanding how well the task was performed (Schraw, 1998). For example, if a student is working on a physics problem cognition involves reading the problem while metacognition occurs when a student assesses if they understand the problem as shown in Table 2. Cognitive skills tend to be more content specific while metacognitive skills tend to be more general and span multiple content areas (Schraw 1998). Although different, cognition and metacognition are closely related and can be difficult to distinguish due to the fact that they are depended on one another, creating a circular relationship (Veenman, Van Hout-Wolters, & Afflerbach, 2006).

Table 2

Examples of how a student may use cognition and metacognition while solving a physics problem.

Metacognition has two distinct components, knowledge of cognition and regulation of cognition (Schraw, 1998; Schraw & Dennison, 1994; Taasoobshirazi & Farley, 2013 The two components of metacognition further break down into eight subcomponents as shown in Figure 6. Knowledge of cognition includes declarative knowledge, procedural knowledge and conditional knowledge. Regulation of cognition includes planning, information management, comprehension monitoring, debugging, and evaluation (Schraw, 1998; Schraw & Dennison, 1994; Taasoobshirazi & Farley, 2013).

Figure 6. The two components and eight sub-components of metacognition.

Knowledge of Cognition

Knowledge of cognition refers to what a student knows about cognition in general and more importantly about their own cognition. There are three types of metacognitive knowledge: (a) declarative, (b) procedural, and (c) conditional (Schraw, 1998; Schraw & Dennison, 1994; Taasoobshirazi & Farley, 2013). Declarative knowledge is knowledge that a student has about themselves as a learner, strategies, and what conditions impact their performance. For example, a student may think they are good at mathematics but struggles with writing. Procedural knowledge refers to knowledge a student has about how to do a task. This may include a student knowing how to apply a problem-solving strategy. And finally, conditional knowledge is the understanding a student has about when and why to use declarative and procedural knowledge. In physics, an example of this would be a student knowing when to use Newton’s Laws as opposed to conservation laws to solve a problem (Schraw, 1998; Taasoobshirazi & Farley, 2013). Knowledge of cognition allows a student to gage their learning, but it does not help them to organize and check their learning.

Regulation of Cognition

Regulation of cognition is a student’s ability to control and monitor their learning. Within regulation of cognition, there are five subprocesses: (a) planning, (b) information management, (c) comprehension monitoring, (d) debugging, and (e) evaluation (Schraw, 1998; Schraw & Dennison, 1994; Taasoobshirazi & Farley, 2013). Planning involves selecting strategies, allocating resources, and setting goals prior to working in a task. A student working on a lab may decide what materials they need before starting the lab. Comprehension monitoring refers to a student’s real time assessing of their progress, comprehension, and goals. While problem solving, a student may check their work every few steps to make sure they have not made any mistakes. Evaluation is the process that occurs when the student evaluates their work or product once it is completed. For example, when a student is done with a problem, they may judge how correct their answer is. (Schraw, 1998; Taasoobshirazi & Farley, 2013). Debugging involves using strategies to fix errors and alter learning. Debugging can be as simple as a student seeking help when they do not fully understand a concept. Information management are strategies that help students be more effective. In physics, an information management strategy is to draw and label a picture or diagram before starting to solve a problem (Taasoobshirazi & Farley, 2013).

Metacognition Development

Metacognitive skills continue to grow and develop with age (Veenman & Spaans, 2005; Veenman, Wilhelm, & Beishuizen, 2004). The first awareness of metacognitive abilities begins in children around ages three to five (Dimmitt & McCormick, 2012; Veenman et al., 2006). At this stage, children have theory of mind, or an ability to understand and attribute mental states to themselves and others. In doing so, they are able to start to distinguish reality from false beliefs (Dimmitt & McCormick, 2012). By age 11 or 12, children begin to develop and apply metacognitive knowledge and skills. (Veenman & Spaans, 2005). By high school, when most students first take physics, students are able to engage in a variety of metacognitive strategies and apply these strategies to different contexts (Dimmitt & McCormick, 2012). Additionally, metacognitive skills are highly interdependent, so developing one skill often leads to developing another (Veenman & Spaans, 2005).

Not only does metacognitive ability depend on age, it is also found to be correlated with intelligence (Veenman & Spaans, 2005; Veenman et al., 2006; Veenman et al., 2004). Intelligence is defined as to the magnitude and quality of cognitive knowledge and skills (Veenman & Spaans, 2005). Highly intelligent students tend to exhibit more metacognitive activities (Veenman & Spaans, 2005). Intelligence and metacognitive knowledge develop in a parallel path (Veenman & Spaans, 2005) while intellectual ability mediates the development of metacognitive skills (Veenman et al., 2004). Additionally, it was found that both metacognition and intelligence individually and collectively accounted for the variance in mathematics performance for secondary students (Veenman & Spaans, 2005).

Metacognition in Physics

Research has explored how metacognition is used in high school and college physics classes as well as the effect of metacognition on student learning. One such study investigated how metacognitive tools support conceptual change (Wade-Jaimes et al., 2018). Throughout a physics unit on circuits, a class of high school students were offered multiple experiences and resources to conceptually engage with the circuits content knowledge. This variety of representations provided students multiple opportunities to make connections between their mental models of circuits and the scientifically accepted physics conception with the hopes of creating a discrepant event that could start the process of conceptual change. Some students in the study were able to demonstrate a correct explanation of a concept, but still needed more time to resolve uneasiness with the more abstract aspects of the concept. Teacher questioning and probing of students was found to be key in getting students to use metacognition. This is because students did not always use a specific metacognitive tool as the teacher intended (Wade-Jaimes et al., 2018). A student may simply use a tool that a teacher asked them to use but may not use the tool in a way to seek deeper meaning or understanding. Students may need help and prompted to use metacognition while learning physics.

College students enrolled in an introductory physics class were asked to use a physics tutorial. In the tutorial students were asked to solve a set of physics problems and watch a video of an expert’s explanation of the answer. Students were also asked to answer a set of metacognitive prompts that were gradually scaffolded away (Osman, 2010). As a result of the tutorial, students showed an increase in their mean metacognitive awareness test score. Students commented that they became more aware of their thinking process, planning strategies, and their ability to check for accuracy. The researcher suggested that metacognition about problem solving strategies may be more important than the problem solving strategies themselves when cultivating students’ physics knowledge (Osman, 2010). Many students can use a problem solving strategy, get the problem correct, but still not understand the underlying physic concept of the problem. The metacognitive strategies, more so than the problem solving strategies, raise the student’s awareness of their ongoing thought processes and check for accuracy (Osman, 2010). This may help in achieving a greater understanding of the underlying concept itself.

A second study also used prompts to help high school students enrolled in introductory physics to plan, monitor, and judge their own work (Jax, Ahn, & Lin-Siegler, 2019). This specific study was investigating the use of contrasting cases in the prompts during a physics circuit simulation. Contrasting cases show students a good example as well as a bad example of the problem solving and circuit building the students were learning in the simulation. Prior research noted that when students have a range of examples to compare, they notice more features within the examples. The results indicated that students who were exposed to the contrasting cases, rather than just the good example were more accurate at assessing their own performance and demonstrated a higher performance on their final assessment (Jax et al., 2019). The use of contrasting cases could help students’ metacognitive awareness by making students aware of good and bad examples of work, allowing them to compare their work to those examples, gauge their understanding, and evaluate their cognition.

Phang (2009) used grounded theory to develop a model how secondary students solve physics problems and where metacognition fits into the problem solving process. As shown in Figure 7, students typically follow a path that begins by reading the problem. After the student reads the problem, they tend to plan their strategy for solving the problem by arranging information and analyzing the problem. The next step in problem solving is to perform the calculation. Occasionally, students will pause during the calculation step to check their work. Following the calculation, students will answer the question. The last possible step in a typical problem solving session is to check the answer. While this is a typical path, students can skip steps, repeat steps, or loop back to an earlier step based on their understanding of the problem (Phang, 2009; 2010). A second study was conducted that confirmed the model (Phang, 2010).

Some of the steps in physics problem solving model represent cognitive knowledge and other metacognitive knowledge. As demonstrated with the dashed boxes, reading the problem, arranging information, calculating, and answering the question are all typically cognitive processes. Phang (2009; 2010) identified the metacognitive processes, as shown in the solid boxes, are the planning, analyzing, and checking steps while problem solving. Different students employ different strategies while problem solving, changing the amount of cognitive versus metacognitive knowledge the student uses. For instance, if a student does not check their work at any step during the problem solving process, they decrease their opportunities to use metacognition (Phang, 2009; 2010). This model shows the potential places in problem solving where students implement metacognition, if they are engaging in metacognitive processes.

Figure 7. Phang (2009; 2010) pattern of physics problem solving.

Simulations are frequently used to help students visualize and more easily manipulate physics concepts in an attempt to address misconceptions. Moser, Zumbach, and Deibl (2017) used prompts in a conservation of energy simulation in physics lesson for secondary students to see if a combination of metacognitive training and metacognitive prompts would promote better performance from students on an assessment of knowledge on conservation of energy. At first glance, the data showed no statistically significant difference between the four groups: (a) no prompting or training, (b) prompting but no training, (c) training by no prompting, and (d) training and prompting. The only significant predictor of the students’ posttest knowledge of energy score was prior knowledge as assessed on the pretest. Researchers went back through their data and coded not only if the students were provided a metacognitive prompt, but also how the student used the prompt. During the second analysis, researchers found that students who more effectively and intensely applied the metacognitive prompts scored higher on the posttest with a statistically significant difference as compared to students who did not apply the prompts. Students who purposively use the prompts by taking notes and repeatedly using the strategies were those who gained the most benefit from the metacognitive prompts. The effectiveness of the supports provided in a simulation depends on how the student uses those supports (Moser et al., 2017). This demonstrates the importance of not only understanding if a student in using metacognitive learning strategies, but also how the student is using the strategy.

A similar finding was found when analyzing the metacognition of university physics students in a laboratory setting (Kung & Linder, 2007). Researchers coded student conversations during a laboratory activity for comments that were metacognitive in nature, statements that were part of the logistics of the lab, and statements that were off task. Comments were analyzed by looking at the quantity of metacognitive statements as well as the time during the lab when the comments were made. Researchers concluded that it did not matter how many metacognitive statements were made, nor when they occurred in the lab. What was more important is what the students did following the metacognitive statement. If a student made a metacognitive statement, such as a statement that expressed a misunderstanding, but neither the student nor their lab partners worked to clarify the misunderstanding, the metacognitive statement did not seem to impact the students’ learning. If instead that same metacognitive statement resulted in the group of students trying to make sense of the misunderstanding, the metacognitive statement proved to be more fruitful (Kung & Linder, 2007). The usefulness of metacognition in physics is not in whether it is used, but how it is used. For a student to change their understanding and start the process of conceptual change, a student not only has to be metacognitive and assess their understanding, but they must also act on the misunderstanding and try to understand why they do not understand.

Measures of Metacognition in Physics

Overall, there has been less research within physics research examining the use of metacognition specifically in problem solving (Phang, 2009; Taasoobshirazi & Farley, 2013). The few research studies that do look at metacognition in physics problem solving use think aloud protocols and interviews for small samples of students (Phang, 2009). Taasoobshirazi and Farley (2013) developed the Physics Metacognition Inventory to provide researchers with a tool to assess physics student’s metacognition during problem solving and open new opportunities for research. The Physics Metacognition Inventory is 26-item self-report survey that uses a five-point Likert scale. The 26 items load into six factors: (a) knowledge of cognition: declarative, procedural, and conditional, (b) regulation of cognition: information management, (c) regulation of cognition: monitoring, (d) evaluating, (e) regulation of cognition: debugging, and (f) regulation of cognition: planning (Taasoobshirazi, Bailey, & Farley, 2015). Exploratory factor analysis, confirmatory factor analysis, and Rasch analysis were used to confirm the overall reliability and construct validity of the Physics Metacognition Inventory (Taasoobshirazi et al., 2015; Taasoobshirazi & Farley, 2013). The Physics Metacognitive Inventory item reliability was 0.97 (excellent) and the person reliability was 0.86 (good) (Taasoobshirazi et al., 2015). The Physics Metacognition Inventory will allow future research to quantitatively asses the impacts of metacognition on physics problem solving.

By better understanding how students use metacognition while solving physics problems, we can gain a perspective as to how students are engaging in conceptual change while solving problems. To start the process of conceptual change, a student first needs to be dissatisfied with their current understanding of a physics concept (Posner et al., 1982). To find the understanding dissatisfying, the student needs to monitor, reflect on, and evaluate their current understanding. These are all metacognitive processes, specifically regulation of cognition processes (Schraw, 1998; Schraw & Dennison, 1994; Taasoobshirazi & Farley, 2013). The process of conceptual change begins with metacognition.

Future Research

As Hammer et al. (2005) concluded their book chapter, if physics education research is going to focus on long term learning and not just short term fixes, “we must take into account the metacognition/epistemology literature… and the importance of helping students become deliberative and reflective about their own learning processes” (p. 23). Students who use metacognition tend to have less erroneous conceptions and mental models (Rozencwajg, 2003). But research has shown that it is not enough to have students engage in metacognitive strategies, it is more important to understand how and when students engage with their metacognitive knowledge (Kung & Linder, 2007; Moser et al., 2017; Osman, 2010). More research is needed to better understand how, when, and why students use metacognition (Dimmit & McCormick, 2012) especially in regard to their decision to undergo the conceptual change process. Specifically, how is metacognition used by students to evaluate their prior knowledge to decide if they are satisfied or dissatisfied with their prior conception.

My focus is specifically how students use metacognition during problem solving in physics. Physics problems, particularly higher order thinking problems, tend to encourage the use metacognitive strategies (Abdullah, Malago, Bundu, & Thalib, 2013). In a traditional physics classroom, problem solving is a main focus and teaching tool (Mulhall & Gunstone, 2012). My overall research goal is to better understand how students use metacognition in problem solving. The research questions for the proposed study is:

1. Quantitative: What is the correlation between current high school physics’ content knowledge in physics as measures by the Force Concept Inventory and metacognition in physics as measured by Physics Metacognition Inventory?

2. Qualitative: How do current high school physics students use cognition and metacognition to solve physics problems?

3. Qualitative: In what ways do current high school physics students voice dissatisfaction with their content knowledge while solving a physics problem?

4. Mixed: What are differences in problem solving processes for current high school physics students who have high, middle, and low physics content knowledge as measure by Force Concept Inventory and high and low physics metacognition as measure by Physics Metacognition Inventory?

Methods

This study will employ a complementarity, explanatory, sequential mixed method design (Creamer, 2018; Greene, Caracelli, & Graham, 1989). Quantitative analysis of student scores on of physics conceptual understanding as measured by the Force Concept Inventory (Hestenes, Wells, & Swackhamer, 1992) and metacognitive use in physics problem solving measured with the Physics Metacognition Inventory (Taasoobshirazi et al., 2015; Taasoobshirazi & Farley, 2013) will be used to inform a purposively selected, nested sample for the qualitative think aloud interview portion of the study (Creamer, 2018; Yin, 2006). Integration will occur at the research question, unit of analysis, sample, data collection, and analytics parts of the study (Yin, 2006). Table 3 shows a visual breakdown steps of the mixed-methods research design.

Table 3

Visual of mixed-methods design procedure (adapted from Gasiewski, Eagan, Garcia, Hurtado, & Chang, 2012)

References

Abdullah, H., Malago, J. D., Bundu, P., & Thalib, S. B. (2013). The use of metacognitive knowledge patterns to compose physics higher order thinking problems. Asia-Pacific Forum on Science Learning and Teaching, 14(2), 1-12.

Banilower, E. R. (2019). 2018 NSSME+: Status of high school physics. Chapel Hill, NC:

Chi, M. T. H., Slotta, J. D., & de Leeuw, N. (1994). From things to processes: A theory of conceptual change for learning science concepts. Learning and Instruction, 4, 27-43.

Creamer, E. G. (2018). An introduction to fully integrated mixed methods research. Thousand Oaks, CA: SAGE Publications, Inc

Dimmitt, C., & McCormick, C. B. (2012). Metacognition in Education. In K. R. Harris, S. Graham, & T. Urdan (Eds.) APA Educational Psychology Handbook: Volume 1 Theories, Constructs, and Critical Issues (pp. 157-187). doi: 10.1037/13273-007

Disessa, A. A. (1996). What do “just plain folk” know about physics. In D. Olson & N. Torrance (Eds.), The handbook of education and human development (pp. 709-724). Cambridge, MA: Blackwell Publishers.

Dole, J. A., & Sinatra, G. M. (1998). Reconceptualizing change in the cognitive construction of knowledge. Educational Psychologist, 33, 109-128. doi: 10.1080/00461520.1998.9653294

Eryilmaz, A. (2002). Effects of conceptual assignments and conceptual change discussions on students' misconceptions and achievement regarding force and motion. Journal of Research in Science Teaching, 39, 1001-1015. doi: 10.1002/tea.10054

Etkina, E., Gentile, M., & Van Heuvelen, A. (2014). College physics. Pearson Education, Inc.

Fink, J. M., & Mankey, G. J. (2010). A problem-solving template for integrating qualitative and quantitative physics instruction. The Journal of General Education, 59, 273-284. Retrieved from http://www.psupress.org/journals/jnls_jge.html

Flavell, J. H. (1979). Metacognition and cognitive monitoring: A new area of cognitive–developmental inquiry. American Psychologist, 34(10), 906-911. doi: 10.1037//0003-066x.34.10.906

Flavell, J. H. (1987). Speculations about the nature and development of metacognition. In F. E. Weinert & R. H. Kluwe (Eds.), Metacognition, motivation, and understanding (pp. 21-29). Hillsdale, NJ: Lawrence Erlbaum Associates.

Gasiewski, J. A., Eagan, M. K., Garcia, G. A., Hurtado, S., & Chang, M. J. (2012). From gatekeeping to engagement: A multicontextual, mixed method study of student academic engagement in introductory STEM courses. Research in Higher Education, 53(2), 229-261.

Greene, J. C., Caracelli, V. J., & Graham, W. F. (1989). Toward a conceptual framework for mixed-method evaluation designs. Educational Evaluation and Policy Analysis, 11(3), 255-274. doi: 10.3102/01623737011003255

Gunstone, R. F., Gray, C. R., & Searle, P. (1992). Some long‐term effects of uninformed conceptual change. Science Education, 76(2), 175-197. doi: 10.1002/sce.3730760206

Hammer, D., Elby, A., Scherr, R. E., & Redish, E. F. (2005). Resources, framing, and transfer. In J. Mestre (Ed.) Transfer of learning from a modern multidisciplinary perspective (pp. 89-119). Greenwich, CT: Information Age.

Havekost, P. C. (2019). 2018 NSSME+: Status of middle school science. Chapel Hill, NC: Horizon Research, Inc.

Hestenes, D., Wells, M., & Swackhamer, G. (1992). Force concept inventory. Physics Teacher, 30, 141-158. Retrieved from http://scitation.aip.org/content/aapt/journal/tpt

Hewson, P. W. (1992, June). Conceptual change in science teaching and teacher education. Paper presented at the meeting on “Research and Curriculum Development in Science Teaching,” National Center for Educational Research, Documentation, and Assessment, Ministry for Education and Science, Madrid, Spain.

Jax, J., Ahn, J. N., & Lin-Siegler, X. (2019). Using contrasting cases to improve self-assessment in physics learning. Educational Psychology, 39(6), 815-838. doi: 10.1080/01443410.2019.1577360

Knight, R. D. (2013). Physics for scientists and engineers. Pearson Education, Inc.

Kung, R. L., & Linder, C. (2007). Metacognitive activity in the physics student laboratory: Is increased metacognition necessarily better?. Metacognition and Learning, 2(1), 41-56. doi: 10.1007/s11409-007-9006-9

Kuo, E., Hull, M. M., Gupta, A., & Elby, A. (2013). How students blend conceptual and formal mathematical reasoning in solving physics problems. Science Education, 97(1), 32-57. doi: 10.1002/sce.21043

Moser, S., Zumbach, J., & Deibl, I. (2017). The effect of metacognitive training and prompting on learning success in simulation‐based physics learning. Science Education, 101(6), 944-967. doi: 10.1002/sce.21295

Mulhall, P. & Gunstone, R. (2012). Views about learning physics held by physics teachers with different approaches to teaching physics. Journal of Science Teacher Education, 23, 429-449. doi: 10.1007/s10972-012-9291-2

Nandagopal, K., & Ericsson, K. A., (2012). Enhancing students’ performance in traditional education: Implications from the expert performance approach and deliberate practice. In K. R. Harris, S. Graham, & T. Urdan (Eds.) APA Educational Psychology Handbook: Volume 1 Theories, Constructs, and Critical Issues (pp. 257-293). doi: 10.1037/13273-010

O'Donnell, A. M. (2012). Constructivism. In K. R. Harris, S. Graham, & T. Urdan (Eds.) APA Educational Psychology Handbook: Volume 1 Theories, Constructs, and Critical Issues (pp. 61-84). doi: 10.1037/13273-003

Osman, M. E. (2010). Virtual tutoring: An online environment for scaffolding students' metacognitive problem solving expertise. Journal of Turkish Science Education, 7(4).

Phang, F. A. (2009). The pattern of physics problem solving from the perspective of metacognition (Unpublished doctoral dissertation). University of Cambridge, Cambridge, UK.

Phang, F. A. (2010). Patterns of physics problem solving and metacognition among secondary school students: A comparative study between the UK and Malaysian cases. International Journal of Interdisciplinary Social Sciences, 5(8). doi: 10.18848/1833-1882/cgp/v05i08/51816

Plumley, C. L. (2019). 2018 NSSME+: Status of elementary school science. Chapel Hill, NC: Horizon Research, Inc.

Posner, G. J., Strike, K. A., Hewson, P. W., & Gertzog, W. A. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Science Education, 66, 211-227.

Pretz, J. E., Naples, A. J., & Sternberg, R. J. (2003). Recognizing, defining, and representing problems. In J. E. Davidson & R. J. Sternberg (Eds.) The psychology of problem solving (pp. 3-30). Cambridge, UK: Cambridge University Press.

Ranellucci, J., Muis, K. R., Duffy, M., Wang, X., Sampasivam, L., & Franco, G. M. (2013). To master or perform? Exploring relations between achievement goals and conceptual change learning. British Journal of Educational Psychology, 83, 431-451. doi: 10.1111/j.2044-8279.2012.02072.x

Redish, E. F., & Hammer, D. (2009). Reinventing college physics for biologists: Explicating an epistemological curriculum. American Journal of Physics, 77, 629-642. doi: 10.1119/1.3119150

Rowlands, S., Graham, T., Berry, J., & McWilliam, P. (2007). Conceptual change through the lens of Newtonian mechanics. Science & Education, 16, 21-42. doi: 10.1007/s11191-005-1339-7

Rozencwajg, P. (2003). Metacognitive factors in scientific problem solving strategies. European Journal of Psychology of Education, 18(3), 281-294. doi: 10.1007/bf03173249

Schraw, G. (1998). Promoting general metacognitive awareness. Instructional Science, 26(1-2), 113-125. doi: 10.1023/a:1003044231033

Schraw, G., & Dennison, R. S. (1994). Assessing metacognitive awareness. Contemporary Educational Psychology, 19(4), 460-475. doi: 10.1006/ceps.1994.1033

Sherin, B. (2006). Common sense clarified: The role of intuitive knowledge in physics problem solving. Journal of Research in Science Teaching, 43, 535-555. doi: 10.1002/tea.21136

Slotta, J. D., Chi, M. T. H., & Joram, E. (1995). Assessing students’ misclassifications of physics concepts: An ontological basis for conceptual change. Cognition and Instruction, 13, 373-400.

Taasoobshirazi, G., Bailey, M., & Farley, J. (2015). Physics metacognition inventory part II: Confirmatory factor analysis and Rasch analysis. International Journal of Science Education, 37(17), 2769-2786. doi: 10.1080/09500693.2015.1104425

Taasoobshirazi, G., & Farley, J. (2013). Construct validation of the physics metacognition inventory. International Journal of Science Education, 35(3), 447-459. doi: 10.1080/09500693.2012.750433

Taasoobshirazi, G., Heddy, B., Bailey, M., & Farley, J. (2016). A multivariable model of conceptual change. Instructional Science, 44(2), 125-145. doi: 10.1007/s11251-016-9372-2

Taasoobshirazi, G., & Sinatra, G. M. (2011). A structural equation model of conceptual change in physics. Journal of Research in Science Teaching, 48, 901-918. doi: 10.1002/tea.20434

van Someren, M. W., Barnard, Y. F., & Sandberg, J. A. C. (1994). A practical guide to modelling cognitive processes. London: Academic Press.

Veenman, M. V., & Spaans, M. A. (2005). Relation between intellectual and metacognitive skills: Age and task differences. Learning and Individual Differences, 15(2), 159-176. doi: 10.1016/j.lindif.2004.12.001

Veenman, M. V., Van Hout-Wolters, B. H., & Afflerbach, P. (2006). Metacognition and learning: Conceptual and methodological considerations. Metacognition and Learning, 1(1), 3-14. doi: 10.1007/s11409-006-6893-0

Veenman, M. V., Wilhelm, P., & Beishuizen, J. J. (2004). The relation between intellectual and metacognitive skills from a developmental perspective. Learning and Instruction, 14(1), 89-109. doi: 10.1016/j.learninstruc.2003.10.004

von Aufschnaiter, C., & Rogge, C. (2010). Misconceptions or missing conceptions?. Eurasia Journal of Mathematics, Science & Technology Education, 6, 3-18.

Vosniadou, S. (1994). Capturing and modeling the process of conceptual change. Learning and Instruction, 4, 45-69.

Vosniadou, S., & Mason, L. (2012). Conceptual change induced by instruction: A complex interplay of multiple factors. In K. R. Harris, S. Graham, & T. Urdan (Eds.) APA Educational Psychology Handbook: Volume 2 Individual Differences and Cultural and Contextual Factors (pp. 221-246). doi: 10.1037/13274-009

Wade‐Jaimes, K., Demir, K., & Qureshi, A. (2018). Modeling strategies enhanced by metacognitive tools in high school physics to support student conceptual trajectories and understanding of electricity. Science Education, 102(4), 711-743. doi: 10.1002/sce.21444

Weinert, F. E. (1987). Introduction and overview: Metacognition and motivation as determinants of effective learning and understanding. In F. E. Weinert & R. H. Kluwe (Eds.), Metacognition, motivation, and understanding (pp. 21-29). Hillsdale, NJ: Lawrence Erlbaum Associates.

Yin, R. K. (2006). Mixed methods research: Are the methods genuinely integrated or merely parallel? Research in the Schools, 13(1), 41-47