Evaluating the effects of the analogical learning approach on eighth graders’ learning outcomes: the role of metacognition
Chia-Yu
Wang
Graduate Institute of Digital Learning and Education, National Taiwan University of Science and Technology, 43, Keelung Rd sec. 4, Taipei, 106, Taiwan, Republic of China. E-mail: chiayuwang@mail.ntust.edu.tw
First published on 5th December 2022
Abstract
Teaching with analogies is an important pedagogy that helps learners construct abstract conceptions through reasoning with something familiar. Heat concepts were chosen for this study because they have an intangible nature and involve complex mechanisms that often challenge school-aged learners. Learning this kind of complex concept with analogies involves complicated mental processes that could demand learners’ metacognitive abilities; yet, to date, the influence of metacognition has been left unexamined. This study therefore investigated how metacognition differentially affected adolescents’ processes and outcomes of analogical learning about abstract heat concepts. Eighty-three eighth graders participated in the study and attended two units of Teaching-With-Analogies on specific heat and heat transfer. This study adopted a mixed-method approach along with within-group comparisons. Among them, eight individuals from each of the high-, moderate- and low-metacognitive groups were interviewed to explore the utilized metacognitive activities and their relation with the ability to reason with analogies. The quantitative findings revealed that analogies benefited the moderate metacognitive learners, and yet did not alter the conceptual understanding of the high and low metacognitive cohorts. A unique explanatory power of metacognition was also observed on the learners’ post conceptual understanding, in addition to on their prior knowledge. Verbal process data illustrated that metacognitive abilities substantially influenced every stage of solving heat problems with analogies. The differential outcomes of the analogical learning approach were explained by in-depth case analyses considering the use of prior knowledge and the absence of metacognition during analogical reasoning. Metacognitive characteristics of the dynamic analogy-inferring process for different metacognitive groups were synthesized. The associated implications for the analogical learning approach and accommodations for adolescents of different levels of metacognition are also discussed.
Introduction
Analogy is an important tool of representation, inferencing, and communication in science communities and schools. Science analogies have been used to support comprehending complex science concepts (e.g., Chuang and She, 2013; Chen and She, 2020) and conceptual change (e.g., Chiu and Lin, 2005). Analogies can serve as conceptual representations that support reasoning and bridge inferences between what is familiar and what is new (Gentner, 1989; Vosniadou, 1989). Learning by analogy typically involves recognizing a set of systematic correspondences between a better-known base (the analogy) and a novel system (the target concepts). Analogies that incorporate visual and spatial cues can facilitate learning through helping learners create a concrete and perceptible model of abstract scientific explanation or intangible phenomena (Richland et al., 2007; del Mar Aragon et al., 2014). Although studies have shown encouraging results indicating that elementary learners benefited from analogical-based approaches (e.g., Mason, 1994; Chuang and She, 2013; Han and Kim, 2019; Vosniadou and Skopeliti, 2019), thinking with analogies may not be as easy as it looks. Reasoning with an analogy may become challenging when the to-be-learned concept involves a complex mechanism (Cho et al., 2007).Effective use of analogies requires learners to carefully analyze the targeted concepts and activate prior knowledge to form a mental model as well as related hypotheses about the base analogy. Learners compare salient properties between base and targeted concepts and then evaluate the analogy in the target phenomena. Mechanisms of analogical reasoning (e.g., Gentner, 1989; Vosniadou, 1989) imply that successful reasoning requires learners to be constantly mindful of the task demands and their decisions (task analysis and planning), to oversee the multiple-step inferring and evaluating process (monitoring and evaluation), and to make alternative moves as needed (action regulation); in other words, reasoning with analogies demands metacognition. Students may also need to be able to reflect on the learning episode and to evaluate the fruitfulness of their understanding of the topic resulting from the outcomes of analogical reasoning in order to acknowledge analogy as a plausible and fruitful tool for future learning (adaptation; Winne and Hadwin, 1998). Lacking or not knowing when to activate metacognition would impair effective learning with analogies and would therefore limit its pedagogical value when the learners have not yet developed sufficient metacognitive skills to support analogical reasoning (Veenman and Spaans, 2005). Despite models of analogical reasoning (e.g., Gentner, 1989; Vosniadou, 1989) being proposed three decades ago and several analogical-based teaching approaches having been built upon these assumptions, the metacognitive aspect of analogical reasoning has not been thoroughly examined since the recommendation of Zohar and Barzilai (2013) in a review study. The importance of metacognition has been neglected when discussing factors affecting learning outcomes in the recent related literature. This study raises a question regarding whether and to what extent learners’ metacognitive abilities influence their thinking and learning with analogies for complex science concepts. Empirical evidence of whether and how metacognition influences the process and outcomes of analogy-based learning is needed to shed light on the development of effective metacognitive supports.
Contemporary metacognitive theories depict metacognition as a multi-constructed, complex mechanism. This study, therefore, aims to fill the gap through utilizing a mixed-method approach with multiple data sources. A self-reported metacognitive inventory was used to identify learners’ levels of metacognitive abilities and to categorize them for further comparisons across high, moderate, and low metacognitive groups. The relations between and among prior knowledge, metacognition, ability to understand analogies, and post knowledge were explored with correlation and regression analyses. Within-group comparisons across the high, moderate, and low metacognitive groups were conducted through incorporating multiple data sources to depict differentiated learning characteristics across groups quantitatively and qualitatively. Cognitive and metacognitive challenges that adolescents may face were also depicted in order to synthesize insights for improving analogical learning approaches.
Heat transfer is one of the core ideas in science curricula (National Research Council, 2012). Concepts of specific heat and heat capacity are first introduced at middle school and are developed at high school and college. Learning the concepts of specific heat and heat transfer is challenging because of their abstract and intangible nature. Learners hold alternative ideas about heat and temperature which they derive from everyday experiences and on some occasions from misrepresented instruction in science classrooms (Luera et al., 2005). Concepts of heat, temperature, and thermal equilibrium are closely interdependent; thus, educators recommend introducing these concepts in a coherent model in order to display their inter-relationships (Gentner, 1989; Arnold and Millar, 1996). The water analogy has been applied for teaching these concepts. In this study, we adapted Gentner's as well as Arnold and Millar's design of the water analogy to display these abstract and interrelated heat concepts in a concrete and visible way, and focus on students’ metacognitive monitoring during the learning process.
Theoretical framework
Analogical reasoning
Analogical reasoning is conceptualized as mapping similarities of propositional structure between a base and target embedded in a specific context, and transferring certain structural relations of the base to the target (e.g., Gentner, 1989; Vosniadou, 1989). It is not merely a matter of matching certain features of the base and target, but requires perceptive interpretation of the base and target systems to form an image-based mental model (Wilbers and Duit, 2002). Learning science concepts with analogies is a heuristic exploration of the targeted concept by forming hypotheses as a model with the analogy, and evaluating their mental model against the target phenomenon. Reasoning with an analogy composed of processes includes accessing properties of the base and attributes of the targets, forming individual potential correspondences and combining them into a system, inferring and generating the higher order attribute from the base to the target to generate new knowledge, and evaluating global matches and identifying limitations of the base (Mozzer and Justi, 2012). Common instruction models that support learning complex science concepts using analogies, such as the General Model of Analogy Teaching (Zeitoun, 1984), the Teaching-With-Analogies (TWA) model (Glynn, 1991), or the Bridge Analogies model (Brown and Clement, 1989) generally reflect features of the aforementioned process. In this study, the widely used TWA model was adopted.Challenges in reasoning science conceptions with analogies
Analogies are recognized as useful sources for facilitating conceptual understanding and conceptual change (e.g., Chiu and Lin, 2005; Duit and Treagust, 2003) in physics (e.g., Arnold and Millar, 1996; Chen and She, 2020), and chemistry (e.g., Sarantopoulos and Tsaparlis, 2004; del Mar Aragon et al., 2014). While the results were encouraging, not all learners benefited from the use of analogy, even when the analogical instruction was clearly implemented. A considerable proportion of participants, particularly elementary and middle school learners, have difficulties mapping attributes of the base to those of the target systems when learning abstract concepts. For example, less than half of fifth graders showed clear and complete understanding of the relational structure when learning concepts of the human circulatory system through the analogy of a mail delivery system (Mason, 1994). Likewise, less than one fifth of third and fifth graders attained some degree of understanding of the day/night cycle using an analogy (Vosniadou and Skopeliti, 2019). Similar obstacles were observed when using analogies to teach thermal equilibrium (Arnold and Millar, 1996). Abstract conditional reasoning is complex and difficult, even for older adolescents (Markovits and Doyon, 2011). Children and novices often fail to benefit from such analogical learning approaches when they are presented without support (Martin et al., 2019).Previous literature has documented some learners’ challenges concerning learning science concepts using analogies. Firstly, Harrison, and Treagust (1993) revealed that learners are able to establish basic structural relations, but fail to map the complex ones if an unfamiliar analogy is used. All too often instructors assume that all students possess prior knowledge of the base. Secondly, learning with a complex analogical task demands reasoning ability. Learners who had a higher level of reasoning ability performed better in an abstract analogical reasoning task (Markovits and Doyon, 2011).
Thirdly, it is difficult for students to identify and suppress misleading information or to be aware of the limitations of an analogy. Cho et al. (2007) manipulated the complexity of analogical reasoning by increasing the number of inferences and by adding misleading information. When the participants were required to integrate multiple relations while simultaneously being asked to attend to and actively suppress misleading information, their performance of analogical reasoning decreased. This may be attributed to the fact that, during analogical reasoning, both distinguishing and inhibiting misleading information as well as actively maintaining information in working memory for relational integration share and may compete for working memory resources. Simply put, the benefits of using analogies may be diminished when the complexity of the base and the target systems increase, or when the learners are immature and have insufficient reasoning ability to handle a complex analogy task.
The above-mentioned studies mainly addressed the cognitive aspects of analogical reasoning, but rarely touched upon the metacognitive aspect. Mason (1994) reported that metacognitive awareness concerning the meaning and purpose of analogy in developing new knowledge was highly correlated with conceptual understanding of the new topic. When learners were specifically prompted to infer with similarities of structural relations, they outperformed those who were not prompted to do so (Brown et al., 1986). Interviews of the unprompted group indicated that they succeeded in mapping the structural relations and yet were not aware of the need to infer with the structural relations; they paid attention to similarities of minor features instead. Both Mason's (1994) and Brown et al. (1986) findings imply that metacognition may play a substantial role during the analogy process. To the best of my knowledge, the influence and the role of metacognition has not been put to the test in the past two decades.
Potential role of metacognition in learning abstract concepts with analogies
Metacognition refers to a learner's knowledge of his or her processes of cognition, and the ability to utilize a repertoire of knowledge to control and monitor the cognitive processes toward achieving goals and optimizing outcomes (Schraw et al., 2006). A number of metacognitive skills have been discussed in the literature. Among them, three essential skills are highlighted in most accounts: planning, monitoring, and evaluation (Winne and Perry, 2000; Veenman and Spaans, 2005; Schraw et al., 2006; Zohar and Barzilai, 2013). Planning includes establishing task demands (Meijer et al., 2006), setting goals, and managing efforts and resources (Meijer et al., 2006; Schraw et al., 2006). Monitoring is the process by which an individual oversees his or her cognitive state or thinking process (Yürük et al., 2009). Evaluation refers to appraising the outcomes and the learning or task-solving process (Schraw et al., 2006).Abundant evidence has shown that metacognition is highly adaptive to the task characteristics and specific content knowledge (Azevedo et al., 2010) and is dynamically deployed during a learning or task-solving section (Wang, 2015a). When using analogies to learn abstract and complex concepts such as thermal equilibrium, learners need to recognize and differentiate surface features from the structural relations. They then need to map several inferences of structural relations while ignoring irrelevant but salient properties in order to infer the explanatory structure for new knowledge. Such productive use of analogies may rely on individuals appropriately and adequately monitoring the process and evaluating outcomes of analogical reasoning. The capability of evaluating the fruitfulness of their understanding of the topic resulting from reasoning with analogies may support learners acknowledging analogy as a plausible and fruitful tool; reflecting on corresponding steps and learning episodes of processing analogy tasks, such as being aware of the need to infer with the structural relations, may support adaptation for future learning (Winne and Hadwin, 1998). However, students may not possess adequate metacognitive knowledge nor consciously regulate their learning (e.g., Greene et al., 2008). Lacking adequate planning and monitoring skills may result in inappropriate matching between attributes of the base and target. Without adequate evaluation, students may not recognize the conflict between their preexisting mental model and the new conceptions. They may also mistakenly use an analogy for reasoning without being aware of where the analogy breaks down. Students who possess insufficient metacognitive skills may not benefit from using analogies as a thinking tool.
Accordingly, there is a substantial need to understand the critical role of metacognition in analogy-based learning, especially for adolescents who have yet to develop mature metacognitive ability. The results would reveal adolescents’ capabilities and difficulties encountered while applying the newly learned analogies and effective support to facilitate analogy-based learning. Thus, this study addresses three research questions:
RQ1. Does an analogical learning approach equally benefit students with different levels of metacognition?
RQ2. Is metacognition related to understanding analogies and gaining conceptual understanding? If so, to what extent?
RQ3. How does the utilization of metacognition during analogy reasoning influence adolescents’ successfulness in using analogies to solve heat problems?
Methods
Participants
The participants were recruited from four eighth-grade public school classes in a middle school in southern Taiwan. They had received traditional lecture-based instruction on heat concepts before they attended the instruction based on the TWA model. Eighty-three of the 130 students elected to participate, and completed at least two of the three research instruments, including the Inventory of Metacognitive Self-Regulation (IMSR), a concept test, and a near transfer task. Procedures for protecting the participants and obtaining informed consent were executed.IMSR was used to categorize learners into the high-, moderate-, and low-metacognitive groups on the basis of the percentage of their scores. High- and low-metacognitive students were individuals in the top and bottom 33% for the IMSR, respectively. Eight students from each of the high-, moderate-, and low-metacognitive groups were interviewed. Among these 24 students, two from the low-metacognitive group and one from the moderate group withdrew from the study. In addition, the video recording of a low metacognitive learner was damaged, leaving 20 interviews for the case analyses.
Teaching specific heat and heat transfer with a TWA model
A water analogy was developed to frame heat, temperature, specific heat, and heat transfer in an integrative way. Arnold and Millar (1996) as well as Gentner (1989) introduced a similar heat/water analogy. Adapting key features from both sets of instruction, we told students that heat flow can be understood just like water. We used “pouring the same amount of water into vials of different diameters yielding different increments of water level for each,” to form an analogy for explaining “when gaining the same amount of heat, objects with different specific heat yield different temperature change.” Building up this analogy, we also used the phenomenon of two connected vessels with different diameters and the concept of communicating vessels to form the second analogy for explaining the concepts of heat transfer. A science educator (the author), an experienced middle school science teacher, and a science teacher who is also a Master's student in science education, formed a pedagogical team which worked together to develop the analogies and the two corresponding TWA units on specific heat and heat transfer, respectively. Each unit lasted about two hours. The last member of the pedagogical team conducted the TWA units. She fully participated in designing the analogies and the TWA units. The TWA units are introduced in the following sequences:1. The teacher helped the students recall the target concepts consisting of heat, temperature, specific heat, and heat transfer.
2. She then discussed with students what they knew about the analogies, such as how the level of water may differ when pouring water into two vials with different diameters and observation of how the water level of the two vessels changes when filling a system of communicating vessels with water.
3. The teacher explained and demonstrated how to map the attributes and structural relations of the analogy base to that of the target concepts accompanying the visual representations for the analogies and for the targeted phenomena. The teacher ensured that the students understood the basic matches before moved on to explaining the complex matches.
4. The teacher summarized by extracting the similarities between the base and target systems to generate new inferences about the target concept. The process of mapping and of carrying over were repeated in different conditions (e.g., heat transfer when the specific heat of object A is greater than, equal to, or smaller than that of object B) to help the students become familiar with analogical reasoning.
5. Last, the teacher showed how to evaluate the system of the established matches and discussed where the analogy broke down.
Instruments
A stone of 50 grams at a 100 °C is dropped into a cup of water with 100 grams at 20 °C. Thermal equilibrium is reached after 10 minutes. Which of the following is correct?
(a) The total heat content of both is the same at the end;
*(b) Both reach the same final temperature;
(c) The decreased temperature level of the stone is the same as the increased temperature level of the water;
(d) The amount of heat given off by the water is equal to the amount of heat absorbed by the stone.
Note: *: The correct answer.
Understanding of heat analogies
Upon completion of the two units, students were given a near transfer task that was similar to the problem that the teacher demonstrated in the TWA units, only the numbers in the problem were altered. The purpose of the near transfer tasks was to understand if the students could apply the taught analogy to a very similar context (Perkins and Salomon, 1992). The problems of the near transfer tasks for specific heat and heat transfer were:Specific heat: “If we heat up 10 g of sand and 10 g of water with the same oven for 5 min, which one will increase more in temperature? Which one will gain more heat?”
Heat transfer: “There are two objects with different temperatures. When they contact, heat will be transferred from the one with a high temperature to the one with a low temperature. Assume object A has a higher temperature than object B. When they contact and reach heat equilibrium, will the range of the dropped temperature for object A be equal to the range of the increased temperature for object B?”
Participants were prompted to reason and to solve the problems using the analogy they had just learned. Students specified their inferences and reasoning process by writing on a worksheet.
The participants’ responses to the near transfer tasks were analyzed for the number of correct structural relations indicated between the base and the target. Students received 1 point for each correct basic or complex relation. Since understanding of complex structural relations is based on correct understanding of basic structural similarities, the score for indicating correct complex structural relations was granted only when the students received full points on the basic ones. The possible maximum score for the specific heat and for the heat transfer problems were 5 and 9, respectively. Scores of both transfer tasks were added up to represent the students’ understanding of the given analogies.
Procedure
All participants completed two two-hour TWA units on specific heat and heat transfer. The students took a concept test before and after the TWA units to examine their understanding of and gain in the related concepts. The IMSR questionnaire was implemented before the instruction to assess their level of metacognition. At the completion of each TWA unit, a near transfer task was given on a worksheet to assess the participants’ understanding of the analogies.An interview was conducted to elicit whether and how the water analogy was used to solve the heat problems. The interviewer was a member of the pedagogical team, who had received training in the think-aloud technique by an educational qualitative researcher (the author). The case students from the high, moderate, and low metacognitive groups were invited to think aloud while solving similar heat problems using the instructed analogies. The purpose of utilizing the think-aloud technique was to elicit the participants’ spontaneous mental process with the least interference. The students were encouraged to externalize their mental representations using a marker to draw on a large white poster during the interview. If the case students paused for over 20 seconds, the interviewer would probe by asking, “What's going through your mind?” The process of drawing and oral reporting was video-taped for further analysis. Participants gave permission for video-taping. They were also assured that participation in the study was independent of their classroom assessment and that their responses would not be identified to their teacher. All interviews were conducted on a one-on-one basis after completion of the TWA units. Each interview was approximately 30 minutes in length. Participants’ verbalization was transcribed and later analyzed for their ability to reason with analogies and their spontaneous use of metacognitive skills. TWA units and all the research instruments, including interviews, were conducted in Mandarin.
Data analysis
To answer RQ1 regarding the effectiveness of the analogies for students with different levels of metacognition, gains of conceptual understanding were analyzed using paired sample t tests for each metacognitive group. We also ran a one-way ANCOVA using the level of metacognition as the independent variable, the score of concept pretest as a covariate, and the score for understanding of analogies as the dependent variable.To explore whether and to what extent prior knowledge and metacognition may influence understanding of analogies and the concept posttest (RQ2), Pearson's correlations were calculated among students’ scores of IMSR, concept pretest and posttest, and understanding of analogies. Two multiple linear regression analyses were conducted to further investigate the influence of the concept pretest and the IMSR score on understanding of the analogy and on the concept posttest, respectively.
To answer the third research question, the videos and protocols of the case students were first analyzed to judge their level of ability to reason with analogies and to count their spontaneous metacognitive activities when solving the transfer tasks. With the revealed characteristics of metacognition and of analogical reasoning in mind, we returned to the data of different metacognitive students to find specific examples that illustrate how content knowledge and metacognition influences process and outcomes of analogical reasoning.
Assessing metacognitive activities
Azevedo and colleagues’ coding scheme (Azevedo et al., 2004) was adapted and modified for analyzing what metacognitive activities may be observed in the analogical reasoning situation. Descriptions of potential metacognitive activities demonstrated during analogical reasoning are presented in Table 1. A metacognitive activity was counted if it was clearly present. The participants received no points if the activity was absent (Veenman and Spaans, 2005). The researchers analyzed and coded not only the presence of quality metacognitive activities, but also negative indicators. While the presence of metacognitive activities indicates learners’ capacities in regulating their process of analogical reasoning, the negative indicators signify constraints and difficulties in deploying metacognition when the tasks were too demanding. The negative indicators are denoted with (−) in Table 1.| Categories and codes | Descriptions of the metacognitive activities |
|---|---|
| Note: (−) denotes negative indicators. | |
| Planning | |
| Task analysis | Reading the completed problem statements. |
| Planning | Accessing and coordinating similarities between the base and the target. |
| Monitoring | |
| Monitoring knowledge adequacy | Assessing the adequacy of related scientific knowledge retrieved from long-term memory |
| Monitoring knowledge adequacy (−) | Misusing concepts or using incorrect concepts without being aware of doing so |
| Monitoring the mapping process | Overseeing the entire process when mapping features of the base to those of the target |
| Identifying conflicts | Assessing whether conflicts occur while mapping the base to the target |
| Identifying conflicts (−) | Being unaware that conflicts occurred during the mapping process when prompted |
| Strategy use | |
| Using alternative strategies | Using strategies (e.g., reasoning with content knowledge) other than the analogy to solve the problems. |
| Drawing or notetaking | Making notes and drawing diagrams to assist with the analogy-inferring process |
| Evaluation | |
| Evaluating | Assessing the quality of the mapping process and of the revised mental model |
| Evaluating (−) | Errors occurred in their conclusions and yet they did not verify or correct the flaws when prompted |
Two independent coders (the interviewer and the author) discussed and coded a verbal protocol from each high, moderate, and low metacognitive group together and then independently coded two additional protocols from each high, moderate, and low metacognitive group. The inter-rater agreement was 0.89. Discrepancies of the nine protocols were resolved through discussion. One of the two coders then coded the remaining 11 protocols. Analysis of the metacognitive activities was independent of the scoring of the participants’ ability to reason with analogies. Frequency of metacognitive activities for the specific heat and heat transfer problems were summarized and compared across the high, moderate, and low metacognitive groups. A case student from each group was selected to illustrate how metacognition which unfolded during analogy reasoning influenced the success in solving heat problems with analogies.
Ability to reason with analogies
We analyzed the participants’ verbal transcriptions to rank their ability to reason with analogies from level 0 to level 5, along a progression from not being able to indicate any similarities between the base and the target to successfully mapping the relational structure and being able to indicate where the analogy breaks down. We adapted and modified Mason's (1994) five levels and added level 0. The levels were the following:Level 0 – not able to indicate any similarities.
Level 1 – can indicate some basic elements of similarities but no clear relational structure.
Level 2 – can indicate several basic elements of similarities and some relational structure.
Level 3 – can indicate all basic elements and shows complete understanding of the relational structure.
Level 4 – shows complete understanding of the relational structure and indicates where the analogy breaks down.
The same two independent coders of metacognitive activities rated the ability to reason with analogies, with inter-rater agreement reaching 0.96. The discrepancy was resolved through discussion.
Results
Reponses to research questions
| Level of metacognition | n | Understanding of analogies M (SD) | n | Concept pretest M (SD) | n | Concept posttest M (SD) | t |
|---|---|---|---|---|---|---|---|
| Note: the maximum scores for understanding of analogies and of the concept pretest are 14 and 20, respectively.a p < 0.01. | |||||||
| High | 25 | 8.53 (4.35) | 26 | 12.12 (3.39) | 24 | 11.83 (4.06) | −0.29 |
| Moderate | 27 | 5.18 (4.46) | 28 | 7.82 (3.32) | 23 | 9.26 (3.44) | 1.44a |
| Low | 28 | 3.17 (2.96) | 25 | 7.70 (2.90) | 20 | 7.03 (3.09) | −0.67 |
Paired sample t tests were used to examine any increase in students’ mean scores of the concept tests. Only students in the moderate metacognitive group showed a significant increase in mean scores (t = 1.44, p < 0.01). Scores of the high and low metacognitive groups had similar scores from the pretest to the posttest. Learning with heat analogies only benefited conceptual understanding for the moderate metacognitive learners.
Multiple regression analyses were used to test if scores of the concept pretest and of IMSR significantly predicted the students’ understanding of analogies as well as the concept posttest, respectively. The results of the regression (in Table 4) indicated that the two predictors explained 29.7% of the variance for understanding of analogies (F(2, 98) = 22.10, p < 0.001). It was found that the concept pretest significantly predicted understanding of analogies (β = 0.45, p < 0.001), yet metacognition did not (β = 0.17, p = 0.09). The two predictors explained 40.3% of the variance for the concept posttest (F(2, 98) = 34.8, p < 0.001). The concept pretest significantly predicted the concept posttest (β = 0.53, p < 0.001), as did metacognition (β = 0.19, p < 0.05).
| Variables | B | SE (B) | β | p | F(2,98) | p | adj. R2 |
|---|---|---|---|---|---|---|---|
| Note:a dependent variable. | |||||||
| Understanding of analogiesa | |||||||
| Overall model | 22.10 | <0.001 | 0.297 | ||||
| (Constant) | −2.00 | 1.53 | 0.20 | ||||
| Concept pretest | 0.49 | 0.11 | 0.45 | <0.001 | |||
| IMSR | 0.03 | 0.02 | 0.17 | 0.09 | |||
| Concept posttesta | |||||||
| Overall model | 34.81 | <0.001 | 0.403 | ||||
| (Constant) | 1.18 | 1.27 | 0.35 | ||||
| Concept pretest | 0.52 | 0.09 | 0.53 | <0.001 | |||
| IMSR | 0.03 | 0.02 | 0.19 | <0.05 | |||
| High-meta (n = 7) | Moderate-meta (n = 7) | Low-meta (n = 6) | |
|---|---|---|---|
| M (SD) | M (SD) | M (SD) | |
| Note: high-, moderate-, and low-meta: learners of the high-, moderate-, and low-metacognitive groups, respectively. | |||
| Ability to reason with analogies | |||
| Level 3–4 | 5 | 0 | 0 |
| Level 2 | 2 | 3 | 0 |
| Level 1 | 0 | 4 | 2 |
| Level 0 | 0 | 0 | 4 |
| Numbers of correct matches | |||
| Correct basic matches (max = 8) | 7.71 (0.76) | 5.71 (2.63) | 0.83 (1.33) |
| Correct complex relational matches (max = 6) | 5.57 (0.79) | 2.14 (2.73) | 0.00 (0.00) |
| Correct indications for where the analogies break down (max = 6) | 1.14 (0.69) | 0.00 (0.00) | 0.00 (0.00) |
Metacognitive activities demonstrated by the high-, moderate- and low-metacognitive students are summarized in Table 6. Overall, there were fewer frequencies of identifying conflicts between the base and the target concepts and evaluating the outcomes. The unfolded metacognitive activities during analogical reasoning can be viewed as a spectrum. The high-metacognitive students, at one end, revealed more task analyses and planning while carefully monitoring adequacy of the activated related knowledge when reading the problem statements. Misuse of concepts was less likely to occur. They frequently and spontaneously drew the diagrams of analogy and marked or took notes while applying propositions on the analogies for inference. Careful monitoring was frequently observed and consistently appeared throughout the entire mapping and inferring process. Conflict or reasoning flaws were rarely identified, and if identified, they would make revisions or corresponding adjustments. Once a conclusion was drawn, they verified if the problem was solved by reevaluating their mapping process. Nevertheless, the evaluation frequencies were less than 50%. Although these students were relatively more capable of utilizing metacognitive skills in general, their ability of monitoring to identify reasoning flaws and for evaluation remained far from mature.
| Steps of analogical reasoning | Metacognitive codes | High-meta (n = 7) | Moderate-meta (n = 7) | Low-meta (n = 6) |
|---|---|---|---|---|
| Note: high-, moderate-, and low-meta: learners of the high-, moderate-, and low-metacognitive groups, respectively. | ||||
| Initial information processing | Task analysis | 13 | 9 | 1 |
| Planning | 10 | 5 | 0 | |
| Monitoring knowledge adequacy | 11 | 8 | 2 | |
| Monitoring knowledge adequacy (−) | 0 | 8 | 6 | |
| Mapping and inferring the base to the target | Monitoring the mapping process | 21 | 12 | 0 |
| Identifying conflicts | 5 | 6 | 1 | |
| Identifying conflicts (−) | 1 | 24 | 15 | |
| Drawing or notetaking | 10 | 4 | 1 | |
| Evaluating the outcome of mapping and drawing a conclusion | Evaluating | 6 | 5 | 1 |
| Evaluating (−) | 0 | 2 | 3 | |
When moving down to the other end of the spectrum, frequencies of the positive metacognitive strategies gradually decreased from the moderate- to the low-meta groups; meanwhile, frequencies of negative indicators increased. Although the moderate-metacognitive students were capable of utilizing some positive metacognitive moves across the steps of analogical reasoning, frequencies of negative metacognitive activities simultaneously increased and hindered the problem-solving outcome. The increasing negative indicators may be attributed to having difficulties managing their limited cognitive resources for the complex analogical inferences and for the demanding metacognitive process.
Metacognitive activities demonstrated by the low-metacognitive students were representative of adolescents who have yet to develop mature metacognitive ability. They read the problem statements but did not extract all crucial information to construct the corresponding relational structure of the analogy. They might occasionally monitor the accuracy of the activated knowledge, but rarely allocated efforts to overseeing the matching and reasoning process, nor did they evaluate the adequacy of the conclusion; therefore, errors or conflicts occurred frequently and yet were not recognized even when prompted. During the problem-solving process, drawing or notetaking were rarely used to facilitate analogical reasoning.
In the next sections, a case student of each of the high, moderate, and low metacognitive groups is used to depict the metacognitive characteristics of the dynamic analogy-inferring process and to illustrate how possessing metacognitive abilities influences the analogical-inferring process and yields different outcomes. Pseudonyms are used. Participants’ hand drawings were redrawn by the researcher for clarity. Characteristics synthesized from the high, moderate, and low metacognitive groups are also summarized in Table 7.
| Problem-solving stages | Characteristics | High-metacognitive learners | Moderate-metacognitive learners | Low-metacognitive learners |
|---|---|---|---|---|
| Problem representation | 1. Utilizing task analysis and planning to analyze the problem at hand | Yes | Yes | Yes |
| Analogy and mental model construction | 2. Spontaneously and appropriately drawing 2D diagrams and taking notes according to the information extracted from the problem statements | Yes | Yes | Yes, yet some errors appeared in the 2D diagrams but were left unidentified |
| 3. The annotated 2D diagrams are aligned with the internal model | Yes | Some contradictions occurred between the drawn analogy and the mental model | No | |
| Mapping and inferring the base to the target | 4. The analogy served as an externalized visualization tool to facilitate inferring to the mental model | Yes | No, mainly using the mental model to solve the heat problem | No, did not hold an internal representation but, instead, applied propositions to the 2D drawing for inferencing |
| 5. Automatically and fluently oversaw the entire analogy-target matching process | Yes, if a reasoning flaw occurred or when he/she was not sure about certain steps, he/she self-questioned or immediately double checked, and made adjustments accordingly | Yes, but did not examine the internal mental model against the externalized analogy; thus, the contradictions were neglected and were not reconciled | No, did not monitor knowledge adequacy nor the mapping and inferring process; thus, the contradictions were neglected and were not reconciled | |
| Evaluate the outcome of mapping and drawing a conclusion | 6. Seamlessly switched between the analogy and the system of heat concepts | Yes | No, the drawn analogy was not a functional thinking tool but an object to be revised based on the mental model | No, the drawn analogy was used for inferencing, but its correctness was not the object for evaluation. The flawed representation could not serve as a visual aid for evaluating the adequacy of the relational structure, nor for evaluating the mental model |
| 7. Reviewed whether the problem was adequately solved | Yes | No, did not reexamine the mapping process, nor reconfirm the conclusion even when prompted | No, did not reexamine the mapping process nor reconfirm the conclusion even when prompted |
Portraying metacognitive characteristics of the dynamic analogy-inferring process
| Think-aloud protocols | Metacognitive codes |
|---|---|
| Heidy: Object B was 30 °C, and this was the original water level [drew communicating vessels and added the water level, marked 30 and added shade on vessel B]. Object A was 80 °C [drew the water level on vessel A, marked 80 and added a shade, Figure 1a]. Object B became 40 °C, and this became 40 [added a new water level on vessel B and marked 40]. This side [vessel A] dropped to 40 [added a new water level on vessel A and marked 40, figure 1b]. | Task analysis |
|
Planning |
| Drawing and note-taking | |
| Heidy: Because object A was 80 °C and its temperature was higher than object B, so it [pointing to vessel A with a finger] would transfer the heat [to vessel B]. I did not know how much heat was transferred. Since they both increased 10, so object B has a greater specific heat. Is that right? | Monitoring the mapping process |
At the analogy/mental model construction stage, Heidy appropriately drew a 2D analogy of communicating vessels correspondingly and spontaneously noted on the diagram based on the information extracted from the problem statements to facilitate inference and reasoning (characteristic 2). She correctly coordinated several basic and complex relational similarities step-by-step, including matching the initial and final temperatures of objects A and B to that of the water levels of vessels A and B. When the interviewer asked her, “How do you know which one has a greater specific heat?” Heidy elaborated:
| Think-aloud protocols | Metacognitive codes |
|---|---|
| Heidy: Because its temperature [pointing to vessel A] is higher, it passed temperature to the one of 30 °C [vessel B], while itself losing heat and dropped its temperature to 40 °C. The amount of the heat lost will…let me think. The amount of the heat lost will be equal to the amount of heat gained? | Monitoring the mapping process |
| I: Are you asking me or asking yourself? | Monitoring knowledge adequacy |
| Heidy: I am asking myself. | |
| Heidy: [looking at the drawing and said] The loss equals the gain. The amount of [water] lost equals the amount of [water] gained. It [pointed to vessel A] was 80 °C and had a temperature change of 40 °C; whereas that [pointed to vessel B] increase merely 10 °C. So object B has a greater specific heat. | Evaluation |
On the basis of the drawn communicating vessels, Heidy related propositions to the analogy and inferred, saying, “Heat is transferred from the object of a higher temperature to the one of a lower temperature” and “The amount of heat lost equals the amount of heat gained.” Heidy was able to correctly label information of the problem statements to the diagram, apply propositions to it, and manipulate the mental model accordingly for reasoning to estimate the degrees of change to the water levels of the two vessels. She actively utilized the drawn analogy system as a visualization tool and formed a functional mental model (characteristic 4). When she explained what was going on in her mind, she simultaneously pointed to the corresponding elements of the drawn analogy, as if the mental model and the 2D diagram were aligned (characteristic 3).
Heidy also closely oversaw the entire analogy-target matching process. When she was not sure about certain reasoning steps, she paused and self-questioned. She immediately double checked her conclusion by reapplying the propositions to the analogy for inferences (characteristic 5). From there she derived a conclusion that the vessel with the greater loss of water level has a smaller diameter; whereas the vessel with a smaller gain of water level has a greater diameter. She then carried the conclusion derived from the analogy system over to the heat concepts and claimed: “Object B has a greater specific heat.” She stopped thinking aloud when she had successfully solved the heat problem using the analogy (characteristic 7).
When mapping the analogy to the context of the problem, Heidy was aware of some limitations of the analogy but could not articulate where the analogy broke down. Thus, she was ranked as level 4 in her ability to reason with analogies. Throughout the analogical-reasoning process, Heidy fluently and seamlessly switched between the analogy and the system of heat concepts (characteristic 6).
| Think-aloud protocols | Metacognitive codes |
|---|---|
| Mark: Specific heat of object A is 0.1. Specific heat of object B is 0.3, and the specific heat of B is greater than that of A. If those were water and containers, the diameter of cup A would be smaller and the diameter of cup B would be larger [drew two cups labeled A and B in figure 2a]. | Task analysis |
|
Planning the mapping |
| Mark: If object A is heated from 30 °C to 40 °C, it increases 10 degrees [drew two lines and marked 10 on cup A]. Object B is heated from 60 °C to 70 °C; it increases 10 degrees as well [drew two lines and marked 10 on cup B at a higher position]. | Drawing and note-taking |
| Mark: They should gain the same amount [of water]. [Paused for 30 seconds.] |
It was apparent that, similar to the high-metacognitive learners, Mark constructed a correct analogy based on the information extracted from the problem statements (characteristic 2). He also correctly matched basic similarities between the heat concept and the analogy, including mapping the specific heat of each object to the diameter of each cup as well as matching the objects’ initial temperature and the increase of that for objects A and B to the initial and the change of the water level for the two cups.
Next, Mark simultaneously held a mental model but related an inappropriate concept to it for reasoning. Thus, he derived an incorrect conclusion, saying: “They [the two objects] should gain the same amount [of heat].” When the interviewer asked him for clarification, Mark responded:
| Think-aloud protocols | Metacognitive codes |
|---|---|
| Mark: Because the specific heat of object A is smaller than that of object B, the temperature change of object A will be greater than that of object B. | Monitoring knowledge adequacy (−) |
| I: The problem asks you about which object would gain a greater amount of heat. | |
| Mark: Both objects have increased 10 [degrees]. But because A yields a greater change, so it needs more heat. | Identifying conflicts (−) |
| I: Your answer is that object A needs more heat. Let's use the amount of water increased to indicate the amount of heat gained. If you compare the amount of water in the two areas [pointing at the increment of water level for cup A and for cup B in the drawing], which area is greater? | |
| Mark: Cup A should be the greater one. | |
| I: Do you mean that what you have drawn here is incorrect? | |
| Mark: Yes. Cup A should have a greater increment! [He added another line to cup A above the initial two lines and shaded the area to indicate a greater amount of water (figure 2b).] | Drawing |
| I: The problem statements indicate that both objects increase 10 degrees. | |
| Mark: Object A increases 10 degrees. Since it [cup A] has a smaller diameter, the change of water level for this one will be greater. | Evaluating (−) |
Mark made a deduction with a preconception that he seemed to strongly hold, saying: “For two objects that have the same mass, temperature change for the one with a small specific heat is greater than that for the one with a large specific heat,” but he neglected the precondition “if both objects gained the same amount of heat” when using this concept. He did not realize that he used this concept in an inappropriate context, which in turn yielded a wrong conclusion.
Introducing the water analogies supplied Mark with a visualized thinking tool, since he understood and was capable of establishing all the basic relational similarities (level 3 for the ability to reason with analogies). When Mark utilized his partially completed analogies for problem solving, some features of his internal model differed from that of the external representation he drew. He chose to use his mental model, rather than utilizing the drawn analogy to continue with the remaining problem-solving steps (characteristic 4). Mark possessed two competing models, his mental model and the drawn analogy, but did not realize the need to evaluate the internal model against the externalized analogy. Despite the fact that Mark oversaw the process of mental model reasoning, he neglected and did not reconcile the contradictions which occurred between his mental model and the propositional structure of the drawn analogy (characteristic 3 and 5).
When the interviewer pointed out his reasoning flaws, Mark did not reexamine his mapping process using the analogy, nor did he verify his conclusion (characteristic 7). Mark revised the water level in the drawn analogy according to features of his mental model rather than evaluating his own mental model against the analogy. The drawing of the analogy was not a functional thinking tool but an object to be corrected according to the deducted outcome of the mental model (characteristic 6).
| Think-aloud protocols | Metacognitive codes |
|---|---|
| Lucy: Object A is heated from 30 °C to 40 °C. We need to map the temperature to the water level. So…, I would draw…30 °C to 40 °C [drew two cups with different diameters to represent object A, figure 3a, and drew a line as the water level on each cup and labeled 30 and 40, respectively]. The temperature of object B increases from 60 °C to 70 °C [drew two cups to represent object B but with a smaller diameter, figure 3b; drew a line as the water level on each cup and labeled them 60 and 70, respectively]. | Task analysis and planning |
|
Drawing and note-taking |
| Identifying conflicts (−) of drawing | |
| Lucy: Let me think. They both increase 10 °C, but their specific heat was different. [The specific heat of] object A is 0.1 cal g−1°C−1[added a note of the specific heat to figure 3a] and that of object B is 0.3 cal g−1°C−1[added a note of the specific heat to figure 3b]. | |
| Monitoring |
Lucy successfully matched the temperatures of the objects to the water levels of the cups, but failed to correctly represent the extent of specific heat to the size of the diameters. She mistakenly used a cup of a larger diameter to represent object A of a smaller specific heat, and vice versa. Once she had drawn the 2D analogies on the paper, she revisited the problem statements and reread the information for basic similarities but failed to identify the mistakes in her drawing (characteristic 3). She continued to think aloud:
| Think-aloud protocols | Metacognitive codes |
|---|---|
| Lucy: Mmm. The object with a greater specific heat should show a smaller increment? I think so. | Monitoring knowledge adequacy (−) |
| Lucy: Both objects have increased 10 degrees, so it [object B] received more heat than object A. Because [the specific heat of] object B is 0.3 cal g−1°C−1, so its temperature increases faster? Faster. [The specific heat of] object A is 0.1 cal g−1°C−1, so it would need more heat, and then its temperature would increase gradually. | Monitoring knowledge adequacy (−) |
| I: Please describe to me how you map the analogy to the target. | Evaluating (−) |
| Lucy: I have matched the degree of temperature to the level of water, and matched the amount of heat gained to the extent of specific heat. | Monitoring (−) |
Similar to Mark, Lucy recalled the same inappropriate proposition for reasoning, and yet did not assess if it was suitable for this problem condition. She held another misconception relating the fast or slow temperature rise to the specific heat. She made deductions by inferring the two improper propositions using the misrepresented drawings (characteristic 4), and, therefore, yielded an incorrect conclusion saying that “Object A is 0.1 cal g−1°C−1, so it would need more heat, and then its temperature would gradually increase.”
Similar to the moderate-metacognitive learners, Lucy used some improper ideas about heat but did not monitor the knowledge adequacy. She neither monitored her mapping nor inferring process; thus, the contradictions were neglected and were not reconciled (characteristic 5). When the interviewer prompted Lucy for clarification, she neither used the opportunity to evaluate her mapping process nor reexamined her drawings or conclusions (characteristic 7). In addition, she made another mistake saying that she would “match the amount of heat gained to the extent of specific heat.”
Lucy's case indicated that, when lacking monitoring and evaluating skills, obstacles may occur, including inferring with inappropriate ideas as well as making mistakes when drawing or mapping similarities between base and target. Although the 2D drawings were used for inferencing, the flawed representation could not serve as a visual aid for evaluating the adequacy of the relational structure between the base and the target, nor for evaluating the internal representations (characteristic 6).
To sum up, seven characteristics were synthesized from the cross-group comparisons to characterize the adolescents’ dynamic analogy-inferring process. It was observed that possessing adequate heat concepts allows the students to construct sufficient external and/or internal representations to infer and deduct with less effort. Although the learners across metacognitive groups were able to construct some kinds of drawings and/or mental models based on the problem conditions or their prior knowledge, and use them as tools of reasoning, only the high-metacognitive students were aware of the needs to evaluate the internal or the external model. Metacognitive abilities also showed substantial influences at every stage of solving heat problems with analogies. The moderate- and the low-metacognitive students with flawed monitoring may not recognize their inappropriate use of ideas or the contradictions in their internal and/or external models. They may not recognize the flaws of reasoning through evaluating their mapping and inferring process or of their conclusions and, therefore, missed opportunities to make corrections and to make adaptive moves accordingly.
Discussion
This study concerns whether an analogical learning approach such as TWA equally benefits adolescents with different levels of metacognition. To what extent and how prior knowledge and metacognition influence the process and outcomes of analogical reasoning were also explored using quantitative and verbal process data.With regard to the first research question, it was observed that teaching abstract heat concepts using structural analogies facilitates conceptual understanding to some extent, but showed a differential effect. Data of cross-group comparisons indicated that analogies benefited conceptual understanding of the moderate metacognitive learners, yet did not alter conceptual understanding of the high and low metacognitive cohorts. The interview data suggested that the absence of identifying conflicts and evaluating outcomes eliminates an additive effect for the high-metacognitive learners. Although both low- and moderate-metacognitive students received similar low scores on the concept pretest, the former did not take any advantage from the analogies. A possible explanation for the moderate-metacognitive learners was that, accompanying some metacognitive activities, their initial knowledge can provide the basis for forming deep relations of the analogy base and of the science concept system (Mozzer and Justi, 2012). The futile result of the low-metacognitive learners was attributed to a lack of metacognitive skills, and findings of the verbal process data support this explanation.
With regard to the second research question, results of the correlation analyses illustrate that both prior knowledge and metacognition are moderately associated with quality understanding of the analogies. These two factors contribute to learners’ gain of conceptual understanding as well. Prior knowledge significantly predicts the quality of analogy understanding and the post conceptual understanding, suggesting that the students’ quality of the constructed analogy as well as the outcomes of conceptual construction were dominated by their preconceived concepts. This finding supported Vosniadou and Skopeliti's (2019) results on elementary students’ learning and explaining the day/night cycle. Although the level of metacognition did not significantly predict understanding of analogies, they were significantly correlated. The regression analysis further showed that level of metacognition significantly predicts post conceptual understanding. Metacognition appears to have a unique explanatory power, in addition to prior knowledge, on post conceptual understanding. I consider the influence of the initial conceptions as a double-edged sword, affecting conceptual construction. At one end, the learners need the least amount of prior knowledge to comprehend and assemble an initial mental model of the analogy for further knowledge development and reconciliation; at the other end, flawed preconceptions impair reasoning if they are not identified through monitoring or are not confronted and resolved during model evaluation. The paradox of prior knowledge elucidating an influential but facilitative role of metacognition on conceptual construction was evident in the cross-case comparisons of the moderate- and the low-metacognitive cohorts. Previous studies mainly inspected the cognitive challenges of analogy-based instruction (Harrison and Treagust, 1993; Martin et al., 2019; Vosniadou and Skopeliti, 2019) or disclosed the importance of metacognitive awareness of the analogy (Mason, 1994). Findings of this study add new knowledge to the field through identifying two crucial factors, prior knowledge and metacognitive skills, and explaining their roles in the adolescents’ processes, and their impacts on outcomes of analogical reasoning. To the best of my knowledge, these results have not been reported elsewhere.
Regarding the third research question, frequencies of metacognitive strategies and the negative indicators across different metacognitive groups were compared, and excerpts of the case students were used to reveal characteristics of the dynamic analogical reasoning process and to explain the differential outcomes. The verbal process data disclosed that the low-metacognitive students suffered from inadequate planning and monitoring, and mismatched attributes of the drawn analogies to wrong problem conditions without being aware of the mistakes they made. They recalled partial basic relational matches, and this incomplete analogy could not support their problem solving. The metacognitive obstacle is also evident in the frequent negative indicators, even when cues were provided. They may have related an inappropriate idea to their mental model but did not realize the error due to not realizing the need for model evaluation. An analogy was often drawn but was later discarded rather than being used to evaluate their mental model. The insufficient metacognition affected not one but all analogical reasoning stages. They derived faulty conclusions or developed alternative concepts when no corresponding supports were provided.
Although holding partial prior knowledge, some moderate-metacognitive learners utilized task-analysis and monitoring to construct a functional mental model consisting of a basic relational structure. The introduced water analogies served as a visual aid supplementing them with a partially completed thinking tool. When inferring propositions with the mental model or the drawn analogy, they were able to monitor and resolve some of the conflicts while reasoning flaws occurred occasionally. Although they successfully deducted some new knowledge from the analogy and carried it over to solve the heat problem, it would be important to prompt the moderate metacognitive learners to evaluate their internal model against the externalized analogy and to reconcile the conflicts which arose between the two. Not realizing the essential need to evaluate and reconcile the flaws of their mental model limited the benefit of reasoning with analogies. The analogical approach such as TWA, therefore, helped the moderate-metacognitive students to some extent, but was incapable of raising their conceptual understanding to a much higher level.
It was surprising to me that the high-metacognitive students who also possessed relatively more prior knowledge and better understanding of the analogy did not have better post conceptions. The qualitative findings for the high-metacognitive students revealed that, although they were capable of metacognitively reasoning with analogies in general, using analogies was still an effortful process for these adolescents whose metacognitive skills are still under development. When they were prompted to use the analogies, they fluently switched between the drawn analogy and the targeted heat concepts. They were capable of using concepts to evaluate their conclusions of problem solving with analogies. However, fewer evaluation behaviors were observed. This was also evident in their being less capable of indicating where the analogies break down. Due to their insufficient monitoring and evaluation in particular, they may not consciously link the conclusions drawn from analogical reasoning back to examining the quality of their mental model of heat. This may explain why the TWA units did not show an additive effect on the high-metacognitive learners.
Another alternative explanation for the absence of conceptual gain was that these high-metacognitive students may possess their mental model which deviates from the given analogies. Although they could comprehend the given analogies, understanding them did not guarantee a spontaneous use of the analogies in the related tasks. Several high-metacognitive students were observed to first solve the near transfer problem utilizing related knowledge instead of reasoning with the analogies. They may not see the need to use analogies since they have gotten the correct answer. The introduced analogies served as an alternative approach to problem solving and, yet, it was not a fruitful reasoning tool. Niebert et al. (2012) reported some similar observations when reanalyzing previous literature for identifying why some analogies did not work. If differences existed between the taught analogies and their self-generated mental model or problem-solving approach were not reconciled, the given analogies may have hindered some learners from developing a cohesive mental model. This explanation was supported by the fact that the standard deviation of the concept posttest was substantially larger than that of the concept pretest of this group. Wilbers and Duit (2002) argued that analogical reasoning is not simply the discovery of correspondences between certain features of base and target, but being perceptive and interpreting the base and target systems to form an image-based mental model. Students would form their own hypothesis as a model with the analogy and go back and forth between the base and target to examine their model against the target phenomenon. My observations support Wilbers and Duit's theory and further illustrate that, when learning complex concept systems like heat, forming a functional mental model of the analogy is a crucial step in analogical reasoning. I argue that lacking mental model evaluation may diminish the advantage of using the drawing of the analogies as a visualization tool.
Thinking with analogies may not be as easy as it looks, especially for adolescents. Markovits and Doyon (2011) related better performance to possession of better reasoning ability. I argue that level of reasoning ability does not exclusively explain the performance of abstract analogical reasoning. Unlike Markovits and Doyon's (2011) and Cho et al. (2007) studies, which used pure matching psychological analogies, the heat concepts and the analogies used in this study comprise multiple relational similarities and involve an abstract and complex mechanism. Reasoning with the analogies and the concepts demands that learners generate and effectively use a functional mental model of the analogies as a thinking tool. The process data from the verbal protocols also echo previous findings of the metacognitive characteristics in mature mental modeling ability (Wang and Barrow, 2011).
A limitation of this study is that data were collected from learners who had received lectures on heat concepts before learning about heat analogies through the TWA model. Whether providing prior concepts would facilitate the effect of learning using the TWA model on students with different metacognition levels is worth exploring. Additionally, in this study, the TWA model was provided as a one-shot intervention. These young adolescents may need multiple practice opportunities to master the reasoning steps demonstrated in the TWA model. Future studies should reexamine the findings of this study and explore the learning trajectories of different metacognitive groups with multiple cycles of TWA.
Conclusions
This study examined the effectiveness of an analogical learning approach utilizing a mixed method approach, and reported a differentiated effect on metacognition. This paper summarizes that both prior knowledge and metacognition are crucial prerequisites, affecting middle school students’ analogical understanding and their capacity to use analogies as a thinking tool for conceptual construction or problem solving. It is also observed that about one third of the participating adolescents had not yet developed sufficient metacognitive skills, particularly monitoring and evaluating, and failed to use and to reason with the analogies. The pedagogical value of using analogies to promote conceptual understanding will be undermined if the developmental aspect of metacognition is not taken into account.Findings of this study contribute to the field through providing empirical evidence showing that metacognition should be considered when explaining the mechanism and predicting student outcomes, and the extent to which the effectiveness of an analogical learning approach may be impaired due to learners lacking metacognition. I suggest that metacognitive ability should be one of the prerequisites for learning and teaching abstract concepts with analogies. Identifying the level of capacity and/or the ratio for the learners of lower metacognition through a metacognitive survey, as well as planning explicit metacognitive prompts along with teaching implementation may increase the efficiency of the analogical learning approach.
The metacognitive characteristics during the analogy-inferring process deserve much more research attention as they may provide fresh insights into how to support analogical reasoning at appropriate times while taking capacity of metacognition into consideration. The in-depth analysis of the present study delineates detailed metacognitive characteristics of the adolescents’ analogical reasoning process. Comparisons across students of different metacognitive levels suggest different directions for improving analogical teaching to better suit their differentiated needs. It is clear that one design of the TWA model does not fit all.
For the high metacognitive learners, eliciting mental models they have held and guiding them to evaluate both a previously held mental model and an alternative one (e.g., the given analogy) for reconciliation may facilitate construction of a more coherent understanding. Providing opportunities for them to generate, share, and peer- or self-evaluate their analogies may further enhance students’ metacognition (Haglund and Jeppsson, 2014). Providing them with more challenging or far transfer tasks to create some fruitful experiences in applying analogies for learning and problem-solving may also motivate these learners to internalize analogies as a useful cognitive tool. To support the moderate metacognitive students, prompting for monitoring accuracy of the activated knowledge and overseeing steps of inferences will be helpful. Explicitly guiding the moderate metacognitive learners to evaluate the quality of their mental model and of the drawn analogies as well as to reconcile the apparent contradictions may further raise their conceptual understanding. For the low metacognitive learners, supporting the metacognitive process may not be sufficient; additional supports such as supplementing related conceptions are needed to lift their understanding of the analogies before the analogies can be used as a learning or thinking tool. Various metacognitive supports have been used to facilitate inquiry (e.g., Wang, 2015b; Zhang et al., 2015), or problem-solving (e.g., Gonzalez and Paoloni, 2015), and some substantial learning enhancements were reported. More scaffolding studies might be devoted to supporting analogical learning approaches and to examining the effectiveness of different cognitive and/or metacognitive scaffolding designs.
It also appears to us that an effective learning scientific concept system through analogies demands the learners to form a functional mental model as a thinking tool. For those learners who possess relatively lower mental modeling ability, explicitly introducing the drawing of analogies as a visualization tool and explaining its value for supporting the monitoring inference process and for mental model evaluation is suitable. Eye movement evidence from a recent study suggests that providing a pictorial analogy, in comparison to giving a textual one, benefits mapping and integration between attributes in the analogy base and the target concepts (Chen and She, 2020). Using visualizations (e.g., animations) to represent the analogy, and highlighting the mapping between the elements of the base and target with spatial cues also sounds promising (Richland et al., 2007) to support mental model construction and reduce the burdens on working memory during mental model reasoning.
Data from the verbal protocols were valuable to help understand how the adolescents reasoned with the instructed analogies and why the instruction did not work as expected. However, coding the deployed metacognitive strategies was laborious and could only illustrate metacognitive processes retrospectively. Analyzing trace data in a digital learning environment to explore and validate some indicators of metacognition may provide solutions for timely diagnosis (please see the review studies, for example Yen et al., 2018). With assistance from the blooming technology of artificial intelligence, exploring models of learners using learning analytic approaches may provide new insights for developing adaptive cognitive and metacognitive supports for the analogical learning approaches.
Conflicts of interest
There are no conflicts to declare.Acknowledgements
This work was supported by the National Science and Technology Council, Taiwan under Grant MOST106-2628-S-011-001-MY3 and MOST108-2511-H-011-008-MY4.References
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