Conceptual Transformation and Cognitive Processes in Origami Paper

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Journal of Problem Solving

Folding Thora Tenbrink1 and Holly A. Taylor2

1Bangor University, 2Tufts University

Research on problem solving typically does not address tasks that involve following detailed and/or illustrated step-by-step instructions. Such tasks are not seen as cognitively challeng- ing problems to be solved. In this paper, we challenge this assumption by analyzing verbal protocols collected during an Origami folding task. Participants verbalised thoughts well beyond reading or reformulating task instructions, or commenting on actions. In particular, they compared the task status to pictures in the instruction, evaluated the progress so far, re- ferred to previous experience, expressed problems and confusions, andcruciallyadded complex thoughts and ideas about the current instructional step. The last two categories highlight the fact that participants conceptualised this spatial task as a problem to be solved, and used creativity to achieve this aim. Procedurally, the verbalisations reflect a typical order of steps: readingreformulatingreconceptualisingevaluating. During reconceptualisa- tion, the creative range of spatial concepts represented in language highlights the complex mental operations involved when transferring the two-dimensional representation into the real world. We discuss the implications of our findings in terms of problem solving as a mul- tilayered process involving diverse types of cognitive effort, consider parallels to known con- ceptual challenges involved in interpreting spatial descriptions, and reflect on the benefit of reconceptualisation for cognitive processes.

Correspondence: Correspondence concerning this article should be addressed to Thora Tenbrink, Bangor University, Bangor, Gwynedd, LL57 2DG, UK, or via email to [email protected]

Acknowledgments: This research was generously supported by the DFG (SFB/TR 8 Spatial Cognition, project I6-[NavTalk]), the Hanse Institute for Advanced Studies, and the SILC Spa- tial Intelligence and Learning Center. We are also grateful for the support of our very reliable student assistants.

Keywords: problem solving, instructions, text in- terpretation, cognitive processes, verbal data analysis, reconceptualization

Origami is the well-known Japanese art of creating 3-D objects by folding paper in a particular manner and order. Often, this is achieved by following written instructions sup- ported by pictures, for example, from a book or webpage. How do people interpret abstract action descriptions to cre- ate a concrete object resembling what is shown in a picture? Anyone who has ever struggled with the challenge of folding Origami, or used any kind of manual to assemble an object or comprehend a newly acquired technical device, will be familiar with potential misinterpretations and conceptual traps. Learning a new procedure based on pictures and text may represent a problem requiring considerable mental effort to solve.

Some cognitive complexity arises when conceptually transfering from an abstract medium toward concrete actions. Moreover, language and depictions, even together, as communication media are notoriously underspecified, leaving more room for interpretation than one might desire (Carston, 2002; Hegarty & Just, 1993; Van Deemter & Peters, 1996). In general, if intended actions need instruc- tions, then there is a problem to solve, and instructions can support the task. Even with instructions, subtle deci- sions and individual conceptualisations engaged during problem solving mean that the outcome may not always be successful.

Research in problem solving in general has mainly focused on identifying creative problem solving, for instance, in order to propose adequate sets of step-by-step instructions (e.g., Anderson, Douglass, & Qin, 2004). However, the act of following instructions has not received extensive research attention. Since instructions guide people along a conceptual path, the need for creativity and/or individual strategies might seem limited.

In this paper, we challenge this assumption by treating a complex instruction-based task, namely Origami folding, as a problem needing a solution via a range of conceptual steps. We start by reviewing the role of operations and cog- nitive strategies in the problem solving literature, and then consider insights from research examining text and picture comprehension, particularly in the spatial domain. Then we report our study in which participants folded an Origami object (a flower stem) while thinking aloud. Our analysis first addresses the extent to which participants verbalisa- tions reflect creative problem solving processes beyond read- ing or reformulating and expressing task execution, and then focuses on the types of conceptual steps represented in the verbalisations. We highlight how participants iteratively interpret and reconceptualise each folding step until satis- fied with the produced object. Then we focus on the recon- ceptualisation process as a main component of the complex problem solving of Origami.

http://dx.doi.org/10.7771/1932-6246.1154

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T. Tenbrink & H. A. Taylor Conceptual Transformation and Cognitive Processes

Mental processes in probleM solving tasks

Following the seminal approach by Newell and Simon (1972), human problem solving means conceptually break- ing down a problem into separate and manageable steps or operations. In his representative account of the state of the art, Anderson (2004, p. 245) characterises problem solving as goal-directed behavior that often involves setting sub- goals to enable the application of operators. Here, the term operator refers to an action that will transform the problem state into another problem state. The solution of the overall problem is a sequence of these known operators, and the challenge is to find some possible sequence of operators in the problem space that leads from the start state to the goal state (Anderson (2004, p. 245). Accordingly, much of the problem solving literature addresses how people identify problems and operators to solve them, and how these oper- ators are ordered into a sequence of actions so as to reach a suitable solution, mediated by expertise (Chi, Glaser, & Rees, 1982). This is reflected in the relevant literature such as Newell and Simon (1972), and more recently in many contri- butions in the Journal of Problem Solvingcompare discus- sions in Carruthers and Stege (2013) and Fischer, Greiff, and Funke (2012), and in introductory reviews such as Anderson (2004), which focus on the complex high-level operations that need to be mentally organised, based on the range of possible actions and problem states.

It is in this area that think-aloud protocols as data sources have been most successful (Ericsson & Simon, 1984). This is because the identification and ordering of operators hap- pens on a high cognitive level; solution steps to a complex problem are verbalisable to a great extent, as they are con- sciously accessible and can be adequately represented in lan- guage. A vast amount of problem solving research drawing on verbalisation data confirms this (e.g., Chi, Bassok, Lewis, Reimann, & Glaser, 1989; Gero & McNeill, 1998; Kuipers, Moskowitz, & Kassirer, 1988; Ritter & Larkin, 1994; Van Gog et al., 2005), in spite of issues about the verbalisability of specific kinds of problems such as those involving read- ing (Afflerbach & Johnston, 1984) or instantaneous insights (Schooler, Ohlsson, & Brooks, 1993).

One way of representing a solution path is by way of a process model (Fischer, Greiff, & Funke, 2012; Myers, Gluck, Gunzelmann, & Krusmark, 2010), for instance, using a cog- nitive architecture such as ACT-R (e.g., Gugerty & Rodes, 2007). Such models can be used as a basis for producing efficient and cognitively supportive instructions (Anderson et al., 2004). The emphasis on creating supportive instruc- tions strongly suggests that not all instructions can be fol- lowed in a cognitively straightforward manner. As such, our focus in the present paper lies in the opposite direction understanding how humans deal with existing instructions

for a complex task. This differs from the kinds of problems addressed in problem solving research typically (or perhaps always), that is, ones for which the problem solvers do not have access to instructions or manuals.

Instructions reduce a given problem considerably, by offering a breakdown of the original problem into separate solution steps (operations) delineating a predetermined solution path. What remains is a more fine-grained cognitive challenge of moving from a declarative representation and a slow interpretation of the task to a smooth, rapid proce- dural execution of the task (Anderson et al., 2004, p. 1046). Highlighting this challenge, Anderson, Kline, and Lewis (1977) as well as Ball (2004) proposed cognitive models for language processing in general. However, to our knowledge, the interpretation of instructions (in terms of guided actions) has not been addressed directly as a problem-solving task for which cognitive processes can be modeled.

A possible reason for this is that cognitive processes in fol- lowing instructions are not expected to be accessible via exist- ing measures such as behavioural performance outcomes or verbalisation protocols. Transforming a given declarative representation into action may conceivably involve entirely low-level cognitive processes, since no further identifica- tion of problem solving steps is required. If that is the case, humans who follow instructions to solve a problem should not have much to verbalise beyond reading and perhaps reformulating the instructions. However, anyone who has tried to follow complex instructions would likely attest that problem solving opportunities arise in this context.

In this paper we address this assumption, and ask if fol- lowing instructions for a complex and cognitively challeng- ing task such as Origami folding may elicit thought processes that can, to some extent, emerge in task-concurrent ver- balisations. In order to see what kinds of challenges may be involved in following instructions, we now turn to research on the interpretation of textual and visual representations.

interpretation of text, pictures, and instructions

Reading a text activates a number of mental processes toward comprehension. According to a bottom-up model of discourse comprehension proposed by Kintsch (1988), spreading activation of concepts based on linguistic cues leads to the construction of a mental representation of the text. Zwaan and Radvansky (1998) further suggested that readers construct a coherent situation model that integrates every newly read clause with the information accumulated so far. This process involves complex interactions of long- term memory retrieval and short-term memory activation. Furthermore, intricate grounding processes with respect to temporal and spatial domains are necessary for the situation model to be consistent. Readers may develop a mental image

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(Kosslyn, 1980) of the textual content, which may amount to a simulation of the situation (Barsalou, 1999), representing details such as spatial structures in the visual field (Bergen, Lindsay, Matlock, & Narayanan, 2007).

Common to all discourse comprehension approaches is the insight that the original text formulation serves as a trig- ger for accessing conceptual frames, logical and common- sense based inferences, and knowledge elaborations that are not directly expressed in the text. Readers quickly identify a messages gist and typically cannot remember the original wording after a very short time (Bransford & Franks, 1972; Sachs, 1967). While readers quickly derive a suitable context- dependent interpretation from their mental model of the situation related through a text, more complex inferences require further cognitive effort and are not as readily incor- porated (Garrod, 1985). This effect is similar to problem solving in general in that intuitive and effortless reasoning is replaced by meta-cognition and higher-level conscious pro- cesses (only) when particular challenges or problems occur (Alter, Oppenheimer, Epley, & Eyre, 2007).

Pictorial information can support text interpretation. For instance, Bransford and Johnson (1972) found that people better recalled a text illustrated by a picture that provided essential context. In terms of comprehension, picture and diagram interpretation proceeds similarly to reading com- prehension in that the gist and conceptual frame are iden- tified quickly, guiding attention towards relevant aspects to serve a particular purpose (Franconeri et al., 2012; Henderson, 2003). The process is facilitated by the fact that depictions can resemble the mental abstractions necessary for remembering and visualising relationships (Tversky, 2011). When combining pictures and text, comprehen- sion can be hampered or supported by particular features of spatial integration, visual complexity, relevance, and the like (Florax & Ploetzner, 2010). Altogether, the comprehen- sion of descriptions and depictions draws on similar but not identical principles, which in the ideal case work together to allow for a thorough understanding (Schnotz, 2002; Schnotz, Baadte, Johnson, & Mengelkamp, 2012).

Since different contexts and contents call for different rep- resentations, identifying an ideal form remains a challenge in every case. Ultimately, no representation is complete or directly accessible to the human mind; intricate comprehen- sion processes are required to gain an adequate interpreta- tion. Different modes of representation affect the distribu- tion of cognitive load in systematic ways, depending on the represented content and its adequacy relative to the recipi- ents level of expertise (Cook, 2006). For instance, the extent to which complete and detailed information is necessary or beneficial for a reader depends on their background. With a high level of previous knowledge to draw on, readers benefit from the challenge posed by less complete representations

that call for deeper processing. Texts that leave room for the readers inferences support a more thorough understanding due to the increased activation of interpretive processes and linking to ones knowledge base (McNamara, Kintsch, Butler Songer, & Kintsch, 1996). Relatedly, different types of learn- ing materials are useful for different purposes (Belenky & Schalk, 2014); while initial learning is enhanced by grounding in background information, transfer is easier when abstract- ing across contexts (Gick & Holyoak, 1980). However, learn- ers differ in the extent to which they can generalise from examples. Crucially for our purposes, learners who success- fully generalised provided explanations for themselves while reading, displaying their deep understanding, more than those who failed to generalise (Chi et al., 1989).

Comprehending instructions and manuals involves these general interpretation processes (Franck, 2004) with their complex interplay of context, represented information, background knowledge, and expertise, plus the challenges of resolving references to relevant objects (Wei, Pfeiffer, Eikmeyer, & Rickheit, 2006), and transforming the infor- mation towards a practical purposeactions to be under- taken in the real world (Daniel & Tversky, 2012). Paralleling the more general findings on text comprehension, Marcus, Cooper, and Sweller (1996) argue that the addition of dia- grams can reduce cognitive load, making instructions easier to follow. Mediated by their ability and expertise in the sub- ject area, readers construct a mental model by incremen- tally combining local with global information (Hegarty & Just, 1993). This is supported by situation-based affordances provided through experiential (non-propositional, non- abstract) background knowledge (Glenberg & Robertson, 1999). Real-world objects and displays offer visual feedback cues supporting action directly, reducing memory load and instantaneously suggesting possible actions (Larkin, 1989).

The processes and requirements involved with follow- ing instructions have been quite thoroughly researched in the context of route descriptions. For instance, Lovelace, Hegarty, and Montello (1999) proposed elements that make up good route directions. Completeness, mention of seg- ments and turns, and particular types of landmarks contrib- uted to route description quality ratings. Additionally, Allen (2000) showed that preserving the natural order and focus- ing on action information at choice points is important, as is taking the addressees knowledge into account (this also affects the route planned, cf. Hlscher, Tenbrink, & Wiener, 2011). While visual information such as maps is just as useful for wayfinding as verbal route descriptions (Meilinger & Knauff, 2008), Lee and Tversky (2005) suggest that adding visual landmark information supports comprehension, in line with the insight that visual imagery can promote reason- ing, especially in spatial settings (Knauff, Mulack, Kassubek, Salih, & Greenlee, 2002; Tversky, 2011).

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Particular challenges arise where spatial descriptions are underspecified or ambiguous, as is frequently found. The analysis of dialogues provides hints about the mental activity engaged in such cases. For instance, Tenbrink, Coventry, and Andonova (2008) found that addressees frequently suggested reformulations of, or additions to, spatial descriptions. Such reconceptualisations arise because of complex inference pro- cesses involved in spatial settings, as specified by Krause, Reyle, and Schiehlen (2001). Muller and Prvot (2009) iden- tified types of feedback addressees provided as a function of the information given by the speaker, enabling the dia- logue partners to negotiate spatial representation challenges. Overall, the dialogic patterns reflect the need to integrate spatial descriptions into a coherent spatial mental model. Together, these results point to a high amount of creativity and cognitive processing on several levels (direct and effort- less, as well as mediated and meta-cognitive) when following verbal descriptions of space. In other words, they point to the need for problem solving when following instructions.

following origaMi instructions: a probleM-solving task?

For tasks like Origami folding, few studies have explored mental processes involved in interpreting illustrated instruc- tions. In face-to-face instruction of Origami, learners rely intensely on the instructors gestures and actions to support the learning process (Furuyama, 2000). Because Origami can enhance spatial thought processes, training can lead to student gains when implemented into school curricula (Higginson & Colgan, 2001; Robichaux & Rodrigue, 2003; Taylor & Hutton, 2013). Algorithms for automatically inter- preting graphical depictions of the folding process high- light the conceptual challenges and routines involved (e.g., Shimanuki, Kato, & Watanabe, 2003). While Sabbah (1985) provided a connectionist model for recognising line draw- ings of Origami objects, to our knowledge, the problem solv- ing stages or conceptual steps of following Origami instruc- tions have not been addressed.

Our aim in this paper is to provide insights about higher- level cognitive processes involved with interpreting illus- trated instructions for folding a complex 3-D object. Rather than attempting to capture the finer processes involved in reading and picture comprehension, we focus on procedures and patterns reflected in think-aloud protocols, collected while following Origami instructions, and address patterns of variability in relation to individual and situation specific differences. Based on the research summarised above, we contrast alternative outcomes of our study:

If instructions already spell out the main problem solving components typically found in verbalisable reports and thus accessible on a high level of cogni- tion, and if there is no actual problem left to solve, then

participants should simply follow instructions step by step, and carry out the task as outlined. Verbalisations would then consist of reading and slightly reformulat- ing or adapting the instructions during the reading comprehension process, and commenting on how the given task is put into action.

If following instructions is a problem to solve in itself, this should be expressed in the think-aloud protocols in terms of creative thinking or additional ideas that are not expressed in the instructions. Furthermore, participants might express problems in carrying out the task, and verbalise considerations as to how they might be solved.

Whether or not following Origami instructions can be seen as a problem solving task might differ depending on various factors. We expect variation based on participants Origami experience, and we expect instruction steps to differ in terms of difficulty. These factors should be reflected in the verbal protocols, revealing how the conceptual challenge of following instructions is met according to the diverse factors involved, and what types or parts of instructions are particu- larly challenging.

Beyond identifying the existence of the relevant verbali- sation types and indicators of the phenomena just outlined, we ask (qualitatively) how these thoughts are expressed in language, and what kinds of problem solving strategies and relevant verbalised concepts may occur, as the previous lit- erature does not provide a sufficient basis for making direct predictions in this regard.

In response to the assumption that cognitive processes involved in interpreting instructions may be too low- level to be captured in think-aloud protocols, we employ Cognitive Discourse Analysis (CODA; Tenbrink, 2015) to address systematic features of the data. CODA was devel- oped to capture deeper insights into cognitive processes, including those speakers might not be able to consciously verbalise, but nevertheless emerge in systematic patterns of verbalisations. The methodology extends the seminal approach to verbal protocol analysis by Ericsson and Simon (1984) by taking a closer look at the features of the language used to express thoughts and cognitive processes captured in a verbal protocol. The rationale behind this approach is that speakers make specific choices out of the more gen- eral network of lexicogrammatical options at their disposal. Such choices are meaningful in ways that speakers may not be aware of; for instance, they reflect a particular concep- tual perspective and granularity level that appears natural to the speaker, but is in no way predetermined by the task. In this paper, the main CODA-based contribution concerns speakers choices of spatial terms that were not directly part of the verbal instruction given to them, expressing their conceptual creativity while doing the task.

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origaMi study

procedure

This study was reviewed and approved by the Tufts University Institutional Review Board. Twenty-four Tufts University undergraduates (14 male, 10 female), all native English speak- ers, participated in this study after having been fully informed about the procedures. They were trained to think aloud (see Appendix A), following suggestions by Ericsson and Simon (1984). Then their first task was to fold the Origami tulip, first the stem and then the blossom, following instructions provided on a computer screen. During these tasks they thought aloud while following the instructions (Appendix B). Participants could move through the instructions at their own pace, scrolling back and forth as they saw fit. The experi- menter gave no advice except in the case of being stuck fol- lowing a mistake. In such cases the experimenter provided a simple hint to reconsider the previous folding step. In cases of inactivity or silence, participants were encouraged to go on trying and to keep thinking aloud. Also, the experimenter provided positive feedback. A pilot test showed that, due to the considerable challenge of this task, such encouragement was vital. In spite of these adjustments, which were necessary to ensure a smooth task procedure and an actual outcome of each participants efforts, it was made clear that there was to be no interaction about the task. The think-aloud expectation was transparent to the participants, who accordingly did not address the experimenter while verbalising their thoughts.

The participants second task was to determine, in a series of trials, which of three Origami objects matched the crease patterns of an unfolded object. Finally, they completed three spatial abilities tests: the redrawn Vandenberg and Kuse mental rotation (Peters et al., 1995), mental paper folding (Shepard & Feng, 1972), and the Santa Barbara Solids Test (Cohen & Hegarty, 2012). We focus here on the cognitive processes reflected in verbalisations while folding the stem, without action coding (see Taylor & Tenbrink, 2013, for a dif- ferent analysis of the same data set). The instruction for this task (represented in Appendix C) showed 13 folding steps as pictures associated with a brief textual instruction (e.g., Put the paper in front of you, with the point toward the top).

results

Participants took between 3:05 and 10:07 minutes to fold the flower stem (mean = 04:54; standard deviation = 1:36). Eleven of the 24 participants received no hints by the experimenter, and the most hints given were four (mean = 1.16; standard deviation = 1.34). While folding, participants varied consid- erably with respect to how much they verbalised, producing between 113 and 1,738 words each (mean = 402.38; standard deviation = 337.75).

Folding success was assessed by independent ratings (7-point Likert scale) of the photographed stems. A sepa- rate group of 25 Tufts undergraduate students, who were not informed about the major goals of this study, rated each pho- tograph. They rated success by comparing the photographs to the Origami instruction picture (see Appendix B), indicat- ing the perceived similarity. Ratings ranged from 1.28 to 5.48 (mean = 3.97; standard deviation = 0.90). In other words, Origami folding results were judged as quite varied, cover- ing almost the full range from failure to considerable suc- cess, although none of the resulting stems were unanimously considered entirely successful.

As would be expected, success ratings were marginally negatively correlated with the number of hints (r = -0.37, n = 24, p = .073). More interestingly, success was reliably neg- atively correlated with the number of words read (r = -0.44, n = 24, p < .05) rather than produced in more creative ways (see more detailed analysis of verbalisations below). That is, the more successful people were, the less they read instruc- tions aloud. Apart from that, success was not related to any of our analysis criteria (including time to fold the stem), and will therefore not be further addressed as a determining factor in the analysis of the problem solving process as expressed in the verbalisations. Verbosity (i.e., the total number of words produced by a participant), for instance, was not related to folding success (r = 0.081, n = 24, p>.05), although it cor- related with time to fold the stem (r = .674, n = 24, p < .01). No effects of gender emerged for any of our analysis criteria.

content categories and verbal creativit y

All think-aloud data produced while folding the stem were transcribed and segmented into units containing a single thought or piece of information, such as um, alright so Im just trying to make sure its as close to the fold as possible. Each unit was annotated in relation to the specific folding step (cf. Appendix C) to which it belonged.

As our first analysis goal, we explored the extent to which the verbalisations exhibited creative thought, as opposed to directly following the instructions. To assess this, we associ- ated the content of units, or partial units if appropriate, with one of the following operationalised categories:

Reading task description: parts that are read aloud or repeated from the written instruction about the rel- evant folding step.

Reformulating description without new thoughts: con- veying the same content as the instruction in a differ- ent syntactic or lexical form.

Additional ideas about a step: introducing new ideas in describing this step. These were further subcat- egorised into the following (not mutually exclusive) types:

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orientation of the paper to be folded object quality: trying to get a nice result alignment of the folds or edges with respect to

each other crease quality: making nice and sharp folds comparison to instruction: trying to match partici-

pants own result with the instruction (including the picture)

within-step repetition: doing the same action twice (e.g., for left and right sides) within a folding step

across-step repetition: the current step repeats a previous one (i.e., is described as identical)

across-step difference: the current step is compared to a previous one, identifying a difference

spatial description: patterns in the current status of the object

adding semantics: associating meaning with some part(s) of the current status of the object

other. Evaluation: the speaker evaluates their own work or prog-

ress so far in general terms, beyond the current folding step. References to background knowledge: for example, not-

ing patterns based on experience. Expression of problems: considering how to do this

step, expressions of matching problems, and so on. Task communication: the participant seeks confir-

mation about the procedure, comments on general aspects, refers to action (including looking at the pic- tures), explicitly starts the next step, or evaluates the instructions (as in that makes sense).

Other: anything ambiguous or not fitting into the pre- vious categories.

As discussed above, we predicted that Reading task description, Reformulating description without new thoughts, and Task communication categories would reflect simple text interpretation and relevant action. All other categories go

beyond this basic instruction-following process and were identified post hoc. They therefore represent a qualitative analysis of the types of thoughts participants verbalised.

Annotations were complete (all verbalisations were cat- egorised) and (by our definition) mutually exclusive (i.e., no partial unit was associated with more than one main category, although the subcategories within the category Additional ideas about a step were not mutually exclusive). Annotation was achieved through an iterative multi-annotator coding process, ensuring optimised operationalisation of annota- tion definitions through repetitive in-depth scrutiny of the data, as well as consistency in coding by revisiting each data set multiple times as required. Following preliminary annota- tion by two independent student assistants, the process was only declared complete after both authors agreed with every instance of the annotations suggested by the students, follow- ing extended discussions of individual cases where needed. This iterative process was considered more adequate to the nature of this particular data set than a quantitative assessment of an inter-coder reliability measure (which is more typical).

Verbalisations coded as Additional ideas and Expressions of problems in particular reveal the conceptual issues asso- ciated with the Origami task (see Table 1 for examples of Additional ideas). Twelve of the 24 participants produced spatial descriptions such as theres a straight line across here at the top, making it more narrow, touching the middle, I have a triangle, that one is horizontal, and so on, reveal- ing that they identified spatial patterns within the folding process and resultant objects. This reflects a reconceptuali- sation of the original Origami instruction. Altogether there were 50 spatial descriptions of this kind.

Descriptions like these involved spatial vocabulary not included in a particular steps original instruction. To opera- tionalise and verify this intuitive, content-based impression, we identified all instances of spatial terms used in relation to an instructional step, but not included in the relevant

Table 1. Examples (taken from various individuals) for reconceptualisations categorised as Additional ideas

Instruction step no.

Instruction Utterance Subcategory

2 Fold the left corner over to the right one, and firmly straighten out the fold.

so that I get a triangle Spatial description

5 Fold the bottom edges onto the midline. this looks like a crane Adding semantics

5 Fold the bottom edges onto the midline. just take one corner and its gonna go down a little bit

Spatial description

8 Fold the lower tip onto the upper one. it looks like I have to match the height

alignment; comparison to instruction

11 Fold it back, and then diagonally to the left. try and make it symmetrical

alignment

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instruction (referred to as new spatial terms for short). We found a reliable correlation of new spatial term use with the spatial description subcategory within the Additional ideas category (r = 0.57, n = 24, p < .01; see also Taylor & Tenbrink, 2013). Th us, participants read the instruction and associated diff erent spatial (and related) concepts with the action described, and expressed this in new spatial terms. Th is provides insight into their cognitive fl exibility in deal- ing with this task. Figure 1 shows the number of occurrence of the 25 most frequently used new spatial terms, along with how many participants used each term. Th e most fre- quent term used in this way was side; 17 participants used it 104 times in situations where it was not part of the instruc- tion. Th e remaining terms used, along with their frequency of occurrence, can be found in Appendix D. Th is impres- sively wide range of spatial terms highlights the creativity of thought employed by our participants.

As further illustrated in Figure 2, participants varied considerably in the extent to which they used new spatial terms throughout their verbalisations; counts ranged from 1 to 130 (mean = 21.38, median = 15). Th e production of spatial terms by individuals was (expectedly) correlated with

the overall number of words produced (r = 0.88, n = 24, p < .01) as well as with other subcategories of Additional ideas)clearly, the more verbose participants were, the more creative they became in their (spatial) language use. Also, use of new spatial terms was correlated with previous experience, as we report in more detail below.

Importantly, participants were not necessarily repetitive in their reformulations; each instruction step contained its own challenges and could therefore lead to new reconceptualisa- tions and (as a consequence) diff erent term use. To illustrate this, a closer look at the highest scoring dataset (130 new spa- tial terms) reveals that this participant produced 15 diff erent spatial nouns: angle, baselines, corner, crease, direction, end, edge, fl ap, line, position, shape, side, symmetry, three dimen- sion, way. In addition there were 7 diff erent verbs: bisect, end up, go, intersect, match up, switch, turn, and 30 other spatial terms: along, around, at, back, center, close, diagonal, down, even, fl at, halfway, here, in, in half, into, lopsided, on, open, opposed, out, outside, over, overlap, straight, symmetrical, three dimensional, to, toward, up, vertical. So, in total, this participant produced 52 diff erent spatial terms, each about three times on average, to total 130. Of these terms, only 3

Figure 1. Frequency of new spatial terms used, along with the number of individuals who used the term at least once in a creative way.

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nouns and 10 other spatial terms occurred anywhere in the original instructions. Th is participant also produced the second highest amount of utterances categorised as spa- tial description (namely seven), including further interest- ing references to concepts such as a kite like shape, valley vs. mountain folds, small fl aps on the side, and rationalisations such as that little crease, that little corner, that obtuse angle right there, was meant to intersect with the centre line.

Obviously, this particular participant was both highly ver- bal and outstandingly creative in range of spatial vocabulary. Other participants did show a similar kind of fl exibility, albeit with lower frequencies of new spatial terms (cf. Figure 2). Although the types of spatial descriptions produced by the participants varied considerably, these examples provide a representative impression of verbalisations when consider- ing spatial instructions. Th e details and frequencies may dif- fer, but the procedure appears to be comparable across those participants who produced spatial descriptions and new spatial terms.

Verbalisations of problems were typically less explicit; participants said things like that doesnt seem right or I was a little confused of this, without specifying further. More explicit statements in this category include I wonder if that was still supposed to be folded somehow, does the angle sort of matter?, thats a little lopsided, and I think is

just opening it up, right? Th us, participants wondered aloud (without interacting with the experimenter) about the pre- cise action to be carried out or the degree of precision to be pursued, were unsatisfi ed with the product, or tried to interpret the formulation used in the instructions. Oft en enough, this included some degree of spatial term use as well (i.e., verbalisation of spatial thinking).

verbalisation patterns

Aft er having identifi ed the content and signifi cance of the verbalisation categories as just outlined, the next step was to address patterns of recurring thoughts or processes as refl ected in the think-aloud data. For this purpose, we ana- lyzed the frequency and distribution of the categories (ignor- ing the Other category, which was rarely used and contained unintelligible parts that did not lend themselves to counting) in relation to folding steps and participants, and determined the order of category mention within each step.

Th e category Reading was used most oft en (232 times, aver- aging 0.74 per participant and step), and Background knowl- edge least oft en (28 times, averaging 0.09). Th e other catego- ries fell in between (Reformulating: 154 (0.49); Additional ideas: 165 (0.53); Evaluation: 49 (0.16); Problems: 105 (0.34); Task communication: 191 (0.61)). Participants used most

Figure 2. Number of new spatial terms used by individual participants, sorted according to frequency.

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categories frequently, though not necessarily for each step. All but two participants read parts of the instructions ver- batim, all participants reformulated something at least once, and all but two formulated additional ideas about at least one step. Seventeen participants evaluated their own work, 20 expressed problems, and all except one communicated about the task. Only references to background knowledge were less frequent, occurring with only 8 participants (although 22 of 24 reported some previous Origami experience; see further details below). Figure 3 illustrates the frequency with which each participant used a category.

Th e distribution of the categories across the folding steps (i.e., associated to the steps shown in Appendix C) was infor- mative. Readings and reformulations were fairly evenly dis- tributed across the folding steps (ranging between 8 and 18 mentions by diff erent participants in each of the 13 steps), indicating that the content of a folding step did not aff ect (in any obvious way) whether an instruction was read verbatim, reformulated, or just comprehended without verbalising. Th e other categories were not distributed equally. For instance, the instruction for folding step 4 was Turn around 180 degrees, which never induced any further ideas, nor evalu- ations or references to background knowledge, and only one expression of problems. In contrast, folding step 6 was Fold the bottom edges onto the midline once again, which led 15

(of the 24) participants to formulate additional ideas such as so the same thing (across-step repetition), the same with the left (within-step repetition), or so in half again (spa- tial description). Th e other categories were represented more frequently in other steps. Figure 4 visualises the distribution of category usage across folding steps.

To shed further light on diff erences between individual folding steps in terms of behaviourally refl ected cogni- tive complexity, we calculated the mean number of words produced as well as the time needed for each folding step. Divided by 10 to matc h scale, the mean number of words is imposed within Figure 4 (dashed line) to reveal a clear visual eff ect: the number of words used along with a specifi c folding step generally matches the pattern of number of participants producing verbalisation types for the same step. Th e number of words peaks at folding step 3 (mean = 72.04 words pro- duced) followed by folding step 10 (mean = 50.71); these are the steps for which most participants explicitly mentioned problems. Th e lowest number of words were produced along with folding steps 4 (mean = 11.46) and 7 (mean = 16.33). Both of these triggered few problems or additional ideas, and the like, as shown in Figure 4. Th e folding times needed for these steps matched this pattern, with a relatively high aver- age fold time of 47 seconds for step 3 followed by 30 seconds for step 10. In contrast, the simpler folding step 4 required

Figure 3. Stacked frequency of category usage across participants.

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only 10 seconds on average, and step 7 took 13 seconds. Th is converging evidence points to systematically diff erent levels of cognitive complexity as refl ected by various behavioural measures, leading to diff erences in the verbalised problem solving processes.

In addition to diff erences between steps, there were also diff erences between individuals. For instance, three partici- pants read verbatim parts of every step, while two never read. Based on the ratio of reading to reformulating, we identifi ed 10 readers, 5 reformulators, and 9 participants who were neu- tral in this respect (ratio ranging between 0.7 and 1.83 or, in one case, producing only one reformulation and no read- ings). Th is indicates individual approaches to dealing with the original formulation and reverbalisation. Furthermore, one participant produced additional ideas for as many as 11 of the 13 steps, while most others did this far less frequently (overall mean = 5.17). Also, 8 participants never explicitly referred to the picture, while the others did this at least once and up to four times throughout the folding task (overall mean = 1.54).

Given this diversity in verbalising concepts and ideas rel- evant to the folding process, we looked for systematic pat- terns based on the order in which these ideas were men- tioned, if they occurred at all within a folding step. While the above analysis merely established whether or not a category

appeared in a folding step, a closer look revealed that they did not appear in random order, in spite of a high diver- sity of combinatorial possibilities. Consider the example in Table 2. Aft er a discourse marker alright marking the start of the task, the participant reads step 1, with a slight gram- matical reformulation at its end (me rather than you). Th is is followed by an action comment (task communication): Im doing that. Th e phrase next thing I need to is again a comment on carrying out the task, introducing the reading of the next instruction. In the next line, so its lined up expresses the additional concept of alignment, not explicitly given in the instruction. Th is is followed by a slight reformulation of the next part of the instruction, straighten out the fold. From here, the participant proceeds to the next step, which starts by reading the instruction and communicating about the task. Th e phrase so I guess that means indicates a certain con- cern about the correct interpretation, followed by a reformu- lation of the task (to the center rather than midline), without expressing a diff erent idea. Th e next three utterances refl ect the participants conceptual development moving away from the original instruction; none of these are directly expressed in the instruction. While the instruction only uses a plural form (edges), the action itself needs to be carried out twice, which is expressed by I gotta do it with the other side (coded as within-step repetition).

Figure 4. Amount of participants using a category in each folding step (113), and mean number of words used for each step (divided by 10 to match scale).

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In contrast, the Table 3 example reflects an inability to move away from the original instruction. The task instruction is repeatedly read, interspersed by expressions of confusion.

A close scrutiny of the linguistic data led to the identifica- tion of a basic recurring pattern as follows:

readingreformulatingreconceptualisingevaluating

Participants started out by reading a folding step, (possi- bly) followed by reformulations. Conceptually moving away from the original wording, they would then (in more fortu- nate cases than the one shown in Table 3) verbalise additional ideas about this folding step, and then possibly evaluate their product. Although past experience could be verbalised at any point in the process, it typically appeared only after evalua- tion (if any). Although folding actions are not reflected di- rectly in the verbal data and were not annotated in this study, participants sometimes referred to action (e.g., which I did here), and this was categorised as task communication. This emerged as a free-floating category, appearing anywhere in

the process (including leading over to next step). This reflects how participants were continuously acting on their object (as expected), following the instructions as soon as they were able to interpret them, based on comprehension and recon- ceptualisation processes. Problems led to disruptions of this process, with participants either unable to move away from the instruction at all as in the above example, or starting again by reading, or anywhere else within the overall process.

To verify this intuition, we identified for all utterances made by participants in relation to individual folding steps whether or not they were consistent with the pattern read- ingreformulatingreconceptualisingevaluating, treating expression of problem as a reset to start, and ignoring task communication and other. Steps could be skipped, since think-aloud protocols can never be expected to represent all thought processes exhaustively). A paired t-test (compar- ing consistent vs. inconsistent patterns within each folding step) showed that the verbalisations within steps were con- sistent with this overall process scheme significantly more

Table 2. Think aloud example, moving from reading to reconceptualising

Step Category Utterance

1 read, reformulate alright. so put the paper in front of you with one corner pointing towards me 1 task communication Im doing that 2 task communication, read next thing I need to fold the left corner over to the right one 2 task communication, additional

idea, reformulate so Im folding that so its lined up and then straightening out the fold

3 task communication, read so its telling me to open the paper again 3 task communication, read so I do that and fold the bottom edges towards the midline 3 express problem, reformulate so I guess that means fold this part to the center here 3 additional idea and Im trying to do that so its as even as possible 3 additional idea now I gotta do it with the other side 3 additional idea and crease that part there

Table 3. Think aloud example involving expression of problems

Step Category Utterance 3 read uh, open the paper again 3 read, reformulate fold the bottom edges towards the middle 3 express problem okay, um, how should I do that? 3 read uh, open the paper and fold the bottom edges toward the midline 3 express problem but how did it turn out like that? 3 express problem thats kinda confusing; also kind of annoying 3 other so, do do do 3 reformulate fold open

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often than they were inconsistent (p < .001). However, even within-step verbalisations that did not precisely fit this pat- tern seemed close enough to support the overall scheme, as in the Table 2 example (so Im folding that so its lined up and then straightening out the fold): Here, the process of reading was interrupted as a partial step triggered some thoughts (here: alignment of the folds, as a type of additional idea). Nevertheless, the overall scheme ranging from mere read- ing via slightly reformulating to reconceptualising and eval- uating (and possibly reminiscing previous experiences) was generally followed, in a flexible way.

experience

Since previous work on problem solving consistently showed effects of background knowledge and previous experience, affecting not only overall performance but also problem solving strategies and pathways, we finally addressed how reported Origami experience related to verbalisation in the given task. Of our 24 participants, when asked about their background, 19 reported having some previous experience with Origami, 3 a lot, and 2 none. In spite of the somewhat uneven distribution in this regard, we were able to detect some interesting associations using Pearsons correlation. Experience was positively correlated with overall verbos- ity, that is, number of words produced (r = 0.48, n = 24, p < .05); this corresponded to a higher number of units (r = 0.37, n = 24, p < .05) as well as a higher number of words per unit (r = 0.48, n = 24, p < .05). Looking at content, it turned out that the verbalisations were more creative with more experi- ence; experience was marginally negatively correlated with the number of words read (r = -0.35, n = 24, p = .091), but positively with the number of words expressing additional ideas (r = 0.38, n = 24, p = .067). More experienced Origami users carefully compared their work with the instruction often (r = 0.56, n = 24, p < .01), and they used more new spatial terms to verbalise their thoughts (r = 0.48, n = 24, p < .05). Also, they reliably used more words to communicate about the task (r = 0.56, n = 24, p < .01), and they (expect- edly) talked more about past experience (r = 0.58, n = 24, p < .01). Along these lines, previous experience affected how people distributed their verbalisations, without fundamen- tally changing the overall pattern (as there were no outliers with respect to any of our analysis categories).

discussion

Most problem solving research focuses on unaided tasks, reflecting an implicit assumption that instructions guide cognitive processes sufficiently to leave few or no problems to be solved. Generally, the extant literature suggests that step-by-step instructions lead rather than trigger trains of

thought; complete instructions should leave little room for creativity. Accordingly, think-aloud protocols when fol- lowing such instructions should not contain much content beyond a reflection of the guidance the instructions provide. However, because findings on reading and visual compre- hension point to a more complex process when interpret- ing action instructions, our study set out to challenge this assumption. We used a task that followed established tradi- tions in the Japanese art of Origami folding. It used step-by- step instructions that were complete in the sense of guiding the reader through the whole process from a blank piece of paper to the completed product, without omitting any actions. Indeed, none of our participants mentioned a need for further instructions; any problems that were expressed had to do with the actions involved within an instruction step. The guidance was complete at the overall tasks high- est level. Nevertheless, it left room for interpretation, high- lighting a different layer of problem solving processes. Our results, drawn from verbalisations uttered throughout the task, point to distinctcognitive processes involved in under- standing and completing the instructions.

Notably, the level of problem solving we see here does not correspond, as might have been assumed, to an automated subconscious level of task execution. Instead, our results sug- gest interpretation processes that are consciously accessible and verbalisable to a high extent, even where the main solu- tion steps are available in both verbal and pictorial format.

Our results speak to a range of findings across domains such as general problem solving, instruction interpretation, spatial reasoning, discourse comprehension, educational practices, and verbalisation of thought. We will address each of these in turn.

Research on problem solving, in general, typically aims to identify the main solution steps (sub-goals) and cognitive strategies employed commonly by humans solving complex problems (following Newell & Simon, 1972). Once these have been determined, for example based on verbal proto- cols (Ericsson & Simon, 1984), they can be represented in terms of computational models and cognitive architectures (Anderson, 2004; Gugerty & Rodes, 2007; Pizlo et al., 2006). Beyond high-level cognitive operators, such models also include more fine-grained representations of how the action steps are accomplished. However, typically these are not expressed in terms of problem solving processes as such.

Our research suggests a different picture. Apparently, specifying the main solution steps in a complete set of step- by-step instructions does not eliminate the need for problem solving. Instead, the main solution steps provide a coarse level of problem solving, but leave room for more fine-grained challenges. Our verbal data highlight the cognitive complex- ity and creativity involved in this process, going well beyond the immediate and automatic interpretation of clearly laid out

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instructions. In our data, verbalisations coded as Additional ideas signaled how the participants went beyond the original instruction, that is, the surface of the formulation. This was a frequent category in our data, used in about half of the folding steps by each participant; with two exceptions, all participants did this at least once. Therefore, the reconceptualisation of the original instruction by adding related ideas played a major role within the procedural pattern detected in our data.

However, such reconceptualisation was not engaged within every instruction step to the same extent. Very sim- ple instructions (e.g., turn paper around) could be directly transformed to action and did not appear to trigger further thoughts. With increasing task complexity, participants took consistently more time to accomplish and words to verbal- ise an instruction step. These reconceptualisations highlight the active consideration of how to appropriately follow the instructions. Thus, rather than simply following the instruc- tions verbatim and activating automated processes, par- ticipants actively engaged in thought processes, going well beyond the step-by-step guidance given to them. In line with previous literature on cognitive complexity (Alter et al., 2007; Garrod, 1985), this effect was mediated by the level of challenge posed by any individual action step. More complex instructions led to more verbalised thoughts and inferences, as well as increased expression of problems.

The literature pointing to the existence of complex inter- pretation processes and inferences involved in reading and pictorial comprehension (Hegarty & Just, 1993; Kosslyn, 1980; Zwaan & Radvansky, 1998) corroborates our results. These processes take the reader well beyond a messages sur- face representation (Bransford & Franks, 1972; Franck, 2004) and trigger cognitive effort at levels similar to other problem solving processes (Alter et al., 2007; Garrod, 1985). Some of these processes include selective attention (Franconeri et al., 2012) guided by relevance (Florax & Ploetzner, 2010) and background knowledge (Glenberg & Robertson, 1999). In fact, the necessity of activating inference processes may be beneficial for deep understanding (McNamara et al., 1996). However, coming from research unrelated to problem solv- ing, this work does not reveal any particular sequence of interpretation processes. Our analysis of thoughts verbal- ised during Origami paper folding sheds more light on these issues in the form of recurring patterns in the language data. Participants gradually moved away from the original wording toward a reconceptualisation of an instructional step. Starting out by reading parts of the instructions verbatim, they quickly turned to minor reformulations, then added additional ideas, before evaluating their product. To our knowledge, our approach provides the first operationalisation for the system- atic analysis of verbalisations related to an instruction inter- pretation process (including reading and picture comprehen- sion and transfer toward real world action).

Task reconceptualisation, as reflected in our annotation category of Additional ideas, may be viewed as a verbal rep- resentation of a cognitive process essential to Origami paper foldingnamely, transferring the abstract textual content (supported by a 2-D picture) to concrete action. To do this, people need to understand the instruction and (creatively) interpret (or, indeed, reconceptualise) it in relation to their own productgoing well beyond a direct or (nearly) auto- matic transfer from readily laid out operations that leave no room for problem solving. In some cases, they formulate specific additional ideas that are particularly clear in their own minds. In other cases, the interpretation and reconcep- tualisation processes may not be verbalised even if they do occur on some, perhaps less consciously accessible, level. Generally, people do not explicitly formulate the transfer process when thinking aloud (e.g., by saying I am now try- ing to transfer this instruction to the piece of paper in my hand)this would be easily accessible through content analysis (Krippendorff, 2004). Instead, the present study gained insights into participants thoughts through a close analysis of the language data. This analysis revealed insights beyond the content of the explicit verbalisations by identify- ing utterance types relative to the instruction, and by analys- ing spatial term use. This approach is in line with Cognitive Discourse Analysis (CODA, Tenbrink, 2015), with its main goal of interpreting language use in relation to thought. The present analysis highlighted thought processes dur- ing instruction interpretation, and led to further insights about the role of verbalisation. As suggested by Taylor and Tenbrink (2013), access to relevant vocabulary for an idea can be helpful when implementing that idea on subsequent tasks. Another striking aspect of the reconceptualisation, as observed here, is the fact that many participants actually volunteered revised spatial descriptions, associating various concepts and spatial relationships. This suggests that partici- pants actively sought to thoroughly understand the spatial situation, and expressed their own representation beyond the one provided.

The idea that people transform and reconceptualise a description in relation to the real world situation at hand resonates with findings in other areas of spatial discourse. According to Tenbrink et al. (2008), recipients of spatial instructions frequently provide insightful ideas that comple- ment the verbal instruction given to them, filling in con- ceptual gaps using available perceptual information. More generally, interpreting spatial language inevitably depends on intricate inference processes that may involve drawing on background knowledge and judgments about the speaker providing the description (Gagnon et al., 2012; Gondorf, Bergmann, & Tenbrink, 2012). In this light, adding ones own ideas while interpreting an instruction seems only natural, since a direct mapping of linguistic descriptions to

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real-world objects is rarely possible. In route instructions, for instance, the main route is laid out in the descriptions, but there is still potential to go wrong in the real world for many reasons, including miscommunication, memory fail- ure, reference resolution problems, underspecification, false information, and perspective and orientation problems. In short, following instructions in a spatial setting introduces a range of problems to solve, necessitating creative and active thought processes such as those reflected in our think-aloud protocols. To our knowledge, our study is the first to outline these phenomena in detail based on language data analysis.

Another frequent and everyday observation relevant to our findings is that, upon receiving a complex explanation in a face-to-face situation, it may be perceived as insuffi- cient to simply acknowledge the information by nodding or responding OK. Such feedback may be due to (or attrib- uted to) politeness rather than true understanding. Arguably, the more complex an instruction or explanation is, the more reconceptualisation will be needed to demonstrate deeper understanding. This is particularly pertinent in school edu- cation. Teachers actively elicit summaries and reformulations on a regular basis; as written text types, they are integral parts of teaching approaches. Being able to summarise and refor- mulate is thus a skill to be learned because it can demonstrate comprehension that goes beyond the input itself (e.g., Chi, De Leeuw, Chiu, & Lavancher, 1994).

While reconceptualising and reformulating upon request by a teacher may be a cognitive challenge, it may also sup- port the learning process. Verbalisation and access to asso- ciated terminology can support cognition, as demonstrated by research in two directions. First, various studies have indicated an enhancement of problem solving processes via verbalisations while doing the task. Fairly uncontro- versially, providing good and elaborate explanations while studying examples correlates with success in problem solv- ing (Chi et al., 1989); being asked for explanations and back- ground information supports depth of thought and therefore enhances the problem solving process (Bielaczyc, Pirolli, & Brown, 1995; Neuman & Schwarz, 1998). However, whether or not simply thinking aloudrather than providing expla- nationsserves to support cognitive processes appears to be dependent on the problem solving task and the way the instruction is formulated (Ericsson & Simon, 1984; Fox, Ericsson, & Best, 2011; Schooler et al., 1993).

The present study was designed to address the nature of verbalisable cognitive processes rather than their effects on performance (with performance measures only affecting minor parts of our analysis); a control group without ver- balisation would not have led to any insights in this regard. However, based on the insights gained here, an informative next study could explore whether thinking aloud helps par- ticipants accomplish the Origami tasks successfully. In our

study, we did not find correlations between success in the Origami paper folding task and reconceptualisations in the verbal data. However, as discussed in Taylor and Tenbrink (2013), use of new spatial terms was correlated with another measure, namely performance in the crease-pattern match- ing task given to participants after the folding task. This indi- cates that creative verbalisation can relate to performance in spatial tasks in somewhat intricate ways. The ability to verbalise spatial relations may enhance spatial thinking in a general sense, even if it does not directly affect the currently verbalised task.

The second research direction relevant to the cognitive effects of verbalisation addresses the relationship between language and thought, as critically inspired by Whorf (1941). In particular, evidence is accumulating that inner speech and labeling systematically support cognition at various lev- els, ranging from perception to categorisation and memory (Lupyan, 2012). Linguistic formulation of perceived catego- ries appears to support ongoing conceptualisations by cap- turing fleeting impressions in a temporary way, supported further by previous linguistic experience and knowledge. It appears that fairly similar processes may be at work in our Origami task, in spite of the fact that labels exist, through the instructions. Our participants made heavy use of these existing formulations by reading aloud and modifying them only slightly at first, but then moved on to new conceptuali- sations and associating linguistic labels with them. Clearly, since they were not asked to formulate anything in partic- ular (just think aloud), they chose descriptions relevant for them (i.e., they found labels and highlighted spatial relation- ships as they became obvious in their minds). Thus, while the research reported here was not designed to test whether reformulations and reconceptualisations actually support the problem solving process, our empirical findings do show that this cognitive process is an integral part of a cognitive task that is considerably more complex than the labeling of a newly encountered object.

conclusion

Our study provides insights about the cognitive processes involved in following Origami paper folding instructions, challenging the assumption that following instructions leads to straightforward action execution. Instead, problem solving can be viewed as a multilayered processnot only in terms of high-level (conscious) and low-level (automated) processes, but also in terms of main problem solving steps (provided in complete instructions) and intermediate problems needing to be solved to accomplish these main steps. This level involves both high-level and low-level cognitive processes and is there- fore in part explicitly verbalisable, and in part reflected in the linguistic features and patterns of the verbalised data.

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Our results suggest a recurring pattern of gradually mov- ing away from the original instruction by reading, reformu- lating, adding ideas and associated concepts, and evaluating the folding effort (with a possible addition of background experience). This pattern highlights the necessary conceptual path involved in interpreting an abstract instruction in such a way as to act appropriately in the real world. Specifically, it supports the theory that reconceptualisationbe it through explicit verbalisations, or only silently in the mindis an important and supportive part of this comprehension pro- cess. Further research is required to explore the extent to which explicit verbalisation introducing new formulations can support problem solving processes.

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appendix a

Instructions given to the participant to explain and train how to think aloud, following Ericsson and Simon (1984):

I will, in a minute, give you a task to perform. While you do that, I will ask you to THINK ALOUD during the whole procedure of the task. We are interested in what you think about as you perform the task. Therefore I want you to say EVERYTHING you are thinking from start to finish of the task. Dont try to plan out what you say and dont talk to ME. Just act as if you were speaking to yourself. It is most important that you keep talking, even though you wont get any response or feedback. Do you understand what I want you to do? If I do not hear you talking for a bit, I will remind you that you are to say aloud what you are thinking.

Good, now we will begin with some practice problems. First, I want you to multiply two numbers in your head and speak out loud what you are thinking as you get an answer.

What is the result of multiplying 24 x 36?

Good. Any questions? — Heres your next practice problem:

How many windows are there in a house you used to live infor example your parents house?

appendix b

Instruction for Task 1Origami paper folding

Okay, we are now ready to start with your first task. Here [show participant the instruction on the screen] is an instruction for an Origami paper fold- ing task. The aim is to create an Origami paper tulip made of two pieces of paper, following these instructions. Start with the STEM, which is easier. Dont forget to THINK ALOUD while doing so.

Take as long as you like. I wont interrupt you, and I wont judge what you have done. We are interested in your thoughts while you do the paper folding.

Okay? You can start right away. When youre done with the stem, proceed directly with the bloom.

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4. Turn around 180 degrees

5. Fold the bottom edges onto the midline.

6. Fold the bottom edges onto the midline once again.

7. Turn the paper over so that the back side is up.

8. Fold the lower tip onto the upper one.

appendix c

Illustrated Origami instructions for the flower stem

Instructions are identical to those used in the study except the numbering, which was added here for purposes of refer- encing in this paper.

This is how you can make the stem Youll need:

Square green paper

Instructions for the stem 1. Put the paper

in front of you, with one corner point- ing towards you.

2. Fold the left corner over to the right one, and firmly straighten out the fold.

3. Open the paper again. Fold the bot- tom edges toward the midline.

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T. Tenbrink & H. A. Taylor Conceptual Transformation and Cognitive Processes

9. Fold the left half over the right one. Fold it back again.

10. Turn the paper over. Fold the over- lying layer of the upper tip diagonally to the right (kind of like in the picture)

11. Fold it back, and then diagonally to the left.

12. Fold the tip back. Fold the upper tip toward the inside along the fold lines.

13. Push the left and the right half of the stem together.

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T. Tenbrink & H. A. Taylor Conceptual Transformation and Cognitive Processes

appendix d

Remaining new spatial terms (complementing Figure 1) sorted according to the absolute number of occurrence.

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