Kindergarten Children’s Learning of Computational Thinking With the “Sorting Like a Computer” Learning Unit

ABSTRACT

Computational thinking (CT) activities are increasingly being integrated into early childhood schools. We focus on studying children’s learning using an “unplugged” (non-computational) learning unit that considers a teacher’s knowledge and classroom space and affords seamless adaptation into the classroom given the objects used in the unit and activities that are reminiscent of classic class activities and games. The gap in research that we address is the focus on unplugged activities, which are less common. A learning unit with card games was developed, focusing on two fundamental sorting algorithms: Linear Sort and Category Sort. Sixteen kindergarten children participated in the study. Their CT skills were assessed using a pretest-intervention-posttest single group research design. An increase in CT skills was observed from an intermediate to a sophisticated level; the number of attempts to completion decreased and the average number of attributes the children could sort with increased. Two children’s interactions with the activities were analyzed in depth and compared. It was found that two concepts related to algorithms had to be learned separately and sequentially: multiple repeating actions and a stopping rule for repeating actions. With advanced challenges that involved multiple attributes and more than one sorting algorithm, children needed significant support.

KEYWORDS:

• Computational thinking
• computer science unplugged
• early childhood education
• kindergarten
• tabletop games

Computational thinking (CT) has recently entered the limelight in education at all levels, including preschool and kindergarten education, as a fundamental competency that is to be learned in school (Wing, 2006). CT can be described as practices and thinking skills that are related to fundamental ideas in computer science but can be used elsewhere to solve problems. For example, planning a sequence of actions to organize a closet can be compared to constructing a computer algorithm using a series of simple steps to be performed sequentially (e.g., take items out of the closet, then inspect each item), and some of these steps repeat several times until completion (an item is inspected and then categorized, followed by the next item, until the closet is empty). Another example is the CT concept of abstraction, where during a task, one can focus on only a certain feature of objects such as the size of nails when sorting them into useful groupings.

As the integration of CT activities and learning environments into early childhood education gradually becomes widespread, a central issue needs to be addressed: How can we consider children’s developing capabilities, teachers’ knowledge, and classroom spaces to allow such an integration on a wide scale? Most of the research into developing CT in early childhood focuses on the use of advanced technologies such as coding (from the earlier Logo, Clements & Gullo, 1984; to the more recent ScratchJr., Flannery et al., 2013) and in programming robots (from the earlier programming of a physical turtle, Papert, 1993; to more recent KIBO, Bers et al., 2022; and Talis et al., 2010). Our view is that these technologies are important to help children become acquainted and comfortable with today’s adaptive and responsive computational and physical tools and environments. However, scaling up and reaching many kindergarten classrooms is hindered by the fact that, at present and in the foreseeable future, most teachers are less familiar with such technologies and lack the confidence, and sometimes the means, to implement these ideas (Nikolopoulou & Gialamas, 2015; Parette et al., 2010). In this article, we approach the issue by developing and researching learning with the games in the “Sorting Like a Computer” learning unit, an “unplugged” learning environment that does not involve computational tools. These games attempt to align with children’s developmental resources and teachers’ prior experience and budding knowledge of computation. We focus on studying children’s learning using an “unplugged” learning unit that considers a teacher’s knowledge and classroom space and affords seamless adaptation into the classroom given the objects used in the unit and the activities that are reminiscent of classic class activities and games. While research into developing CT in early childhood education is expanding, these studies address unplugged activities only to a very small extent. It is this gap we wish to address.

In this research, children’s initial and developing CT skills were analyzed. The study makes two main contributions. One involves the design of appropriate tool for learning CT in the earlier years. The other is the analysis method that we have developed for detailing young children’s computational problem-solving skills, which enables observing the smaller and larger changes in the child’s understanding that is taking place.

This article provides a literature review on the relevant issues, a rich description of the learning environment used in the study, and the methodology. Then, results are presented through two perspectives – the overall group learning and contrasting case studies into the process of learning – and then discussed. The goal of this study is to explore young children’s strategies and learning regarding two sorting algorithms and their ability to select the more appropriate one for different conditions.

Literature review

The review focuses on computational thinking, its application in early childhood settings, and related developmental aspects.

Computational thinking

Computational thinking (CT) has been conceptualized in a variety of ways. Wing (2006), in her seminal paper that helped launch much of the recent educational work related to CT, defined it as solving problems by drawing upon concepts that are fundamental to computer science. She presented CT as a combination of four thinking skills – abstraction, decomposition, pattern recognition, and forming algorithms. She explicitly distinguished these skills from the actual practices of programming, describing them as basic forms of thinking in computer science that can be applied outside the realm of computers to other problems. Abstraction relates to the notion and tools that allow focusing on the important components of a problem and filtering out of aspects and components that are irrelevant to the problem at hand. Decomposition is the process of dividing a problem into smaller components that are easier to understand and solve. Pattern recognition involves finding similarities between problems, allowing a better understanding of the problem and ability to transfer solutions from one problem to another. Forming algorithms or algorithmic thinking is the process of creating a plan composed of a set of ordered instructions to solve a problem. These thinking skills are often integrated and used together; thus, a problem may first undergo abstraction, with only the relevant components considered, which then may be decomposed into sub-problems each of which will be presented with a solution either by finding similarities with a problem for which a solution exists or by developing an algorithm to solve the problem.

For example, when a child is to clean up her room, she might consider putting away the pile of books and the pile of balls as two separate sub-problems, thus decomposing the larger task into smaller ones. In doing so, she abstracts certain properties from the books and balls. In this case, the titles of the books may be irrelevant to the task and so can be ignored when the books are replaced on the shelf; however, the color of the balls may be relevant as the balls are placed in their separate-colored bags. Organizing the balls into their colored bags is a problem that the child has seen before (e.g., organizing blocks into colored boxes) and the steps required can be duplicated (pick up a ball, select same colored bag, place ball in bag, repeat). This repeating sequence of steps can be viewed as an algorithm.

Weintrop et al. (2016) created a taxonomy of CT practices in the domains of STEM, most of which require computer and prior computational knowledge. Brennan and Resnick (2012) created a framework for analyzing CT that relates specifically to programming with the block-based Scratch (Maloney et al., 2010) toolkit.

This study focuses on early education, and most of these teachers do not have the background knowledge required to support learning through CT activities that are based on digital technologies without, at least some, initial support (Nikolopoulou & Gialamas, 2015). Many teachers feel uncomfortable teaching programming with digital technologies, as the computational interfaces, devices, and tools present challenges that are both technical and conceptual (Love et al., 2022; Parette et al., 2010; Rich et al., 2021). As a result, many teachers do not begin or persevere in using them in their classes (Blackwell et al., 2014). Thus, we used the Wing conceptualization that clearly separates between the computerized/programming medium and the thinking skills and sought a learning environment that would help teachers feel more comfortable with the medium of CT learning and would resonate with their prior knowledge.

Algorithmic thinking, as one of the four cornerstones of CT, is a major aspect of the current study. It is often linked with programming and computers; however, it is a basic tool in everyday life (from baking a cake to organizing a closet). In Peel et al. (2020), algorithmic thinking is formalized through concepts and skills termed Computational Thinking Through Algorithmic Explanations. In their study, they analyze students’ thinking about STEM processes. In the current study, we exploit this formalization in order to analyze young children’s understanding and use of algorithms.

We will consider the following concepts:

1. Branching – conditional steps where the next move depends on a [binary] question, often represented as IF/THEN/ELSE steps. (Example: If the number on the card in hand is greater than the number on the card on the table, then place the card on the table [else move to the next card on the table].)

2. Iterations – step or steps that are repeated (often until a condition is met); these are often termed loops. (Example: Repeat comparing the card in hand with the cards on the table until a larger card is found.)

3. Variables – values that can change. (Example: Take the first card from the pile, consider its number. The number may be any value between 1 and 10.)

Considering these practices in our study is tricky, as students are not actually writing and developing algorithms; rather, they are attempting to understand and follow them, as well as identify when a certain algorithm (category or ordered sorting) is to be used. Nevertheless, some practices will be considered in this study, albeit under our new interpretation:

1. Sequencing – a) Understanding that the algorithm is composed of ordered steps. (Example: First pick card from pile, then compare cards, then act.); b) Understanding that the algorithm consists of ordered parts. (Example: first, pick card from pile and compare to first card on table; second, repeatedly compare card with cards on table until correct position to place the card is found.)

2. Abstracting – Understanding that a pattern of steps is repeated. (Example: for each card in the pile, repeat the steps required to find its correct position on the table.)

3. Generalization – Realizing that the same algorithm is applied regardless of the value of the variable. (Example: regardless of the number on the card selected from the pile.)

4. Recognizing patterns – Realizing that a problem is similar to a previously encountered problem. (Example: realizing that ordering balls by size is similar to ordering numbered cards by value.)

Computational thinking in early childhood education

In three recent reviews of the topic (McCormick & Hall, 2022; Su & Yang, 2023; Zeng et al., 2023), it was found that relatively few studies have been conducted into CT in ECE that passed the review criteria: 44 in eight years, 26 in 12 years. Among younger children (3- to 5-year-olds), there are even fewer papers: 17 papers in 14 years. All reviews highlighted the high proportion of research contributed by Marina Bers and her colleagues at the DevTech laboratory (e.g., Bers, 2019; Strawhacker et al., 2022).

Conceptual framing of CT activities in the different papers related to social constructivism, Piagetian developmental theory, developmental neuroscience, sociocultural approaches, and play-based learning. The justifications for these research papers were mainly economic in their perspective, highlighting the need for a skilled workforce. Additional justifications were efficiency in promoting children’s problem-solving abilities, developmental goals such as hand-eye and motor skills, and teamwork skills.

More than half of the learning environments were robotics (such as the KIBO kit and Bee-bot), and a fifth used digital applications (such as ScratchJr http://www.scratchjr.org and code.org). Only about a tenth of these studies involved unplugged activities, activities that use non-digital tools, as in the present study. The CT concepts explored in these studies include mainly sequences, loops, events, conditionals, algorithmic design, and pattern recognition.

Most of the activities were more heavily structured by adults in the introductory phase, with studies diverging in the degree to which children engaged in free play with the related tools as well as the scaffolding and mediation provided by adults. Few studies were completely open-ended.

Learning outcomes were assessed mainly through direct knowledge assessment for CT concepts and problem-solving skills, and observation. The studies showed that 4- to 6-year-old children can learn both CT and coding and particularly improved in pattern recognition, sorting, algorithm design, debugging, and procedures. Non-cognitive outcomes showed improved collaboration and communication.

Developmental aspects of computational thinking

CT skills related to and supported by the present learning unit are considered from the developmental perspective. Finding patterns is related to categorization, sorting, and ordering of objects by some attribute. Being able to flexibly shift between categorization methods is described via relationships with metacognition and executive control (e.g., the Wisconsin Card Sorting Test, WCST; Grant & Berg, 1993). Previous research regarding the development of abilities related to decomposition and abstraction (two additional processes related to CT) is not explored, as it does not align with constructs typically investigated in early education and developmental research.

Young children’s categorization begins at infancy with the broad categories of inanimate, people, and other living things (Wellman & Gelman, 1998). This categorization supports understanding the unique concepts that apply to each subdivision (Keil, 1979) and allows for making inferences about unknown objects. Going beyond these broad categories, infants spontaneously sort objects into categories, such as cats versus dogs (Quinn et al., 2006). Perceptual categorization based on similarity of appearance is dominant in the earlier years (Cohen & Cashon, 2006). In the present study, the children categorize based on such perceptual information of color and shape. Categorization comprises several cognitive processes and is impacted by domain-specific aspects, such as whether the task is explicit (by the teacher/experimenter) or implicit (in self-initiated activities) and the role of language and the complexity of the tasks at hand (review by Gelman & Meyer, 2011). For example, by preschool and earlier, children can categorize based on shape, color, gender, number, and more. Sorting as an activity is also central to children’s cognitive development, as it supports their construction of general categories that further support their evolving concepts, and in expanding their classification abilities (Sarama & Clements, 2009). To highlight the importance of these activities, we can see central developmental tests that focus on sorting, such as the Wisconsin Card Sorting Test (Grant & Berg, 1948) and the Category Test (Reitan & Wolfson, 1993). Being able to flexibly select among types of sorting processes is important as well, as there is no single process that is most efficient for all situations and because selecting among strategies is an important problem-solving ability. In this study, we focus on children’s metacognition as metastrategic control in applying strategies to new challenges (Kuhn, 2000).

Shifting between categorization methods

According to Blaye and Jacques (2009), children’s executive abilities develop between the ages of 4 and 5, enabling categorical flexibility. Zelazo et al. (1996) also contend that young children’s ability to transition between simple categorization criteria (shape and color) develops between the ages of 3 and 5. These developmental trends point to two important conclusions. One is that kindergarten children, the target population of the educational intervention in this study, have the budding resources to contend with challenges in the card games. Second is that these are budding abilities, so that learning with tools has the potential of further developing them.

Computational thinking as related to teachers and classrooms

At present, most early education teachers do not have the background knowledge required to support learning through CT activities that are based on digital technologies without, at least, initial support (Nikolopoulou & Gialamas, 2015). This is a new type of knowledge and tools that were not part of their professional training. This issue is related to CT integration in ECE, rather than teacher training. Many teachers feel uncomfortable in teaching programming with digital technologies, as the computational interfaces, devices, and tools present challenges that are both technical and conceptual (Parette et al., 2010). As a result, many teachers do not begin or persevere in using them in their classes (Blackwell et al., 2014). This state of affairs motivated our search for learning environments that would help teachers feel more comfortable with the medium of CT learning and would resonate with their prior knowledge.

Early childhood classrooms are usually organized in a modular fashion that may include dedicated areas for building, board games, art, home role-playing, reading, and math learning. This organization has several educational and practical goals. One goal is encouraging children to work independently on creative, fun, and intellectual activities, in a way that implicitly or explicitly distinguishes between different types of knowledge and supports independent activity. In practice, early childhood educators cannot interact on a personal one-to-one basis with each child during all parts of the day. As a result, many activities, such as the learning unit in the present study, are designed for initial guidance (e.g., a board game, painting with colors, putting together parts of a construction game) followed by autonomous activity with minimal support.

“Sorting like a computer” learning unit

The Computer Science Unplugged approach presents activities and games that include student role-play and non-computerized simulations or solving puzzles, that support learning of central ideas in computer science (Bell et al., 2009). Previous studies have used this approach for learning about computation in early childhood educational settings, with tabletop games that include board and card games (Horn et al., 2012; Poole et al., 2021). In the design presented in this article, we build upon this approach and other previous applications by presenting activities that do not require actual programming or engaging with digital technologies. In the present research, the learning activities are based on card games, which can be placed in the board games learning area in the classroom space and can be independently used by children after initial guidance. Moreover, the design is based on familiar sorting and categorizing games that are familiar both to the children and their teachers, making it a ramp-up activity into computational coding activities for young children. Using such activities to help teachers build up their capabilities to support CT learning in familiar and understandable formats can open the way to going beyond them into digital formats.

The learning unit we designed is geared toward young learners and focuses on understanding sorting algorithms, a basic CT skill, in which objects are organized in a specific pattern to enable further actions. This topic was selected because sorting algorithms are important, both in computers and in daily life. It is easier and more time efficient to search and find specific items in a sorted setting than in an unsorted one; for example, finding a fork in a cutlery drawer is easier when the objects are sorted by kind – spoons, forks, and knives. Sorting skills are associated with many daily life activities, even for young children, such as organizing toys, finding a specific dress, arranging books on a shelf, or emptying the dishwasher.

The unit was designed to take advantage of materials often present in the classrooms, such as numbered cards, colored cards, picture cards, and Lego blocks. The games in the unit also use procedures that are familiar to children and teachers, such as classifying by kind and color and ordering by attributes such as size. An example for a classification game is matching the colors on a spinner with the colors on a mat in the Twister game. Such games are geared to support children’s formation of categories and concepts by recognizing commonalities within one category and differences from another category. An example of an ordering game is stacking rings on a pole by size; these games are meant to encourage focusing on attributes and the differences in their quantity in order to typify objects. The present design takes the child one step beyond by uniting classification and ordering in the same activity, so that one needs to determine which procedure to use.

The learning unit includes hands-on activities that help children learn how to sort “like a computer” using the “Linear Sort” and “Category Sort” strategies (see Appendix A for details on Linear Sort).

The children experience “Sorting Like a Computer” in ordering cards by number (Linear Sort), and sorting cards by color and shape (Category Sort) (see more extensive explanation with examples in Appendix A).

Three main principles in computer sorting characterize the difference in the way we sort objects: 1) There is sequential entry of new objects into the system; imagine randomly picking one piece of cutlery out of the dishwasher to be sorted. 2) There is no global view of the sorted objects in the array or in the cutlery drawer, so that new objects can be compared with only one object in the cutlery drawer at a time. 3) There is the simplicity and repetition of the individual steps in the algorithm used to sort the objects.

These three characteristics are made apparent in the rules of the card games and relate to computerized procedures.

The activities of the learning environment aim to teach the participant how to sort a collection of items, using two sorting algorithms, and to determine which is appropriate for a given problem. While the collection of CS Unplugged activities (Bett et al., 2005) includes sorting activities, these are geared toward older children. Thus, we developed the activity to be developmentally appropriate for kindergarten-age children. For a full description of the activities, see Appendix B.

The CT practices that can be used and developed through the unit’s activities include data representation for efficient search, decomposition of a problem into simpler problems, algorithmic thinking (selecting a method and planning its execution), and pattern recognition (noting similar features across different items).

The learning unit was designed for the experimental setting of individual interactions of experimenter and child; however, the unit activities can be expanded to group work in classrooms. Although Category Sort is a skill acquired and well versed by age 5–6, we intentionally chose to start the learning unit with the less versed Linear Sort. By doing so, we hoped to prevent participants from affixing to a well-known procedure and allow for learning a new concept and procedure.

The learning unit consists of four activities performed in order.

1. Numbers Go Up or Down – Linear Sort

2. What Color? – Category Sort

3. Slide Show – When to Use Linear Sort and Category Sort

4. Maram’s Box of Cards – Using Both Linear and Category Sort

Figure 1 displays the cards and slides used in the four activities.

Figure 1. Cards and slides used in the four activities of the learning unit.

Upon reading about the tasks, the reader may be reminded of the dimensional change card sort task (DCCS), a cardinal measure of executive function for 3- to 7-year-old children (Zelazo, 2006). This task includes cards that can be sorted according to one or two dimensions, such as color and shape. This test first requests sorting by one dimension, such as color, and then shifts to sorting the same set of cards by another dimension, such as shape. However, the cards in our learning unit differ from those of the test in that they use two distinct kinds of dimensions – one is categorial (shape or color) and one is numerical (ascending numbers up to 10), the numerical not being part of the DCCS task. The method by which the children sort is more constrained, as they are learning typical computer algorithms for sorting. They are required to select between methods of sorting according to the information available on the cards or objects. Finally, they are asked to use both dimensions to sort in the more advanced problems, creating a greater challenge.

Research questions

In this study, we explore how young kindergarten children can develop CT skills in a school-related and age-appropriate learning environment. We show that children can understand and solve problems using appropriate strategies, developing the ability to solve a problem by translating it into a simpler and better-understood representation, which is then easier to solve. We focus on both learning outcomes and the process of learning, considering what CT skills are learned through the learning unit and what characterizes the learning processes. The research questions are summarized as follows:

1) What computational skills (decomposition, pattern recognition, algorithmic thinking) and problem-solving capabilities (number of trials to success) are learned through the hands-on activities of the learning unit?2) What are the characteristics of young children’s learning processes while solving CT problems within the learning unit, as seen in their sorting strategies across successive steps and the level of adult support required?

Method

Approach and design

This research uses mixed methods (Creswell, 2012) to enable observation of group results and understanding the learning processes. Quantitative analysis was performed on the pre- and post- interviews through which learning gains of computational skills were evaluated. Qualitative analysis was performed by comparing the process of learning of two participants. The research is a pretest-intervention-posttest design.

Participants and setting

The participants were 16 kindergarten children between the ages of 5–6 years selected from a pool of around 40 children, reduced according to three criteria: (1) mid-range cognitive abilities according to the teacher, (2) an equal number of boys and girls, and (3) verbally articulate. All stages of the study took place individually in a small room that is part of the classroom. The Ministry of Education’s head scientist and the University of Haifa’s ethics committee approved the research. All participants submitted a signed consent from their guardians.

For the qualitative analysis, two participants were selected to represent high and low learning gains. To avoid outliers, the two participants were selected from the middle third of all participants ranked according to their learning gain scores. Noah (male) was chosen to represent a high learning gain participant and Alleen (female) was selected to represent a low learning gain participant (names are fictitious).

Data sources

The data collection tools included a learning unit (Appendix B), pretest, and posttest interview protocols (Appendix C), video-recordings, and field notes. Both the pretest and the posttest interview protocols focused on activities that are similar to those in the learning unit. The pretest focused on numbered and colored cards and tested for sorting abilities. The children were first asked to find a specific card among a set of downturned cards. The number of trials until the card was found was recorded. The children were asked to organize (first the numbered, and then the colored) cards so that finding a specific card would be easier to find (i.e., required fewer search trials). Thus, the children’s concept of sorting, its advantages, and the types of sorting that the participants were acquainted with could be explored. The posttest interview protocol was very similar to the pretest protocol, but involved sorting of Lego blocks, which could be sorted by either color, size, or both attributes. Sorting of Lego blocks rather than cards was chosen to disambiguate the learning effects from the activities’ medium. It also allows to test for transfer of learning. The interviews took approximately 10–15 minutes.

Validity and reliability

Increased reliability was achieved by relying on three coders (the three authors) to formulate the structure and elements of the coding table. Coding of 20% of the data was then performed by all three authors and tested for reliability. The reliability rates are described in the findings section.

Results

The results are presented in two main parts. The first part focuses on the whole group of children and describes their change in CT skills between the pretest and posttest interviews. The second part presents two contrasting case studies with one child who learned much and one child who learned little in the study.

Computational skills and problem-solving capabilities

To evaluate the computational skills that were learned and to typify the children’s problem-solving, we analyzed the pre- and posttest interview data. We present here an assessment of the children’s CT skills, the number of attributes the children could sort with, and the number of trials until a successful implementation of a sorting algorithm.

CT was analyzed based on Wing’s framework (Wing, 2006), focusing on decomposition, pattern recognition, and algorithmic thinking as elementary skills in solving problems, using a computational perspective. We did not include abstraction in the evaluation, as no independent measure could be developed. Decomposition, or dividing a problem into sub-problems, is conceptualized as using a sorting criterion or two criteria to sort the pack of cards into smaller groups or in a line. Pattern recognition, detecting patterns that repeat across items, is operationalized as recognizing repeating patterns across the set of cards using a systematic criterion. Algorithmic thinking is operationalized as following a consistent set of steps of one of the sorting algorithms, regardless of whether it is suitable. Each CT skill was defined at three levels of sophistication. Table 1 is the coding table, providing definitions and examples for coding each of these skills and levels. See also Figure 2.

Figure 2. Illustrations of sorting games at different levels of CT skills.

Table 1. Coding table for computational thinking skills. Figure 2 is referenced in the example column.

CT skill	Definition	Example
Decomposition (D)	Level 0 (D-0): The problem at hand is not divided into subproblems. The sorted items are arranged with no sorting criterion, attributes are not considered.	The cards are arranged in a line in random order not taking into consideration any of the items’ attributes (Figure 2a).
	Level 1 (D-1): The items are sorted according to one criterion (correct or not).	Cards are paired together according to one attribute (the color of the cards), while disregarding the other attributes (type and number of elements on the card) (Figure 2b).
	Level 2 (D-2): The items are sorted using two criteria, where one subsumes the other (correct or not).	Lego bricks are sorted according to two attributes; the blocks are grouped by color and within each color group they are sorted by size (Figure 2c).
Pattern Recognition (PR)	Level 0 (PR-0): The ordering of the items does not follow a specific pattern.	The cards are placed in a line randomly (Figure 2a).
	Level 1 (PR-1): A pattern is not detected and/or followed for part of the task.	The cards are sorted while changing criteria: pairing cards sometimes by color and sometimes by color and icon (cat or flower) (Figure 2b).
	Level 2 (PR-2): A pattern is detected and followed throughout the task.	Lego bricks are sorted while applying a pattern throughout the whole task; bricks are organized according to their color and then size (Figure 2c).
Algorithmic Thinking (AT)	Level 0 (AT-0): No detectable application of a sorting method.	Items are placed randomly on a table without a detectable application of a sorting method (Figure 2a).
	Level 1 (AT-1): An incorrect sorting method is used, but implemented correctly.	Cards are paired according to their color as a sorting criterion, yet it is not the correct method for these specific items (Figure 2b).
	Level 2 (AT-2): A correct sorting method is used and implemented correctly.	Lego bricks have been chosen to be sorted according to both color and size, and sorting was implemented correctly (Figure 2c).

The coding table was used to code the transcribed interviews. Every task in the interview protocol was coded according to the three categories in the coding table and was awarded a score between 0 and 2 according to the levels of sophistication. The three authors coded 20% of the interviews to test for reliability (0.83). Differences were resolved through discussion. The first author coded the rest of the interviews. The results are presented in Table 2, where the average score across all participants is shown for each of the CT skills.

Table 2. Children’s computational thinking scores with regard to the pretest and posttest interviews (range 0–2; N = 16).

CT Skill	Pretest Mean (SD)	Posttest Mean (SD)	Statistics paired t(15) (p)
Pattern Recognition	1.00 (0.632)	1.63 (0.500)	−2.825 (.013)
Algorithmic Thinking	1.06 (0.854)	1.94 (0.250)	−3.656 (.002)
Decomposition	0.94 (0.443)	1.44 (0.512)	−3.162 (.006)

Results show a significant increase in all computational skills between the pretest and posttest interviews across all three CT skills. The initial performance (at pretest) for each of the CT skills is around 1 (range of 0–2), implying some, but not full, understanding. The posttest performance is between 1.5 and 2 for all CT skills, approaching a full execution of the skill.

The number of attributes (color, size, or number) the children used to sort items was coded for each of the two tests. In the pretest, most children (12 out of 16) used one attribute to sort items while in the posttest the majority of children (10 out of 16) used two attributes (mostly color and shape) when sorting the items, increasing from a mean of 1.25 (.45) to 1.62 (.50).

To evaluate problem-solving efficiency, the number of trials until success at solving a sorting task was coded. It was found that the number of trials in the pretest ranged between 1–4 (average 2.3 (0.70)); in the posttest, all children required a single trial to solve the task.

To conclude the analysis regarding the children’s CT and problem-solving capabilities:

• For all three evaluated CT skills (decomposition, pattern finding, and algorithmic thinking), the children advanced from an intermediate level to a more sophisticated level.

• From pretest to posttest, they became more efficient in sorting the cards with the new algorithms.

• They also increased their ability to sort from one attribute to two attributes.

Characteristics of young children’s learning processes

To understand the children’s learning process, we considered the Linear Sorting task (Activity 1) and the Category Sorting task (Activity 2). As most children reached the maximal assessment value in the posttest, we were interested specifically in the earlier stages when the ideas are constructed. The findings are based on a qualitative analysis presented through two contrasting cases (Creswell, 2012) where two children’s problem-solving strategies are analyzed and compared. Two children were selected to represent high [Noah] and low learning gains [Alleen] through the activities (see Methods Section).

Linear Sort learning unit analysis

The two children’s processes of learning how to conduct the Linear Sort algorithm were analyzed. Their actions on the cards and their intermediate strategies when learning how to execute the complete algorithm were analyzed as well as the order of appearance of these strategies.

In the Linear Sorting task, the participants were taught to sort using a simple Insertion Sort algorithm (Appendix A). Sorting was performed on 10 cards numbered 1–10. The Linear Sort task involves selecting a card from the central pile and positioning it in the correct position in a linearly sorted line by repeatedly comparing and swapping neighboring cards. There were 10 cards to be sorted. Thus, the performance of the Linear Sort task was segmented into 10 events, each of which involved dealing with one card. Each event involved six types of actions associated with the steps of the sorting algorithm.

The two children’s performance in Activity 1 was recorded and coded according to these six actions. Tables 3 and 4 display the coding results for Noah and Alleen, respectively, showing their unassisted actions during the activity.

Table 3. Noah’s unassisted actions during the Linear Sort Task. Each event represents working with one card from the pile to be sorted.

Table 4. Alleen’s unassisted actions during the Linear Sort Task. Each event represents working with one card from the pile to be sorted.

Noah started the sorting by saying the number of the card out loud (action A1) for all the cards that he picked (excluding event 4 and 7). When reaching event 4, he started to implement new strategies. He placed the card to be sorted in front of the sorted line (A2), thinking out loud about which card is bigger (A3) and switching the card that is being sorted with the one next to it (A4). However, he stopped at this point and required assistance. In event 6, we begin to see a form (though not yet complete) of implementing the Linear Sort algorithm, by comparing and switching the card to be sorted along the sorted line (A5); however, he had difficulty stopping when the card to be sorted reached the correct position and continued moving it along the line beyond its correct position. Toward the end of the task, Noah started to perform the complete sorting algorithm (A6).

Alleen also started performing her task while saying the card’s number aloud (A1). When she reached event 4, she began to apply two more actions: placing the card in front of the sorted line (A2) and thinking out loud as to which card number is bigger (A3). In event 5, she began switching the card being sorted without assistance (A4). In event 6, she started to grasp the necessity of continuing the comparing and switching along the sorted line (A5); however, she had difficulty stopping the iterative process when reaching the correct card position. Finally, in the last event, she was able to perform the sorting task on her own by fully implementing the Linear Sort algorithm (A6).

Both children executed the Linear Sort in a similar manner. They both initiated the sorting by stating the card number they were holding. It took them several trials to add a second and third new action to their performance, placing the card in front of the sorted line and thinking out loud about which card is bigger. By event 6, both children were comparing and switching the card to be sorted along the line of sorted cards; however, they both had difficulty in applying the stopping criterion when the correct position of the card was reached. Toward the end, they were able to implement the Linear Sorting by themselves (without any form of guidance). Noah showed this in event 8, yet Alleen took two more events before she could execute it independently.

The qualitative analysis described above led us to define three learning phases that arise from Noah’s and Alleen’s behavior and that appears across all children in our experiment when learning to perform Linear Sorting. These phases can be interpreted as transitioning between three possible algorithms for solving the sorting task, each algorithm showing increased ability:

Algorithm 1

– “Single shot sorting – no repeats.” Compare the card being sorted only with the first card in the sorted line and then stopping. At this point, the repetitive nature of the algorithm is not yet grasped.

Algorithm 2

– “Sorting ad infinitum – no stopping.” Compare and swap the card being sorted with each card along the sorted line one at a time, but not realizing the need to stop when reaching the correct location of the card. The repeating nature of using an algorithm has been grasped; however, another component – the stopping rule – is not yet incorporated.

Algorithm 3

– “Sorting till stop condition attained.” Compare the card being sorted with each card along the sorted line one at a time until reaching the correct card position. At this point, the child grasps both the card comparison repeating process and the stopping rule, so that once the cards are sorted, they are able to terminate the algorithm.

Examples of these learning phases as expressed in children learning to perform Linear Sort are given in Table 5.

Figure 3 displays the three levels of understanding depicted as three algorithms that are used by the participants while learning the Linear Sort algorithm. Arrows depict the transition between algorithms during the learning process. From our research, we find that the transitions children make are typically from Algorithm 1 to Algorithm 2, or from Algorithm 1 directly to Algorithm 3.

Figure 3. The phases of learning of Linear Sort depicted as three algorithms and transitions between them.

Table 5. Examples of the three learning phases expressed in children’s attempts to perform the Linear Sort Algorithm.

Phase of Learning	Example
Algorithm 1 Single shot sorting: Compare the card being sorted only with the first card in the sorted line and then stop	Alleen picked a card from the pile (it is numbered 5), then said, “5 is bigger than 2” (first card in line was numbered “2”); briefly peeking at the researcher, she switched the two cards while looking at the sorted line and scratching her neck.
Algorithm 2 Sorting ad infinitum: Compare and swap the card being sorted with each card along the sorted line one at a time but not realizing the need to stop when reaching the correct location of the card	Noah studied the sorted line and declared that 7 is bigger than 5 while switching their places. Following that, Noah rubbed his neck and looked at the sorted line, then said in a hesitating voice, “7 is bigger than 6;” the researcher encouraged him to switch the cards, so Noah swiftly swapped the two cards and continued even when reaching the next card “7 is bigger than 9.”
Algorithm 3 Sorting till stop condition attained: Compare the card being sorted with each card along the sorted line one at a time until getting to the correct card position	Noah picked the last card from the pile (numbered “4”) and said while smirking, “4;” then he placed the card at the beginning of the sorted line (before the card numbered 1) and said, “4 is bigger than 1,” then swapped the places of the two cards. He carried on in this manner until reaching card number “5,” saying, “4 is smaller than 5.” He stopped and looked up at the researcher triumphantly.

To conclude the analysis characterizing the young children’s learning processes of the Linear Sort algorithm:

• The two children were similar in their learning phases while learning the Linear Sort algorithm, shifting from “Single shot sorting – no repeats” to “Sorting ad infinitum – no stopping,” and then to “Sorting till stop condition attained” algorithms.

• Transition between these phases was slightly slower for the child who learned less through the process.

• Both children reached a full execution of the algorithm, which involved both multiple comparisons and card swaps to order the cards and stopping the process once the correct card position was determined.

• Children had to first learn to execute one part of the algorithm (the multiple sequential comparisons with cards in the sorted line); only when this was grasped could they further incorporate the stopping rule algorithm.

Category sort learning unit analysis

The second analysis involved the children’s learning process of the Category Sort in which we included three steps: Step 1 - sorting cards according to one attribute (color); Step 2 - sorting according to two attributes (color and icon); and Step 3 - merging Category Sort with Linear Sort. The data for this study were collected in Activity 4 (Maram’s Box of Cards – Linear and Category Sort Combined) in which colored cards with one or two icons (flowers or cats) were used. We recorded, transcribed, and coded Activity 4 of the learning unit of the two selected children Noah and Alleen. Results were then compared qualitatively with performance of other children by visual analysis of the video recordings.

Both Noah and Alleen, as well as most of the children in this research, had no problem performing the first step of Category Sorting by one attribute (color) and required no assistance. As we can see in the following excerpt, at this point in the learning unit, Alleen was proficient in sorting the cards with one attribute.

Table

Alleen picked a green card from the pile looked at it, said “green,” and then placed it in the green group. When she was done sorting all the cards, she had formed four groups of same-colored cards (Figure 4).

Figure 4. Alleen`s completed category sort by color.

Step 2 (sorting with two attributes) required the researcher to provide some assistance. Specifically, the researcher needed to direct the children to focus on a single sorted group from Step 1 (e.g., the group of red cards). Only when focused within the group were the children capable of completing the sorting with the second attribute within the group. Often, children required further guidance by focusing them on a single card with an icon (cat) and asking them to compare other icons in the group. This is demonstrated in the following excerpt.

Table

Referring to the red group of cards, the researcher asked, “Is there anything in common across these cards, or things that are the same in the cards so that you can place them together?” Noah looked at the red group and nodded his head slightly in the affirmative. Pointing his fingers at the cards he says, “Cats together and flowers together.”

Both Noah and Alleen performed the Step 2 Category Sort. It was found that sorting within each color group resulted in different relative positions of cards with the same icons (cats, flowers). Thus, the cards with the cats sometimes were positioned on the right and sometimes on the left within the color group (Figure 5). This indicated that the Category Sort in each group was considered independently of other groups. This behavior was consistent across most participants in this study.

Figure 5. Alleen`s category sort with two attributes (color, then icon). Note the inconsistency of the icons’ order in each color group.

To complete Step 3, verbal assistance was insufficient, and the experimenter was required to demonstrate a Linear Sort within one of the sorted groups. Following the demonstration, most children were able to complete the Linear Sort within the other groups of categorically sorted cards (Figures 6 and 7). This intervention is seen in the following excerpt.

Figure 6. Alleen`s final sorting with two attributes (color and icon) and Linear Sort within each group (by number of icons per card).

Figure 7. Noah`s final sorting with two attributes (color and icon) and Linear Sort within each group.

Table

The researcher said to Alleen: “We learned how a computer can sort according to big and small numbers (Linear Sort); let us also apply it here.” The researcher then sorted the red cards according to Linear Sort based on the number of icons on each card. Alleen moved on to sort the yellow cards; she took the flower cards while mumbling, “One and Two,” and sorted them according to Linear Sort placing the cards on one side, and the linearly sorted cat cards on the other side. She did the same with the rest of the color groups (Figure 6).

We view the three steps of the activity as three phases of sorting at increasing levels of difficulty: Phase 2 due to the integration of more than one attribute and Phase 3 due to both the integration of the attributes as well as combining of two different algorithms.

To conclude, in combining more than one sorting attribute and more than one type of sorting algorithm, we can observe phases of difficulty in the children’s learning. The first phase involved executing Category Sort according to one attribute (color) and required minimal help. The second phase involved executing Category Sort according to two attributes (color and icon) and required intermediate-level guidance and help. The third phase involved executing Linear Sort within the already Category Sorted groups, thus requiring integration of two attributes (color and icon) together with the numeric attribute as well as applying a sorting method that is more complex and that differs from the sorting used in the previous two steps. This phase required strong support, which included a demonstration of the sorting process that the child then imitated. Both children met the same hurdles and required similar support throughout the activity.

Discussion

We focus on studying children’s learning using an “unplugged” (non-computational) learning unit that considers teacher’s knowledge and classroom space and that affords seamless adaptation into the classroom given the objects used in the unit and the activities that are reminiscent of classic class activities and games. While research into developing CT in early childhood education is expanding, previous studies address unplugged activities only to a very small extent. It is this gap we wish to address.

The broader challenge this research addresses is integrating the learning of CT in early childhood education, while considering children’s developmental abilities, teachers’ knowledge, and the structure of early childhood classrooms and activities. In this study, we developed a learning unit geared at developing CT among young children, and researched kindergarten children’s learning with this unit. The learning unit takes advantage of materials often present in the classrooms, such as numbered, colored, and picture cards and Lego blocks. It uses tasks that are familiar to children and teachers, such as classifying by kind and color and ordering by attributes such as size. The research explored children’s interactions with such activities, specifically their computational thinking and problem-solving skills and the process by which they come to develop these skills. The discussion summarizes the findings and interprets them in light of previous research.

The learning unit is based on card games that introduce the topic of sorting algorithms. It aims to support developing an appreciation of having a sorted set of items to increase efficiency of searching for an item, to teach how to sort a collection of items using the Linear Sort or Category Sort algorithms, and to promote an understanding of which of the two sorting methods is most appropriate for a given problem. Moreover, by experiencing how computers sort information, children begin to appreciate that computers are not monolithic black-box objects, as they perform comprehensible procedures that are different from the way people do the same procedures. These procedures are typified by local vision, sequences of simple and well-defined actions that can repeat and have stopping rules.

In this study, children’s learning was analyzed in terms of improvement in three CT skills (Section Computational Skills and Problem-solving Capabilities) and in terms of stages of learning a complex problem (Section Characteristics of Young Children’s Learning Processes).

In quantifying the changes between pre- and post-testing (Section Computational Skills and Problem-solving Capabilities), it was found that children showed improvement in all three CT skills: namely decomposition, pattern finding, and algorithmic thinking. It was also found that the number of attributes used in sorting increased after completing the unit from one dimension to two dimension (color and shape), and that the children’s proficiency in problem solving increased in terms of the number of trials until reaching success completing a sorting task.

To study the stages in learning to solve a complex problem, we considered three tasks: learning the Linear Sort, learning the multi-dimensional Category Sort, and learning a hierarchy of Category and Linear Sort algorithms.

The Linear Sort algorithm is a challenging task with several steps, including a complex step of iterations that requires understanding the stopping criterion. It was found (Section Linear Sort Learning Unit Analysis) that children’s first interpretation and understanding of the algorithm is a simple incomplete version of the algorithm, which eliminated the more complex steps of iterations (repetitions) and disregarded algorithm conditions such as the stopping condition for terminating the repetitions. The children showed several transitions from the simpler version of the Linear Sort algorithm, where a single compare-and-swap step was performed, to a more advanced version of the algorithm, where repetition of the compare-and-swap steps was performed, and finally reaching the complete algorithm, where the stopping criterion for the repetition was implemented.

The multi-dimensional Category Sort task (Section Category Sort Learning Unit Analysis) required children to sort cards according to one dimension (color) and then to sort according to a second dimension (shape) within each color group. Whereas all children were able to complete the color sorting easily, sorting of the second dimension required assistance. Specifically, children were directed to focus on a specific color group in order to complete the secondary sort. It was seen that children had difficulty considering both dimensions simultaneously and required a disentanglement of the dimensions by focusing on a single-color group at a time to complete the shape sort within. This disentanglement was further supported by the fact that sorting by shape within each color group was not consistent across the color groups (with the same shapes placed on the right in some color groups and on the left in others).

Finally, we considered an additional hierarchical step in the sorting task where children were asked to linearly sort within the categorically sorted groups (Section Category Sort Learning Unit Analysis). This required a change of attribute by which to sort as well as changing the type of sorting (sorting algorithm). This formed a challenging problem for the children and they required a demonstration of the sorting process, which they then imitated.

These three findings show that children are capable of learning and following a structured step-by-step algorithm. The findings show that children can come to understand and solve problems using appropriate strategies and develop the ability to solve a problem by translating it into a simpler and better-understood representation, which is then easier to solve. In the Category Sort task, the difficulty of sorting using two dimensions was overcome using a divide and conquer simplification approach, where the problem was divided into distinct sub-problems (sorting each color group by shape, independently). In the Linear Sort task, the difficulty was addressed by simplifying the task, (learning only the first step) and subsequently adding complexity to the task (adding additional algorithmic steps) incrementally.

These findings point to the nascent powers among children that enable them to develop these abilities and places a limit on what can be achieved in less-supported contexts. These possibilities and constraints are well known in the developmental research literature, where young preschool children’s thinking is typified by unidimensionality and support is needed for them to consider more than one attribute at a time (Siegler, 1991). In a study with children on construction of robot behaviors and water flow systems, it was seen that this unidimensionality constraint was overcome with support – either by the constructed object itself or by the interviewer/teacher (Mioduser, 2010; Levy, 2012). Thus, the current study connects well with previous work, showing how well-designed and mediated learning environments can support children in developing more sophisticated thinking, which are initially restricted by developmental constraints.

Limitations of the study include the lack of a comparison group, which could have helped control for other logic-developing activities, which do not focus on CT. Another limitation is the selection of participants, particularly the criterion of verbal fluency, which is related to early math abilities, and also could be related to CT skills. Finally, prior testing regarding general abilities, such as executive function and math abilities, could have helped us analyze the contribution of the learning environment to a variety of abilities. Future research that addresses these issues could help deepen our understanding of young children’s spontaneous and learned CT skills, and their relationship with more general abilities.

Conclusion

CT skills have become important, if not essential, in many domains; thus, schools have been incorporating the topic into the curriculum. This study concerns young pre-elementary children, with whom much less work has been performed. The study serves as a basis to widen our understanding of children’s learning, specifically regarding CT skills and concepts. We show a structure in children’s learning that may assist in developing practices to promote additional CT skills, the shift toward understanding the need for repetitions (iterations) and then to perceiving the role of a stopping rule. Understanding such processes is critical to appropriate adult support. For example, this can be used by teachers to assess where the children are along the learning path and provide supports and mediation to help notice conflicts between their goals in sorting and the strategies they are using. In consideration of teachers and their classrooms, the learning unit can serve as a template for additional designs of CT-related activities that are based on staying within teachers’ comfort zone with slight extensions; and allowing for a combination of supported and independent children’s work, thus adapting to modular classroom structure.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Research was supported by the Israel Ministry of Science & Technology Grant # 315721 and by two University of Haifa scholarships that supported the first author while conducting her master’s thesis: the Silver Scholarship for students’ research in educational technologies and the Baranowsky Scholarship for students’ research in early childhood education. We have no conflicts of interest.

Appendix A.

Linear Sort using Insertion Sort

Linear Sort is an algorithm typically run by computers. It is a standard topic that is taught at the basic level of computer science and programming. The goal of Linear Sort is to organize items in a “single line,” ordered according to a monotonic attribute (e.g., ordering according to height, size, age, alphabetical order). The Linear Sorting activity in this research uses a deck of 10 numbered cards that can be sorted according to the numbers on the card (Figure A1).

Figure A1. Unsorted (top) and sorted (bottom) line of numbered cards.

In the learning unit in this research, participants are taught to sort the 10 numbered cards using a simple Insertion Sort algorithm (Knuth, 1998). The Insert Sort algorithm follows a sequence of well-defined steps as follows (Figure A2):

Assume all cards are in a single pile on a table. The cards will be sorted into a single ordered line on the table.

First Step: Top card is picked from the pile and placed face up on the table. The card on the table marks the beginning of the sorted line.

Repeat following steps until no cards are left in the pile:

1. Select the next card from the pile. Call it the card to be sorted.

2. Place the card to be sorted to the left of the of the first card in the sorted line.

3. Compare the number on the card to be sorted with the card on its right.

4. Swap: If the card to be sorted is greater, then swap the position of the two cards. Go to Step 3.

5. Stopping criteria: If the card to be sorted is not greater, OR there are no more cards to the right, then the card to be sorted has been positioned in its correct place in the sorted line.

Figure A2. Linear Sort using the Insertion Sort algorithm. All cards are in a pile on the table.

Appendix B.

Activities in the learning unit

The learning unit “How to Sort Like a Computer” consists of four activities performed in order. Each activity is performed in a one-on-one setting between child participant and the researcher.

1. Numbers Go Up or Down – Linear Sort

2. What Color? – Category Sort

3. Slide Show – When to Use Linear Sort and Category Sort

4. Maram’s Box of Cards – Using Both Linear and Category Sort

Activity 1: Numbers Go Up or Down - Linear Sort

The first activity focuses on Linear Sort using the Insert Sort algorithm. The goal of Linear Sort is to organize items in a “single line” ordered according to a monotonic attribute (e.g., ordering according to height, size, age, alphabetical order, etc.). The activity uses a deck of 10 numbered cards, which are to be sorted according to the magnitude of the numbers on the card (Figure A1). Details of Linear Sorting using the Insert Sort Algorithm are given in Appendix A1.

During the activity, the cards are introduced to the participant by the researcher. Then the following steps are followed:

a) The researcher shuffles the cards, lays them face down on the table and they play “Find the Number.” The researcher or participant chooses a number and the latter flips cards until the number is found. They record the number of trials (flipped cards) required to find the number. The game is repeated several times. Table B1 presents an example from the data of how this plays out.

b) The researcher then places the cards face up in a line ordered from 1 to 10. The researcher interacts with the participant to induce an understanding that the cards are now sorted (“ordered in a line”). The researcher then flips the cards face down maintaining card positions. They again play the “Find the Number” game, again recording the number of trials (card flips) required to find the desired card. The game is repeated several times.

c) The researcher and participant discuss the table of recorded trials and compare the number of trials in the unsorted and sorted conditions. The conclusion should be that the sorted condition required much fewer trials to find the desired card.

d) The researcher coaxes the participant to think of situations in their daily life in which objects are sorted and are easier to find.

e) Main part of the activity: The researcher shuffles the cards and places them in a single pile face down. The researcher then demonstrates how to sort the set of cards using the Insert Sort algorithm (Appendix A1). The algorithm is novel to most participants and thus requires several demonstrations. Following the demonstrations, the participant is invited to sort the reshuffled deck of cards. Scaffolding and assistance are given as needed during the participants attempts at sorting.

Table B1. Number of trials required to find a numbered card – example from the data.

	Number Sought	Number of Trials to Reaching the Number Sought
Unsorted Pile	5 3 7	|||| ||||||| |||||
Sorted Pile	9 4	|| |

Activity 2: What Color? - Category Sort

The second activity focuses on Category Sort where objects are organized into groups. The activity uses a set of 16 cards of 4 different colors (Figure B1). They are introduced to the participant by the researcher.

1. The researcher lays the cards face down on the table in random positions and they play “Find the Color.” The researcher or participant choose a number and the latter flips cards until a card of the correct color is found. They record the number of trials (flipped cards) required to find the card. The game is repeated several times.

2. The researcher then places the cards face up in groups of colored cards. The researcher interacts with the participant to induce an understanding that the cards are now Category Sorted (“ordered in groups”). The researcher then flips the cards face down maintaining card positions. They again play the “Find the Color” game, again recording the number of trials (card flips) required to find the desired card. The game is repeated several times.

3. The researcher and participant discuss the table of recorded trials and compare the number of trials in the unsorted and sorted conditions. The conclusion should be that the sorted condition required much fewer trials to find the desired card.

4. The researcher coaxes the participant to think of situations in their daily life in which objects are Category Sorted and are easier to find.

5. Main part of the activity: The researcher shuffles the cards and places them in a single pile face down. The researcher then demonstrates how to perform Category Sort. Following the demonstration, the participant is invited to sort the reshuffled deck of cards. Scaffolding and assistance are given as needed during the participants attempts at sorting.

Activity 3: Slide Show – When to Use Linear Sort and Category Sort?

The third activity focuses on determining which sorting method (linear or category) are most appropriate for a given task. The “tasks” are defined by pictures showing the objects to be sorted. The slide show includes five pictures containing sets of items: a pile of books, matryoshka dolls, and clothing items (Figure B1). The researcher shows the participant a slide at a time and asks which of the two sorting algorithms is most appropriate for the set of items.

Figure B1. Examples of images used in activity 3.

Activity 4: Maram’s Box of Cards - Linear and Category Sort Combined

The fourth activity focuses on combining both Linear Sort and Category Sort hierarchically. The activity uses a deck of 16 cards that are colored in four different colors (red, blue, yellow, green). Each card has one two or three objects of the same type (balls, flowers, or cars). The cards are introduced to the participant by the researcher.

1. The researcher lays the cards face down on the table in random positions and they play “Find the Card.” The researcher or participant chooses a specific card (color, object, and number of objects). The participant flips cards until a card of the correct color is found. They record the number of trials (flipped cards) required to find the card.

2. The researcher asks the participant to sort the pile of cards in a manner that will help her “win” the “Find the Card” game.

3. The participant sorts the cards according to her choice (all participants chose the Category Sort method based on color).

4. The researcher then flips the cards face down maintaining card positions. They again play the “Find the Card” game and record the number of trials (card flips) required to find the desired card.

5. The researcher initiates a discussion on how to “improve” the order of cards so that the participant can “win” even faster (fewer card flips).

6. In the research, all participants chose to start with category sort. The participant then sorts each group of cards previously Category Sorted by color.

7. The researcher initiates another discussion on how to further “improve” the order of cards so that the participant can “win” even faster (fewer card flips).

8. The participant then sorts each group of cards with similar color and icons using Linear Sort according to the number of objects in the cards.

Appendix C.

Pretest and posttest interviews

Similar to the activities, the interviews were conducted in a one-on-one setting between child participant and the researcher. The interview activities and questions concern first the Linear Sort algorithm (Find the Number game) and then the Category Sort algorithm (Find the Color game).

The pre-interview was often preceded by an introduction. In the introduction, the researcher first introduced herself, then described the study’s goals and its structure. The children were encouraged to ask questions. The children were also encouraged to share their feelings if they felt uncomfortable in any way so that any such issues can be resolved.

Pretest interview protocol

During the pretest interview, the following steps were taken:

a) The researcher introduces a set of 10 single-color cards with numbers 1–10. The researcher lays the cards face down on the table in random locations and explains the “Find the Number” game. The participant chooses a number, and the researcher flips cards until the number is found. The researcher and participant then exchange roles in the game.

b) The researcher invites the participant to organize the cards anyway they like to help them “win.” No scaffolding is given.

c) Regardless of the reordering or sorting performed by the participant, the researcher asks a series of questions:

1. How did you organize the cards to help you win?

2. Why do you think this order will help you win?

3. Can you think of other ways to order the cards on the table to help you win?

4. Did anybody teach you how to order it this way? Can you tell me what you learned from them?

d) The researcher introduces a set of 16 colored cards (four cards of each color: red, green, blue, yellow). The researcher lays the cards face down on the table in random locations and explains the “Find the Color” game. The participant chooses a color, and the researcher flips cards until the color is found. The researcher and participant then exchange roles in the game.

e) The researcher invites the participant to organize the cards anyway they like to help them “win.” No scaffolding is given.

f) Regardless of the reordering or sorting performed by the participant the researcher asks a series of questions:

1. How did you organize the cards to help you win?

2. Why do you think this order will help you win?

3. Can you think of other ways to order the cards on the table to help you win?

4. Did anybody teach you how to order it this way? Can you tell me what you learned from them?

The post-interview, administered individually to each participant, was performed after the intervention (activities of the learning unit). The participant was asked to perform sorting of Lego blocks.

Posttest interview protocol

During the posttest interview the following steps were followed:

a) The researcher introduces a pile of Lego blocks spread out randomly on the table. The blocks are of 4 colors and of 5 sizes.

b) The researcher then shows the participant a “wall” made of Lego blocks, where every row of the wall is made up of Lego blocks of a single color of different sizes (Figure C1, right).

c) The researcher asks a series of questions:

1. Do you have Lego blocks in class?

2. Do you know how to build with Lego Blocks?

3. Let’s build a wall like this one. Can you find a green Lego block in this pile?

4. What can we do to help us find Lego blocks of a certain size and color?

If the participant does not volunteer the response of sorting the researcher may continue:

(v) Can you think of how to order the blocks on the table so it will be easier for us to find Lego blocks?

Figure C1. Lego blocks in a random pile (left) and Lego blocks “wall” (right) used in the posttest interview.