Relationships Between Executive Functions and Computational Thinking

Definition of Computational Thinking

The core principles and practices of CT are closely linked with computer science, which shares its computational fundamentals with other disciplines like science and mathematics (Lye & Koh, 2014). Consequently, many CT frameworks draw upon computer science concepts, incorporating components like programming and computational theory. For example, Denner et al. (2012) developed a CT framework to evaluate the programming skills and CT knowledge of middle school students, comprising three key components: programming, documentation and understanding, and design. Similarly, researchers such as Weintrop, Holbert, et al. (2016) have proposed CT frameworks that encompass four dimensions for acquiring CT concepts and practicing related skills, which are particularly suited for considering CT in programming contexts. These frameworks offer guidance on how students can systematically improve their CT skills through structured learning experiences (Lye & Koh, 2014).

In parallel to the effort of bringing CT into K-12 education, a growing number of educators developed CT framework from a broader range of learning situations that beyond programming or coding (Kazimoglu et al., 2011). Scholars have contended that CT represented a robust cognitive competency that was linked to children’s intellectual development (Horn et al., 2012; Schneider & McGrew, 2012), emphasizing the importance of general CT frameworks that highlight how students approach various subject domains (Barr et al., 2011). In 2011, Computer Science Teachers Association defined CT as a problem-solving process that involves abstraction, recursion, and iteration. This definition places a primary emphasis on the cognitive processes employed by students, as opposed to the mere production of tangible artifacts or evidence in CT activities (Csizmadia et al., 2015). From this vantage point, students are required to cultivate domain-specific knowledge and problem-solving skills to adeptly comprehend and reason about both natural and artificial problems, adopting the perspective of a computer scientist within real-world scenarios.

Adopting a broader perspective, it becomes evident that CT transcends the confines of computer science and should be recognized as a problem-solving process comprising several stages, including abstraction, reflection, application, and self-regulation (Voskoglou & Buckley, 2012). Researchers have explored innovative approaches for nurturing students’ CT skills across diverse domains by incorporating intelligent agents into the CT framework (Weese, 2017). For instance, Kalelioğlu (2015) described CT as a mental ability that enables individuals to abstract information, generalize problem-solving processes, and automate algorithmic solutions. This perspective highlights the generalizable nature of CT skills, extending its relevance beyond specific programming contexts. Thus, a key aspect of the CT definition lies in the capacity to apply computer science knowledge and problem-solving strategies to domains outside the field of computer science.

Typically, the process of achieving CT knowledge mastery involves distinct phases (Alanazi, 2016) within problem-solving scenarios. Initially, students engage in problem decomposition to uncover implicit CT knowledge embedded within the problem-solving scenarios. Subsequently, they identify useful patterns and employ various strategies to design effective solutions. Finally, they put these solutions into practice and subject them to critical evaluation during specific CT activities. Drawing from insights gleaned from various sources in the field (Grover, 2017; Shute et al., 2017; Weintrop, Beheshti, et al., 2016), Rowe, Almeda, et al. (2021) has developed a learning progression for CT that aligns with the existing literature and maintains perfect congruity with the observed practices within this study:

• Problem decomposition: Decomposing a complex problem into its constituent elements that is smaller and more manageable.

Computational Thinking Assessment

The current landscape of CT assessment in K-12 education reveals a significant gap in the availability of reliable and efficient CT measures (Mühling et al., 2015). Many existing CT assessments are predominantly aligned with computer science frameworks, limiting their applicability and accessibility to students with limited coding experience. For example, Werner et al. (2012) developed a CT test focused on measuring middle school students’ CT performance using pre-designed, semi-finished programming artifacts within a programming course. Similarly, Von Wangenheim et al. (2018) applied a rubric of CT measures to analyze students’ static code in a block-based programming environment. Additionally, Brennan and Resnick (2012) described a three-dimensional assessment of CT development (i.e., CT concepts, CT practices, and CT perspectives) specifically tailored for Scratch.

Although these CT assessment measures have provided valuable insights, their dependence on programming environments creates constraints in assessing the core CT skills of students who possess limited programming knowledge (Rowe, Asbell-Clarke, et al., 2021). As a result, there arises a demand for more comprehensive and adaptable CT assessment methods that can proficiently evaluate students’ CT abilities in diverse learning settings. Such measures would enable a wider range of students to demonstrate their CT proficiency, regardless of their programming background.

In parallel, recent efforts have been made to explore students’ psychological states and perceptions that may reflect their CT competency, drawing from cognitive science and self-efficacy research. For instance, Sáez-López et al. (2016) utilized a questionnaire to evaluate primary school students’ perceptions of CT concepts, while Chen et al. (2017) developed an instrument with multiple-choice and open-ended questions to examine how students applied their CT skills to solve authentic problems. Additionally, Bean et al. (2015) introduced a self-efficacy survey to measure teachers’ understanding of CT concepts in relation to their coding experience.

In this study, the Interactive Assessment of Computational Thinking (IACT) was employed as the measurement tool for assessing students’ CT skills. The IACT, as developed by Rowe, Asbell-Clarke, et al. (2021), stands out as a dependable and easily accessible means of evaluating the foundational CT skills. IACT assessment is tailored to students with varying levels of EFs and eliminates potential barriers, such as excessive text, multiple programming tasks, or other obstacles that might impede their ability to showcase their underlying CT capabilities. It consists of interactive logic puzzles that assess four key CT practices, which are aligned with the frameworks outlined in this study: problem decomposition, pattern recognition, abstraction, and algorithm design. To ensure both concurrent validity and test-retest reliability of IACT, prior research (Rowe, Asbell-Clarke, et al., 2021) engaged thousands of students in the validation study. The findings revealed moderate evidence of the validity and reliability of IACT items in large-scale studies that included students with and without cognitive diversity.

Definition of Executive Functions

Defining EFs precisely has been challenging due to the absence of a single behavior directly tied to EFs (Cristofori et al., 2019). Nevertheless, numerous studies have underscored the complexity and importance of EFs concerning human adaptive behaviors (Sabat et al., 2020). EFs empower individuals to apply their existing knowledge and adapt their cognitive processes flexibly to varying circumstances. This adaptability is crucial for achieving success in learning and work environments (Jurado & Rosselli, 2007).

Zelazo (2020) highlighted several factors that contribute to the development of EFs in students. One significant factor is flexibility, which is often studied in the context of perseveration. Perseveration refers to the tendency to continue with a particular behavior or response even when it is no longer appropriate or effective (Van der Linden et al., 2003). The ability to flexibly adapt one’s behavior and switch between tasks or strategies is crucial for executive functioning (Jacques & Zelazo, 2001). Another important factor is working memory, which refers to the ability to hold and manipulate information in mind over a short period of time (Gathercole & Alloway, 2004). As students’ working memory capacity improves, they become better equipped to actively hold and manipulate information, which supports their ability to plan, solve problems, and make decisions (Jurado & Rosselli, 2007). Inhibition is also a crucial mechanism related to EFs. This factor refers to the ability to suppress or inhibit prepotent or over-learned response tendencies (Richard Ridderinkhof et al., 2011). Students who have effective inhibition mechanisms can resist impulsive behaviours, ignore distractions, and inhibit automatic responses that may interfere with goal-directed actions (Happaney & Zelazo, 2003). This executive function is essential for maintaining focus, self-control, and goal-directed behaviour.

As an influential taxonomy, Miyake et al. (2000) developed a conceptual framework of EFs consisting of three core functions: working memory, inhibition, and shifting. Working memory allows individuals to maintain relevant information and mentally work with it, facilitating complex thinking and problem-solving. It helps individuals resist the interference of irrelevant information (Hofmann et al., 2012), enabling them to focus on the task at hand. Inhibition refers to the capacity to suppress dominant and automatic behavioral responses when necessary (Miyake et al., 2000). It helps us question the possible assumptions and refrain from irrelevant stimuli or perseverative errors (Jurado & Rosselli, 2007). Shifting indicates the competency of transferring the mental sets to adapt to changeable situations (Monsell, 2003). Switching among different tasks allows to develop cognitive flexibility and establish alternative solutions from different perspectives (Monsell, 2003). As the results, higher-order EFs such as problem-solving, reasoning, and CT are crucial for students’ cognitive development and success in various domains, including school and real-life situations (Collins & Koechlin, 2012). The related cognitive mechanisms of the three core functions emphasized in this work are conceptualized in Table 1.

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Table 1.

Executive Functions and the Related Cognitive Mechanisms.

EFs	Related cognitive mechanisms
Working memory	Representing goal-oriented components. Shielding goals from interference. Top-down control of goal-relevant attention
Inhibition	Suppression of habitual and mindless behaviors. Inhibiting dominant or automatic responses.
Shifting	Flexible switching between similar goals. Switching back and forth among multiple goals.

Executive Functions Assessment

Given the complexity and multifaceted nature of EFs, the development of reliable and valid assessment measures is a challenging task. Researchers commonly employ test-based measurements that involve complex problem-solving scenarios to gain insights into the development of children’s EFs. However, the use of performance-based tests in assessing EFs faces certain limitations. One is that the structural features of these assessment scenarios may restrict critical processes associated with EFs (Holmes-Bernstein & Waber, 1990). In other words, the assessments with ordered and organized structures provides executive control for children’s optimal performance (Isquith et al., 2013). Furthermore, Hughes and Graham (2002) has argued that most measures of EFs are flawed and unreliable due to their inability to distinguish between automatic and controlled behaviors, which are considered to reside at opposite ends of a circular continuum. Additionally, many contemporary assessments of EFs overlook the isolation and quantification of specific EFs, such as reasoning and problem-solving (Karr et al., 2018). As a result, the assessment of EFs remains a topic of ongoing debate within the field.

Recently, the University of California, San Francisco (UCSF) introduced a novel mobile assessment battery referred to as Adaptive Cognitive Evaluation (ACE) to measure students’ EFs (Anguera et al., 2016). It provides a reliable way to evaluate EFs by including adaptive, psychometric staircase algorithms, and trial-wise feedback (Anguera et al., 2016). To examine the effectiveness and performance of ACE, extensive empirical research (Hsu et al., 2021; Younger et al., 2021) has been conducted to evaluate its validity and reliability within the EF assessments. For example, Hsu et al. (2021) provided preliminary evidence suggesting that ACE tasks offer a reliable method for EF assessment, ensuring an appropriate challenge level without encountering ceiling or floor effects.

The ACE tasks consists of various modules, and within each module, students are required to respond to probes or targets within a given time frame. The evaluation utilizes adaptive algorithms that adjust the difficulty level based on the student’s performance. As the student’s accuracy and response time improve, the difficulty of the subsequent trials is appropriately increased to ensure an optimal level of challenge. The ACE tasks also provides trial-wise feedback to students, indicating whether their responses were correct, incorrect, or made after the allotted time.

ACE tasks encompass two working memory tasks, two response inhibition tasks, three interference resolution tasks, a cognitive flexibility task, one response time control task, and several other related tasks. In this study, four specific tasks have been chosen to evaluate students’ working memory, response inhibition, interference resolution, and cognitive flexibility. Additionally, response time is included as a covariate to account for its potential impact on the measured EFs. All these measures are aligned with the conceptual framework of EFs, as depicted in Figure 1.OPEN IN VIEWER

Working Memory and Computational Thinking

Working memory refers to the cognitive processes involved in the temporary storage and manipulation of information, which are crucial for complex cognitive tasks such as reasoning, problem-solving, and learning (Baddeley, 1992). Gerosa et al. (2021) conducted a study utilizing mixed-effects linear regressions to examine the relationships between students’ CT skills and working memory. The study by Román-González et al. (2017) further supports these connections. Their findings revealed that well-developed working memory enables students to retain and process logical connections among subjects without constant reference, thereby enhancing problem-solving performance. These studies collectively contribute to the growing body of research that establishes the connections between CT skills and working memory.

In CT activities, working memory plays a crucial role in various cognitive processes, including top-down control of attention and protection of goals from interference with goal-oriented information (Hofmann et al., 2012). For instance, during the problem decomposition stage, students must retain the final goals in their working memory while breaking down complex problems into smaller, more manageable components. Well-developed working memory allows students to effectively maintain and manipulate stored information while resisting attention-grabbing stimuli (Wang et al., 2021), thereby supporting essential mechanisms within individuals’ CT processes.

Inhibition and Computational Thinking

Inhibition refers to the ability to suppress habitual, dominant, and mindless behaviors that are unnecessary in dynamic and ever-changing situations (Verbruggen & Logan, 2008b). Current understanding of the relationships between CT and students’ inhibition development is still limited (Di Lieto et al., 2017). However, research has begun to shed light on this topic. For example, a study by Senn et al. (2004) found that inhibition skills can predict problem-solving abilities and social prerequisites in preschool children. In the context of problem-solving scenarios, inhibition plays a crucial role in enabling students to maintain and update relevant information while inhibiting prepotent responses that may hinder problem-solving (Di Lieto et al., 2017).

Arfé et al. (2019) highlighted the significance of developed inhibition and planning skills in CT practices among young children. This study employed four neuropsychological tests to assess changes in students’ EFs. The results demonstrated that response inhibition skills developed rapidly during the elementary school years. Building upon this work, Arfé et al. (2020) investigated the impact of age-related inhibition development on students’ computational problem-solving performance. The findings revealed that children between the ages of 5 and 7 exhibited heightened sensitivity to CT practices. Given the rapid development of inhibition during childhood, it becomes particularly important to consider the effects of inhibition on students’ CT activities, especially within this developmental time span (Arfé et al., 2020).

Shifting and Computational Thinking

Shifting refers to the ability of flexibility and creativity (Miyake et al., 2000). This ability involves the capacity to adapt and switch between different strategies, tasks, or mental sets. Gerosa et al. (2021) aimed to explore CT skills from a cognitive development perspective, with a specific focus on providing targeted interventions for every individual. In this research, shifting, or cognitive flexibility, was considered as a foundational aspect of complex CT skills that undergoes exponential improvement during childhood. When students encounter complex problems, they may experience frustration and boredom. However, cognitive flexibility can offer a fresh perspective on these situations, enabling individuals to approach problem-solving with a new mindset and establish the belief that desired problem-solving goals can be achieved (Zapata-Rivera et al., 2019).

In CT practices, students with higher cognitive flexibility possess the ability to effectively switch between multiple goals and identify the most efficient methods to attain those goals (Hofmann et al., 2012). Flexible adjustments in behavior within problem-solving environments are vital for successful CT knowledge acquisition and skill development. For example, during the problem decomposition stage, repeatedly making the same errors indicates the need for a switch in problem-solving approaches. In such cases, students must reallocate their attention, inhibit the previous response, learn from their mistakes, and reconfigure their strategies to overcome the challenges (Monsell, 2003). This process of shifting requires cognitive flexibility, allowing students to adapt their thinking and behavior to address different aspects of a problem.

Computational Thinking-IACT Assessment

Students with diverse learning challenges may encounter difficulties when attempting standard CT tests that involve complex, context-dependent scenarios. IACT assessment overcomes these challenges by incorporating logic puzzles designed to minimize text and eliminate the requirement for prior programming experience. By reducing these potential barriers, IACT allows students to engage in the assessment and demonstrate their performance without being hindered by language or programming constraints (Rowe, Asbell-Clarke, et al., 2021). It promotes a more inclusive assessment environment, where students can demonstrate their CT skills in a context that is accessible and conducive to their individual learning needs.

Table 2 provides details about the IACT puzzles that assess four CT constructs: problem decomposition, pattern recognition, abstraction, and algorithm design. Each puzzle is designed to target a specific CT practice and challenges students to apply relevant strategies and thinking processes to solve the given problem. These puzzles are carefully crafted to encourage students’ engagement with the core principles of CT and their practical application within the game environment. Figure 2 displays screenshots of four specific puzzles: P_1 for problem decomposition, P_3 for pattern recognition, P_2 for algorithm design, and P_4 for abstraction.

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Table 2.

Operationalization of CT Practices in IACT Assessment.

Puzzle type	CT practice	Task
Mastermind	Problem decomposition	Finding correct combinations of colors and shapes of item within required moves
Raven’s matrix	Pattern recognition	Select correct piece that completes a pattern with limited attempts
Sudoku	Abstraction	Correctly fill grid spaces with colors and shapes
Maze solving	Algorithm design	Design the least moves to complete the maze

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Figure 2.

Four tasks of IACT assessment.

Executive Functions-ACE Assessment

The ACE tasks are used to measure specific aspects of students’ EFs. The assessment process involves presenting students with probes or targets, and they are required to respond before reaching the maximum reaction time. Immediate feedback is provided after each trial, indicating whether the response was correct, incorrect, or if the time limit was exceeded. In this study, four specific tasks are selected to measure working memory, response inhibition, interference resolution, cognitive flexibility. Studies (Christ et al., 2001; Fry & Hale, 1996) suggested that information processing speed could influence the improvements of EFs. ACE tasks evaluate students’ basic response time before students start other regular tasks. Therefore, the response time control task was included as a covariate to be regressed from performance metrics in all other tasks. Figure 3 shows the screenshots of these four tasks.OPEN IN VIEWER

Canonical Correlation Analysis

Suppose we are given n instances S = ( ( x 1 , y 1 ) , … , ( x n , y n ) ) , where S x denotes students’ ACE tasks measures as ( x 1 , … , x n ) , and S y denotes students’ IACT assessment scores as ( y 1 , … , y n ) . Consider projecting x onto a direction w x and y onto a direction w y to build a new coordinate, where the new x coordinate is:

S x , w x = ( 〈 w x , x 1 〉 , … , 〈 w x , x n 〉 )

(1)

S y , w y = ( 〈 w y , y 1 〉 , … , 〈 w y , y n 〉 )

(2)

The goal is to find w x and w y that can maximise the correlation between ACE task measures and IACT assessment scores:

ρ = max w x , w y c o r r ( S x w x , S y w y ) = max w x , w y 〈 S x w x , S y w y 〉 ∥ S x w x ∥ ∥ S y w y ∥

(3)

Suppose E [ f ( x , y ) ] is the empirical expectation of the function f ( x , y ) :

E [ f ( x , y ) ] = 1 m ∑ i = 1 m f ( x i , y i )

(4)

ρ = max w x , w y E ^ [ 〈 w x , x 〉 〈 w y , y 〉 ] E ^ [ 〈 w x , x 〉 2 ] E ^ [ 〈 w y , y 〉 2 ]

(5)

= max w x , w y E ^ [ w x ⊺ x y ⊺ w y ] E ^ [ w x ⊺ x x ⊺ w x ] E ^ [ w y ⊺ y y ⊺ w y ]

= max w x , w y w x ⊺ E ^ [ x y ⊺ ] w y w x ⊺ E ^ [ x x ⊺ ] w x w y ⊺ E ^ [ y y ⊺ ] w y

The covariance matrix of ( x , y ) is:

C ( x , y ) = E ^ [ ( x y ) ( x y ) ⊺ ] = [ C x x C x y C y x C y y ] = C

(6)

Therefore, equation (5) is rewriting as:

ρ = max w x , w y w x ⊺ C x y w y w x ⊺ C x x w x w y ⊺ C y y w y

(7)

According to equation (7), ρ is note affected by w x or w y . We can replace w x by a w x and w y by a w y . The goal to is maximize the numerator subject to:

w x ⊺ C x x w x = 1

w y ⊺ C y y w y = 1

(8)

The corresponding Lagrangian is:

L ( λ , w x , w y ) = w x ⊺ C x y w y − λ x 2 ( w x ⊺ C x x w x − 1 ) − λ y 2 ( w y ⊺ C y y w y − 1 )

(9)

Taking derivatives in respect to w x and w y :

∂ f ∂ w x = C x y w y − λ x C x x w x = 0

∂ f ∂ w y = C y x w x − λ y C y y w y = 0

(10)

Rewrite equation (10), then obtain:

0 = w x ⊺ C x y w y − w x ⊺ λ x C x x w x − w y ⊺ C y x w x + w y ⊺ λ y C y y w y = λ y w y ⊺ C y y w y − λ x w x ⊺ C x x w x

(11)

Suppose λ = λ x = λ y and C y y is invertible:

w y = C y y − 1 C y x w x λ

(12)

Then we get:

C x y C y y − 1 C y x w x = λ 2 C x x w x

(13)

To find the coordinate system that optimizes the correlation, we have to follow two steps: first, solving the generalized eigenproblem of the for A x = λ B x ; second, using equations (12) and (13) to identify w x and w y .

To gain deeper insights into the potential connections between students’ EFs and their CT skills, Pearson correlations and linear regressions were subsequently used to investigate the associations between the sub-dimensions of these two domains.