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Since the 1960s, a few, yet very influential, educational researchers have investigated how computer programming can be used to foster mathematics learning. However, since the term ‘computational thinking’ was popularised by Jeannette Wing in 2006, the number of studies in this area has grown substantially. In this article, we present a systematic...

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This research aims to determine the perceptions of middle school pre-service mathematics teachers regarding the concept of "mathematical thinking" through the usage of metaphors. The phenomenology method, which is one of the qualitative research methods, is adopted in this study. Data of the research was obtained by the pre-service mathematics teac...

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... But also, pre-service teachers expressed that this work could allow children to learn other mathematical aspects such as representing, communicating, and connecting mathematical ideas, namely, working with numbers, spatial orientation, directions, and pattern recognition (retrieved from the written task delivered by pre-service teachers). This aspect shows that pre-service teachers identify an intersection between CT and mathematics learning once they assume that both CT and mathematical reasoning are used to decompose the problem, think abstractly, produce, or choose an algorithm appropriate to the problem, and debug any errors that might arise [12]. ...

... Their knowledge retention of math increased significantly, and they were able to perceive the relevance between math and coding that further deepened their understanding of said math concepts while helping them realize the value of math in problem solving. This finding reconfirmed the potential of CT integration to invigorate math instruction, as evidenced in prior literature (Hickmott et al., 2018;Niemelä & Helevirta, 2017;Rodríguez-Martínez et al., 2020;Weintrop et al., 2016;Wright et al., 2013). ...

Students need to learn and practice computational thinking and skills throughout PreK-12 to be better prepared for entering college and future careers. We designed a math-infused computer science course for third to fifth graders to learn programming. This study aims to investigate the impact of the course on students’ knowledge acquisition of mathematical and computational concepts, motivation, and perceptions of the computing activities. Fifty-one students at a Boys and Girls Club participated in the study. Data collection procedures include pre- and post-tests, pre- and post-surveys, in-class observations, and one-on-one interviews. Results indicate that students have improved significantly on mathematical and computational concepts. They also tended to believe computer programming is fun, comprehensible, enjoyable, and were able to perceive the value of learning it. Implications and recommendations for future research are also discussed.

... Another review study on CT in K-12 mathematics classrooms considered linking mathematical concepts and CT with reporting. Notably, more studies incidentally linked mathematics learning with CT as opposed to creating explicit links (Hickmott et al., 2018). The aforementioned studies showed that multiple concepts in CT overlap significantly with elements of mathematics compared to other subjects. ...

... The results of the criterion validity of the two measurements proved that CT abilities were associated with and predicted by mathematical abilities such as logical sequence, identifying a subset, or matching sets, and mathematical knowledge such as patterns, counting, or comparison to solve a problem (Gadanidis et al., 2017;Hickmott et al., 2018;Lavigne et al., 2020;Sung et al., 2017). The correlation coefficient ranged from 0.22 to 0.37, indicating that the correlation was weak despite a significant positive relationship. ...

Computational thinking (CT) in young children has recently gained attention. This study verified the applicability of the Korean version of the Bebras cards and TACTIC-KIBO in measuring CT among young children in South Korea. A total of 450 children responded to the Bebras cards, TACTIC-KIBO, and Early Numeracy tasks that were used for the following analyses. Item response theory analysis, confirmatory factor analysis, correlation analysis, and calculation of Cronbach’s alpha were conducted to examine the psychometric properties of the validity and reliability of the two measurements. The results showed that these two measurements are acceptable for assessing CT among young children, demonstrating good validity and reliability, despite limitations such as the weak factor loadings of some items and low internal consistency of subfactors. These two CT measurements were significantly and positively correlated with early mathematical ability. Thus, these two measurements are acceptable for assessing CT among young children with varying CT ability, as they present good psychometric properties of the overall scores even though they have low internal consistency of subfactors and slightly weak correlations between subfactors.

... CT has been included in various educational settings, ranging from early childhood and preschool education to university levels (Grover and Pea, 2013;Lyon and Magana, 2020;Fagerlund et al., 2021). The inclusion of CT notions in formal education has taken many forms, which include its integration in both computer science courses and its embedding in different disciplines, such as math (Weintrop et al., 2016;Hickmott et al., 2018), science (Sneider et al., 2014;Swanson et al., 2019), and art (Bell and Bell, 2018). Moreover, CT has reached classrooms during the instruction of programming (Zhang and Nouri, 2019;Papadakis, 2021Papadakis, , 2022 through robotics (Ioannou and Makridou, 2018) and unplugged activities, such as board games or storybooks (Huang and Looi, 2021). ...

Computational thinking (CT) is a broadly used term in education to refer to the cognitive processes underlying the application of computer science concepts and strategies of problem-solving. Recent literature has pointed out the value of children acquiring computational thinking skills (i.e., understanding and applying concepts, such as conditionals, iteration, or generalization), especially while learning STEM subjects. Robotics has been used as a tool to introduce computational thinking and STEM knowledge to children. As physical objects, robots have been proposed as developmentally appropriate for the early childhood setting, promoting motivation and allowing young learners to represent abstract ideas in a concrete setting. This study presents a novel educational robotics (ER) intervention using RoboTito, a robot programmable through tangible elements in its environment designed for kindergarteners. We used a quasi-experimental design with an active control group. In addition, we conducted a structured observation of the filmed material of the sessions to gather data on children’s attention and motivation throughout the activities. Fifty-one children (male = 33; mean age = 66 months, SD = 5.49 months) attending level 5 (kindergarten) at a Uruguayan public school participated in the study. Children in our experimental condition participated in an intervention programming RoboTito using tangible elements, while children in our control condition played with the robot through sensory-motor activities using a remote control and did not engage in programming. Motivational and attentional factors were assessed through video-recorded sessions of the ER activities. Four trained observers blind to the experimental conditions participated in the coding. Children’s interactions were assessed in four categories: task engagement, distractibility, oral participation, and objective fulfillment. Our results suggest children’s task engagement mediated their gains in CT after the intervention; post-hoc Tukey contrasts revealed non-significant pre-test to post-test gains for the control and low engagement groups, and significant for the high engagement group. Overall, we conclude task engagement played a central role in children’s learning gains and our robotics intervention was successful in promoting CT for engaged children. We discuss the practical implications of our results for early childhood education and developmentally appropriate ER targeted for young learners.

... such as studies from Barcelos et al. (2018) and Hickmott et al. (2018). In these earlier reviews, there is no detailed information about the types and forms of CT tools, and the assessed CT competencies and mathematics topics in the integrated instruction. ...

... Another review study was performed by Hickmott et al. (2018) by recognizing peerreviewed articles on CT in K-12 educational settings that were published between 2006 and 2016 and figuring out how these research-related CT to mathematics learning. The results indicated that the majority of the studies: (1) originate from computer science academics rather than education experts, (2) involve mathematics but primarily focus on teaching programming skills, and 2017, to identify studies that looked at how the relationship between mathematics and CT has been proven through didactic activities at all levels of education. ...

... Scratch was the most prevalent CT tool. The usage of Scratch enabled the students to engage with tough mathematical concepts in new, meaningful, and generalizable ways (Benton et al., 2018). By using Scratch, students were able to create computer programs without worrying about syntax or spelling in block-based coding environments (Gadanidis et al., 2018). ...

The importance of computational thinking (CT) as a 21st-century skill for future generations has been a key consideration in the reforms of many national and regional educational systems. Much attention has been paid to integrating CT into the traditional subject classrooms. This paper describes a scoping review of learning tools for integrating CT and mathematics in current empirical studies published from 2015 to 2021. The review showed that most of the studies implemented CT-intensive Math-connected integration. Five major types of CT tools had been identified, i.e., digital tangibles, apps and games, programming languages, formative or summative assessments, and other technological tools. In many instances, the tools also provide functions of assessment of CT skills. The most assessed CT competencies were including algorithms and algorithmic thinking, abstraction, testing and debugging, loops, and sequences. Geometry and Measurement was the most assessed mathematics topic. Our scoping review is beneficial in the investigation of the literature on CT and mathematics education, as well as guides those who are interested in developing curriculum, programs, or assessments that involve the integration of CT and mathematics.

... On the other hand, the studies in which experimental and control groups were formed with random assignment were rarely observed (Cetin, 2016;Jun et al., 2017;Pala & Mıhçı Türker, 2021;Sung et al., 2017). Similarly, Hickmott et al. (2018), in their review of CT studies in math, concluded that none of the studies conducted experiments with random assignment. ...

Cluster randomized trials are frequently used in educational research for methodological reasons. This study aims to improve the efficiency of cluster randomized trials on computer/information literacy and computational thinking. The study employs a two-level hierarchical linear model to estimate (i) intraclass correlation coefficients, (ii) the amount of explained variances given selected predictors, and (iii) minimum detectable effect sizes given the set of plausible scenarios. Two data cycles from the International Computer and Information Study were used. The covariates at the student level are gender, interest in ICT, parents’ highest education level, ICT self-efficacy, and experience with computers. The covariates at school/teacher level are teacher’s ICT use, ratio of school size to the number of computers for student use, availability of ICT resources at school, approximate teacher age, and ICT self-efficacy. Findings showed that the most precise effect could be measured when student and teacher/school covariates are both adopted. Lastly, it was revealed that increasing the number of schools is effective to get the most precise effect.

... This is not to say that the application of CT in mathematics is non-existent. For example, Hickmott et al. (2018) analysed literature from the fields of both computer science (CS) and mathematics education, with the aim of identifying peer-reviewed studies published from 2006 to 2016 that related to CT in the K-12 educational context. They sought to determine whether, and in what ways, these studies linked CT to the learning of mathematics. ...

... Hence, while this does not necessarily show the full picture of CT in mathematics, it helps give an impression of how prevalent it is worldwide to include CT in primary mathematics education (see Table 3). With regard to mathematics content domains, in line with Hickmott et al. (2018), we found that all but one of the domains (i.e. data and chance) were prominent in (at least) one of the papers, with geometry and numbers being the most frequently addressed. ...

... Weintrop et al. (2016, p. 139) similarly stressed that computer programming is important for students to learn when working with CT, because they develop the ability to encode instructions in such a way that a computer can execute them, which is a powerful skill that can also be applied when solving mathematical problems. Hickmott et al. (2018) concluded that full integration of CT in mathematics is complicated. There are hindrances that make fully integrated approaches far from straightforward; as Shute et al. (2017) reminded us, teachers tend to be unfamiliar with CT and, for that reason, struggle to see the connections between it and the learning of mathematics. ...

Computational thinking (CT) has acquired the status of a necessary 21st-century skill and is currently being introduced in school curricula around the world, despite a lack of consensus about what it entails. The aims of this review are to provide an overview of the existing literature on CT activities in primary mathematics education, and to articulate how it is integrated into the teaching and learning of primary mathematics. This systematic review presents and analyses the findings of 10 empirical studies, revealing a recent increased focus on the inclusion of CT in primary mathematics classrooms, as most studies are published around 2020. Our findings indicate two categories of such activities, one focusing on skills (such as mainly sequencing, looping, conditionals, debugging, decomposition, and abstraction) and one on process-oriented activities (communication, creativity, exploration, and engagement). Furthermore, we found that, while there are studies reporting on mathematics being taught directly through CT activities (full integration), in most studies, the mathematics content was emphasised, with CT built in as a way for students to demonstrate their understanding of mathematics concepts (partial integration). This review identifies current gaps in the field and the need to investigate further such process-oriented activities, the use of these activities in accelerated mathematics, and the need for different methodological approaches in primary mathematics.

... These studies frequently occurred within technology-related courses and contexts such as computer science and programming activities. A scoping review of CT in K-12 mathematics similarly showed that many studies were conducted within the field of computer science and focused on participants' perceptions of computer science careers (Hickmott et al., 2018). The previous scoping reviews demonstrated that most studies have examined CT development with computers and programming languages as the primary tools as opposed to the use of robotics or Content courtesy of Springer Nature, terms of use apply. ...

... unplugged activities (Hickmott et al., 2018;Ilic et al., 2018). Additionally, participants in CT studies have most often been elementary school students followed by in-service and pre-service teachers; scholars have recommended that more future studies of CT should be conducted with preschool children (Ilic et al., 2018). ...

When implemented appropriately, computational thinking (CT) experiences in early childhood settings build essential literacy skills and foster initial explorations of sequencing, engineering design principles, and cause-and-effect relationships. While existing research explores CT in K-12 settings, there is insufficient research documenting the true scope of CT skills for preschool-age children (ages 3–5 years old). Thus, the paucity of research in this emerging area warranted a scoping review approach. This scoping review surveys existing CT studies with preschool-age participants and maps what is known of CT learning experience design, intended educational outcomes, and CT study design. Evidence from the reviewed articles (n = 17) indicate most studies used physical kits, task-oriented activities, and varying experience timeframes and adult scaffolding. Most studies focused on learning sequencing and events with few embedding remixing and reusing skills. Additionally, studies primarily implemented pre-post research design approaches, and few utilized qualitative methods. The analysis of the reviewed articles indicates gaps exist in CT experience designs, scope of CT interventions, and CT tool research and development. We conclude with recommendations for closing the knowledge gaps by providing specific future research directions.

... While Wing's (2006) article about computational thinking and its benefits reinvigorated discussions among educators, researchers, and policymakers about its role in K-12, it initially gained popularity in mathematics classrooms in the early 1980s as a result of Papert's work and his programming language, LOGO. During the last two decades, programming and CT in K-12 settings have gained more attention by researchers and educators (Hickmott et al., 2018;Kalelioğlu et al., 2016;Lye & Koh, 2014). This literature review will first provide an overview of the current landscape of such research in K-12 settings, followed by a synthesis of research on programming in primary mathematics education, and conclude with a discussion about teacher preparation and the gap in the literature. ...

... She found that engaging young students in coding activities can support higher levels of mathematical thinking about mathematical patterns and structures. Hickmott et al. (2018) reviewed studies that involved computational thinking in mathematics classrooms. They noted the need to integrate it with mathematical topics such as probability, statistics, and measurement, and identified gaps in investigations of explicit links between them. ...

... There is a need to build on the successes of this intervention to seek more opportunities for effective mathematics teaching with robots. In addition, there is a need to examine how integrating robots in mathematics classes influence students' mathematical reasoning in areas such as arithmetic, geometry, algebra, and statistics (Hickmott et al., 2018). Exploring concrete ideas and examples of how to integrate robots in mathematics teaching can heighten PSTs' perceptions of the affordances and usefulness of these technologies for mathematics learning. ...

While programming was introduced to mathematics classrooms in the 1980s, emerging robotic technologies have encouraged more widespread integration of these technologies to support the development of K–12 students’ mathematical reasoning. The recent emphasis of programming and computational thinking in K–12 education has highlighted the need to prepare future teachers appropriately to incorporate these technologies in their teaching. This study draws from the technology acceptance model and the theory of planned behavior to examine how pre-service teachers’ (PSTs) interaction with robots might influence their intent to use them in teaching. Two groups of such participants engaged in solving mathematical problems using robots in this quasi-experimental pre-/post-test study. Additionally, one of these groups had the chance to design and implement activities that integrated robots with first-grade students. The robots used in this study were Bee-Bots, simple programmable robots that can store up to 40 commands. At the beginning and end of a semester, both groups of participants completed a questionnaire about their perceptions, attitudes, and intentions towards using robots in teaching. In addition, the group who designed and implemented activities with robots provided qualitative reflections about their experience. The study’s quantitative and qualitative findings show that both groups of participants reported significant increases in their intention to use robots in teaching. These findings highlight that opportunities for PSTs to explore, ponder, and experience robotic technologies can promote the integration of these tools in their future teaching.

... A SIGCSE paper (Al-Zubidy et al., 2016) showed that empirical validation is common among SIGCSE papers, with about 70% of papers using some form of empiricism. There is a large variety in methods however: studies are performed both in the classroom (Grover, Rutstein & Snow, 2016;Hickmott, Prieto-Rodriguez & Holmes, 2017;Kazakoff & Bers, 2012) as well as in extracurricular settings (Maloney et al., 2008). Not all studies involving K-12 CSEd include subjects: in addition to small scale studies in classrooms, programs created by learners have also been analyzed by researchers. ...

Computer science education (CSEd) research within K-12 makes extensive use of empirical studies in which children participate. Insight in the demographics of these children is important for the purpose of understanding the representativeness of the populations included. This literature review studies the demographics of subjects included in K-12 CSEd studies. We have manually inspected the proceedings of three of the main international CSEd conferences: SIGCSE, ITiCSE and ICER, of five years (2014–2018), and selected all papers pertaining to K-12 CSEd experiments. This led to a sample of 134 papers describing 143 studies. We manually read these papers to determine the demographic information that was reported on, investigating the following categories: age/grade, gender, race/ethnic background, location, prior computer science experience, socio-economic status (SES), and disability. Our findings show that children from the United States, boys and children without computer science experience are included most frequently. Race and SES are frequently not reported on, and for race as well as for disabilities there appears a tendency to report these categories only when they deviate from the majority. Further, for several demographic categories different criteria are used to determine them. Finally, most studies take place within schools. These insights can be valuable to correctly interpret current knowledge from K-12 CSEd research, and furthermore can be helpful in developing standards for consistent collection and reporting of demographic information in this community.