Criteria employed by teacher educators when reflecting upon a problem-solving activity involving robots

Abstract

This study aims to identify the criteria employed by teacher educators and researchers in mathematics education when evaluating an activity designed to foster computational thinking through the use of the BlueBot educational robot. The proposal is targeted at pre-service early childhood education teachers, with the objective of preparing them to effectively teach this content. In recent years, several countries have incorporated computational thinking into their curricula as part of educational reforms responding to evolving social demands. The study involved twenty experts in mathematics education and teacher training who participated in a 90-minute workshop organised by the authors at a Catalan university. During the session, the participants carried out the proposed activity, reflected on their experience, and contributed to a group discussion in which they shared their evaluations. They were audio-recorded and subsequently transcribed for analysis. The data were examined using the didactic suitability criteria of the ontosemiotic approach. Although the participants were not familiar with this theoretical framework, their evaluations revealed indicators consistent with its criteria, enabling a theoretically grounded reinterpretation of their views. The findings show that the instructional activity was perceived as highly suitable from a didactic perspective, with particular emphasis on its epistemic, cognitive, and ecological suitability. These results underscore the need to design and implement teacher training programmes – both pre-service and in-service – that support the development of mathematical thinking through computational thinking, with a strong focus on reflective practice.

Keywords:
Criteria of didactic suitability; early childhood education; teacher training; computational thinking; educational robot

Resumen

El objetivo de este trabajo es identificar los criterios que utilizan formadores de docentes e investigadores en Didáctica de las Matemáticas para valorar una actividad orientada al desarrollo del pensamiento computacional, mediante el uso del robot educativo BlueBot. La propuesta se dirige a la formación de futuros maestros de Educación Infantil, con el fin de formarlos para enseñar este contenido, recientemente incorporado en diversos países a través de reformas curriculares que responden a las demandas sociales actuales. Participaron en el estudio veinte expertos en Didáctica de las Matemáticas y formación del profesorado, quienes asistieron a un taller de 90 minutos organizado por los autores en una universidad catalana. Los participantes realizaron la actividad, reflexionaron sobre ella y, en una puesta en común, compartieron sus valoraciones, las cuales fueron grabadas y transcritas. El análisis de estas intervenciones se llevó a cabo mediante la herramienta de los Criterios de Idoneidad Didáctica del Enfoque Ontosemiótico. Aunque los participantes no estaban familiarizados con dicho marco teórico, sus valoraciones permitieron identificar indicadores alineados con estos criterios, posibilitando su reinterpretación fundamentada. Los resultados evidencian que la actividad fue valorada como altamente idónea desde una perspectiva didáctica, destacándose, especialmente, la idoneidad epistémica, la cognitiva y la ecológica. Finalmente, es necesario diseñar e implementar programas de formación para orientar a las futuras maestras y a los maestros y maestras en activo, con el fin de promover el desarrollo del Pensamiento Matemático a través del Pensamiento Computacional, donde la reflexión sobre la práctica educativa toma un papel primordial.

Palabras clave:
Criterios de idoneidad didáctica; Educación infantil; Formación del profesorado; Pensamiento computacional; Robot educativo

1 Introduction

In recent decades, there has been significant progress in the development of technology, leading countries all over the world to reconsider their public policies in various fields, especially in education.

Wing (2006) defined computational thinking (CT) – beyond being a technological skill to be developed by computer scientists – as a fundamental skill for everyone, considering it to be a core competence to be developed at school level. One of the strategies used to develop CT in the early years of schooling (Grover; Pea, 2013; Jara; Hepp, 2016) has been through programming and educational robotics (Conde et al., 2021; García-Peñalvo; Mendes, 2018; Llorens Largo et al., 2017). However, teachers are often left to face this challenge alone, which can sometimes result in the abandonment of innovative teaching practices aimed at fostering digital literacy and technological skills through the use of educational robots. Mondada et al. (2017) maintain that providing guidance on the potential uses of these resources encourages teachers to incorporate them into their teaching practices.

In Spain, a recent curriculum reform has been introduced in basic education with the objective of promoting the development of technology-related competences among students. For instance, the updated curriculum in Catalonia, an autonomous community in Spain with legislative authority over educational matters, explicitly states that by the end of primary education, students should have developed specific mathematical competences related to CT, enabling them to solve problems and engage in efficient mathematical modelling (Departament d’Educació, 2022). At earlier educational stages, CT has also been incorporated into the second cycle of early childhood education (ECE), which serves children aged 3 to 6. The current Catalan curriculum (Departament d’Educació, 2023), along with the Spanish curriculum, introduces CT within the learning area focused on discovering and exploring the environment. The curriculum aims to foster the development of problem-solving skills among young learners (Ministry of Education and Vocational Training – MEFP, 2022). Consequently, the curriculum proposal developed by the Spanish Ministry of is a clear example of how CT and mathematical thinking (MT) can be integrated across different stages of the educational system.

The design and implementation of teacher training programmes are proposed as one of the alternatives for guiding pre-and in-service teachers to enable them to meet the demands of the new curriculum, including the development of MT through CT.

Recent studies have shown that educational robotics holds particular potential from early childhood onwards (Bers, 2008; Bers; Horn, 2010; Kazakoff; Sullivan; Bers, 2013). Likewise, research on the use of the BlueBot educational robot or similar robots in the development of MT reveals two main areas of interest: teacher training and types of tasks to be used in mathematics lessons. With regard to teacher training, evidence has been provided on various aspects when participants use and handle educational robots: a) types of errors made by pre-service ECE teachers when using educational robots (Seckel; Vásquez, et al., 2022); b) reflections of future ECE teachers when planning learning situations including educational robots for mathematics lessons (Seckel; Breda, et al., 2022); and c) primary school teachers’ conceptions regarding the use of this resource in their mathematics lessons (Seckel et al., 2021). With respect to the types of tasks, research has been conducted on: a) the development of logical-mathematical skills in ECE and the first year of primary education (Muñoz et al., 2020); b) the development of spatial thinking (Aranda; Estrada Roca; Margalef Martí, 2019; Palmer, 2017); c) the development of algebraic thinking (Alsina; Acosta, 2018); and d) the development of mathematical skills (Diago Nebot; Arnau Vera; González-Calero Somoza, 2018; Pérez Buj; Diago Nebot, 2018). However, none of these studies place particular emphasis on the computational concepts or practices developed through the use of educational robots, nor on how these are connected with the curricular aspects of the educational level for which the proposed robotic tasks or problems are designed.

Research from the past five years has focused on the study of educational practices and teachers’ conceptions regarding the use of educational robots and the development of CT through robotics (Casey; Pennington; Mireles, 2021), and more particularly on the use of these robots with young children (Papadakis, 2020; Seckel et al., 2021). Those studies highlight the interest in studying the knowledge, for instance, technological knowledge (Mishra; Koehler, 2006), teachers require for their teaching beyond pedagogical content knowledge (Shulman, 1986).

Within this context, the theoretical framework of the ontosemiotic approach (OSA) (Godino; Batanero; Font, 2007, 2019) offers a model of didactic-mathematical knowledge (DMK) that interprets and characterises teachers’ knowledge based on three dimensions: the mathematical dimension, the didactic dimension, and the meta-didactic-mathematical dimension (Pino-Fan; Godino, 2015). This study focuses on the meta-didactic-mathematical dimension, as it characterises the knowledge teachers require to reflect on practice (their own or that of others). In particular, it involves identifying and analysing the set of norms and meta-norms that regulate the processes of teaching and learning mathematics, as well as assessing their didactic suitability in order to propose potential improvements in the design and implementation of these processes (Breda; Pino-Fan; Font, 2017).

This research seeks to answer the following research questions: What criteria do teacher educators and expert researchers in mathematics education employ to assess an activity on CT using the BlueBot educational robot aimed at training future ECE teachers? How could the criteria identified in the participants’ evaluations be interpreted in terms of the didactic suitability criteria (DSCs) and their components and indicators?

This study therefore aimed to identify the criteria teacher educators and expert researchers in mathematics education relied on to evaluate a CT-based task using the BlueBot educational robot designed for preparing future ECE teachers. To this end, the criteria implicit in their comments were reinterpreted in terms of the DSCs and their components and indicators.

2 Theoretical framework

Several proposals aimed at teacher training focus on equipping teachers with the knowledge required to foster CT among their students (Estebanell et al., 2018; Kong; Lai; Sun, 2020). For instance, Estebanell et al. (2018), propose a model for initial teacher training that encompasses four levels for the development of CT: 1) user level: teachers ask themselves questions about how to use a specific computational language to solve problems involving a robot, video game, application, etc., 2) reflective user level: teachers reflect on what they did when developing a computational problem, 3) teacher level: teachers face the challenge of deciding what to teach, what they expect their students to learn about CT, and which resources and strategies to use, and 4) reflective teacher level: teachers reflect on the teaching and learning process related to CT.

With regard to problem-solving involving CT, teachers should be able to recognise two fundamental aspects when designing problems (Arlegui; Pina, 2016). The first aspect is related to the nature of robotics-type problem tasks, whose resolution requires the robot to move from an initial position to a final one through planning a sequence of actions (intermediate positions that are programmed). The second aspect concerns the criteria that should guide the formulation of a problem or a sequence of problems: 1) presenting progressive complexity, 2) referring to both known and unknown elements, and 3) situating the problem within a specific environment or scenario.

The framework proposed by Brennan and Resnick (2012) provides an operational definition of CT, characterising it through three observable dimensions: computational concepts, practices, and perspectives. Computational concepts include sequences, parallelism, loops, conditionals, events, data, and operators. Observable practices encompass the following four: experimenting and iterating, testing and debugging, reusing and remixing, and abstracting and modularising. The perspectives considered include expressing, connecting, and questioning.

In addition to these specific aspects of CT, it is also necessary to consider the meta-didactic-mathematical dimension of teachers’ knowledge, which constitutes the focus of this study. The OSA provides a tool known as the didactic suitability criteria (DSCs) (Breda; Font; Pino-Fan, 2018) whose understanding enables teachers to evaluate and redesign instructional processes. It consists of six DSCs (Font; Planas; Godino, 2010): the epistemic suitability criterion, which assesses whether the mathematics taught represents “good mathematics”; the cognitive suitability criterion, which evaluates -prior to instruction- whether the learning content is at a reasonable distance from what students already know, and -after instruction- whether the learning acquired approximates the intended learning goals; the interactional suitability criterion, which assesses whether classroom interactions help resolve students’ doubts and difficulties; the mediational suitability criterion, which evaluates the adequacy of the materials and time used in the instructional process; the affective suitability criterion, which considers student involvement, interests, and motivation in the learning process; and the ecological suitability criterion, which assesses the alignment of the teaching process with the school’s educational project, curriculum guidelines, and social and professional context. In order for the DSCs to be operational in the analysis and evaluation of instructional processes, they are further broken down into a set of components and indicators (Breda; Pino-Fan; Font, 2017).

3 Methodology

This study is framed within a qualitative interpretative paradigm (Cohen, Manion, & Morrison, 2007) aimed at identifying and understanding the criteria used by expert teacher educators to evaluate an activity—comprising a sequence of tasks—designed by the authors of this paper to foster the development of CT among future ECE teachers.

The activity, which involved the use of the educational robot BlueBot, was designed following a systematic review of its alignment with the new ECE curriculum (Departament d’Educació, 2023). The activity was implemented by the first two authors as a workshop integrated into the programme of a research conference held at a Catalan university in 2023. All conference attendees participated in the workshop, as no parallel sessions were offered. The workshop had an approximate duration of 90 minutes.

The participants were 20 researchers in didactics of mathematics and teacher educators responsible for training ECE, primary, and secondary mathematics teachers from various Spanish universities. Although all participants have extensive professional experience in teacher education and are recognised researchers in the field of mathematics education, none of them had in-depth knowledge of the use of educational robots or similar technologies in the classroom for the development of CT, nor were they specialists in technology. Furthermore, the participants were not regular users of the DSCs in their research, as they typically work with theoretical frameworks other than the OSA.

At the beginning of the workshop, a presentation was delivered explaining its objective: to evaluate an activity designed by the authors and previously implemented with future teachers at a Catalan university (Catalonia, Spain). The workshop was organised in two phases. In the first phase, the participants completed a sequence of tasks as if they were pre-service ECE teachers, following an adapted version of the original implementation carried out with future teachers, due to the more limited time available for the workshop. In the second phase, the participants, from their actual professional role as educators of future teachers, reflected on the activity and shared their insights during a final group discussion.

The authors took field notes based on observation of the different groups of teacher educators as they interacted with the robot to solve the tasks proposed. The idea-sharing session that concluded the workshop was audio-recorded. The audio recording was analysed by the first two authors, who selected comments and contributions from the discussion that could be identified as reflecting the criteria used by the participants to evaluate the activity. These comments were transcribed and subsequently reinterpreted in terms of the DSCs and classified in a table in accordance with the indicators corresponding to each of the identified DSC components. The components and indicators used can be found in Breda and Do Rosário Lima (2016).

The identification of evaluative comments, as well as the classification of their reinterpretations based on the DSC indicators, were triangulated with the other two authors of this paper and with an expert in the OSA theoretical framework whenever discrepancies arose. To this end, the two co-authors and the expert reviewed both the audio recording and the transcription of the participants’ original comments, discussing the classifications until at least four of the five researchers (the four authors and one collaborating expert involved in the triangulation) reached agreement. These triangulation meetings were held periodically throughout the data analysis process.

This study followed the code of ethics on integrity and best practices of the university of Barcelona and was approved by the academic committee of the doctoral programme in teaching and learning of sciences, languages, arts and humanities at the university of Barcelona on July 18, 2023.

3.1 Description of the activity

First, a brief presentation was given to explain the purpose of the activity in which the participants were about to engage. This activity formed part of a sequence of tasks that had recently been implemented with two groups of future ECE teachers at a Catalan public university – and subsequently analysed with the aim of identifying their mathematical and computational knowledge when solving problems using the BlueBot educational robot, as well as the justifications they provided when reflecting on the design of such tasks. The original instructional sequence implemented with students and the corresponding results can be found in Sala-Sebastià et al., 2023.

Thus, the implemented activity and its curricular rationale (presented in more detail in subsection 3.3) were explained, along with the aim of the workshop, which was for the participants to evaluate that activity previously implemented with pre-service teachers. The participants were first asked to carry out the activity proposed (an adapted and shorter version of the original due to time constraints) as if they were students, namely future ECE teachers. Subsequently, they took part in an idea-sharing session in which they evaluated the activity from their actual role as teacher educators of future ECE and mathematics teachers.

To carry out or experience the activity from the perspective of students, the participants were organised into pairs or groups of three. Each group was given a BlueBot educational robot, a small bag containing manipulative materials (Figure 1) without instructions on how to use them, and a dossier including a set of robotics questions or problems (Table 1) to be solved using the robot within the classroom space where the workshop was held or in the immediate surroundings.

Figure 1
– Manipulative materials used in the activity: the BlueBot robot; cards to represent the robot’s route algorithm; and a 15 cm rectangular card

Table 1
– List of robotic questions or problems from the dossier of the activity

Task	Questions included in the dossier
1	Does anyone know how to play this? Could it be a toy? Are you sure? How do you switch it on? What does it do?
2	It looks like the robot moves when you press the buttons… Could we send it wherever we want?
3	Are there different commands that could be used to reach the same place? Does the robot take the same time to get there with one algorithm as with another? How could we represent the commands we give the robot?
4	Can the robot go far? How far does it move with each “move forward” command? How could we find out how far it can go? Could it reach the classroom of…?
5	Could we use the robot to communicate with another part of the school (the classroom next door/ the caretaker/ the canteen, etc.)? How far is it from our classroom to the other classroom? Which route is best for the robot to take? What is the best route? (Think about what “the best route” means)
6	How can we represent the return instructions? In other words, what will the return programming sequence look like, bearing in mind that the route is the same? Can any part of the programming sequence (or algorithm) be reused?
7	Could the robot be used to transport things? What sort of things could it carry? How could it carry them? What sort of container could be attached to it? Could we use a container from the classroom, or would it be better to build one? Is it necessary to make any changes to the route when the robot is pulling the trailer? Which parts of the programming need to be changed to modify part of the route?

The different groups were given time to solve and discuss the seven tasks in the dossier that made up the activity. This was followed by an idea-sharing session, during which the participants specialising in mathematics education evaluated the activity using their mathematical pedagogical knowledge, now adopting the perspective of educators of future ECE teachers. This paper focuses primarily on analysing this idea-sharing session.

3.2 The BlueBot educational robot

The educational robot used in this implementation is commercially available under the name BlueBot (Figure 1). It is an analogue robot, meaning that to give it instructions for the movements to be performed, the user must press the buttons located on its back. The robot stores the sequence of button presses executed by the user. Therefore, each time a new sequence of commands is to be initiated, the “clear” button must be pressed not to add the new sequence of commands to the previously programmed one. Each press of the forward (or backward) button moves the robot 15 cm forward (or backward). Pressing the turn buttons (right or left) rotates the robot 90 degrees without any forward movement. The programming may also include stops along the route, which are executed by pressing the corresponding “pause” button.

The participants in the implementation were able to use the manipulative materials shown in Figure 1. The small laminated cards represent each of the robot’s keys and can be used (their use is recommended) to write or represent the sequence of commands (key presses to be executed) or the algorithm. Each card can be reproduced as many times as necessary so that the students can write or represent the entire algorithm of their programme, allowing the robot to follow the required path, either before or after executing the programme. The rectangular card shown on the right of Figure 1 is 15 cm long, which is the exact distance the robot moves with each forward or backward command. This card can be used by the robot users to calculate how many key presses are needed to move from one point to another in space, or by the teacher to design paths with precise measurements relative to the robot’s capabilities.

3.3 Curricular justification of the activity

To justify the design of the activity aimed at developing CT in ECE and to situate the tasks in the dossier within the curriculum, an analysis of the current Catalan ECE curriculum, summarised in this sub-section, was performed. The recently published Catalan curriculum (Departament d’Educació, 2023) used to analyse this activity, operates within the same legal framework as the Spanish national curriculum (MEFP, 2022). However, it specifies certain regional particularities of Catalonia - such as the language of instruction, official monitoring and assessment documents, and the number of hours allocated to specific subjects, amongst others), given that the Catalan government has competencies in the field of education.

The ECE curriculum is organised into two cycles: the first one for children aged 0 to 3 years and the second one for children aged 3 to 6 years. It is governed by eight pedagogical principles that serve as a manifesto for the type of teaching and learning pursued. Furthermore, in line with these principles, eight general objectives have been established for the specific competences (SCs) young learners are expected to develop. The elements that make up the curriculum and which must be specified in learning situations are defined as follows: key competences, specific competences, assessment criteria for specific competences, knowledge, and learning situations. There are eight key competences, defined as the learning outcomes considered essential for children to progress in their educational path and to address the main local and global challenges of the future: 1) competence in linguistic communication; 2) multilingual competence; 3) mathematical competence and competence in science, technology and engineering; 4) digital competence, 5) personal, social, and learning to learn competence, 6) citizenship competence, 7) creative thinking competence, and 8) cultural awareness and expression competence.

Key competences are the learning outcomes young learners should develop within the specific context of their environment in order to resolve the different life situations they may encounter. They are organised and classified around the following four axes of development and learning: 1) a child that grows up with autonomy and confidence; 2) a child that communicates using different languages; 3) a child that discovers the world with curiosity; and 4) a child that is part of the diversity of the world around them. Each axis complements the other three, adopting a holistic view of teaching and learning. Axis 1 comprises four SCs, axis 2 comprises two SCs, axis 3 comprises three SCs and axis 4 comprises two SCs. All four axes include SCs related to the development of mathematics in early childhood. However, the SCs explicitly refer to mathematical language and mathematical reasoning skills in axes 2 and 3, respectively.

The assessment criteria serve as the benchmarks for assessment, and each is linked to a specific competence. They indicate the degree of children’s development and acquisition of learning that has taken place in the different activities, situations, and tasks at a specific point in the learning process.

The knowledge areas are the content through which learners must develop the SCs in different meaningful and functional situations and contexts. These knowledge areas are presented as a list organised by educational cycle (first or second cycle, linked to the learners’ age) and with several options for each of the SCs.

Thus, the axes, the SCs, the assessment criteria, and the knowledge areas are all presented with corresponding relationships. In other words, if the activity implemented has been designed to develop a particular SC, situated within one of the axes, it will need to be carried out whilst considering some of the knowledge areas related to this competence listed in the curriculum. The extent to which learners have managed to develop it must be evaluated using some of the assessment criteria corresponding to that SC (more than one assessment criterion may correspond to each SC). It is worth noting that the assessment criteria of the curriculum refer to what students should have mastered by the end of the stage. Those criteria should therefore be adapted to the specific moment of assessment.

Learning situations are defined as experiences children “live” and which teachers use to facilitate learning. They are geared towards the development of SCs and take place within a specific context, presenting a challenge, question, or problem – in a broad sense – to which a response is required and in which learners are actively involved.

The learning situation for the second cycle of ECE, designed by the authors and adapted for implementation, aimed to develop the participants’ CT. This learning situation was originally implemented with future ECE teachers together with expert teacher educators and mathematics teachers. Its implementation is the subject of the study presented in this paper. For the first time, the new Catalan curriculum explicitly refers to CT, specifically in the explanation of SC2 — “To progressively develop different forms of reasoning and scientific thinking procedures through observation and manipulation, to start interpreting the environment, and respond creatively to different challenges and situations” (Departament d’Educació, 2023, p. 33). It states the following:

The processes inherent to both the scientific method and computational thinking skills will be introduced gradually at this stage, through exploration and inquiry, the formulation and testing of hypotheses, the proposal of different solutions, the breaking down of a task into simpler ones, the interrelation of different areas of knowledge, the development of cause-and-effect learning, decision-making through trial and error, and the proposal of creative and original ideas and solutions (Departament d’Educació, 2023, p. 33, authors’ own translation).

However, neither the assessment criteria nor the learning outcomes provide any further explanation of what is meant by “processes […] specific to computational thinking skills” (Departament d’Educació, 2023, p. 33), although it could be inferred that it refers to a type of process associated with inquiry-based learning.

To ensure that the objective of developing CT of the learning situation designed by the authors met the requirements of the Catalan curriculum, an analysis of the activity was carried out from an overall perspective and of each of the tasks set out in the dossier (Table 1) for which a tool specifically designed in Excel was used. Elements were extracted from the curriculum and assigned an a priori categorisation to highlight the possible relationships between the different types of curriculum elements (principles, axes, levels, key competences, specific competences, assessment criteria, and knowledge) in a systematic manner. This was agreed upon by the first two authors of this paper.

Through the learning situation, the aim was to offer the participating students opportunities to develop the following key competences: 1) competence in linguistic communication (which includes mathematical communication), 3) mathematical competence and competence in science, technology and engineering, and 7) competence in creative thinking. Likewise, the activity focuses primarily on the development of various key competences within themes 1 (a child that grows up with autonomy and confidence), 2 (a child that communicates using different languages), and 3 (a child that discovers the world with curiosity). With regard to the other elements of the curriculum covered in the different tasks of the designed learning situation, Table 2 is included below as a summary of the analysis carried out.

Table 2
– Elements of the curriculum identified in the tasks of the dossier

Axis (A)	Specific competence (SC)	Assessment criterion (AC)	Knowledge cycle 1 (KC1) Knowledge cycle 2 (KC2)	Tasks in which they are identified
1	A1 SC3 Recognising the influence of space and time in everyday situations based on experiences lived in order to grow with confidence and understand the world	A1 SC3 AC1 Using basic temporal and spatial concepts based on one’s own experiences	A1 SC3 KC2 1 Using basic concepts of time and space in relation to the body, objects and other people in one’s own experiences. A1 SC3 KC2 2 Identifying some changes and continuities in daily life and the immediate environment, and predicting their continuation A1 SC3 KC2 4 Recognising sequences and the chronological order of events and activities in daily life. Identifying series, repetitions and patterns	Task 5, task 6, and task 7
		A1 SC3 AC2 Developing spatial reasoning skills through exploratory games and everyday situations	A1 SC3 KC2 5 Organising and representing space based on personal experiences, using different forms of expression A1 SC3 KC2 8 Interpreting representations of familiar routes A1 SC3 KC2 9 Use of simple maps and/or following verbal directions in situations of playing and familiar surroundings
2	A2 SC1 Interpret, understand, and express messages, using resources and knowledge drawn from personal experience to improve with regard to communication and the development of new learning.	A2 SC1 AC3 Making functional use of spoken language by expanding learners’ linguistic repertoire and expressing ideas, wishes, feelings and emotions.	A2 SC1 KC2 1 Progressive acquisition of a new communicative repertoire	Tasks 6 and 7
		A2 SC1 AC4 Using spoken language as a means of constructing one’s own thoughts and regulating behaviour in interactions with others, progressively developing more organised and coherent discourse in different contexts	A2 SC1 KC2 6 Gradual use of spoken language in everyday situations to guide one’s own actions
	A2 SC2 Express oneself in a comprehensible, personal, and creative manner through different languages, exploring and enjoying possibilities in order to respond to different communicative contexts	A2 SC2 AC1 Demonstrating skills in communicating and interacting through different forms of language, adapting expression to verbal, mathematical, physical, artistic, musical, and digital contexts	A2 SC2 KC2 15 Recognition and use of mathematical language, numbers, symbols, and codes that can be read by others and which have meanings shared by society in real contexts and progressively more complex situations A2 SC2 KC1 5 Introduction to understanding and expressing the use of mathematical language in everyday situations involving relationships of quantity, measurement and/or spatial position: much/little, long/short, and near/far	Tasks 3, 5, and 6
3	A3 SC1 Observe and recognise characteristics of materials and elements and establish relationships between them, through experimentation and sensory manipulation in order to progress towards increasingly complex thought structures by developing mathematical reasoning skills	Axis 3 SC1 AC1 Using personal strategies and ways of reasoning to solve a challenge and explain the process used	A3 SC1 KC2 1 Observation, exploration, and identification of elements in the environment: objects, materials, animals, plants, landscapes, etc., adopting a respectful attitude	Tasks 1 and 7
		A3 SC1 AC2 Establishing relationships between elements, distinguishing qualities or attributes, identifying patterns and knowing how to communicate them	A3 SC1 KC2 3 Qualitative and quantitative relationships. Recognition of patterns, anticipation, and verbalisation of regularities in everyday situations. A3 SC1 KC2 5 Estimations and predictions using non-standard units in a contextualised and functional manner A3 SC1 KC2 7 Progressive use of strategies for measuring length, capacity, mass, time and temperature A3 SC1 KC2 15 Graphical representation and communication of the processes followed in experimentation and the interpretation of results
	A3 SC2 Progressively develop different forms of reasoning and scientific thinking processes through observation and hands-on exploration to begin interpreting the environment and respond creatively to different challenges and situations	A3 SC2 AC3 Formulating and testing hypotheses through manipulation and experimentation with different elements and materials in order to understand their behaviour	A3 SC2 KC2 3 Introduction to the scientific method: question formulation, inquiry, contrasting, positioning, and its application to new contexts to reformulate new question A3 SC2 KC2 4 Development of strategies for proposing solutions: creativity, dialogue, and discovery	Tasks 2, 3, 4, and 5
		A3 SC2 AC4 Taking part in collaborative challenges in small groups, sharing one’s own ideas and listening to those of others with respect	A3 SC2 KC2 5 Advancement in strategies for planning and organising one’s own actions through dialogue, cooperation, and consensus with others
	A3 SC3 Explore and recognise elements and phenomena of the natural world, establishing relationships between one’s own actions and the resulting consequences to encourage sustainable habits and environmental conservation	A3 SC3 AC1 Establishing connections between phenomena in the natural environment and their impact on daily life, based on knowledge and observation of the natural environment	A3 SC3 KC2 2 Use of both analogue and digital observation tools: magnifying glasses, scales and sensors for data collection and subsequent analysis	Task 5

4 Results

An analysis was conducted of the recording of the discussion between the experts in mathematics education and the teacher educators that took part in the workshop in which the activity was evaluated. Comments that can be interpreted in terms of components and indicators of the DSCs were identified, as indicated in the methodology section. The results are presented below, organised in accordance with the suitability criteria identified.

4.1 Epistemic suitability of the activity

With regard to epistemic suitability, four of the participants (P) referred to the richness of processes, one of the indicators of this suitability that were developed through the activity. For example, P1 comments that the tasks foster relevant processes, such as estimating the measurements required to solve the tasks of the activity, particularly in tasks 3, 4 and 5 of the dossier (see Table 1).

P1: Relevant processes for measuring length and time can be performed (Participant 1, 2023).

Another noteworthy comment is that of P3, who notes that by manipulating the robot to solve task 7 in the dossier, the concept of inverse proportionality can be observed empirically thanks to a physical property of interaction between materials. Indirectly, they allude to the perspective of CT of connecting different areas of knowledge.

P3: Inverse proportionality can be observed empirically. With a constant force [exerted by the robot to move], if I increase the weight by attaching something [to the robot] for it to carry, the acceleration decreases and you can see that the robot moves more slowly (Participant 3, 2023).

P7’s perspective concerns the contribution of the activity to the development of spatial orientation strategies in ECE children:

P7: Processes are promoted that enable the shift from an egocentric reference frame to an external reference frame (Participant 7, 2023).

There were also comments regarding representativeness, the indicator that refers to bearing in mind the complexity of what one wants to teach by considering the diversity of partial meanings, the use of different languages or modes of expression, etc. For example, P2 highlights that a different meaning [this meaning is directly related to the concept of CT called sequence] is worked on compared to the traditional use of the algorithm:

P2: The activity offers a different meaning from the traditional one for the algorithm [referring to the algorithm for solving an operation], such as an instruction for [the robot] to reach a location. Given an instruction, see where it arrives, or create an instruction for it to reach a location (Participant 2, 2023).

P8 points out the task is approached through a series of constraints determined by the type of resource used—the robot—which require reflection on the concept of the “shortest path” in order to solve the task effectively. This comment refers to the perspectives of questioning and connecting of CT.

P8: It gives an idea of a different kind of measurement, since the robot, because of how it can move [referring to the limitation of 90° turns], makes you think about what the shortest path is, as it is not the usual one because it cannot move diagonally. It moves on a Cartesian plane (Participant 8, 2023).

P11 comments on the role of the cards representing the different commands that can be given to the robot as an introduction to the use of code as a language. P11 refers to the perspective of expressing of CT, which focuses on the fact that the code itself that is used to implement the programmes intrinsically constitutes a new way of expressing ideas.

P11: The code on the cards used as a computing language is interesting (Participant 11, 2023).

Seven comments related to the epistemic suitability criterion were identified and reinterpreted. Four of them referred to the indicator of richness of processes and the other three to the representativeness of the mathematics taught. None of the comments identified indicators of the components of errors and ambiguities of teachers in these tasks.

4. 2 Cognitive suitability of the activity

Of the comments gathered, only two were identified and reinterpreted as criteria for cognitive suitability. The comment made by P5 referring to the previous knowledge indicator shows this participant observed how the different mathematical contents are introduced through the progression of tasks proposed in the dossier for the intended meanings to be achieved, and for the difficulty to be manageable for the students:

P5: The mathematical content related to computational thinking, as presented in this activity, falls within the zone of proximal development of future teachers (Participant 5, 2023).

An indicator of high cognitive demand was also identified in the comment made by P6, referring to task 6 in the dossier, when the participants had to consider whether the same algorithm could be used for the robot to go to a place and then return to its initial position. From the perspective of questioning in CT, critical thinking skills are developed:

P6: [In response to the question of whether the same algorithm works for the robot to go to a place and then return], this “go and return” task promotes reversibility of thought (Participant 6, 2023).

P6 also acknowledges that this activity is a challenge for future teachers when they have to put themselves in the position of their future students:

P6: It encourages the future teacher to consider how a child would think to solve the task

(Participant 6, 2023).

It was not possible to identify any indicators related to the component of adapting the curriculum to different individual needs in the participants’ comments. No indicators were identified regarding the learning component of this suitability. The topic of evaluating this type of activity did not arise.

4. 3 Interactional suitability of the activity

Only two comments that could be interpreted as being related to interactional suitability were identified. With respect to the indicators of student-student interaction and teacher-student interaction, P9 expressed concern about the importance of discussing the activity and formulating objectives to ensure future teachers have a clear understanding of the objective of the activity and what they should focus on because, according to this participant, it is common for students to focus on details such as the robot’s user-friendly design rather than on what is important (the development of CT).

In contrast, P10 highlighted that the activity promotes autonomy, another indicator for this component, as the tasks are self-validating (if the robot is programmed to move to a point and fails to reach it, it is the path itself that validates the completion of the task). There is hence no need for the teacher to provide validation.

No comments were identified regarding the formative assessment component this activity may support. As outlined in the previous section, the topic of evaluation did not arise during the idea-sharing session.

4. 4 Affective suitability of the activity

Affective suitability refers to the students’ motivation to participate and maintain interest in the activity proposed. The notes taken in the anecdotal records indicate that the participants actively engaged with the robot both at the tables and throughout the room, with the other groups, and with the authors leading the workshop. The participants completed all the tasks with evident enthusiasm, making positive comments and asking questions about them.

It can therefore be said that the tasks carried out in the workshop were motivating for the participants. However, only P9’s explicit comment regarding the appropriate selection of tasks and emotions—indicators of affective suitability—was identified. In the group discussion, this participant commented the activity was fun and motivating. No comments were identified regarding the attitudes these tasks might promote in students.

4. 5 Mediational suitability of the activity

As expected, given the prominence of the educational robot used in the workshop and the novelty it represented for the participants, numerous comments referred to mediational suitability. Seven comments were transcribed and reinterpreted. Six of them concerned the material resource used and the benefits of using technology associated with the BlueBot robot. For instance, P5 indicates this technology is easy to use and understand and does not constitute a limitation for future teachers in terms of having to determine how to teach with it, as may occur with video games, applets, or applications, which are often more complex to use and understand.

There is one comment made by P4 that concerns the time indicator for this component. This participant was reluctant to spend an entire session playing with the robot, given the time available to cover the rest of the mathematics content set out in the teaching plan.

No comments were identified regarding indicators for the component related to the number of students or the classroom conditions required to carry out this type of activity.

4. 6 Ecological suitability of the activity

With regard to ecological suitability, based on the comments regarding adaptation of the activity to the curriculum – particularly concerning the development of the core curriculum and the creation of learning situations as defined in the new curriculum – a debate arose as to whether teacher training should focus on the current curriculum. The participants raised the question of whether teacher training should be shaped by current educational policies or positioned independently of them. The discussion stressed the importance of preparing teachers to work with a curriculum, that is, to operate within its established guidelines while maintaining sufficient flexibility to adapt to the succession of curricula teachers are likely to encounter throughout their professional careers.

There were also highly positive comments regarding the interdisciplinary nature of the activity, as it allowed for connections with other disciplines such as physics, and with different mathematical concepts, in addition to computational ones, such as measurement, counting, etc.

There were contributions regarding the definition of CT (as the participants were not familiar with the theoretical framework presented in this paper) and there was a lack of consensus on the matter. However, the prevailing view was that it is part of mathematics and is closely linked to mathematical logic as a language that enables giving (and receiving) instructions to/from another (object or person) to perform an action, such as a movement, a turn, etc. Technology (for instance, an educational robot or a programme) can be used, but it is not strictly necessary, thus giving rise to the idea of “unplugged” CT. This latter notion refers to giving verbal instructions to an individual that subsequently enacts them through bodily movement.

No explicit comments were identified concerning the socio-occupational utility of the activity or its pedagogical innovation.

5 Discussion and conclusions

It is worthy of note that the expert mathematics teacher educators who participated in the workshop were neither familiar with the conceptual framework of CT (Brennan; Resnick, 2012) nor with the DSC construct (Breda; Font; Pino-Fan, 2018). However, they are specialists in mathematics education and are used to designing, planning, and evaluating educational practices, For the majority of them, this represented the first interaction with an educational robot such as BlueBot, and none had previously taken part in a workshop aimed at developing CT through its use.

In recent decades, substantial technological advancements have prompted countries worldwide to reconsider their public policies across multiple sectors, particularly in education (Wing, 2006). This shift has, for instance, led to the integration of CT into educational curricula as a core competence to be developed from the earliest stages of schooling (Grover; Pea, 2013; Jara; Hepp, 2016).

Hence, in relation to the levels proposed by Estebanell et al. (2018), the participants initially operated at the user level during the first part of the workshop, in which they engaged with the activity from the perspective of ECE students. Subsequently, they progressed to the reflective user level when they expressed and shared their reflections and evaluations of the activity. In this respect, their engagement corresponded to the levels typically observed in pre-service teachers when such activities are introduced during their training. However, the depth of reflection and evaluation shown by the participants was considerably greater, owing to their extensive didactic-mathematical knowledge, grounded in both their professional training and their experience in teaching and research.

The aim of this study was to identify the criteria that teacher educators and expert researchers in mathematics education employ when evaluating an activity on CT using the BlueBot educational robot, and to interpret these criteria through the lens of the DSCs. The findings show that the activity received highly positive evaluations, reflecting a high degree of didactic suitability, as inferred from the analysis and reinterpretation of the participants’ evaluations in terms of the DSCs. In particular, the BlueBot robot was considered as an effective technological resource for promoting the development of CT in ECE, as well as in teacher education by supporting an interdisciplinary approach. This approach facilitates connections across disciplines, such as mathematics and physics, as well as among diverse mathematical concepts, including measurement, number concepts, and proportionality, and across different meanings associated with the same mathematical concept, such as the various meanings of measurement.

The experts in mathematics education, who are also researchers and teacher educators, structure their evaluations according to certain criteria that can be reinterpreted in terms of DSC indicators, although they are not familiar with them. However, not all the criteria could be identified. This finding is consistent with that reported by Font et al. (2018) in their analysis of future teachers’ narratives. It may be explained by the consensual basis underpinning the indicators and components of the CDSs.

Similarly, despite not having explicit knowing of the conceptual framework defining CT, the participants’ evaluations made reference to several of its dimensions, especially those grouped under computational perspectives. These include aspects whereby computational problem-solving enables individuals to position themselves in relation to technology, for instance by using it as another means of expression, connecting it with other areas of knowledge, and fostering critical thinking through inquiry (Wing, 2006). This finding reinforces the notion that both the concepts and practices of CT, as defined by Brennan and Resnick (2012), while sharing certain features with MT, possess distinctive characteristics that require CT to be addressed using specific educational practices.

The participants, apart from evaluating mediational suitability—which is obvious given the central role of the technological resource used—mainly focused on evaluating and justifying epistemic and ecological suitability. Consideration was also given to cognitive suitability, whereas comparatively less attention was devoted to interactional and affective suitability. This contrasts with that typically observed among pre-service teachers, who tend to prioritise interactional and affective dimensions in their evaluations (Sala-Sebastià, Breda, & Farsani, 2022).

Evaluating aspects of curriculum alignment (ecological suitability) sparked a productive debate that questioned whether educators should stick to teaching a specific curriculum—which changes depending on the prevailing political climate—or whether they should focus on teaching how to navigate a curriculum in order to learn to adapt to working within its guidelines. Another aspect that generated discussion was how to define CT, although a consensus was reached that it refers to the use of language to give (and understand) instructions for others to carry out. Like logic, the development of CT from an early age promotes the organisation and structuring of thought, which facilitates solving mathematical (and everyday) problems.

Finally, the innovative nature of this research, which is based on the analysis of the feedback provided by teacher educators after participating in a workshop focused on developing a CT activity for ECE teachers should be stressed. The duration of the workshop was much shorter than that of the original implementation with future teachers. This could have been a limitation had the objective of the implementation been the same. However, the aim of the workshop was not to develop the teaching strategy or the participants’ pedagogical knowledge associated with it (as they are not students, but expert specialists in the field). The workshop was intended to ensure they gained an in-depth understanding of this type of activity and for its evaluation during the idea-sharing session to be productive.

The idea-sharing session offers the strength of contrasting opinions and debate amongst the participants, but it is also worth highlighting the limitation imposed by the specific nature of the workshop and its duration within the timetable of the day on which it took place. This limitation has implications regarding the possible generalisation of the results. However, this was not the aim of the research, as a broader implementation of the workshop would be required.

This study is original and innovative, given the fact it analyses the evaluations of a CT development activity using BlueBot for future ECE teachers. It was carried out by experts after “experiencing” this activity. The results provide an initial idea of which aspects the experts prioritise when evaluating activities to be able to focus on them and improve the design and implementation of this type of activity.

As a general conclusion, it is understood that the design and implementation of training programmes are essential to meet the demands of the new curriculum. There is a need to design and implement training programmes to guide pre-service teachers (the majority of whom are women) and in-service teachers with a view to promoting the development of MT through CT (Grover & Pea, 2013). Reflection on educational practice is a central aspect of the study presented here.

Acknowledgements

This study was carried out thanks to the following projects: a) Pensament Computacional i robòtica amb perspectiva de gènere a l’educació Infantil i Primària (CT and Robotics with a Gender Perspective in ECE and Primary Education) (EDU145/23/000006), funded by the Catalan government, Departament d’Educació; b) Criteris i recursos per al desenvolupament del Pensament Computacional amb robots educatius i per a la seva avaluació a l'Educació Infantil i Primària (Criteria and resources for the development of CT with educational robots and for its evaluation in ECE and Primary Education (2024 ARMIF 00017), Government of Catalonia (AGAUR); c) Trayectoria de enseñanza y aprendizaje para la alfabetización digital en la asignatura de matemática de educación básica: un estudio longitudinal en las regiones del Maule, Biobío y La Araucanía (Teaching and learning pathway for digital literacy in the basic education mathematics subject: a longitudinal study in the Maule, Biobío and La Araucanía regions) (Fondecyt No. 1251801); and d) PID2021-122326OB-I00 funded by MCIN/AEI/10.13039/501100011033. We wish to express our gratitude to Ann Swinnen for her invaluable assistance with the article’s translation and for her insightful comments, which significantly enhanced its clarity and readability for the reader.

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• Data Availability:
  The data generated or analyzed during this study are included in the published article.

• Editor-in-Chief:
  Prof. Dr. Roger Miarka

• Associate Editor:
  Prof. Dr. Jhony Alexander Villa-Ochoa

Data availability

The data generated or analyzed during this study are included in the published article.

Publication Dates

• Publication in this collection
  10 July 2026
• Date of issue
  2026

History

• Received
  30 Oct 2023
• Accepted
  05 Nov 2025