1 Introduction

In Brazil, Early Childhood Education serves children from zero to five years and eleven months, with the main objective of their integral development. To achieve this purpose, it is essential that practices are carried out based on the guiding axes of interaction and play, promoting learning that involves living together, playing, participating, exploring, expressing oneself and knowing oneself (Brasil, 2010). Therefore, it is important that teachers are clear that this learning happens constantly, whether through routine practices, free practices or intentional practices. This knowledge leads them to be attentive to all moments of the child, whether they are of care and/or education, seeking to observe reactions, interactions and discoveries.

Regarding the potential of intentional practices, when they are carried out with problematization and investigation, they can be immense, since, in order for children to solve and research something, they need to develop notions in the most diverse areas. This knowledge of the teacher enhances their practice and, consequently, the children's learning.

[...] Early Childhood Education needs to promote experiences in which children can make observations, manipulate objects, investigate and explore their surroundings, raise hypotheses and consult sources of information to seek answers to their curiosities and questions. Thus, the school institution is creating opportunities for children to expand their knowledge of the physical and sociocultural world and to be able to use it in their daily lives

(Brasil, 2017, p. 43, our emphasis).

In this context, Belo and Burak (2020, p. 7) state that, in Early Childhood Education, it is important that pedagogical practice be carried out “based on playful activities, such as games, music, children's stories, games and others that are of interest to children”. In other words, it is essential to start from what is important to them, enabling the mobilization of their prior knowledge.

In addition, several researchers, such as ^{Amarilha (1997)}, ^{Coelho (1991)} and ^{Monteiro et al. (2020)}, have affirmed the relevance of children's stories and contact with books by children for their integral development. Faria et al. (2017, p. 31) assure that “it is in childhood that the first life experiences are constructed that will support the formation of character, personality and conscience. In this sense, children must be inserted into a culture that stimulates thinking, feeling, expressing and experiencing”, which occurs when they have access to children's stories.

In turn, ^{Coelho (1991)} emphasizes the importance of children's books both in the area of ​​literary arts and in pedagogical practices so that the child is surrounded by an environment in which entertainment and education occur simultaneously. Thinking about the development of mathematical notions and language, ^{Arnold (2016)} and ^{Carcanholo and Duarte (2016)} discuss, in their research, the potential of using the contexts explored in children's stories, their illustrations and even problematizations elaborated based on them.

^{Monteiro et al. (2020)} state that, in the context of problematization, contact with children's stories stimulates children's creative capacity. This contact helps them create connections between elements and develop original resolutions to problems presented in the story, which can contribute to the understanding of concepts in various areas of knowledge.

Thus, it is believed that the integration between children's stories and the investigation or resolution of problems linked to them, children's learning and development can be enhanced in all areas, including mathematical notions and language. In this sense, Smole, Cândido and Stancanelli (1999, p. 20, emphasis added) state that “reading the text necessarily requires debate, dialogue, criticism and creation. Exploring problems in this context can help students transfer this process to other problem-solving situations”.

The statements by ^{Monteiro et al. (2020)} and ^{Smole, Cândido and Stancanelli (1999)} indicate that, in addition to contributing to children's learning in relation to mathematical notions and language, children's stories and problem-solving contribute to the development of creativity. However, for this creativity to be observed, it is essential that the teacher understands how it manifests itself.

With a focus on promoting creativity and understanding mathematical notions and language, this study aims to discuss the meaning of creative thinking and its characteristics in practices that explore mathematical notions and language through problem-solving related to a children's story. To this end, it presents a theoretical framework on the topic, a description of a practice carried out with children in Early Childhood Education, and an analysis of creative thinking.

It is important to define what is meant by understanding, which, according to ^{Van de Walle (2009, p. 45)}, corresponds to the “number of connections that an idea has with existing ones”.

Initially, this study discusses the concept of creative thinking and creativity in Mathematics, as well as the cognitive activities that represent them. Next, a brief explanation is presented on the relevance of children's stories in Early Childhood Education and the practices that explore problem-solving based on these stories for understanding mathematical notions and language. Finally, the importance of working with problem-solving in Early Childhood Education is addressed, as well as the analysis of a practice carried out.

2 Creativity in Mathematics and practices involving children's stories and problem solving

Higher-order thinking, a uniquely human capacity, involves advanced cognitive abilites such as abstract reasoning, complex problem-solving, critical thinking, and imagination, which plays a crucial role in various spheres of life, including art, science, business, and innovation (^{Gontijo et al., 2019}). In this study it is assumed that imagination is the basis for the development of creativity, so that it constitutes an intrinsically human ability, enabling the generation of original ideas, innovative resolutions, and the production of something new from the combination of information, experiences, and pre-existing knowledge.

Researchers who study the development of creativity, such as ^{Bicer (2021)} and ^{Gontijo et al. (2019)}, state that it dates back to the beginnings of humanity, being understood in different ways: as something mystical, as a capacity related to genius, or as a human construction, depending on the evolution of studies on the subject. Below, a brief description of the meaning of each of these interpretations is presented.

3 Methodological approach

The research followed a qualitative approach of the action research type, since each stage occurred in a continuous process of planning, implementation, description and evaluation, aiming to improve both practice and research throughout the process (^{Tripp, 2005}). Regarding the objectives, it is characterized as a descriptive study. This method allowed a detailed analysis of the interactions and strategies used by children when solving the problems presented, allowing the investigation of the development of creativity in this context.

The research was carried out in Preschool in Blumenau (SC, Brazil), involving 26 children, at the end of 2024. At that time, most of them already had knowledge about the number-quantity relationship up to 10 and understood the number-order relationship. As for writing, they recognized some letters and identified the spelling of some words, even without having learned to read and write.

This experience is part of a broader study, developed within the scope of a Professional Master's Degree, which researches the development of creativity and the understanding of mathematical notions and language. In this specific stage, only one of the practices carried out is described and analyzed, with a focus on the creativity that emerged in the process, its analysis and the mathematical understandings developed.

The intervention was conducted in the reference classrooms, which was properly organized so that the children could move around and discover freely. ^{Barbosa (2010)}, when discussing practices to be carried out with babies, states that it is important to carefully consider the space in which children carry out their practices, so that they are safe and stimulating, allowing them to experience different experiences. This statement is extended to practices carried out with very young children and small children, since they also need care and freedom to develop fully.

The practice presented was based on the book Os mistérios da Caixa: desvendando a Matemática por meio de Problemas [The Mysteries of the Box: unraveling Mathematics through Problems], prepared specifically for this research by the authors of this article. The material was developed in the context of the professional master's degree, which is in the process of being finalized, carried out in the Postgraduate Program in Teaching Natural Sciences and Mathematics, of the Regional University of Blumenau. The problem analyzed corresponds to the second challenge solved by the children, the details of which will be presented in the description of the activity.

Data collection was performed using three complementary methods, providing a broader and more detailed analysis. The first method consisted of the teacher-researcher's records in her logbook; the second included audio recordings of the children's speeches; and the third method involved the analysis of images obtained through photographs of the practice and the children's written records. These three methods were used in a complementary manner, ensuring a more comprehensive view of the practice and enabling a detailed analysis of the children's interactions and learning throughout the process.

The analysis sought to verify whether the practice contributed to the development of the children's creativity. The intervention was conducted based on categories developed a priori, based on the theoretical framework. Thus, cognitive activities that constitute creative thinking were considered: fluency, flexibility and novelty, seeking to observe these characteristics as pointed out by ^{Silver (1994)}.

The following is a complete description of the practice carried out, followed by the analysis based on the highlighted focuses.

4 Description of the practice

The practice was carried out based on a children's book specifically designed to work with problem-solving involving mathematical notions, in order to explore these knowledge with children and stimulate their creativity.

The book contains five generating problems, each exploring a mathematical field: numerical, spatial, magnitudes and measurements, algebraic and statistical. In addition to these, there are five complementary problems, which consist of mathematical questions or challenges that accompany the generating problems, with the aim of expanding or diversifying the possibilities of resolution and deepening the mathematical notion explored a little more.

The problem presented and analyzed in this research was selected because it addresses the field of Measurements, a branch of Mathematics that allows the development of interdisciplinary practices and the exploration of concepts related to different mathematical areas.

The process took place weekly. It was agreed with the children that every Monday they would resume reading the book printed on A3 sheets, continuing the story. In addition, one child would be responsible for taking out the envelope containing the challenge — the name given to the problems — to be solved. The complementary problems would be solved on the same day or distributed on alternative days throughout the week.

On the day of this practice, the room was organized so that the children could sit in a circle and listen to the story, together with the teacher, who was holding the book in her hands. Since this was the second practice carried out with the children, involving the book, it began by recalling the beginning of the children's story. They showed interest and participated by talking about the characters, the context in which they found themselves and the problem solved the previous week. After this resumption, they expressed a desire to continue the story and discover the next challenge to be solved.

In the plot, the characters held a box containing mathematical challenges to be solved. As a way to encourage children to interact with them, the challenges were presented on cards, placed inside individual envelopes and attached to the boxes drawn on the pages of the book. Thus, in each practice, when a character took a card from the box, one of the children was invited to go to the book and take out the envelope with the question to be read.

The book was opened on the page where the envelope with the problem was, and one of the children was chosen to take it out and enable it to be read. The image presented in Figure 1 shows the page of the book and the problem to be solved in the digital version. In the physical copy used in the classroom, instead of the card with the problem, there was an envelope containing the letter.

(^{Kraft and Silva, 2025}, p. 11)

Figure 1 Page of the book with the problem presented to the children 

The child held the letter, observed the drawings contained in it and interpreted that the problem would involve old things, animals and leaves, sharing this observation with his classmates. Next, the curiosity and the challenge were read aloud. Figure 2 presents the letter in detail, to facilitate its analysis.

(^{Kraft and Silva, 2025}, p. 11)

Figure 2 File with the problem to be solved 

The reading aroused the children’s curiosity, and they began to ask how these methods worked. They wondered how it was possible to measure using arms and feet. Taking advantage of the children’s involvement and interest, the challenge in the letter was proposed: “Measure the table with your hand”, leaving them free to interpret the request and carry out the activity as they wished, without the teacher’s guidance.

For students to be able to present the different ways they use to solve problems, it is up to the teacher to provide a space for discussion in which they can think about the problems they will solve, develop a strategy and record the solution found or the resources they used to reach the result

(^{Cavalcanti, 2001}, p. 122).

Free to do the activity as they wished, some children measured the top of the table, while others chose to measure its height, that is, its feet. There were also those who measured the two non-parallel sides of the top. In total, about five different parts of the table were observed being measured. This demonstrates how hands-on learning, combined with children's natural curiosity, can make the experience more engaging.

It can be said that the diversity of perceptions about which part of the table should be measured highlights the fluency of ideas related to the proposed problem. According to ^{Gontijo (2024, p. 197)}, this fluency “corresponds to the ability to present an abundance or large quantity of ideas on the same subject or possible answers to the same problem”, which was clearly observed at this moment in the practice.

After the activity of measuring with their hands, the children wanted to present their resolutions. Socialization took place, in which all presented their strategies orally, while the others listened attentively.

^{Possamai and Allevato (2024)} state, based on work carried out in Elementary School, that it is essential to consider students' involvement and willingness to explore new knowledge. When activities are playful and promote active participation, children demonstrate great interest and enthusiasm, which enhances learning.

It can be seen in this practice that, even though they are small and have a greater tendency to disperse, when involved in the practice, the children remain attentive and participate continuously.

In this stage of the process, they found that they performed measurements in different ways and obtained varied results. Table 1 presents the solutions of four children, selected to exemplify the diversity of strategies used. To differentiate them, they were identified by numbers.

Initially, the children only presented the results they had found, but they soon became curious to understand why the values ​​were so different. Then, each one explained how they had performed the task.

Child 1 mentioned that he had measured the entire table, including the top and the legs. The others measured only the top, but in different ways. Child 2, when explaining his approach, revealed that he had not been careful to position his hands very close together. Child 3 used the distance from the tip of his biggest finger to his wrist, instead of the measurement between his thumb and little finger. Child 4, when presenting his resolution, showed that he had measured the two non-parallel sides of the top and stated that they were equal. None of the children considered measuring the area of ​​the table top, only its length.

The children used different methods to measure the table, demonstrating the active construction of mathematical knowledge and the development of creative thinking. ^{Van de Walle (2009)} highlights that meaningful mathematical learning occurs when children are encouraged to explore different strategies and share their discoveries.

During the practice, it was possible to observe the children's involvement in the process of investigation and experimentation, testing different ways of measuring the table. Table 1 exemplifies the diversity of responses presented by the children. By freely exploring different strategies and comparing the results with each other, they begin to understand concepts such as variability in measurements and the importance of precision, which is a natural introduction to the notion of standards, units of measurement and consistency.

Allowing children to explore problems based on their own understandings, as highlighted by ^{Possamai and Allevato (2024)}, is central to mathematical development, as it allows them, when articulating their discoveries, to build a deeper knowledge about Mathematics and the world around them. Thus, curiosity and the desire to investigate are catalysts for meaningful and lasting learning, encouraging them to formulate questions, test hypotheses and reflect on their practices. In this way, the development of critical thinking, creativity and abilities for solving problems in everyday life is promoted.

After measurement and socialization, each child received a sheet to record the practice carried out, considering that each one used a unique measurement method.

[..] it is important to encourage them to record, even if it is through drawings, and ask them to explain how they thought to solve the problems. At this point, the teacher will be able to understand their reasoning and make the necessary intervention to correct mistakes, in order to contribute to the development of mathematical reasoning

(^{Carvalho, 2014}, p. 159).

The records of four other children were chosen to portray, in Figure 3, the different ways of representing the practice. These records reinforce the previous statement that, when presenting an open question, the children adopted different resolution strategies, arriving at different results. This fact allowed discussions and understanding about the mathematical field involved.

Figure 3 Research Archive 

It was observed that the child who drew the picture in the upper left represented a hand, indicating that he had measured the table with it, and, next to it, he wrote the number nine, showing how many times this measurement was used. In the upper right drawing, the child depicted himself with his hand on the table, indicating that he had measured the side of the top, noting the number of hands used for this measurement.

In the lower left image, the child drew the entire table and the number 13. When questioned, he said that he had measured the top and the legs of the table. In the lower right drawing, the representation shows that the child measured the two non-parallel sides of the table top, verifying that one of them had five hands and the other, six.

The different ways of presenting the results demonstrate the development of cognitive activity associated with novelty (^{Gontijo, 2024}), since Figure 3 exemplifies the originality of the children in their representations.

After the presentations, the children discussed why the values ​​were different and concluded that this was due to the variation in hand size and the way they used to measure. Some used their hands closed, others open; some did not bother to position them together, while others measured using the distance between the largest finger and the wrist. The fact that they used more than five different ways of measuring influenced the divergence of the results.

At this point, the children demonstrated flexibility in their thinking, understanding that the different results were derived from the approaches to solving the problem or from the fact that the measuring instrument, the hand, was of different sizes (^{Silver, 1994}). After reaching this conclusion, at the children's request, the page of the book was turned to show the results obtained by the characters in the story, and they realized that they had also found different values.

Continuing the activity, the next page was read (Figure 4), which presented a complementary problem. Observing the children, it was possible to notice their enthusiasm as they prepared to begin the next practice.

(^{Kraft and Silva, 2025}, p. 13)

Figura 4 Problema Complementar 

After reading, the children took their pencils to measure the table and, this time, it was agreed that they should measure its width. However, when comparing the pencils with each other, they realized that they were of different sizes, which generated a discussion about the differences in measurement that could arise. According to ^{Van de Walle (2009, p. 407)}, “a discussion about the need for a standard unit can be more meaningful after the groups in your class have measured the same objects with their own units and arrived at different answers”.

Given the understanding that the size of the pencils should be the same, new pencils were distributed, all the same size, instructing the children to use them as a standard measurement, without introducing conventional units of measurement, such as centimeters or meters, at that moment.

After this new measurement, the sentence on the board that the character in the story was holding was read. The children began to compare their results with those of their classmates, and most obtained the same value, with only five presenting different measurements.

A boy, seeing the discussion among his classmates about the fact that the previous measurements were different and the current ones were the same, quickly explained why this happened: “Each hand has a measurement, because we are different and the pencil has the same measurement for everyone”. This comment generated collective curiosity, leading the children to confirm, by measuring one pencil with another, whether they were all really the same size. This fact demonstrates that “the appropriation of mathematical knowledge does not occur naturally or intuitively; but through the mediation of cultural instruments and signs, through relationships between human beings” (^{Miranda and Sá, 2020}, p. 16). After the discussions and the conclusion presented by one of the children, most began to understand the process.

When they noticed this difference, the children went to the desks of their classmates who had obtained different results and repeated the process, verifying that, in fact, the measurements were the same as theirs. After this verification, they questioned their classmates about the procedure used. When analyzing the measurement process, they realized that some had not positioned the pencils one after the other correctly, but had partially overlapped one pencil over the next, which generated discrepancies in the results. The children discussed among themselves the best way to measure and understood why their values ​​were different.

After the discussions, the page of the book was turned again, and everyone together checked the measurements of the characters in the story. They realized that, when using the pencil as a reference, they had also obtained the same measurements. This reinforced their understanding and confidence in their findings, showing that the measurement of an object is represented by a number and that, in order to find it correctly, a single reference instrument is necessary, allowing the comparison of its length with that of the measured object.

5 Final Considerations

The aim of this article was to discuss the meaning of creative thinking and its characteristics in practices that explore mathematical notions and language through problem-solving related to a children's story. To this end, the theoretical framework that explores the various conceptions of creativity was initially presented, positioning itself in relation to the one considered most pertinent.

Based on this positioning, the difference between creative thinking and creativity was addressed, highlighting the importance of stimulating the former in order to develop the latter, that is, encouraging creative thinking to become more creative.

Then, the cognitive activities that characterize creative thinking were presented — fluency, flexibility, and novelty —, which allow us to verify signs of creativity in the practices carried out by children. Finally, a practice carried out with five- and six-year-old children was analyzed, seeking to identify signs of the mental processes presented previously and their mathematical understandings.

As final considerations of this study, it is stated, based on the experience and analysis, that this practice allowed us to verify that the work related to a children's story led the children to get involved. They enjoyed following and listening to what happened to the characters and created scripts for the continuation of the narrative.

The exploration of this open problem, based on the story, allowed them to reflect on the situation presented, interpreting it according to their understanding and seeking their own strategy to solve it. This process demonstrated the fluency of ideas and the flexibility of thought in the search for measurement instruments. Furthermore, when analyzing the records, we observed the originality of the ways used by the children to represent the action performed and the result obtained.

It is important to mention that, after solving the proposed problem, the children showed great interest in returning to the story to check if the characters had performed the task in the same way, revealing the bond that was formed between them, the characters and the problems presented.

Regarding the knowledge associated with the field of Measurements, it was noted that, as the practice developed, the children began to understand some related notions, such as the need to clearly define what should be measured and the importance of using the same instrument to ensure that, when measuring the same object, the result obtained is consistent.

Therefore, it was believed that pedagogical practices that relate children's stories to problem-solving have great potential for the development of mathematical notions and language and creativity. When the teacher explores open problems and encourages children to think and seek their own strategies to solve them, in addition to creating spaces for socializing resolutions and results and exchanging experiences, he or she strengthens learning. In this process, the teacher's role should be that of a mediator, questioning the strategies adopted and the results obtained, consolidating correct understandings.