**2.1.1 Causative genes of CHD**

The etiological factors of many genetic syndromes and familial CHD have been identified, but the genetic basis of majority of "sporadic" CHD remains unknown. With the progress in molecular genetics and developmental biology, many genes associated heart development have been identified. When searching computer databases such as NCBI Gene Bank for "cardiac or heart", we can indentify 1154 loci in human. Search for"(heart or cardiac)and development", limited to human, 630 genes were found. A number of selected congenital heart defects and genetic syndromes have been found to be associated with mutations in a variety of single genes. The mutations were found only in affected individuals, were not present in control samples, and were demonstrated to change protein structure or function.

plate-specific expressed genes NKX2.5, SRF, GATA4, TBX5, and HAND2, compose the core regulatory network of cardiac morphogenesis, controlling heart looping, left-right symmetry and chambers formation. SRF regulates the differentiation of coronary vascular smooth muscle cells [17, 18]. Genes that involved in epicardial development include FOG-2, vascular cell adhesion molecule 1, integrins, erythropoietin, and erythropoietin receptor. Specific genes such as the NOTCH receptor, Jagged (JAG), WNT, transforming growth factor beta 2 (TGF ß2) and bone morphogenic proteins have been implicated in cardiac neural crest development in the mouse[12, 19-21]. Retinoic acid signal pathway is involved in the regulation of cardiac looping. Complex signal pathways are implicated in the crosstalk between endocardium and myocardium to form endocardial cushion and heart valves, including VEGF, NFATc1, Notch, Wnt/ß-catenin, BMP/TGF-ß, EGF, erbB, NF1

signal pathways [10, 22-24].

Fig. 1. Eteology of CHD

**2.1.1 Causative genes of CHD**

**2. Molecular mechanisms of congenital heart disease**

The etiological factors of many genetic syndromes and familial CHD have been identified, but the genetic basis of majority of "sporadic" CHD remains unknown. With the progress in molecular genetics and developmental biology, many genes associated heart development have been identified. When searching computer databases such as NCBI Gene Bank for "cardiac or heart", we can indentify 1154 loci in human. Search for"(heart or cardiac)and development", limited to human, 630 genes were found. A number of selected congenital heart defects and genetic syndromes have been found to be associated with mutations in a variety of single genes. The mutations were found only in affected individuals, were not present in control samples, and were demonstrated to change protein structure or function.

Disease genes of CHD identified to date are summarized in Table 1, and the functions of these causative genes are summarized as following [25].

Table 1. Causative genes of CHD

For example, NKX2-5, Homeobox-containing genes play critical roles in regulating tissuespecific gene expression essential for tissue differentiation, as well as determining the temporal and spatial patterns of development. It has been demonstrated that a Drosophila

Molecular Mechanisms of Congenital Heart Disease 125

Homeobox-containing genes play critical roles in regulating tissue-specific gene expression essential for tissue differentiation, as well as determining the temporal and spatial patterns of development. Mutations in NKX2-5 result in loss of heart formation in the embryo,

This gene encodes a member of the epidermal growth factor (EGF)- Cripto, Frl-1, and Cryptic (CFC) family. These proteins play key roles in intercellular signaling pathways during vertebrate embryogenesis. Mutations in this gene can cause autosomal visceral heterotaxy. This protein is involved in left-right asymmetric morphogenesis during organ

Also known as THRAP2, The evolutionarily conserved THRAP genes encode a family of proteins that regulate embryonic development. THRAP2 is involved in early development

The zinc finger protein encoded by this gene is a widely expressed member of the FOG family of transcription factors. The family members modulate the activity of GATA family proteins, which are important regulators of hematopoiesis and cardiogenesis in mammals

The jagged 1 protein encoded by JAG1 is the human homolog of the Drosophilia jagged protein. Human jagged 1 is the ligand for the receptor notch 1. Mutations that alter the

Epidermal growth factor-like repeats are a class of cysteine-rich domains that mediate interactions between proteins of diverse function. CRELD1 is the founding member of a

This gene encodes a member of the GATA family of zinc-finger transcription factors. This protein is thought to regulate genes involved in embryogenesis and in myocardial differentiation and function. Mutations in this gene have been associated with cardiac septal

This gene encodes a member of the ZIC family of C2H2-type zinc finger proteins. Mutations

Activins are dimeric growth and differentiation factors which belong to the transforming growth factor-beta superfamily of structurally related signaling proteins. These receptors

suggesting that NKX2-5 is essential for heart formation [31, 32].

PROSIT240, MED13L, mediator complex subunit 13-like

CFC1, cripto, FRL-1, cryptic family 1

development [33, 34].

of the heart and brain [35].

[36].

defects [39].

ZFPM2, zinc finger protein, multitype 2

Jagged 1, jagged 1 (Alagille syndrome)

family of matricellular proteins [38]. GATA4, GATA binding protein 4

ZIC3, Zic family member 3 heterotaxy 1

ACVR2B, activin A receptor, type 2, beta

are all transmembrane proteins [41].

in this gene cause X-linked visceral heterotaxy [40].

jagged 1 protein cause Alagille syndrome [37]. CRELD1, cysteine-rich with EGF-like domains 1

homeobox-containing gene called 'tinman' is expressed in the developing dorsal vessel and in the equivalent of the vertebrate heart. Mutations in tinman result in loss of heart formation in the embryo, suggesting that tinman is essential for Drosophila heart formation. Furthermore, abundant expression of Csx, the presumptive mouse homolog of tinman, is observed only in the heart from the time of cardiac differentiation. CSX, the human homolog of murine Csx, has a homeodomain sequence identical to that of Csx and is expressed only in the heart, again suggesting that CSX plays an important role in human heart formation. Studies have recently shown that nonsyndromic CHD can result from single-gene defects. Schott et al identified mutations in *NKX2.5* in 4 kindreds with atrial septal defects and atrioventricular conduction delay without other apparent syndromic features. The mutations were found only in affected individuals, were not present in control samples, and were demonstrated to change protein structure or function [26-28].

Noonan Syndrome is a genetic multiple malformation disorder that includes short stature, typical facial dysmorphism, webbed neck, chest deformity, and cardiovascular abnormalities. The cardiac involvement is observed in 80% to 90% of affected individuals, with valvar pulmonic stenosis and hypertrophic cardiomyopathy being the most common. Other congenital heart defects observed in Noonan Syndrome are secundum atrial septal defect, atrioventricular septal defect, mitral valve abnormalities, aortic coarctation, and tetralogy of Fallot. Noonan Syndrome is genetically heterogeneous, which means that there are at least 3 Noonan Syndrome disease genes, *PTPN11*, *SOS1*, and *KRAS* [29]. It is *PTPN11*, which encodes a protein tyrosine phosphatase called SHP-2. SHP-2 plays an important role in signal transduction for a wide variety of biological processes, including the formation of the semilunar valves. Mutations in the *PTPN11* gene are observed in 40% to 50% of Noonan Syndrome patients [25, 30].

#### **2.1.2 Functions of the causative genes of CHD**

Table2 shows the functions of the causative genes of CHD.

NKX2-5, NK2 transcription factor related, locus 5

Table 2. Inborn Errors Causing CHD

Homeobox-containing genes play critical roles in regulating tissue-specific gene expression essential for tissue differentiation, as well as determining the temporal and spatial patterns of development. Mutations in NKX2-5 result in loss of heart formation in the embryo, suggesting that NKX2-5 is essential for heart formation [31, 32].

CFC1, cripto, FRL-1, cryptic family 1

124 Congenital Heart Disease – Selected Aspects

homeobox-containing gene called 'tinman' is expressed in the developing dorsal vessel and in the equivalent of the vertebrate heart. Mutations in tinman result in loss of heart formation in the embryo, suggesting that tinman is essential for Drosophila heart formation. Furthermore, abundant expression of Csx, the presumptive mouse homolog of tinman, is observed only in the heart from the time of cardiac differentiation. CSX, the human homolog of murine Csx, has a homeodomain sequence identical to that of Csx and is expressed only in the heart, again suggesting that CSX plays an important role in human heart formation. Studies have recently shown that nonsyndromic CHD can result from single-gene defects. Schott et al identified mutations in *NKX2.5* in 4 kindreds with atrial septal defects and atrioventricular conduction delay without other apparent syndromic features. The mutations were found only in affected individuals, were not present in control samples, and

Noonan Syndrome is a genetic multiple malformation disorder that includes short stature, typical facial dysmorphism, webbed neck, chest deformity, and cardiovascular abnormalities. The cardiac involvement is observed in 80% to 90% of affected individuals, with valvar pulmonic stenosis and hypertrophic cardiomyopathy being the most common. Other congenital heart defects observed in Noonan Syndrome are secundum atrial septal defect, atrioventricular septal defect, mitral valve abnormalities, aortic coarctation, and tetralogy of Fallot. Noonan Syndrome is genetically heterogeneous, which means that there are at least 3 Noonan Syndrome disease genes, *PTPN11*, *SOS1*, and *KRAS* [29]. It is *PTPN11*, which encodes a protein tyrosine phosphatase called SHP-2. SHP-2 plays an important role in signal transduction for a wide variety of biological processes, including the formation of the semilunar valves. Mutations in the *PTPN11* gene are observed in 40% to 50% of Noonan

Transcription factors Signaling proteins Vascular extracellular matrix

FBN-1 Elastin

were demonstrated to change protein structure or function [26-28].

Syndrome patients [25, 30].

Genes affected

GATA4 TBX1 TBX5 NKX2.5 dHAND TFAP2 ZFPM2

**2.1.2 Functions of the causative genes of CHD**

NKX2-5, NK2 transcription factor related, locus 5

Table 2. Inborn Errors Causing CHD

Table2 shows the functions of the causative genes of CHD.

PTPN11 Jagged 1 DMPK CFC1 SOS1 TGFBR2 KRAS BRAF MEK1 MEK2 HRAS ACVR2B CRELD1 LEFTYA

This gene encodes a member of the epidermal growth factor (EGF)- Cripto, Frl-1, and Cryptic (CFC) family. These proteins play key roles in intercellular signaling pathways during vertebrate embryogenesis. Mutations in this gene can cause autosomal visceral heterotaxy. This protein is involved in left-right asymmetric morphogenesis during organ development [33, 34].

PROSIT240, MED13L, mediator complex subunit 13-like

Also known as THRAP2, The evolutionarily conserved THRAP genes encode a family of proteins that regulate embryonic development. THRAP2 is involved in early development of the heart and brain [35].

ZFPM2, zinc finger protein, multitype 2

The zinc finger protein encoded by this gene is a widely expressed member of the FOG family of transcription factors. The family members modulate the activity of GATA family proteins, which are important regulators of hematopoiesis and cardiogenesis in mammals [36].

Jagged 1, jagged 1 (Alagille syndrome)

The jagged 1 protein encoded by JAG1 is the human homolog of the Drosophilia jagged protein. Human jagged 1 is the ligand for the receptor notch 1. Mutations that alter the jagged 1 protein cause Alagille syndrome [37].

CRELD1, cysteine-rich with EGF-like domains 1

Epidermal growth factor-like repeats are a class of cysteine-rich domains that mediate interactions between proteins of diverse function. CRELD1 is the founding member of a family of matricellular proteins [38].

GATA4, GATA binding protein 4

This gene encodes a member of the GATA family of zinc-finger transcription factors. This protein is thought to regulate genes involved in embryogenesis and in myocardial differentiation and function. Mutations in this gene have been associated with cardiac septal defects [39].

ZIC3, Zic family member 3 heterotaxy 1

This gene encodes a member of the ZIC family of C2H2-type zinc finger proteins. Mutations in this gene cause X-linked visceral heterotaxy [40].

ACVR2B, activin A receptor, type 2, beta

Activins are dimeric growth and differentiation factors which belong to the transforming growth factor-beta superfamily of structurally related signaling proteins. These receptors are all transmembrane proteins [41].

Molecular Mechanisms of Congenital Heart Disease 127

This gene encodes a member of the Ser/Thr protein kinase family and the TGFB receptor subfamily. Mutations in this gene have been associated with Marfan Syndrome, Loeys-Deitz

This gene, encodes a protein that is a member of the small GTPase superfamily. The transforming protein that results is implicated in various malignancies, including lung adenocarcinoma, mucinous adenoma, ductal carcinoma of the pancreas and colorectal

This gene encodes a protein belonging to the raf/mil family of serine/threonine protein kinases. This protein plays a role in regulating the MAP kinase/ERKs signaling pathway, which affects cell division, differentiation, and secretion. Mutations in this gene are

The protein encoded by this gene is a member of the dual specificity protein kinase family, which acts as a mitogen-activated protein (MAP) kinase kinase. This kinase is involved in many cellular processes such as proliferation, differentiation, transcription regulation and

The protein encoded by this gene is a dual specificity protein kinase that belongs to the MAP kinase kinase family. This kinase is known to play a critical role in mitogen growth factor signal transduction. Mutations in this gene cause cardiofaciocutaneous syndrome

This gene belongs to the Ras oncogene family. The products encoded by these genes function in signal transduction pathways. Mutations in this gene cause Costello syndrome.

Phenotypes of CHD vary from small ASD and VSD, which may go undetected throughout life, to large ASD and VSD, which are significantly symptomatic. Clinically significant anomalies range from persistence of fetal circulation (eg, patent ductus arteriosus) to complex defects such as transposition of the great vessels, single ventricle anomaly, hypoplastic left heart syndrome, and complex variants of heterotaxy. The etiological factors of many genetic syndromes and familial CHD have been identified, but the genetic basis of majority of "sporadic" CHD remains unknown. It is hypothesized that susceptibility resulted from single nucleotide polymorphisms or key gene(s), with the interaction of environmental factors, which disturb normal cardiac development, result in cardiac defects. There are six causative mechanisms according to pathogenetic classification of congenital cardiovascular malformations: ectomesenchymal tissue migration abnormalities (causing conotruncal malformations and aortic arch anomalies); intracardiac blood flow defects

Aortic Aneurysm Syndrome, and the development of various types of tumors [52].

TGFBR2, transforming growth factor receptor 2

carcinoma [53].

development [54].

(CFC syndrome) [55].

KRAS, v-Ki-ras2 Kirsten rat sarcoma viral oncogene homolog

BRAF, v-raf murine sarcoma viral oncogene homolog B1

associated with cardiofaciocutaneous syndrome [53]. MEK1, MAP2K1, mitogen-activated protein kinase 1

MEK2, MAP2K2*,* mitogen-activated protein kinase 2

HRAS, v-Ha-ras Harvey rat sarcoma viral oncogene homolog

Defects in this gene are implicated in a variety of cancers [56].

**2.2 Pathogenic mechanisms of congenital heart disease**


Theories emanating from Vygotsky maintain that until the age of seven children learn to their best potential when the learning is embedded in playful activities (El'konin, 1999). Nevertheless, there seems to be a debate concerning how to conduct play-oriented teaching. Burghardt (2011) even experiences that the label "play" might better be avoided in trying to integrate playful activities into school curricula. On the other hand, there are research-based education programs aiming to further the idea of play as young children's primary activity for learning. One such program is Developmental Education (Van Oers, 2014), which takes its starting point in the notion that any activity can be interpreted as more or less playfully formatted. This implies that play is not considered a separate kind of activity but rather part of a continuum, in line with how Roopnarine (2011) conceptualizes play (see quotation above). In accordance with this, the relationship between play and mathematics teaching can be seen both as "mathematics made playful", for instance through games in which counting and mathematical operations are used, and as "mathematizing elements of play" in which the primary act is play and the teacher actively introduces mathematical concepts or operations to the playing child. Regardless of whether a play activity is framed in a context of manipulative or role play, it is usually characterized by children having a high degree of freedom in how they carry out the rule-governed activity. In such a context, the children can encounter tasks that are solved with tools that may look mathematics-like, but can also often be solved through intuition. It is then the actions of the teacher and how s/he articulates mathematical relationships that extend the children's encounters with mathematics and that may induce learning. This means that children's initiatives and explorations are important, but it is not enough that mathematical representations and concepts are present in a play activity – teachers must also provide new content and altering perspectives that extend the children's experiences (Van Oers, 2010).

To support mathematical learning, it is not enough to merely confrm what the child him/herself initiates, as this will not contribute to extending the child's knowledge or skills. Offering strategies for completing a task or a different perspective on how to interpret a problem is more a goal-oriented act that may direct the child's attention toward skills or tools that help him/her complete a task in a more advanced way. The teacher's way of responding to children's initiatives and possible mathematical content in play activities thereby leads to different learning opportunities. Particularly, maintaining a shared focus and handling the balance between foregrounding play or the content for learning is a core issue and is not easily operationalized in educational settings (Björklund et al., 2018). In reality, teaching most likely moves across this continuum, sometimes starting from problems initiated by the children and sometimes from curricular goals determining what mathematics they are expected to learn about, but most often moving in between these. When this occurs, the two dimensions of meaning – the cultural meaning and the personal sense – are likely to be connected (Leont'ev, 1978).

### **The Study**

In this paper, we present an analysis of teaching in Swedish preschool classes. It is not our ambition to classify teaching activities as play or not play; rather, we focus on the term *playfulness* as it comes through in the teaching of numbers. While playfulness does not have a clear-cut defnition in the literature, we nevertheless understand the notion as shared attention and responsiveness to the other's (the child's) perspective and experiences, including imaginary creations, and particularly an openness in the direction of the activity whereby any participant may introduce alternatives and renegotiate the rules of a game, task, or play activity (Pramling et al., 2019; Roopnarine, 2011).

The data for analysis consists of feldnotes and documentation in a protocol (originally developed by Venkat & Askew, 2018) focusing on teachers' talk, gestures, use of artefacts, and notations in bringing forth numbers as the object of learning. Researchers (including the authors of this paper) made observations of teaching that the teachers themselves considered to be about numbers, the features of numbers, and how to make use of numbers in problem-solving. The data was collected during fall 2021. From the large data set, 81 episodes (from 46 individual teachers), observed and documented by the two authors of this paper, were used for analysis.

The object of analysis in this study is mathematics teaching about numbers, conducted in Swedish preschool class. Two features of this phenomenon are of specifc interest: expressions of playfulness that come through in the mathematics teaching, and how mathematics appears as a content for learning. In this sense the analysis is phenomenological, aiming to reduce, describe, and search for essence in the observed phenomenon (Giorgi, 1997). Thus, the analysis started with identifying and describing the context in which the mathematics is being taught, as it appeared to the participants of the activity based on how the mathematics was framed as well as the teachers' and students' actions, freedom to pose suggestions and alternatives, and the nature of their engagement. Several qualitative differences emerged, in which similarities and differences in the intentions of the contexts shaped in the teaching activity came through. In this identifcation process, it was also possible to recognize a pattern in how the mathematical content appeared. In the following process, we condensed the contexts and connected meanings of the mathematical content into thick descriptions that bear a common meaning. Playfulness being the main object or phenomenon of inquiry is the guiding notion in these descriptions. The result of the analysis is thereby a condensed description of playfulness as it appeared in the observed lessons, and of how the content for learning was made discernable for the learners.

### **Results**

In the Results section we present a synthesis of playfulness and the mathematical content for learning as it appeared during the teaching activities in the observed preschool classes. Three different appearances of how mathematics appears as content for learning *in regard to* the playfulness expressed in the teaching situation can be found in the data set. The observations are not exclusively classifed to one or another as there are overlapping observations, but in this presentation, we describe the characteristic pattern of contextualization that was found in the data.

### *The Mathematical Content as the Primary Target*

Firstly, a good many observations have the common characteristic of "completing a task", in which the mathematical content appears as the primary target. The tasks are not contextualized based in the children's experiences or lives. If manipulatives are used for visualizing number relations and operations, it seems irrelevant what kind of objects are used. The mathematical content constitutes the task, and is thereby the center of attention. There is rarely any playfulness observed, such as negotiating about rules or offering imaginary suggestions, and when there is some sense of playfulness this occurs when the teacher is building up tension in activities in which the outcome is not known and the children are involved in making guesses. The following example describes a teaching activity in which the mathematical content appears as the primary task:

The teacher hands out cards with numbers on them (1-20) and asks the children to arrange them in order from smallest to largest. The children take on the task and try to place the cards in the right order. During the activity the teacher supports the children, asking "Do you remember, 17, what number comes before?". Child: "18". Teacher: "What number is before?". Child: "16". Teacher: "Then this is your place" (points at a position on the number track). When all the numbers have been placed on the number track, teacher and children check together that the numbers have been correctly ordered by counting out loud together while the teacher points to one number at a time.

The goal for this group activity is clearly stated and does not allow for alternative solutions. The children are expected to participate in a certain way, and a specifc content is in focus. There is no room for spontaneity and the focus is on completing the task, i.e., placing the number cards in the correct order.

### *Exploring the Mathematical Content in a Relevant Context*

Secondly, playfulness is observed in cases in which teacher and children explore the mathematical content in a relevant context; that is, numbers are a central feature of the activity and exploring mathematical possibilities is necessary for completing the task. Here, the children are involved in activities in which they interact and solve tasks together with their peers and the teacher. Typically, the teacher directs the activity and asks questions like "Why…?" and "How come…?". Mathematics is used as a tool for understanding the outcome of some investigation or suggestion, to help structure the children's experiences. In these observations we can see that a common approach in the teaching takes its starting point in the children's experiences and the teacher extends these by pointing out surprising results and hidden questions, and making them objects of inquiry. For instance, the teacher may introduce "conficts" to highlight issues that can only be resolved through mathematical reasoning. In such cases, the goal for the activity is predetermined and known by the teacher, but the exact direction to take within the activity in order to arrive at the goal is not determined beforehand. This can be seen as a criterion for playfulness, as the approach allows for alternative routes and exploration. By structuring the mathematical content, the children make sense of their experiences and take part in the mediated cultural meaning in the process. Furthermore, this way of teaching mathematics, with playfulness and keeping content foregrounded, is based on either the children's own lived experiences or a collectively created context shaped in the ongoing situation. Both seem to function as facilitators for engaging the children in the activity and connecting cultural and personal mathematical meaning in joint exploration. In the following example, the teacher and the children examine what fruits the children have brought to school as a starting point for a mathematically informed exploration:

Teacher: "Let's try to fnd out which fruit is the most common one today!". The teacher makes a horizontal axis on the whiteboard and asks the children what fruits they have brought with them today, writing their answers under the axis. The teacher then systematically asks for each fruit: "How many of you have apples with you today?", and the children raise their hands. The teacher documents each answer with an X in separate stacks on the board for each fruit, and a stacked bar chart emerges. After this survey, the teacher uses the stacked bar chart to ask questions, helping the children answer them by interpreting the data on the chart: "Which fruit is the most common one today?" "How can we know that without counting?" and "And if we compare pears and bananas?". In the end, the teacher describes the use of diagrams in everyday life and says it is very useful to have the ability to interpret data presented in this way.

In this activity, the children's experiences are taken as the starting point for mathematizing. The teacher helps reduce the "noise" and provides mathematical explanations for the children's experiences. The engagement is strong among the children during the activity. The teacher points out surprising results on the chart, and challenges the children to fgure out answers to different questions and make them objects of joint inquiry. In this activity, mathematics is necessary in structuring the mathematical content and reasoning about the results. Playfulness is also a central part of the activity, in terms of the explorative and curious approach that both teacher and students engage in.

### *Parallel Activities*

Thirdly, the children are involved in activities framed in an imaginary narrative, usually participating by helping a protagonist to complete a task. The mathematical task is then situated in a playful setting, but the narrative and the mathematical content are rather parallel activities. Children are invited to an imaginary setting, within which they are engaged in solving tasks through their own means and suggestions; that is, with a high degree of freedom. Mathematics may become part of the activity, but as the attention is not necessarily directed at exploring the mathematical content in a mathematically relevant context it is possible to participate without extending the children's view on the present mathematical content. The teaching appears to constitute a combination of creating a playful setting in order to (re)gain interest among the children and of completing a task in which the setting does not support the *mathematical* inquiry. In the following example, the teacher invites the children into an activity that is shaped as an imaginary narrative:

The teacher tells the children about Findus (a well known cat in children's literature) who wants to play a joke on Pettson (his owner) by hiding eggs in his boots.  The children are told that Findus needs their help to fgure out how the fve eggs can be divided between the two boots. The teacher captures each suggestion the children offer, and processes them together with the children by writing the solutions in triads on tablets. At the end of the activity, teacher and children state that they have found all the possible ways that the fve eggs can be divided between the two boots.

This example is a teaching activity in which the mathematical task is situated in a playful setting. The task itself is well structured to facilitate an exploration of partwhole relationships in numbers, and its playfulness in playing a joke on a familiar fctional character seems to engage the children in participating in the activity. Nevertheless, the narrative and the mathematical content are parallel activities in the teaching.

### **Discussion**

In this paper we set out to describe how playfulness and mathematics as a content for learning appear in preschool class teaching activities. The analysis is therefore focused on both the playfulness and the content for learning, as a contribution to the discussion on how play (or rather playfulness) may become an informed part of preschool class mathematics teaching. The appearance of these two features of preschool class teaching forms the phenomenon in our inquiry, and the analysis of the 81 observations reveals that the way in which these features emerge shapes the mathematical learning opportunities differently. Thus, we do not intend to make any quantitative comparisons of frequency of observations, as the data can best be described as "touchdowns in time" rather than necessarily being representative of classroom teaching from a broader perspective.

When we frst identifed expressions of playfulness, a continuum of the extent to which play was given space in the teaching activities appeared. At one end of this continuum, we fnd teaching characterized by an orientation toward completing a (mathematical) task with highly limited expressions of playful exploration or openended inquiry. At the other end, we fnd teaching framed in narratives and a use of props with the intention to engage the children in interaction whereby the teacher, through the playful narrative, guides their communication about some mathematical content. In between, we fnd examples of interaction that centers around exploring a specifc content, characterized by active involvement (from both teachers and children), that induces an explorative approach with a high degree of freedom. These inquiries are often (but not exclusively) guided by the teacher's open-ended questions that take their starting point in the children's own experiences or a familiar setting and embrace alternative suggestions and imaginary proposals.

The common content in all our observations is numbers, but the mathematics appear in different ways in the observed teaching. In some observations the mathematics becomes the central task to engage in, often through the mediation of a standard solution to symbolically presented problems (e.g., numerals written on the whiteboard). However, the content can sometimes be presented very well in terms of visualizing mathematical structures and procedures but not connect to contexts outside the mathematical. The mathematical content is thereby heavily foregrounded. In these cases, there is also often a closed solution or expected way to complete the task at hand. Meanwhile, in other observations, there is a more open approach in which the children are invited to offer suggestions for how to complete a task. The teacher still has a clear emphasis on the mathematical content and goal of the activity, but encourages different solutions for reaching the goal.

Numbers are the central feature in the observed teaching acts, and do appear in all the observations. However, the analysis of how the mathematical content is foregrounded, seen through the lens of playfulness, reveals differences in the opportunities for learning mathematics as useful and relevant (and thus meaningful) to the children. The frst and third categories exhibit teaching practices in which the mathematical task to be completed is central and the goal is clearly determined, as are the

methods and tools to be used. In the frst category, in which the mathematics constitute the context, the cultural meaning of mathematical tools and concepts comes through. However, if one focuses on merely the cultural meaning of tools and goals, the teaching risks being reduced to the training of specifc operations (Leont'ev, 1978). This stands out in comparison with the second category, which exemplifes openended inquiries that to a greater extent involve the children's experiences and suggestions as an outset for the teaching and are characterized by an openness in the direction of the activity, whereby any participant may introduce alternatives and renegotiate the rules of the game, task, or play activity. In other words, the children are invited to explore mathematical content in a relevant context, with their experiences taken as the starting point for mathematizing (see Freudenthal, 1981). The teacher helps reduce the "noise" and provides mathematical explanations for the children's experiences. In this way, the interplay between mediating (cultural) meaning and (personal) sense (see Leont'ev, 1978; Van Oers, 2010, 2014) becomes operationalized.

There is no doubt as to the benefts of linking educational goals to play, as play can be seen as a motivating factor for children and make them perceive the learning as meaningful, enjoyable, satisfying, and thereby help to arouse their interest in further learning (Simeonsdotter Svensson, 2009). However, our study may contribute through problematizing how play and playfulness can be implemented in teaching in ways that facilitate the learning of a specifc content, a task that is known to be challenging (Björklund et al., 2018). We claim that it is not enough to embed the content for learning in a playful context, as in the third category. Instead, we argue that there are greater opportunities for learning when the setting facilitates structuring the mathematical content to be comprehensible and useful to the learner. We observed this in the second category. Play then becomes more than simply having fun; it is a valuable educational tool that includes children's experiences and meanings, creating opportunities for their deeper engagement.

The openness and high degree of freedom that playfulness offers can be characterized by a "what if" type of thinking (see Vaihinger, 1924/2001) that arises as children are challenged to go past their current level of understanding. This allows them to realize that changes to or variations in a specifc task, as well as their consequences, can be anticipated and calculated. In this way, what-if thinking provides a kind of prospective thinking whereby the essential direction is forward (not looking back), which is in stark contrast to the commonly used notion of refective thinking that instead presents a meta-perspective on an occurrence. This makes playfulness an asset in mathematics teaching, and our study has provided empirical observations of how this can take place in the Swedish preschool class. We suggest that this is an important insight to consider when developing teaching practice and policy guidelines for how education for six-year-olds should be conducted; particularly in the Swedish context, where the role of the preschool class in the education system is under review. For mathematics to remain meaningful to learners, and for education to provide culturally mediated tools that support individuals' development of mathematical knowledge and skills, it is essential to gain a deeper understanding of the signifcance of play and playfulness in regard to mathematics teaching and learning in early childhood education.

**Acknowledgments** This paper is part of the project SATSA, fnanced by the Swedish Research Council (Grant no. 2020-03712). The research group consists of Angelika Kullberg, Anna-Lena Ekdahl, Maria Alkhede, and Ulla Runesson Kempe, all of whom contribute to the research in the project.

### **References**

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### **Methodological Choices in Research on Early Mathematics Education: Elicitation of Parents' Views**

**Dorota Lembrér**

### **Introduction**

In this paper, I discuss two data collection methods: an online survey and photoelicitation interviews (PEIs) used in my PhD project (Lembrér, 2021). These different ways of gathering data were used to investigate parents' views on mathematics education for young children at home and in Early Childhood Education and Care (ECEC) institutions in Sweden and Norway. The data included parents' stories about mathematics education and provided insights into pedagogical and mathematical aspects of home and ECEC that parents value.

Curricula documents for ECEC in Sweden and Norway highlight the importance of collaboration between teachers and parents for children's learning and development (Norwegian Ministry of Education, 2017; Swedish National Agency for Education, 2018). Yet, parents' views have received little attention in Scandinavian early childhood research. International research highlights the importance of understanding children's learning as embedded in the social, cultural and family contexts in which it occurs (Goodall & Montgomery, 2014; Phillipson et al., 2017). Most studies about parents and mathematics education in ECEC have focused on informing parents about good activities to do at home and how teachers in ECEC could support parents to better understand mathematics-related learning opportunities for young children (e.g. Blevins-Knabe et al., 2000). Some studies have shown that the involvement of parents in their children's mathematics education is considered important in ensuring that they achieve an appropriate academic outcome. For example, Mapp (2003) and Missall et al. (2015) found that informal home mathematics activities, such as when parents highlight number symbols or counting with children, seem to contribute to children's early mathematical skills, which

D. Lembrér (\*)

Malmö University, The Faculty of Education and Society, Malmö, Sweden e-mail<EMAIL_ADDRESS>
<sup>©</sup> The Author(s) 2024

H. Palmér et al. (eds.), *Teaching Mathematics as to be Meaningful – Foregrounding Play and Children's Perspectives*, https://doi.org/10.1007/978-3-031-37663-4\_19

contribute to their achievement at school. Other researchers, such as Anderson and Anderson (2018), have queried the one-way communication from ECEC to home and have stressed the need to understand the mathematics that adults introduce to young children at home. Previous research suggests that a lack of collaboration between ECEC and parents may be linked to the different roles parents and teachers play in children's lives (see for example, Green et al., 2007; Sonnenschein et al., 2012; Van Laere & Vandenbroeck, 2017). Parents may have limited opportunities to share what they already do without awareness of how these differences may interfere with developing opportunities for richer collaborations. Opportunities for collaboration often depend on the context, such as the parents' familiarity with the educational institutions (Murray et al., 2015; Norheim & Moser, 2020). Against this background, research on mathematics education for young children in terms of parents' views can be divided into three themes. The frst theme is about how research fndings should be translated into the home. The second theme identifes research concerned with how parents engage children in mathematical ideas through everyday experience. The third indicates the different roles that parents play in children's lives and the contextual considerations that may interfere with opportunities for such collaboration. Nevertheless, research that values parents' views requires appropriate methodologies that reveal how parents see, think about, and value their children's mathematics at home and in ECEC.

Vázquez Campos and Liz Gutiérrez (2015) stated that points of view are identifed by highlighting of specifc content, related not only to what is experienced but also to what is possible to experience. Therefore, in this paper, I defne a view as a way of seeing the world that comes from the life experiences that people carry with them. A point of view is not only a place from which people view things and events but also how those things and events can be viewed from a certain kind of situation or position. The events that parents share provide insights into their experiences of mathematics education for young children at home and ECEC.

What kinds of parents' views can be identifed in the research is related to methodological choices as these shows how the data collection contexts affect how they are interpreted. In this paper, I discuss the methodological choices in research on early mathematics education framed by two data collection methods: an online survey and photo-elicited interviews (PEIs), with a particular interpretation of insights, gained about parents' views on mathematics education for young children. I argue for the need for more discussion about the methodological choices for investigating parents' views on mathematics education for young children.

In the following section, I present Bruner's theory of narrative construction (1991, 2004), which links people's views and the cultures created and negotiated within a society (Bruner, 2009). Bruner' theory provides the foundation for how investigating parents' views is undertaken. I also briefy describe previous research into parents' views on mathematics education for young children and describe the data collection methods used in my studies (e.g., Lange et al., 2022; Lembrér, 2020). In the last sections, I discuss these methods with particular understanding of how the data collection has affected the research insights from investigating parents' views on mathematics education for young children.

### **Theoretical Perspective About Parents' Views**

Bruner (1991) stressed that narrative construction should be understood as universal, where the personal view is constructed and reconstructed through social interactions and cultural activities. In his work, Bruner used stories to talk about people's experiences, he stated that: "to narrate" derives from both "telling" (narrate) and "knowing in some particular way" (gnarus), the two tangled beyond sorting" (Bruner, 2002, p. 27). He highlighted the power of narrative or storytelling for imposing order on life's uncertainties and one's expectations of life. Therefore, narrative construction shows the importance of contexts and provides opportunities for exploring views on particular topics, such as children and the family culture in which mathematics education occurs.

Bruner (2002) highlighted the importance of meaning as a central process of the individual mind and social interaction. Bruner stated:

There is no such thing as an intuitively obvious and essential self to know, one that just sits there ready to be portrayed in words. Rather, we constantly construct and reconstruct ourselves to meet the needs of the situations we encounter. (Bruner, 2002, p. 64)

From this understanding, parents' views become identifable because narratives do not just recall memories but indicate the values connected to others' expectations and culture as well as their own experiences, ideas, and opinions. Parents' views appear in the problems, dilemmas, or contradictions in the narratives that connect past, present, and future events with mathematics education for young children. Past experiences are connected with what may be yet to come through the values developed from past experiences, as these are likely to be used to interpret future events. Contexts affect what comes to be views or valuable knowledge about mathematics education for young children. For example, institutional views often determine events with children at home. Takeuchi (2018) showed that in Filipino immigrant parents' interactions with children about multiplication methods, the methods used in the children's Japanese school were valued more highly. The parents considered their past experiences with an informal fnger method, commonly used in Filipino culture, to be a counterproductive activity for doing multiplication, even if they knew that it provided correct answers.

For Bruner, a narrative is about "the desire to communicate meaning" (1990, p. 8) and that people use narratives to construct and make sense of their views of the world. As such, he emphasised the importance of language as a tool for understanding the world. Through narratives, people build up a view of themselves and their place in the world. A narrative is, thus, situated in the context of its time and provides a sequence of events with an interrelated, meaningful connection, which allows for the reasons behind these events to be interpreted. Bruner's narrative construction provides opportunities to better understand the meanings that people create from their experiences.  These narratives include people recalling events using particular knowledge or understanding. For example, in a study by Wager and Whyte (2013), parents provided information to ECEC teachers about mathematics activities done at home. The teachers incorporated this information into their planning of mathematics activities at ECEC in two ways. The frst way involved including only activities presented by parents that teachers were familiar with. These teachers disregarded the activities they did not recognise from their own experiences or practices. The second way involved integrating home experiences that teachers were unfamiliar with. In this way, teachers adopted some of the parents' experiences of home activities, but it was a much less common approach. In both cases, the teachers made choices about what mathematics activities should be included based on how the teacher interpreted the narratives told to them by the parents.

Bruner's narrative construction can be used to understand the meanings that parents created from their experiences. The sequences of events described in the narratives may also include what Clandinin and Connelly (2004) describe as the three-dimensional narrative research space. These dimensional spaces are: the personal and social (the interaction); the past, present, and future (continuity); and the place (situation). Narratives are constructed in a specifc place and situation and in a way that the narrative modes of thought generally do not highlight or make clear to those trying to understand them. The sequence of events may include information about the setting or context of participants' experiences. Einarsdottir and Jónsdóttir's (2017) study of collaborations in Iceland between parents and preschool teachers identifed tensions when the parents became more interested in early childhood policy and pedagogical practices. The results indicated that while teachers sought to keep their professional status as educators when talking about children's early years' education, the parents were viewed as providing teachers with informal knowledge about their children. The views of parents were valued only to the extent that it was individualised, so it was only about their particular children. As a result, the teachers did not seek collaboration in implementing the institutional goals and organisation of pedagogical practices at ECEC. Bruner (1991) stated that in interactions, people navigate between their previous experiences and knowledge of the world around them. This kind of navigation could be seen in the teachers' views about what should happen in the Icelandic ECEC institutions affected their interpretation of what the parents told them.

People share their views when interacting by telling narratives about events and experiences. Narratives are social or personal stories which refer to cultural values and traditions as they offer meaningful connections to events. Bruner (1991, 2004) stated that narratives address the meanings people create from their experiences. These experiences include layers of understanding about representations of time, interpretations, what feels right to say or do, cultural norms and contextual background knowledge. Narratives about events to do with mathematics activities for your children appeared in the two data collection methods. The stories told through these methods, either explicitly or implicitly, provided insights into parents' lived experiences in society. Therefore, the connection between parents' narratives and views became apparent in how they constructed their narratives in the individual survey responses and the interactions between parents in a PEI.

In the next section, I describe both methods and then discuss how Bruner's narrative construction was used to identify how the parents' views were constructed by merging their individual and social understandings of the world.

### **Data Collection Strategies**

The two data collection methods were an online survey and photo-elicited interviews (PEIs). Earlier studies indicated that photo-elicitation interviews yielded narratives jointly constructed by the participants and offered a sharing of attention because photos have communicative features when viewed together (Lapenta, 2011). The online survey was useful in describing a population's characteristics (Braun et al., 2021). For my PhD project, Polish immigrant parents and their responses provided opportunities to gain insights into their experiences in their home countries and their new countries.

The frst data collection phase focused on immigrant parents' views on mathematics education for young children; therefore, an online survey was designed to capture some of these views from Polish immigrant parents living in Sweden and Norway. The focus on Polish parents was because there are more Polish immigrants yearly in Norway than any other nationality (Østby, 2016), and Polish citizens were also the fourth-largest immigrant group in Sweden in 2015 (Statistics Sweden, 2016).

The use of surveys for data collection is a common technique for focusing on a specifc population sample. Surveys can be conducted within a limited period of time and are cost-effective for collecting data (Cohen et al., 2000; Trost, 2012). This method allowed participants to remain anonymous. The survey consisted of 16 questions. The majority were open-ended, and two were multiple-choice. These questions are described in detail in Lembrér (2021, pp. 30–34). The survey questions aimed to fnd out about parents' individual views and understand how these views could inform ECEC in both countries. The data from the frst phase were responses to a survey on an online platform (SurveyPlanet), answered between June 2016 and closed in November 2016 (41 Polish parents resident in Sweden completed the survey), and May and September 2017 (54 Polish parents resident in Norway completed the survey). The links to both surveys were made available on the websites of the Polish organisation in Sweden (Polonia info), and an organisation in Norway (Moja Norwegia/My Norway). All the parents that responded to the survey made an explicit or implicit reference to early childhood education in Sweden/Norway and had to have at least one child in ECEC in Sweden/Norway.

The photo-elicitation focus group interviews (PEIs) comprised the second phase of the data collection. Photo elicitation is a method that involves participants taking photos that are later used as stimuli during interviews. Basing the interviews on their own photos helps participants to articulate their interpretations (Hurworth, 2004). This provides insights into how the parents see the relationship between individual views and the wider societal context. Photos as stimuli provide familiarity (Harper, 2002), and the user-generated image is a term often used in research

**Table 1** Overview of data collected

when participants take photos (Epstein et al., 2006). The participants' choice of photos is an initial consideration when investigating specifc groups' views on certain experiences from particular environments. The parents were asked to take photos of their children engaged in mathematical activities, with no information provided about what mathematical activities could be. The data collection for PEIs began in May 2017 and ended in November 2017.

An overview of the data is given in Table 1 and includes the method, data material, and participants' descriptions.

The narratives that were produced from these two data collections were about events and experiences of mathematics education for young children. The initial analysis began with identifying what insights appeared in the surveys, about events to do with young children's mathematics activities, and the transcripts of the photoelicited interviews. Refecting on the data, I describe how the narratives produced from these two data collections provided different insights into parents' views on mathematics education for young children. These narratives were investigated to identify the relationship between parents' individual views and wider societal views. In the next section, I describe the two types of narratives constructed when gathering data from parents.

### **Results and Discussion**

The types of narratives that appeared were produced as a result of the way the survey questions were asked and how the interactions between the participants in PEIs developed. The context in which these narratives were produced provided insights into why various aspects of individual and societal views appeared. The context also gave insight into what can or should be described in the narratives.

The parents' narratives were shaped by the settings in which they were collected and connected to the three-dimensional space narrative enquiry framework (Clandinin & Connelly, 2004). In the narratives about parents' lived experiences, I found patterns, descriptions of what mathematics education is, and evidence of the social infuence that affected parents' views from specifc cultural standpoints (see Chap. 5 in Lembrér, 2021). The narratives brought up the personal and social and were dominated by the autonomy of a parent to be original when telling stories, their commitment to the group, and the values they might share. For example, the interactions show links between personal and social factors of experiences involving sharing life experiences through which a teller looks inside into their feelings, hope, and outside to external environments. The narrative reveals not only the mathematical events but also the settings in which the narratives were collected.

### *The Individual Context of the Online Survey*

In the survey, the questions were designed to elicit narratives, albeit short ones. The questions asked about individual parents' experiences related to the environments of home and ECEC where children might be involved in mathematics education. When designing the survey questions, particular mathematics activities at home and ECEC identifed in earlier research (e.g. Aubrey et al., 2003; Bottle, 1999) were presented, and the parents were asked to identify the mathematics activities their children did at home and ECEC.

The survey results gave a broader view of a particular group of parents on a specifc set of questions about parents' experiences of mathematics education for young children at home, in ECEC in Poland and Sweden, and between Poland and Norway. Overall, the answers to the survey questions were relatively short, making it diffcult to know if more details would have changed the understanding of the values connected.

Although the questions were designed to encourage parents to describe mathematics activities, the shortness of the responses limited the kinds of narratives parents could share, which led to the identifcation of particular kinds of views. The collected set of views that emerged from the survey about participants' experiences of mathematics education for young children indicated an implicit recognition of the infuence of everyday life in the given society (Bruner, 2002).

The narratives allowed for practical and situated knowledge to be identifed. This knowledge suggested a similar view from this group of immigrant parents about what was valuable for the mathematics education of young children. For example, the following two narratives illustrate Polish immigrant parents' dissatisfaction with the ECEC institutions that their children attended in Sweden and Norway.

Survey response (Sweden): I do not think that playing in the sandbox has a greater impact on learning mathematics – unless they count sand molds or distribute a group of toys in equal parts among the children. Survey response (Norway): There is a tragic level of education in Norwegian preschools compared to any preschool in Poland. The Norwegian preschool is a children's storage room until parents take them home. I am very disappointed; I plan to return to Poland because I see that children do not learn anything here, and only at school from the frst Grade, do they start learning anything.

In the frst narrative, the parent valued counting. Other aspects of mathematics, such as volume, measurement or understanding of shapes, which can occur when playing with sand, were not recognised and not valued. The second narrative is from a parent who, infuenced by expectations from the Polish approach to early childhood mathematics education, considered that Norwegian preschool did not provide appropriate experiences to their child. From these two narratives, it is possible to see how an online survey could elicit parents' critical points of view. The complexity connected to the construction of these narratives was apparent in that there were different sources that parents drew on when developing their views, which came from wider societal and institutional expectations and their own previous experience of mathematics education.

Although the survey required individual responses, it was assumed that there would be societal infuences on the narratives through the parents' expectations about the kinds of answers that the survey developer were expecting. There was a range of views presented, from the critical perspective provided earlier, to those which valued the approaches used in the Scandinavian countries. Thus, parents' narrative could include contextual background knowledge from interpreting the pedagogical practices that they were aware of in the ECEC:

Narratives such as these provided insights into the relationship between specifc individual experiences and societal norms in that they emphasised the particularity of mathematics education for young children at ECEC from a particular cultural experience. This can be seen in the description of the valued pedagogical norm, "learning through play", as being a "good approach". The societal infuence appears in the similarity between how play is described by the parent and how it is described in the Swedish preschool curriculum, highlighting that children learn through play (Swedish National Agency for Education, 2018). This narrative indicates that, potentially, this Polish parent had knowledge of and was infuenced by the curriculum. In the second example, Polish parents living in Norway indicated an appreciation of how the Norwegian ECEC supported children to learn in everyday situation and a view of the Norwegian ECEC providing appropriate mathematics education for their children.

The societal impact on parents' general view of the institutional values to do with mathematics education was evident from viewing the whole set of responses to the questionnaires. They provided narratives that included their view, both as being individual and showing the infuence of societal expectations, which had been adopted by the narrator about ways of engaging with mathematics. For example, in response to a specifc survey question, when a series of individual narratives present a similar view about a range of examples of mathematical learning situations, from playing with sand and water, to measuring or jigsaw puzzles, the societal impact on that view becomes more evident.

### *The Context of Interactions in the Photo-Elicited Group Interviews*

The narratives produced in the PEIs refected the specifc context of their construction, including the contributions of other participants about selected photos and related experiences and the impact of broader society on sharing personal memories of events within a group. The PEIs provided a more nuanced understanding of small groups, but were more specifc to the experiences of those groups. In the PEIs, participants elaborated on each other's contributions, contributing to the jointly constructed narratives. As such, the parents' interpretations of their individual events were less apparent, and as the interaction developed, a joint narrative about a set of events was often produced.

Bruner (2002) argued that group interactions grow on the interplay of narratives, on the sharing of common ideas that can be negotiated for their consequences producing an outcome or resolution. In the PEIs, the Norwegian parents described several events in which they played games with their children, often as examples of adapting mathematics in everyday situations. Yahtzee was raised as a general experience of activity that parents engaged with their children at home. Here the emphasis on the social processes that shaped their understanding of people's positions was found. Bruner (2002) described narratives as providing shared meanings and symbolic modes for maintaining original or existing genres that contributed to creating and communicating the world. The narratives produced were not always familiar to those who were listening. Several narratives provided details about how the game involved mathematics and indicated that parents could interpret the features of playing a board game with their children and value playing Yahtzee as it provided mathematical learning possibilities in the home environment. From this discussion, the view seemed to be developed that this was the right or valuable activity to do with young children. For example, parents said:

**Fig. 1** A photo taken by a parent illustrating playing the Yahtzee game

In these examples, the parents focused on encouraging children to count with them and recognise specifc amounts through pattern shapes or from the numerals (Fig. 1). Yathzee was mentioned in both PEIs groups, and this further suggests that parents have valued learning to count into their general view about mathematics education. Talking about the Yahtzee game made at least one parent refect on whether they participated in what was presented as a societal norm and refected on their commitment to the group and the values they might share. This parent said:

PEI Group 2: I have got a little guilty conscience because we almost never played Yahtzee with our other child. So we must go home and do that.

Although PEIs were designed to elicit individual views, the specifc context of the PEIs revealed that there would be societal infuences on the narratives, including the contributions of other parents and the impact of wider society on sharing individual memories within a group.

The narratives produced in the interactions in PEIs were both individual and social and provided insights into what infuenced participants' views beyond what was evident in the responses to the survey questions. Analysis of these narratives aims to understand why or how something happened and the participants' motivation in the events. Parents' views are linked to their intentionality of actions regarding what they value in their roles and the kinds of engagement they described themselves as having with their children. For example, a parent said:

PEI Group 1: I think that there is a strong connection between home and barnehage [ECEC] because children may get [mathematical] ideas in barnehage [ECEC] and can engage with it at home too and learn a little more about it.

This example indicates an appreciation of the Norwegian ECEC and how they might have been infuenced by what was done at the ECEC. This suggests that a parent had subsumed valuing Norwegian ECEC providing appropriate mathematics education, situating the work with children being shared undertaking.

Birkeland (2013) stated that, in PEIs, telling stories about specifc contexts included participants confronting each other with different ideas. The co-constructed nature of the narratives was evident in the transcripts, as the participants drew upon input from each other's narratives when they brought up different points. Therefore, the jointly constructed narratives contained the negotiation of ideas about mathematics education for young children from a set of experiences, using the pictures of their children's engagement in mathematics activities at home as stimuli. The interactions between the participants prompted broader discussions about mathematics education than the individual parents' interpretations of their own experiences.

### **Conclusion**

In this paper, I have discussed two data collection methods, an online survey and photo-elicited interviews (PEIs), for gathering data from parents to identify their views on mathematics education. The different types of narratives produced were affected by the ways the data were collected and provided insights into some of the parents' views on mathematics education for young children. The kinds of narratives that arose in the responses to survey questions brought attention to parents' individual experiences against the backdrop of societal expectations. In the PEIs, as the interactions developed, parents could reconstruct, unpack and contextualise their views, which gave insights into what infuenced those views beyond what had been evident in the survey responses.

In mathematics education research, it is acknowledged that parents contribute to their children's educational outcomes. Many researchers have studied these contributions using different methodologies (see for example, Anders et al., 2012; Colliver & Arguel, 2018; Hoover-Dempsey et al., 2005; Sheri-Lynn et al., 2014). In this paper, I have illustrated how parents' identifable views seem to be situated simultaneously within the individual and social expectations that appeared differently in the data collected through these two methods. Thus, in the support for collaboration stated in curricula documents for ECEC in Sweden and Norway (Norwegian Ministry of Education, 2017; Swedish National Agency for Education, 2018), there are no formal directions about how this is to be achieved. For the research related to parents' views on mathematics education for young children, the study has shown that further refection is needed on the infuence of data collection on what can be said about parents' knowledge, experiences and views. The cultural nature of mathematics education for young children infuences parents' views. The way parents are asked about their views might emphasise particular aspects of their knowledge about differences or similarities in mathematics education, such as between home and ECEC institutions.

The focus on the social also indicates the role of the political context in social interactions. In the case of the Polish parent in Norway, it seemed that they lacked the power to have the Norwegian preschool adopt their view on mathematics education for their children, which led them to consider taking their children back to Poland (Lange et al., 2022). The issue of who had the power to affect the mathematics learning opportunities offered to children came up in different ways when considering what might infuence parents' views. Further refection on the cultural and political nature of data collection is needed.

### **References**

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### **Index**

#### **A**

Actions, and speech, 209, 212 Assessment, 167, 172, 177, 180, 185, 199, 200, 205 Authentic assessment, 199, 200

#### **B**

Barnehage, 97–101, 255

#### **C**

Combinatorics, 119–128 Computational thinking (CT), 97–116 Counting, 2, 7, 57, 60, 63, 65, 66, 81, 98, 99, 102, 106–109, 111–113, 115, 116, 120, 138, 140, 141, 172, 175, 179, 186, 188, 190, 195, 198, 199, 202, 204, 205, 213–215, 217, 218, 227, 235, 237, 238, 245, 252 Cultural historical activity theory (CHAT), 1, 3, 185–189, 192

#### **D**

Diagrammatic reasoning, 209–218 Digital apps, 39–44, 50–52, 100 Division, 69–77, 126

#### **E**

Early childhood education (ECE), 13–23, 39, 40, 55, 98, 99, 145–154, 231, 234–236, 241, 249

Early childhood mathematics education, 221, 228, 252 Early mathematics learning, 157–168 Educational app, 44, 66, 145 Educational technology (ET), 145–154 Ethical reasoning, 70, 71, 73, 74, 76 Evaluation study, 58

#### **F**

Free play, 20, 30–32, 58, 61, 62, 65, 66, 85, 93, 174, 189, 191, 233 Freudenthal, H., 3, 195, 221–223, 225, 231, 234, 241

#### **I**

Individual-adaptive learning support, 132, 172 Interplay of gestures, 211, 215, 217 Interpretative paradigm, 87

#### **K**

Kindergarten, 13, 39–44, 50, 56–60, 62, 65, 66, 81–94, 131–143, 157, 159, 160, 167, 171, 172, 174–176, 185–195, 212, 213, 252 The Knowledge Quartet (KQ), 131–143

#### **L**

Learning support, 22, 28, 57, 58, 65, 132, 175, 179–181 Locating, 39–52, 98, 102, 103, 108, 109

© The Editor(s) (if applicable) and The Author(s) 2024

H. Palmér et al. (eds.), *Teaching Mathematics as to be Meaningful – Foregrounding Play and Children's Perspectives*, https://doi.org/10.1007/978-3-031-37663-4

#### **M**

Mathematical design patterns, 157–160, 163, 166–167 Mathematical profciencies, 185–195 Mathematical reasoning, 70–72, 74, 76, 141, 210, 238 Mathematical teaching opportunities, 28, 29, 31, 32 Mathematics, 2, 14, 28, 39, 55, 69, 81, 97, 120, 131, 145, 157, 171, 186, 197, 210, 221, 233, 245 Mathematics education, 55–66, 81, 86, 92, 120, 123, 133, 134, 145–154, 158, 171–173, 179, 180, 209, 221–223, 234, 245–256 Mathematics teaching, 15, 84, 133, 134, 142, 222, 233–241 Mathematizing, 9, 22, 221–223, 225–231, 235, 239, 241 Methodology, 32, 43–44, 85–87, 100–102, 246, 255

Multimodality, 209, 212, 218

### **N**

Narrative construction, 246–249 Numbers, 2–9, 17, 19, 23, 46, 57, 58, 60, 62–64, 66, 71, 74, 99, 102, 105, 106, 109–112, 115, 116, 119, 124, 127, 131, 132, 134, 139, 142, 145, 148, 154, 160, 172, 175, 186, 188, 189, 195, 197–200, 202, 204, 205, 212–217, 221, 222, 225, 226, 228, 229, 234, 236–240, 245, 253

### **O**

Observation and diagnostic tools, 172, 175–177, 179–181 Online survey, 176, 245, 246, 249–253, 255

#### **P**

Peer interactions, 81–94 Photo-elicitation, 249, 250 Playfulness, 233–241 Play-responsive assessment, 186–188, 192–194 Preschool, 3, 13, 28, 44, 69, 97, 120, 132, 148, 157, 221, 233, 248 Preschool class, 120, 123, 233–241 Pretend play, 7, 27–37 Problem solving, 4, 81–94, 97–116, 119–128, 132, 198, 222, 231, 236 Professional competencies, 172, 173, 180

### **R**

Real world, 2, 55, 221–231, 234 Relations language and mathematics, 4, 8, 83, 197–199, 201, 204, 205 Representation, 2, 5–7, 15, 18, 60, 64, 83, 119–128, 134, 137, 138, 225–227, 235, 248 Responsiveness, 157–168, 186–190, 192, 193, 195, 224, 236 Robots, 97–116, 151

### **S**

Scaffolding, 28–32, 36, 100, 158 School characteristics, 145–154

### **T**

Teacher characteristics, 148, 152

Teacher's practices, 30

Teacher-support, 29, 237

Teaching, 9, 14, 28, 40, 70, 84, 131, 147, 171, 185, 222, 233

Toddlers, 13, 40, 50, 186, 197–199, 201–204, 221–231

#### **Y**

Young learners' mathematical interactions, 134, 157, 209


**8.2 Spinal surgery**

Hart et al. informed on a prospective, randomized, and blinded study in patients with lumbar disease the use of BMC mixed with allograft spongiosa chips during surgical posterolateral fusion (PLF) procedures. Patients underwent instrumented lumbar spine PLF procedures [134]. Fusion status and the degree of mineralization were evaluated by two radiologists blinded to patient group affiliation. X-ray examination, in control patients at 12-month follow-up, showed that the bone graft mass fused in none of the cases and, at 24-months, in four cases (10%). In the BMC treatment group, 6 cases (15%) achieved fusion at 12 months and 14 cases (35%) at 24 months. Computed tomography scans showed that 40% of control patients and 80% of BMC-treated patients had evidence of at least a unilateral continuous bridging of the bones between neighboring vertebrae at 24 months, significantly favoring the mixture of spongiosa bone with autologous BMC (*P* < 0.05) as an efficient option to augment PLF healing.


3. Findings

personality traits of successful entrepreneurs lies in the impact of non-psychological factors including demographics, training and experience, and this has been pointed out in the literature [20, 21]. Brandstätter's [22] study revealed that in order to become and continue as an entrepreneur, one needs to possess some distinctive character attributes such as self-motivation; a moderate risk propensity; an internal locus of control, as well as a personal talent for innovation,

In many of the women entrepreneurship literature, availability of financial resources and government support are indicated as important external environment factors limiting the success of women entrepreneurs ([7, 23, 24]). In a study dedicated to the challenges facing women entering entrepreneurship, Still [25] identified three different classes of barrier that also include availability of financial resources. The first class is composed of the motivational factors that push women to establish their own businesses, including creating the confidence necessary in starting a venture, finding proper sources of help and advice, financial resources, coping with risk and access to networks. The second class of barrier again includes motivational factors, but this time the pull factors include women's lack of access to finance, mentors, knowledge and information. The third barrier class refers to the youth of such entrepreneurs, which elicits discrimination on the basis of age by consumers, insufficient family and peer

In light of this literature review, the motives, personal characteristics and challenges facing

A phenomenological approach allows researchers to get close to participants, penetrate their realities and generate an understanding of the research in question (Bygrave, 1989) [26]. Within this paradigm, an in-depth interview was identified as the most appropriate method to the purpose of the study. The interview guide for the study was designed by a panel of experts, including two entrepreneurship and strategy professors, and one active female entrepreneur. Once piloted, the interviews were conducted face-to-face for a period of about an hour and all tape-recorded and transcribed. The purposive sampling technique was used for this study, since it is a non-random technique that does not need underlying theories or a set number of participants and it enables the researcher to select individuals and groups who are proficient and well-informed within a phenomenon of interest and are willing to assist with the relevant research [27]. As a result, 10 women entrepreneurs who are acknowledged successes and are

The interviews were semi-structured to enable women entrepreneurs talk about range of topics but also specific questions on three key issues of the study: (1) the motivational factors of the respondents to become entrepreneurs, (2) their personality traits and (3) challenges they

pro-activity, a high tolerance for stress and self-efficacy.

1.4. The challenges facing female entrepreneurs

144 Active Learning - Beyond the Future

support, and the lack of proper business advice.

2. Methodology

successful female entrepreneurs in North Cyprus are investigated.

active members of the Business Association in North Cyprus were selected.

#### 3.1. The demographic profile of the female entrepreneurs

The demographic characteristics of those interviewed are presented in Table 1. The mean age of the sample was 46.1, and 80% of the women had a university degree, while the remaining 20% had completed high school. The marital status of the respondents is broken down as 80% married, and 20% divorced. Half of the respondents were active in both the service and productive sectors, while 30% were active only in the service segment and 20% were involved in trading businesses.

Table 1. Demographic profile of respondents.

30% of the female entrepreneurs interviewed were in service businesses such as boutique hotels, car rentals and insurance. 20% were in trading businesses covering the importation of fruit and vegetables or textiles. The majority of this group had both production and service functions within their concerns. Some had had operations in both areas since opening their businesses as they were active both in the production and distribution of their goods. Many of them had added a function when expanding their businesses. 30% of the entrepreneurs had the minimum 5 employees necessary for inclusion in this study, and 2 entrepreneurs had staffs of 70 and 125, respectively, and both are involved in large-scale production and service businesses.