Keywords

Introduction

According to The Norwegian Framework Plan for the Content and Tasks of Kindergartens, “Staff shall create opportunities for mathematical experiences by enriching the children’s play and day-to-day lives with mathematical ideas and in-depth conversations” (Ministry of Education and Research, 2017, p. 54). Enrichment of play has been theorized in Sweden as play-responsive teaching (Pramling et al., 2019). The Norwegian and Swedish traditions are similar, except that the word “teaching” may be more controversial in Norway. Situations of daily life can be seen as cultural activities and be seen through the lenses of cultural historical activity theory (CHAT). Within this approach van Oers (2010, 2013a, b, 2014), theorizes play as a format of cultural activity in which children are highly involved, follow implicitly or explicitly some shared rules and have some degrees of freedom with regard to how the activity should be carried out (Van Oers & Duijkers, 2013). CHAT as a theoretical framework is thus suitable for analyzing whether children are observed in adherence to the ideals of the Norwegian kindergarten context. CHAT has been used in developmental education and play-responsive teaching, two approaches which both acknowledge play and the important role of adults in young children’s development (Pramling et al., 2019; Van Oers & Duijkers, 2013).

Assessment of children’s mathematical competency or proficiencies in Norwegian kindergarten has been investigated from the perspective of mathematical learning difficulties and early intervention. In Norway, ‘kindergarten’ is used for children aged 1–6 years. Reikerås et al. (2012) and Reikerås (2016) have studied quantitatively the results of assessment of competence or proficiency in mathematics, language, social skills and movement in Norwegian kindergartens. The kindergarten teachers in their study assessed every child at the ages of 2.5 and 4.5 years old and were told to do this through observation in daily life and play situations. Reikerås et al. (2012) and Reikerås (2016) used the observation scheme (MIO), which is also available for assessment purposes in Norwegian kindergartens (Davidsen et al., 2008). The referred study and the availability of assessment schemes make it a relevant research question to ask whether kindergarten teachers using that kind of observation scheme really observe children in play and daily life activity, and how the observations interfere with ongoing play and activity. An observation scheme restricted to proficiencies related to numbers and counting was developed for the study this article is based on, in place of the MIO scheme. This is a simplification compared to MIO, but the developed observation scheme adds more detail to the area numbers and counting and makes it possible to avoid a ceiling effect for children who are 4 and 5 years old. The chosen mathematical area had largest variance among toddlers in Reikerås et al. (2012), and it is also most relevant in order to identify children at risk of developing mathematical learning difficulties (Geary et al., 2018). This was a motivation in the study, even though learning difficulties are not discussed in this article.

The concepts responsiveness to cultural meaning and play-responsive assessment will be developed, and the research question will be refined by using these concepts, CHAT and van Oers’ theory of play as a format of cultural activity. The first refined question asks how observations were made, and the second and third ask about responsiveness of observation to cultural meaning and play respectively. Thus, in this article we will investigate the following three research questions:

  • What are the main types of observation of mathematical proficiencies used by the kindergarten teachers?

  • How do observations of mathematical proficiencies relate to the cultural meaning of the activity in which observation was done?

  • How was children’s involvement and freedom during observation related to cultural and personal meanings of the cultural activities in which observation was done?

Theory

Cultural historical activity theory, originating with Leont’ev and Vygotsky, conceives human development as a process based on interactions between humans with the help of cultural tools in the context of historically produced practices (Van Oers, 2013b, p. 189). A central idea is that human activity is part of human culture and develops through history. Learning takes place when children participate in cultural activity, and development is dependent on participation together with adults or more capable peers. Mathematics is a human activity, an abstract one with scientific concepts. Mathematical concepts and actions have to be put into words, and this is crucial for young children’s development of mathematical meaning (Van Oers, 2010, p. 29).

Bearing on El’konin, cultural historical activity theory claims that before school age, the best way of learning is when children take part in playful activity (El’konin, 1999). Play and learning are unified by seeing learning as a format of cultural activity in which children are highly involved, follow implicitly or explicitly some shared rules and have some degrees of freedom with regard to how the activity should be carried out (Van Oers & Duijkers, 2013). Since daily life activities are cultural activities, children’s participation in them may become play when the above definition is satisfied. The three characteristics involvement, rules and freedom of change apply to all cultural activity, and thus can be used also for potential non-play. A sociocultural approach makes it possible to overcome the assessment-teaching dualism. In the Vygotsky-based dynamic assessment theory, mediated interaction is necessary to understand the range of a child’s functioning, but this interaction also guides further development of these abilities (Poehner, 2008, p. 24). From this point of view, assessment may involve proficiencies and activities that children can only approach together with adults or more capable peers. Assessment may start in cultural activity which is non-play, but which may be turned into play. The concept play-responsive teaching includes both adult interference responsive to children’s initiatives and interests, and interference which enables children to have experiences they otherwise would not have had (Pramling et al., 2019, p. 180). Similarities to this will be discussed for the concept play-responsive assessment introduced in this article.

Another kind of responsiveness in assessment is responsiveness to cultural meaning. A cultural activity has a motive which is collective or cultural, and the actions of a participant in the activity will have personal meanings, similar or sometimes different from the cultural motive of the activity. Leontyev (2009) identifies personal meaning with subjective meaning and links this to the German ‘Sinn’ as opposed to objective meaning ‘Bedeutung’. We will follow van Oers (2010, p. 26) and use the phrase ‘cultural meaning’ in place of ‘cultural motive’. An adult intervention in a cultural activity for the purpose of assessment will be called responsive to cultural meaning if the intervention is compatible or faithful to the cultural meaning.

Meaningful learning happens when cultural and personal meanings merge. Play can be seen as imitative participation in meaningful cultural practices (Van Oers, 2010, p. 29). The child’s personal meaning normally is not quite the same as the cultural meaning that the child’s play is based on. Adults’ intervention in children’s play may change the cultural meaning and also be at odds with children’s personal meanings. Responsiveness to cultural meaning must not be confused with the concepts culturally responsive teaching and culturally responsive assessment, which emphasize the multicultural perspective (Gay, 2018).

The concept of teaching is clearly distinguished from the related concept of instruction when play-responsive teaching is conceptualized. Instruction takes place regardless of response to the instruction, but teaching presumes responsiveness to response (Pramling et al., 2019, p. 176). According to Pramling et al. (2019, p. 176), “instruction is an action while teaching is an activity”. A parallel distinction between testing and assessment for the concept play-responsive assessment will be discussed.

Method

This study was planned as a pilot for future studies. The observations involve 47 children aged 2:10–3:1, 3 children aged 3:10–4:1 and 11 children aged 4:10–5:1. The observations were carried out by the kindergarten teachers in 2019 using an observation scheme in the twelve kindergartens that participated in the project. The observation scheme has been developed by the authors, based on Stock et al. (2010) and inspired by the project described in Reikerås (2016), but limited to solely focusing on the children’s proficiencies related to numbers and counting. This article will focus on the following five of a total of eight proficiencies in the observation scheme: ‘recitation of the counting sequence’, ‘counting a set of objects’ (arranged in order and by random placement), ‘fetching N objects by a given number word’, ‘estimation by separating most from fewest’ and ‘seriation and classification’. The observations were carried out during normal practice in the kindergarten.

Four researchers, pairwise, conducted interviews with the kindergarten teachers in groups of one to four, but typically two, in each of the twelve kindergartens. The main content of the interviews was related to how the kindergarten staff carried out the observations and how they themselves and the children experienced these observations. The interviews lasted about 45 minutes and were audio recorded. We analyzed the data using thematic analysis, in which an initial thematic coding was done during transcription. Then as a result of repeated readings of the coded transcriptions, we identified about ten themes of research interest. In the third phase of analysis we both searched for a theoretical framework and tried to restrict attention to a coherent subset of the identified themes. This resulted in four themes defined by how the kindergarten teachers observed children’s mathematical proficiencies and the choice of van Oers’ use of CHAT to theorize play and learning. One of the four themes was excluded because non-participant observation was not found to be central, and daily life situations and play situations were united as one theme that was called natural activity. The fourth theme was initially given the name adult initiated activity, but was renamed organized activity.

The fact that four different researchers conducted semi-structured interviews may have influenced the reliability of the data. For example, the amount of specific follow-up questions versus more general questions could affect the level of details in the answers from the informants. The fact that the project leader participated in ten of the twelve interviews together with one of the other three, has greatly reduced this bias in the collected data material. The reliability is strengthened by the fact that the two authors, largely independently of each other, have read and analyzed the data over time and from different perspectives.

The excerpts from the interviews are labelled with a K, and a number between 1 and 12, which refers to the kindergarten number in our data, followed by the quote’s time point in the interview. The age of the children, except for one excerpt, is 2:10–3:1. Written consent for participation has been given by the parents or guardians of all the children who have been observed and by all the kindergarten teachers who have been interviewed in this project. The project has been approved by the Norwegian Centre for Research Data (NSD).

Results

The thematic analysis combined with the cultural historical activity theory approach resulted in these main types of observation of mathematical proficiencies:

  • Extension of natural activities

  • Organized activities

In a few cases, observation was done without organization or adults extending a natural activity, but this third alternative is beyond the scope of this article. The kindergarten teachers themselves used phrases like ‘natural situations’, in the sense of both daily life activities and play initiated by children.

Extension of natural activities means that the kindergarten teachers for the purpose of observing one or several proficiencies in the observation scheme, take some action which adds to and potentially modifies or changes a cultural activity that has a cultural meaning independent of the need of observation. In the case of children’s free play, the activity is ongoing when the adult takes part or influences it. For daily life activities the adult may initiate an activity like a real meal, but for another purpose than observation.

The term ‘organized activity’ was used by the kindergarten teachers and will be used in the sense of initiating a cultural mathematical activity for the sole purpose of observing a proficiency in the observation scheme. It is not ruled out that an organized activity could turn into a natural activity. Sometimes a natural activity is extended in a way that neither responds to its cultural meaning nor children’s meaning, and such cases may more appropriately be called organized activities.

Responsiveness to Cultural and Personal Meanings

Natural activity was regarded as the typical kindergarten approach by the kindergarten teachers. This means that their preferred way of observation was by extension of such activity, as long as this was regarded as a possible choice. The typical way the kindergarten teachers add to a natural activity is to ask questions with mathematical content, dependent on the proficiency being observed.

When dressing, to ask how many shoes do you need to wear, how many mittens do you need? (K5: 7.40)

Putting on shoes or mittens is an example of a daily life activity which regularly happens in the kindergarten. The questions to the children are consistent with the cultural meaning of the activity and put a mathematical concept into words. Thus, the questions are responsive to the cultural meaning and make the activity mathematical for children.

when we came back from shopping and there were these little tins of liver pate […] instead of lining up something arbitrary and saying that they should count. […] There it was natural, we were unpacking the box of groceries, and they were lying higgledy-piggledy, so then it was just a completely natural activity. (K12: 4.17)

The kindergarten had ordered tins of liver pate, and the kindergarten teacher asked the children (aged 4–5) to count the tins which were randomly placed, probably on a table. For the adult it makes sense to count the tins, in order to be sure that what is brought to the kindergarten is in accordance with what they planned to buy, and so her question to the children was consistent with the cultural meaning of the activity. Introducing counting into the activity makes it mathematical, but in this case children’s personal meanings do not necessarily include the cultural meaning.

A: We were in the woods, playing with leaves and sticks. Where are there most / fewest. M: Was it planned? A: No, then I had someone with me to be observed. So, I thought it was a good idea to use things from nature and include it in the play. (K4: 11.00)

To go for a walk in the woods is a daily life activity in Norway. This is an activity with some degrees of freedom, and for instance, talking about what you see in the woods can be seen as part of the activity. One of the items in the observation scheme was to decide which of two sets is most numerous. This extension of the activity would probably not have occurred without the observation needing to be done and is as such an organized activity. However, it has similarities to rule-based competitive game activities common among children which possibly may be seen as part of a walk in the woods.

Like separating most from fewest, to fetch N objects also was regarded by some of the kindergarten teachers as difficult to observe through natural activity. One example from the data is that children were playing with toy building bricks, and that the kindergarten teacher asked a child to fetch five bricks. Typically, this question was not related to the cultural meaning of building. However, in one situation with building bricks the kindergarten teacher said “We need another two. Can you find two more and build upon this?” This extension of the activity is responsive to cultural meaning.

Children’s Involvement and Freedom During Observation

Observation in extensions of natural activities is described generally in positive terms. Specific examples of situations from the data where the kindergarten teachers mention positively involved children in extensions not changing the cultural or children’s personal meaning are sparse, but sometimes the kindergarten teachers said that they contributed to children’s involvement. Some of them also mentioned learning, even though the study focused on assessment. An expression used by some kindergarten teachers was ‘learning by playing’.

We must be the driving force in free play, make it interesting and ‘play it in’. Even more than we do. We see that what we are involved in, in ‘learning by playing’, shows up in other contexts. That’s what kindergarten is all about. (K1: 39.40)

This kindergarten teacher has an overall belief that play is of utmost importance in the kindergarten, and that adults must contribute to playful learning. Both in this excerpt and in other cases it is unclear whether “free play” is restricted to play initiated by children, or whether they have in mind also other kinds of cultural activities with a playful approach.

Organized activities could also lead to positive involvement, even if the border between play and organized activity sometimes may be discussed.

LB: What kinds of activities did you use when she sorted them from smallest to largest, for example? Then it was families that were the thing. Then it was domestic animals. Mom-horse and dad-horse and the baby(-horse). Sheep and pigs. Then she was eager, then she could line them up by size. But she also wanted to arrange them so that the piglet stood between mom and dad, then she focused on that. (K6: 31.55)

The kindergarten teachers had handed out toy animals and asked children to sort the animals according to size. This girl enjoyed role play and families, and her engagement in that may have influenced her involvement in the extended or organized activity. She was given freedom to change the rules, and she turned the activity into play with another cultural meaning. By placing the baby-animal between its parents she is focusing on social relations rather that ordering by size.

Often organized activity was done with a group of children, a math-group, in a separate room. These organized activities with a playful attitude were popular with many and said to have similarities with engaging activities children were used to doing in the kindergarten.

T1: Then we took some things into a separate room. We were there together so that we could both observe and instruct. […] R: So it was more like a test? T1: Yes. Yes, but I don’t think the kids experienced it like that. T2: No, more like play maybe. T1: It is not unusual for them that we are doing it. […] T2: I found that they were very eager. Everyone wanted to join in. Because it’s like playing. […] It was rather a bit like what I experienced when we were indoors in the kindergarten and played with the teddy bears or the cars and made them count. (K1: 20.52)

Children’s freedom of change was restricted when they were observed in a separate room, and the words ‘instruct’ and ‘like a test’ indicate restrictions in children’s freedom of change. Even so, the kindergarten teachers thought that the activities were a positive experience for the children. The kindergarten teachers argued for this by saying that the children were used to restrictions in their freedom, and the adults managed to maintain a playful attitude and enthusiasm towards the activity.

Children’s negative involvement related to organized activities was mostly described by words like ‘artificial’, ‘like a test’ and ‘schoolish’. The word ‘artificial’ could point to difficulties in relating both to cultural and personal meaning, and ‘like a test’ and ‘schoolish’ express activities with restricted degrees of freedom. One kindergarten teacher related the word ‘artificial’ to a feeling among children that this was not what they wanted to play, and said that the adults took control in order to observe what they needed to see. The adults in these cases sometimes were uninvolved, and the children sometimes expressed bad feelings towards the kindergarten teachers. Children for instance said that they did not want to do this. Some children disliked being observed or understood that something was expected of them. Other times children withdrew from the activity, preferring to do something else, but not necessarily with bad feelings.

Discussion

The research questions will be discussed using cultural historical activity theory, theory of play in the version of van Oers, and the theory of play-responsive teaching (Pramling et al., 2019). Van Oers (2010, 2013a, b, 2014), theorizes play as a format of cultural activity in which children are highly involved, follow implicitly or explicitly some shared rules and have some degrees of freedom with regard to how the activity should be carried out (Van Oers & Duijkers, 2013). A central construct is the idea of cultural activity and that children’s involvement, and children’s freedom of change is what distinguishes play from non-play. A new contribution in this article is the introduction of the concepts responsiveness to cultural meaning and play-responsive assessment, inspired by the concept play-responsive teaching (Pramling et al., 2019).

  • What are the main types of observation of mathematical proficiencies used by the kindergarten teachers?

The main distinction found is between organized activity and extension of natural activity. Natural activity is either play initiated by children or daily life activities which are initiated by adults for other reasons than observation of mathematical proficiencies. Only in a few cases were the kindergarten teachers able to observe mathematical proficiencies passively without any participation. The following two remaining research questions will be discussed together.

  • How do observations of mathematical proficiencies relate to the cultural meaning of the activity in which observation was done?

  • How was children’s involvement and freedom during observation related to cultural and personal meanings of the cultural activities in which observation was done?

Both play and daily life activities have cultural meaning as well as a personal meaning for the participating children. In natural activity the kindergarten teachers in many cases contributed by introducing mathematical vocabulary or procedures in a way that preserved or was consistent with the cultural meaning of the activity. By doing so, adults contributed to the child’s process of gaining mathematical meaning (Van Oers, 2010, p. 29). In the case of ongoing play, such extensions often preserved children’s involvement and so were play-responsive. Responsiveness to play failed in cases when adults were not attentive to children’s meanings or did not give children enough freedom.

A central finding is that children could be engaged also when they were observed in organized activity. Both explanations related to children and explanations related to adults may explain children’s involvement in such activity. Adults’ involvement and the way organized activity is presented are explanations related to kindergarten teachers. Some of the kindergarten teachers said that they have to make it interesting and ‘play it in’, or that involvement is contagious. One child-related explanation was that children are used to similar activities in the kindergarten with restrictions in their freedom. Restrictions in freedom as a reason for involvement is strange, and it is more plausible that enough freedom was still present. If so, it makes sense that similarity to usual activities in the kindergarten explains the involvement. Activities with the sole purpose of observing proficiencies in the observation scheme often were similar to engaging activities like games or rule-based play. Another child-related explanation is that some of them liked to play with the same kind of objects or material as used in organized observational activities. This did not always apply, as children sometimes turned to their preferred way of using the material. Bad feelings in such situations were avoided when children were given freedom to withdraw from the intended adult extension. That children are members of a math-group is another kind of explanation. Such a group is said to be popular, but the data do not contribute to answering why this is so. A final reason related to children is that movement and physical action are engaging. Relay race and collecting sticks in the forest are examples from the interviews. When children later compared the lengths of the sticks, their involvement from the collecting process may be prolonged into the mathematical activity.

The concepts of responsiveness to cultural meaning and play-responsive assessment are inspired by the concept of play-responsive teaching (Pramling et al., 2019), but are about assessment rather than teaching. Especially in the first part of the observation period, kindergarten teachers thought assessment to be clearly distinct from teaching and learning, and had ideas similar to not ‘teaching to the test’. Gradually they began to use observation activities that also led to children’s learning. In principle, assessment may be possible in daily life situations in which children neither are involved nor have freedom of influencing what is going on. The possibility of that kind of assessment could be a question of research, but whether this can be done in an ethically justifiable way is questionable. Even so, the concept of responsiveness to cultural meaning can be defended as a supplement to play-responsive assessment. In language learning, words and concepts are used before children have an ownership to the words, and in the same way mathematical language and procedures may be introduced into daily life situations. When this happens in children’s zone of proximal development, both assessment and learning are possible. However, play-responsive teaching is said not necessarily to start in play, but has to be responsive to play, if it starts in play (Pramling et al., 2019, p. 180). This could be interpreted as if play-responsive teaching also includes teaching that starts in, for instance, daily life situations. Play-responsive didaktik (Pramling et al., 2019) subsumes both play-responsive teaching and play-responsive assessment.

One finding is that the word ‘test’ is used in organized activities which impose restrictions on children’s freedom of change. Kindergarten teachers from one kindergarten also used the word ‘instruction’ for this kind of activities. We argue that play-responsive assessment in play and daily life situations is just as distinct from testing as play-responsive teaching is from instruction according to (Pramling et al., 2019, p. 176). It was found that children could be involved and even have some kind of freedom to influence organized activities, but that sometimes involvement was low and freedom almost absent. When some freedom of change is present, this is, however, not freedom regarding aspects central to the mathematical proficiencies to be assessed in the activity. In play-responsive assessment, as in play-responsive teaching, assessment may start with adult-initiated activity, but must be responsive to how children react.

A possible limitation in the study is that the analysis and discussion use a theory of play, but that the kindergarten teachers’ use of the word ‘play’ is not necessarily always consistent with the theoretical definition. For instance, some talk about play could be interpreted as related to some kind of material or to physical movement, but also to involvement, which is central in the theory of van Oers. In the study such utterances are taken as reasons for children’s involvement. The way kindergarten teachers talk about play also in some cases makes it unclear whether they are talking about child-initiated play, extensions of daily life activities or organized activity. One solution to this can be the term play-responsive didaktik and a playful attitude to all interaction with children, but also the finding that the different kinds of activities transform into each other, and that the borders between them sometimes are unclear. Another limitation is that in some of the interviews, kindergarten teachers who have assessed different children independently, share their experiences, but their individual stories are difficult to distinguish in the transcriptions. Care has been taken to avoid mixing up such stories, but a possible danger is to fit together unrelated individual voices into a false story.

Questions for Further Research

One finding was that extensions of daily life activities can respond to cultural meaning and contribute to mathematical meaning, even if this does not necessarily respond to children’s meaning. An interesting question to investigate is how children’s involvement is in that kind of extensions. A plausible hypothesis is that responsiveness to cultural meaning makes the adults become involved, which may then be contagious. Taking part together with adults in that kind of activity may also in itself be attractive to children, in much the same way as taking part in a math-group.

Some mathematical proficiencies, like to fetch a given number of items or deciding which of two sets is most numerous, were found to be more challenging to assess through natural activity than proficiencies related to counting a given set of items. A question for further research is to investigate why this is so from the perspective of mathematical teacher competency or tasks of teaching. An alternative approach is didactical phenomenology in the sense of Freudenthal (1983), by searching for suitable cultural activities for the mathematical proficiencies that it is most relevant to assess in kindergarten.