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In the following, two different situations of a Grade 1 mathematics class about relational terms will illuminate language and discursive particularities of the different scenes. In this regard, especially the use of a narrative real-world context about a crocodile in order to visualize the relational terms ‘greater than’ and ‘less than’ demonstrates that the pupils’ language use and their learning process is affected in both, positive and negative ways - e.g. by a lack of clarity concerning the mathematical content. This also becomes visible through the language of the pupils during the two presented scenes.

Scene 1. Class discussion at the start of the lesson: What does Croco like to eat?

The excerpt below is from the opening class discussion in Grade 1 about the topic of the relation terms ‘greater than’ (>) and ‘less than’ (<).The teacher (T) is now initiating a discussion about the formal expression of the terms. With the help of a narrative real-world context about a crocodile with an open mouth (named Croco) and towers of two red cubes and five blue cubes on the board (see Figure 11.1, from the images available at https://www.zaubereinmaleins.de, June 2019) the mathematical content is brought to the pupils.

T: Our little Croco always wants to eat a lot.That’s why its mouth is open that

wide. And now he comes and thinks about. Shall I eat the red ones or the blue ones? What do you think, Ina?

INA: I think red.

T: You think red [Turns Croco with the open mouth to the two red cubesj .Why?

INA: Red is like meat.

FIGURE 11.1 The board before and after the class discussion (left and middle). Simplified visualization of Croco

T: Aha.That would be a consideration. Nabil, what do you think he wants to eat?

NABIL: Blue?

T: You say blue is what he wants to eat, why? ... [Nabil does not say anything for

4 seconds). Simply because blue is beautiful. Okay. Rich, what do you think? RICH: Ehm. He wants to eat red because it is like meat and fish.

T: [Turns Croco to the red cubes] Because meat and fish. Mhm. Nagi, what do

you think?

NAGI: Blue. Because that is more.

T: That is our little Croco who always wants to eat the most and that’s why he

looks here [Turns the crocodile between the towers and cubes that it looks to the four blue ones, writes a “>’ between the four blue and the red cubes and again places Croco between them]. Can you see this? Because he always wants to eat what is more.

The extract shows that the teacher packs the mathematical content into a narrative real-world context. This seems to lead to pupil answers which are oriented towards the story and less towards the mathematical content.The answers and explanations of Ina and Rich seem to be bound to the story of Croco (as they give the explanation that they argue for red because of the similarity to meat and fish), until Nagi gives a ‘satisfactory’ answer with a short justification about the mathematical insight, which seems to be less oriented to the story. Ina and Rich, by contrast, seem to be ‘caught up’ in the narrative real-world context and try to argue for ‘red’ as it is similar to the color of raw meat and fish. Although it is visible that there are more blue cubes on the board, two children argue for red, which leads to the assumption that they are too fixated on the story.

This is consistent with the assertion of Neth and Voigt (1991), who state that the use of narrative real-world contexts might disguise mathematical facts, and with the statement of Krummheuer (2000) that the mathematical core is co-delivered and implicitly conveyed. Thus, it is up to the pupils to ‘filter out’ and understand the mathematically significant facts of the story. In the analyzed situation, it is never explicitly expressed which mathematical idea Croco and his food are symbols for. Concerning the realistic content, authenticity and personal involvement of the story, it becomes clear that this is too far-fetched. It is neither taken from the everyday world of children, nor is it relevant to the pupils, nor is it conceivable that a crocodile in such a situation would be in a position to decide on its own which color and ‘amount’ of its food it will have. It remains unclear whether the children understand the mathematical concept behind the given story, since only Nagi contributed something to the situation that can be interpreted as primarily mathematical. The rest of the pupils’ utterances seems to be superficially oriented toward the story of Croco and/or the colors of the cubes. The teacher might interpret Nagi’s answer as oriented to the mathematical content and therefore proceeds from the assumption that Nagi (and by her utterance also the rest of the class) might have understood the mathematical content of abstract quantity and the relational terms. The teacher did not support the children to discover the mathematical purposeful concept (they do not have to argue with the numbers of cubes) and the idea of color is seen as one possible way to answer the question of what Croco wants to eat.

Scene 2. Assistance during individual work on the tasks in the workbook: Do you need help, Nabil?

Directly after this class discussion the pupils were asked to complete some exercises about this topic in their workbooks. After four tasks in the style comparable to those on the board - two towers of cubes and in between the pupils had to place the correct sign - in number two there are neither towers of cubes nor a crocodile that wants to eat them (see Figure 11.2).The pupils seem to be supposed to identify the relationship between the numbers and the correct sign on their own.

After several minutes, Nabil is still working on number two, while his seatmate Dani has already finished the task. When Dani sees that Nabil has not finished yet, the following conversation starts:

NABIL: Why do you want to help me?

DANI: [Takes the pencil out of Nabil’s hand and signs on task 6 О 5 in his workbook] Here. See here. Which he would like to eat? Six or five?

NABIL: ... Six.

FIGURE 11.2 Extract of the children’s workbooks

DANI: Yes. So you do it |Writes something in Nabil’s workbook],

NABIL: | Takes his pencil from Dani]

BAILA: [Comes to the desk of Nabil and Dani, Dani stands on Nabil’s left. Baila stands to the right of him. Looks on Nabil’s workbook] ehm ... you are here. Think about it ... [Shows three fingers with her left hand] nine or three. Which is more?

NABIL: | Writes something in his workbook]

BAILA: That’s right.