# Code-Switching Explorations in Teaching Early Number Sense

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Perspectives

#### 2.1. Language and Mathematics Teaching

#### 2.2. Code Switching and the Language of Mathematics

## 3. Methods

#### Data Collection and Analysis

## 4. Findings

#### 4.1. Educators’ Understandings And Views About Language in Mathematics Teaching

#### 4.2. Code Switching Between the Language of Instruction and the Mathematics Register

- (a)
- they talked about numbers and used expressions such as “how many,” “how many more,” “count,” “counting,” “counting on,” “amount,” and “number combinations” (used only by E1);
- (b)
- they talked about number words such as “one,” “two” “ten;”
- (c)
- they compared sizes, amounts, and weight and used terms such as “more than,” “less,” big,” “small,” “more” “heavier,” lighter,” “tallest,” and “shortest;”
- (d)
- they talked about regularities and used the term “pattern;”
- (e)
- they talked about “groups;”
- (f)
- they brought a lesson to closure (i.e., “That’s a pattern!” “This is called counting forwards”); and
- (g)
- when E1 (the grade 1 teacher) talked about sets and changes in a set, and used terms like “division,” “addition,” “subtraction,” “equal,” “double,” “take away,” “plus,” “number sentence,” “equation,” “equal to,” “two numbers that make,” “combination for what number?”

- (a)
- Re-voiced students’ ideas (i.e., “when I am counting this way, I am counting forwards”);
- (b)
- Explained and then checked students’ actions and thinking (i.e., “you are thinking-ten”);
- (c)
- Explained their own actions (i.e., “Should I cut this one in half?”);
- (d)
- Used contextual clues (i.e., “Daniel is saying that he saw a square to count four”;
- (e)
- Provided new math information (i.e., “This is called making ten”); and
- (f)
- Chose between terms that belonged to the math register (i.e., “When you were making the patterns—the groups with your counters, were some groups easier to make than others?).

#### 4.3. Language Choices

- (a)
- protoquantitative terms [19] (i.e., “a little more”);
- (b)
- everyday language (i.e., How many we will need to borrow from that five to make that nine a ten?”); and
- (c)
- the educators’ explanation of how mathematics happens (i.e., “a pattern repeats over and over again”).

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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Stanza 8 (in math class)Mike had to count how many people were in class. Mary had previously counted clothes pins with the children’s names; Mary had counted 13 names. EP1: Ok, we need to count thirteen heads. EP2: Let’s count… Ch3: one, twooo, three, four, fiiiive, six, seven, eight, nine ten, eleeeeven,tweeelve, thirteen,…THIRTEEN!EP4: Thirteen!! Is it the same?Ch5: YES! | Stanza 8a (educator’s video recall)R: Could you have use the term equal instead of “the same”? EP1: I wouldn’t use “ equal.” I wouldn’t, EP2: I just would never use it because you have to go with the language they understand EP3: Later on I am not sure … EP4: it’s certainly something to think about… |

Stanza 4 (in math class)The teacher and the children were working in small groups. Children were creating masks and gluing different number of paper noses, eyes, and teeth depending on how many they got when they rolled the die. EK1: how many teeth do you have? (pointing at the mask that Sean had created)Sean2: twoEK3: Danny has two teethEK4: and you have two teethEK5: NOW you have something that is THE SAME! Joanna6: I have ONE toothEK7: just like Emma, EK8: you have one tooth and she has one tooth EK9: .. that’s the same! | Stanza 4a (educator’s video recall)R: Could you explain the use of the term “the same” in the clips? EK5: So I think it is EK6: one of those words EK7: that I’m always trying EK8: to have the visual to pair with so…so… EK9: because it is really hard to explain EK10: what “the same” meeeeans … R11: Is it “the same,” or is it “ equal?”EK17: I will use the word “the same” EK18: rather than “ equal,” EK21: “same” is…is a word EK22: that they get, they understand… EK36: when we are making groupsEK37: that are numerically equivalent EK38: I will use “the same” rather than “equal..”… EK44: what I probably should have said was EK45: “make the same NUMBER in your group.” |

Stanza 4 (in class)During morning meeting the educator brought a scale and manipulatives. EG31: Ok, I have five here and I have four here (pointing at each side of the scale)EG32: it’s almost balanced…(she dropped one more block on the side that had 4) EG33: Five and five.EG36: are they balanced now? Mary37: pretty much. EG38: Ok, if it is balanced, EG39: what do we know about those numbers? EG40: They are the.Claire41: Equal.EG42: They are equal, what’s another WORD for equal?Matt43: same.EG44: SAME! Exactly! EG45: THAT’S THE WORD I am thinking about! EG46: If it’s equal IT IS the same. | Stanza 3a (educator’s video recall) R: Was that the first time you were showing them the relationship between equations? EG6: Yes R7: What do you think about the language you use? EG17: like in my mind, EG18: the word “ same”EG19: it’s an easier term EG20: because they can transfer that term “ same” in so many different ways, you know? EG21: Not just in math but also in other ways EG22: I think lots of them DO understand what “ same” means, EG23: and could make that connection EG24: between “ same” and the term “equal” in math. |

Stanza 2c |
---|

R3: Is it important that at some point a teacher starts saying “sets?” |

EK5: I think at some point |

EK6: children will have to be able to understand |

EK7: that sets and groups mean the same thing…you know? |

EK8: ..I think that’s important.. |

EK9: that children need to learn that.. |

EK10: WHEN children need to learn that? |

EK11: I don’t know.. |

EK12: But for me right now... |

EK13: I want them to understand these dots we are looking at |

EK14: so, “groups” is a familiar word, so I can use it |

EK15: and I don’t have to do a lot of teaching before I teach about the dots. |

Stanza 14 (in math class)Five children were asked to stand up in a row. Each child held a poster with a number (from 1 to 5) written on it. EK1: ah…I want to ask you, EK2: what number comes after one? Ch3: tttwoooo..EK4: what number comes after four?(pause, 0.5) Ch5: fffive EK6: ffffive…that’s right...EK7: When I say after I mean… EK8: If I am talking about what number comes after four (touching the head of girl that had number 4) EK9: it means what number comes next (touching the head of the girl that had number 5) EK16: Now, here is a new word, EK17: what number comes BEFORE three? (touching the head of the girl that had number 3) (pause, 0.6) Sam and Lucy18: ttwoooEK19: Two, that’s right,EK20: that means what number do I say first; EK21: I say two and THEENN I say three. EK22: What number comes before two?(touching the head of the boy that had number 2) (pause, 0.5) EK23: Anybody knows? Connor24: OneEK25: yeah, one..EK26: I say one first and THEENN I say two. | Stanza 14a (educator’s video recall)R: Could you tell me more about this scenario? How does your talking help children to understand the idea of the “number after?” EK1: Yeah… “before” and “after” EK2: it’s like...(laughing) EK3: Because now, I have changed that terminology EK4: because that didn’t stick EK5: …they are like “Ah? Ah? We don’t know what she is talking about” EK6: So I thought, EK7: “Ok, using what comes first, what comes next..” |

Stanza 1 (in math class)The educator gathered the group and explained that Julie brought a treat (a rice crispy square) that she would like to share with all her friends. EP21: How many people can have a piece if I just cut it in two? Ch22: Two…EP23: Only two peopleEP24: Oh… Is there more than two people? Ch25: Yeah… EP26: What do you think I should do now? EP27: We’ll cut this side on half and…should we cut this one on half too?Ch28: Yes! EP29: How many are we going to have now?Lucy30: Fifteen!EP31: How many friends do I have?Samuel32: One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen! (he touched each child)EP33: Would these pieces fill fifteen people? Ch34: No EP35: What should I do? Ch36: Cut it! EP37: Cut them in half? Ch38: Yes! EP39: Is this half? (Making a knife mark through half) Ch40: Yes! | Stanza 1a (educator’s video recall)R: How does mathematics language unfold through this clip? Stanza 1cEP1: I also said “ half,”EP2: but I didn’t say “ quarter,” EP3: because I didn’t feel… EP4: because if they got “ half,” that’s good EP5: because some kids would have experience with “ half,” EP6: like “do you want half an apple?” EP7: With “ quarter?” mmm… EP8: If I put it in, I will…consciously put it in. Stanza 1dR: How do you make those decisions? EP1: I think I am aware of the language that I am using… EP2: and I try not to go above their level; EP3: I try to be sure I am down at the level where they are. |

Stanza 1 (in math class)The teacher placed a printed worksheet on the white board entitled “Fact family cones.” The worksheet displayed four columns and four rows of empty squares and a picture of an ice cream cone below each column. In the worksheet, each ice cream cone had 3 numbers. At the bottom of the sheet there were 16 equations for addition and subtraction that matched up with the numbers of the four ice cream cones. EG1: Ok grade one, EG2: you are going to take a look, EG3: there are all kinds of number sentences or equations that are down here, EG4: and you need to figure out EG5: what four equations or number sentences EG6: are going to fit and match up with each cone ok? | Stanza 1b (educator’s video recall)R: As you know, I will be investigating how teachers switch between the language of instruction and the language of mathematics. How do you see that switching happening in this video clip? EG1: That was a conscious choice.. EG2: I was consciously trying EG3: to make that connection EG4: between the terms “ number sentence,” and the term “equation.” R5: Do you think that the term equation…EG6: I feel it’s a higher level… R7: Could you explain please? EG8: I don’t know…(pause, 0.3) EG9: I think… EG10: they understand the term “sentence,” EG11: and we’ve used the simple terms like “ number sentence,” EG12: we‘ve used it soooo much… EG13: now, I think that the term “ equation,” EG14: is just a bigger word, you know? EG15: Just even to get your tongue around EG16: to even say “ e-qua-tion,” EG17: that articulation of the word equation…EG18: for them to say it, and hear it, EG19: and remember it, and understand it… |

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**MDPI and ACS Style**

Arias de Sanchez, G.; Gabriel, M.A.; Anderson, A.; Turnbull, M.
Code-Switching Explorations in Teaching Early Number Sense. *Educ. Sci.* **2018**, *8*, 38.
https://doi.org/10.3390/educsci8010038

**AMA Style**

Arias de Sanchez G, Gabriel MA, Anderson A, Turnbull M.
Code-Switching Explorations in Teaching Early Number Sense. *Education Sciences*. 2018; 8(1):38.
https://doi.org/10.3390/educsci8010038

**Chicago/Turabian Style**

Arias de Sanchez, Gabriela, Martha A. Gabriel, Ann Anderson, and Miles Turnbull.
2018. "Code-Switching Explorations in Teaching Early Number Sense" *Education Sciences* 8, no. 1: 38.
https://doi.org/10.3390/educsci8010038