| SESSION |
GUIDING QUESTIONS AND PRINCIPLES |
PROCEDURES |
| 1) What are numbers for? |
- Where do we find the numbers?
- What are they for?
- How can we count them?
- Is there a right way to count?
- Which one?
- How to know how many are there?
- Stable order
- One-to-one correspondence
- Cardinality |
First moment: ask the children the guiding questions. Ask them to point to the numbers in the intervention room. Counting room objects without following the stable order and then following the stable order, but counting the same item more than once. Ask students if the count was done correctly. Discuss with the children the answers to the guiding questions.
Second moment: distribute the stories to the children and ask what do they have in common. Ask them to tell which numbers appear on their papers and then propose to sort them. Then ask the children how many numbers were counted and how they counted. Explore the idea that one always counts the same way, in the same order, and that the last number counted corresponds to the total number in the set.
Third moment: starting from the idea of constant order and cardinality, propose to play “which one is missing?”. Arrange a sequence of numbers on the table and ask the children to observe it for a few minutes. While arranging the sequence, purposely err the ordering of numbers. Ask the children to help organize them by pointing out possible errors. Then ask them to close their eyes and remove some numbers from the queue, asking them, after opening their eyes, to indicate which numbers are missing. At the end of some rounds (each student will have their turn), have a discussion, asking: how did you know which numbers were missing? How many numbers were there? How did you know that? Resume the guiding questions. |
| 2) How to count? |
- How can we count without getting lost?
- How do I know if I already counted a number?
- How to count a set that is not organized?
- Stable order
- One-to-one correspondence
- Order irrelevance
- Cardinality |
Resume the previous session, discussing the ideas already presented and the guiding questions discussed (we always count the same way and the last number counted corresponds to the total number of objects in the set). The researcher should say that sometimes one gets lost in counting, counting more than once the same object or forgetting to count another object: when the set is not in line, it is difficult to count. Question the children if there are other ways of counting that help us not to get lost. For this, figures containing balls and some chips will be used. Initially, ask what the figures have in common (balls). Then, ask how to find out how many balls there are in each one (count). Set the example collectively: count the balls without using the chips, counting them more than once. Inquire if you counted correctly. After indications that you did not count right, ask how to use the tokens to help with counting. Count again using the tokens to mark the balls already counted. Then ask if it is always necessary to start with the same ball. Count starting with another, discussing the value found. Repeat this movement, starting with another one. Say that we will always find the same number, regardless of the ball that will start counting (cardinality). Distribute three pictures to each and ask students to practice on their own, one at a time. At the end of the activity, the ideas presented will be resumed and discussed, emphasizing the issue of constant order, cardinality, one-to-one correspondence and order irrelevance. |
| SESSION |
GUIDING QUESTIONS AND PRINCIPLES |
PROCEDURES |
| 3) Counting |
- What can we count?
- Where do I start to count?
- Stable order
- one-to-one correspondence
- Cardinality
- Order irrelevance
- Abstraction |
Part One: Resume the previous session by asking the children to remember what was done and learned. After a brief discussion on what the students bring, propose to play two board games, one at a time. The first game will be “color board”. Explain how it works and accompany the children in the rounds, guiding them. One child at a time throws the die and must walk to the indicated color, counting the squares. Then write down, on a small piece of paper, how many houses they walked. After, it is another student’s turn, and so on until it reaches the end of the board. After this game, ask how the kids did to get the color indicated on the dice and if they knew how many houses they had walked in total. The idea is that they perceive counting as a useful tool in the game and indicate paper notes as a way of recording the total number of houses walked. These discussions will be permeated by interventions by the researcher, clarifying that the constant order of counting was followed, that each house was counted once and only once and that if we can count colors, we can count anything.
Second part: After the color board game, play “hand game”. Explain and play with the kids. A student throws the dice and must separate that number of chips, hand them over to the next classmate, and ask them to put them on their fingers, indicating which finger to start with. This will be done by each student, with the researcher following. In the end, other questions will be addressed: how do we count this time? Would we need to have started with the big toe or the little finger, or in marking the counted fingers there was no problem start in another order? Does this apply to other things we count too? If we need to count some objects and they are messy, how can we do it? Or if someone asks us to start counting from a certain place, how can we do it? The focus is to discuss the principle of order irrelevance, taking up what was seen in other sessions. |
| 4) Thinking about counting |
- How can I count in my head?
- How to organize the numbers when counting them?
- How to find a number without knowing its name?
- Stable order
- One-to-one correspondence
- Cardinality
- Order irrelevance
- Abstraction |
Resume previous sessions, talk about what has been seen, done, learned. Discuss guiding questions, resuming what is the right way to count. Propose a challenge to see who better learned the numbers: bingo game. Each student will receive a card and tokens to mark them. Raffle a card with phrases such as “I am the number that comes before 5 and after 3”, asking students to find out what it is. Play until someone does bingo; the rounds can be repeated. Shortly before the end of the game, resume the initial ideas and close the intervention sessions by reviewing what was done at each meeting and asking three questions: each student should answer one thing they have learned, one they found difficult and something they found it easy. |
INTERVENTION ON COUNTING PRINCIPLES: PROGRAM DEVELOPMENT AND INITIAL APPLICATION
Source: Recorded by the authors (2017).
Source: Recorded by the authors (2017).
Source: Recorded by the authors (2017).
Source: Recorded by the authors (2017).
Source: Recorded by the authors (2017).
Source: Recorded by the authors (2017).
Source: Recorded by the authors (2017).