Children have different levels of mathematical understanding in counting principles that depend on their comprehension and the ability to analyze various mathematical concepts critically. Age, experience, and exposure to mathematical concepts contribute to the child’s level of understanding of the counting principles. As the child grow and develop their number sense and mathematical skills, their understanding of the counting principle concept also develops. The stage shown by the video is the “count-all” stage, where the child has to count all the blocks again after new ones have been added. The child also counts the blocks aloud. Each time a new block is added, the child has to go back and count all of them to get the new count. This shows that the child does not have the mental capacity to retain the original count when new blocks are added and has to count them afresh. This represents the “count-all” stage.
As seen in the video, the child goes back to counting the block individually each time the teacher adds a new block to the existing blocks; thus, they may need additional help from the tutors in organizing the objects in groups. They understand the order and sequence of numbers, so it is easy to recite the number of the blocks in order (Zippert et al., 2020). They recognize the concept of counting and can use words, gestures, or even objects to showcase numbers. Thus, as seen in this video, the child’s current mathematical understanding of the counting principle is intermediary counting sense.
The child might count the number of buttons in the picture with various sizes and colors sequentially. First, the child will start by pointing at each button and saying them as blue, red, and yellow to identify the controls of the same colors. Then they will point out the colored button of the same size and put them in different order and categories, such as all red buttons with huge sizes in one class and all blue buttons with a small extent in another category (Zippert et al., 2021). The child might use a specific strategy to count the number of buttons according to color and size. One method is to calculate the colored buttons of the same size separately by saying two big red, three tiny green, and one large blue button and then adding the totals all together. They can also count the button in the pictures by saying the numbers aloud, such as one, two, three, four, and five blue big buttons. However, depending on the experience and exposure of the child to the mathematical concepts of counting, the child may use other advanced strategies, such as grouping the buttons in various shapes.
If the teacher adds three more buttons to the picture, the child will count the buttons differently. They will first recount the existing buttons and then count the added ones. The child will then count all the buttons combined afresh. Also, they may start by calculating the newly added buttons separately and pointing at them while saying one, two, and three. Then the child may add the total number of buttons to the original count, such as two green buttons plus three more, and then make a total sum to know the total number of buttons.
The following steps for the child that can help them better understand the counting principles in math are to encourage the child to practice counting by counting all the provided objects, such as blocks, to develop their counting skills. It is also essential to enable them to say each number aloud as they count. The tutor can provide visual aids to the child, such as number charts and lines, to help the child develop the ability to relate numbers and count (Di Nuovo & Jay, 2019). Also, it is essential to encourage the child to practice counting the objects in the principle of one-to-one correspondence, as this helps the child to touch the objects while counting them, thus preventing them from skipping any object or number that needs counting. Another way is by training them to add and subtract numbers from each other. For example, if there are five blocks on the paper and the teacher adds two more, how many blocks will they have now?
References
Di Nuovo, A., & Jay, T. (2019). Development of numerical cognition in children and artificial systems: a review of the current knowledge and proposals for multi‐disciplinary research. Cognitive Computation and Systems, 1(1), 2-11.
Zippert, E. L., Douglas, A. A., & Rittle-Johnson, B. (2020). Finding patterns in objects and numbers: Repeating patterning in pre-K predicts kindergarten mathematics knowledge. Journal of Experimental Child Psychology, p. 200, 104965.
Zippert, E. L., Douglas, A. A., Tian, F., & Rittle-Johnson, B. (2021). Helping preschoolers learn math: The impact of emphasizing the patterns in objects and numbers—Journal of Educational Psychology, 113(7), 1370.
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