maths test

Concrete stage

Students physically manipulate objects to solve problems, building their understanding of the concept through hands-on experience. Examples include using blocks to represent numbers, fraction circles to demonstrate fractions, or counting coins. 

Representational Stage

Students use pictorial or diagrammatic representations to model the concrete actions. This stage helps bridge the gap between the physical objects and abstract symbols. For instance, they might draw pictures of blocks or create diagrams to visualize mathematical relationships. 

Abstract stage

Students solve problems using abstract notation, symbols, and numbers, without relying on physical objects or diagrams. This stage requires students to understand the underlying mathematical principles and relationships. 

What are the four Precursor Math Concepts?

attribute, comparison, pattern, and change

why are they (4 precursors) important

as they provide foundation for more complex maths skills, and are developed through everyday play experiences

c.r.a importance

students are able to build visual models of complex ideas that helps to deepen their learning.

six concepts of measurement

time, length, weight (mass), capacity, area, and volume.

the three types of patterns

growing, symmetrical, and repeating.

3 pattern types ways of teaching

repeating: by size, colour, and shape

growing: cra approach, and adding on one more manipulative each time

symmetrical: with block play

1-1 correspondence

For each object they are counting, children give it one count and only one count by matching a counting word to an object. Every item is assigned a number word in order as it is tagged. Children demonstrate that they have not fully mastered the one-on-one principle when they tag an object more than once, miss an object, or repeat or miss the counting name.

Stable order principle:

Children begin to realise the counting sequence stays consistent. The number name is used in a fixed order every time. It is always 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and not, for example, 1, 2, 4, 5, 8, 10. The pattern of the numbers becomes quite difficult after 9 (the teen numbers of 11, 12 and 13, for example) as at this point new number names are introduced that are different from what we use with decade counting (for example, 21, 22, 23).

cardinal principle

Children understand that the last object in the count represents how many are in the group. The cardinal number is the final number said and symbolises how many are in the group. When asked how many candles are in the set that they have just counted, a child who re-counts to get the answer has not understood the cardinal principle. The cardinal principle is developed later than one-to-one and stable order and knowing these two principles is necessary for understanding the cardinal principle.

abstraction principle

Children sometimes have difficulty counting things that are not identical objects. Five objects can be made up of all cups, but five objects can also be a cup, a spoon, a fork, a knife and a bowl. Children have grasped the abstraction principle when they can count any range of similar or different objects in a group and know the number is the same. Another example is when children understand that the quantity of four large things is the same count as the quantity of four small things.

order irrelevance principle

Children can begin counting a group of objects from any object in a group and know that the total will stay the same. That is, the cardinal number remains the same whether you begin counting from the middle of the group, at the beginning of the group or at the end.