The Mathematical Thinking

The mathematical thinking is one part of the intellectual education.

The child between 2 and 3 starts to create his mathematical view of the world. The parents can back up the child by:

  • leading him to assemble various cube structures,
  • leading him to sort out the objects based on the size,
  • sorting out the objects according to the four colors (red, yellow, blue, green),
  • sorting out the objects according to the four shapes (a cube, a ball, a triangular prism and a cylinder),
  • discerning objects according to their attributes (e.g. the color – the shape etc.),
  • responding to clauses which give location of things and persons (bring it here, put it on, sit down, stand up, throw away, hang it up etc.),
  • teaching to understand time perception and vocabulary (in the morning, in the evening, now, later, quickly, slowly).

The mathematical thinking of a child between 3 and 4 should enable him to:

  • place the objects in the room based on the instructions (on, in, under...),
  • distinguish (not identify) the objects based on their shape (circular, triangular, square),
  • put simple objects into the slots matching their shape,
  • discern the size of the objects (small – big, long – short),
  • solve simple mazes (to move from the start to a predefined point and to find various options where to move),
  • understand the quantificators (all, none),
  • point out the differences (various attributes like size and color) between two similar objects (show which one of those two objects are e.g. small, red...),
  • organize a group of elements based on the logical order and use respective terms (e.g. to determine the first, second and last object),
  • create groups consisting of a certain number of elements (1 or 2 elements at the most).
  • assign respective number based on the amount of elements (1 or 2) and compare them,
  • assemble various cube structures and construction sets,
  • sort out the objects according to the size and color (red, yellow, blue, green).

By using his mathematical knowledge, the child between 4 and 5 should:

  • know and discern geometric shapes: a circle, a square, a rectangular and a triangle,
  • place the objects under more complex instructions (in front of, behind, under, over, between, the first, the last),
  • point at the objects with a certain attribute – shape, color and size,
  • organize the objects within a group and determine what should and should not be included in the group,
  • assemble simple structures using the instructions,
  • distinguish between the objects according to their shape and call them by the name (e.g. round, angular, pointy etc.),
  • identify stages of sizes and shapes (e.g. big – bigger – the biggest, round – angular – pointy, small – bigger – the biggest, short – longer – the longest, narrow – broader – the broadest),
  • put simple objects into the slots matching their shape,
  • solve simple mazes (searching and highlighting the routes between two points),
  • understand and distinguish between the words (e.g. all, none, every),
  • create sets of elements based on a predetermined attribute: size, color and shape (identify objects sharing these attributes, such as small blue balls...),
  • create couples by matching the words (one coat, one hanger...),
  • discern and use the words expressing the amount and number of things (all, many, more, nothing, few/little, less/fewer, as many as, the same),
  • know how to count at least to 4,
  • apply the knowledge of numbers 1 – 4 (more, less, equally), e.g. 1 = me, 2 = me and you, 3 = me, you and him, 4 = me, you, him and her,
  • divide the set consisting of 2 – 4 elements into more groups and determine number of elements in each group, then assembling the groups back into the set,
  • organize a group of elements based on a certain logic order and a timeframe and use the terms (e.g. in the fairy tale: who was the first, the last, in front – behind, according to the first and the last, what happened at the beginning and at the end of the story...),
  • discern who is at the top, at the bottom, on the left and on the right in the two-dimensional space.

The ever-improving level of the child’s mathematical skills ensures that the child between 5 and 6 can:

  • describe the location of objects with regard to his own person, his body, limbs and body parts using prepositions (e.g. there is a picture in front of me, a desk behind me etc.) and the relative position of two separate objects (e.g. the book is on the table); he can also determine whether an object is located somewhere or not (e.g. whether it is or it is not in the shelf etc.),
  • assemble more complex structures using the instructions, pictures as well as his own imagination,
  • determine his positon on a square grid (the child solves mazes and marks his movement using arrows from one point to the predefined destination),
  • distinguish between geometric shapes (both two-dimensional and three-dimensional objects),
  • sort out the objects based on their prerequisites (etc. are the objects red and wooden?),
  • compare and sort out the objects by their size (length, width, height), weight (lighter, heavier), volume (comparing the amount of liquid fitting into various containers),
  • create sets based on a predetermined attribute (color, shape, size, volume etc.),
  • understand words (at least one, all objects, all people, none, every, some person, some people etc.),
  • draw, sort out and organize the objects and pictures into a table with heading (e.g. there is color in the row and size in the column),
  • divide an object into parts (one half, one quarter) and determines the number, amount and shape,
  • count to six and knows ordinal numbers,
  • create a set consisting of objects sharing common attributes out of 2 or 3 groups of objects.

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