Kindergarten Academic Situations
Numerators and Operators
Key Points:
Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining and separating situations with sets of objects, or eventually with equations such as 5 + 2 = 7 and 7 – 2 = 5. (Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged, but it is not required.) Students choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away.
Common Struggles:

Confusing addition and subtraction concepts, leading to calculation errors. For example, solving a subtraction problem as if it were addition

Some children may still reverse numbers like 2 or 3 when they reach the 2nd grade, indicating a weak foundation.

Relying solely on counting fingers for calculation, which is slower and more prone to errors.
Solution:
Addition and subtraction within 10, and carrying addition within 20, mark the beginning of students' number recognition and calculation. These concepts are widely applied in daily life and serve as the foundation for multidigit calculations. They are essential foundational knowledge for learning mathematical operations. For example, when second graders learn to calculate multidigit sums like 23+35, they need to separately calculate the sum of the units place (3+5) and the tens place (2+3). If students have mastered addition and subtraction within 10 by the first grade, they will be able to accurately and quickly arrive at the correct result.
Geometry
Key Points:
Students describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary. They identify, name, and describe basic twodimensional shapes, such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (e.g., with different sizes and orientations), as well as threedimensional shapes such as cubes, cones, cylinders, and spheres. They use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes.
Common Struggles:

Unclear concept of left and right, unable to distinguish between directions.

Poor spatial awareness, unable to differentiate between solid shapes, unclear about the difference between solid and flat shapes.

Incorrect description of relative positions, confusion about who is in front of or behind whom, reversing positions.
Solution:
Starting with actual objects from everyday life, students can concretely understand solid shapes and begin to classify them. This lays a solid foundation for later observing solid figures and understanding their characteristics.
Consequences:
GK (Kindergarten) is the year before children start formal schooling, a period meant for growth through joyful learning. Many American parents do not emphasize this learning process. For example, some children may still reverse numbers like 2 or 3 when they reach the 2nd grade, indicating a weak foundation. The basis formed during this year can have a very important impact on future learning. The knowledge acquired in the 1st grade may seem simple, but only by understanding the underlying mathematical principles and establishing sufficient cognitive experience can students apply this knowledge in higher grades to achieve the effect of leveraging analogous learning and reaching broader insights.