Introduction
The concept of "Big Ideas" refers to the general principles, core concepts, or essential understandings that are central to a particular subject. These ideas are crucial for students to grasp in order to develop a deep understanding of the subject, especially the big map of the subject. In recent years, the curriculum in China has emphasized the integration of "Big Ideas" into classes. Unfortunately, it is rare to find teachers who can clearly identify the "Big Ideas" within their respective subjects.
It is likely a challenging task to pinpoint the significant "Big Ideas" because it requires teachers or educators to have a comprehensive and nuanced understanding of their subject area beyond the surface level knowledge of facts and processes.
Methods
Progress
Results
Discussion
Appendix
Here, we have a table appendix of big ideas from math experts and this research has been wildly accepted by other researchers. [1].
| Big Ideas
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Examples
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| 1. Numbers - The set of real numbers is infinite, and each real number can be associated with a unique point on the number line.
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Counting Numbers
• Counting tells how many items there are altogether. When counting, the last number tells the total number of items; it is a cumulative count.
• Counting a set in a different order does not change the total.
• There is a number word and a matching symbol that tell exactly how many items are in a group.
• Each counting number can be associated with a unique point on the number line, but there are many points on the number line that cannot be named by the counting numbers.
• The distance between any two consecutive counting numbers on a given number line is the same.
• One is the least counting number and there is no greatest counting number on the number line.
• Numbers can also be used to tell the position of objects in a sequence (e.g., 3rd), and numbers can be used to name something (e.g., social security numbers).
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Whole Numbers
• Zero is a number used to describe how many are in a group with no objects in it.
• Zero can be associated with a unique point on the number line.
• Each whole number can be associated with a unique point on the number line, but there are many points on the number line that cannot be named by the whole numbers.
• Zero is the least whole number and there is no greatest whole number on the number line.
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Integers
• Integers are the whole numbers and their opposites on the number line, where zero is its own opposite.
• Each integer can be associated with a unique point on the number line, but there are many points on the number line that cannot be named by integers.
• An integer and its opposite are the same distance from zero on the number line.
• There is no greatest or least integer on the number line.
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Fractions/Rational Numbers
• A fraction describes the division of a whole (region, set, segment) into equal parts.
• The bottom number in a fraction tells how many equal parts the whole or unit is divided into. The top number tells how many equal parts are indicated.
• A fraction is relative to the size of the whole or unit.
• A fraction describes division.( [math]\displaystyle{ \frac{a}{b} = a \div b }[/math] , a & b are integers & [math]\displaystyle{ b \neq 0 }[/math] ), and it can be interpreted on the number line in two ways. For example, [math]\displaystyle{ \frac{2}{3} = 2 \div 3 }[/math] . On the number line, [math]\displaystyle{ 2 \div 3 }[/math] can be interpreted as 2 segments where each is [math]\displaystyle{ \frac{1}{3} }[/math] of a unit [math]\displaystyle{ (2 \times \frac{1}{3}) }[/math] or [math]\displaystyle{ \frac{1}{3} }[/math] of 2 whole units [math]\displaystyle{ (\frac{1}{3} \times 2) }[/math] ; each is associated with the same point on the number line. (Rational number)
• Each fraction can be associated with a uniqu
References
- ↑ Charles RI 2005. Big ideas and understandings as the foundation for elementary and middle school mathematics. National Council of Supervisors of Mathematics (NCSM). Journal of Mathematics Education Leadership,8(1): 9-24.
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