## Integrating the Shanghai Mathematics Curriculum and US Common Core standards

It is known worldwide that Chinese people are good at calculating (arithmetic). However, arithmetic is the basic level of mathematics which is more of a conditional reflex than true mathematical abilities. What truly distinguishes Chinese students is not calculating skills but rather mathematical thinking. The mathematics curriculum plays an essential role in cultivating Chinese students’ mathematical thinking abilities. For example, the high-demanding geometric proof is the emphasis in middle school from Grade 7 to Grade 9, which accounts for about 40% of the High School Entrance Examination. In contrast to geometry education, probability and statistics only takes an insignificant part in Chinese courses. Probability and statistics, in the US Common Core Standards, however, is one of the main focuses throughout K-12. Moreover, the wide use of technology in teaching and real-life problems are the two advantages of the US curriculum. Therefore, the comparison of the two curricula will help us integrate the strengths and improve the quality of math education.

**Core Contents****Teaching Methods****Level of Difficulty****Unit Activities**

## The Impact of Visualization on Geometric Proofs

Students in Shanghai start to learn geometric proofs in the second semester of Grade 7. It is exactly the time when most students have a hard time going through the transition from concrete to abstract. In terms of the Van Hiele model, the huge leap occurs in level 2 and level 3. (use example to show, do we need to learn geometry, use Michigan’s book)

- GeoGebra helps
- Is visualization helpful to solve Q25?