Liping Ma has undergone research to compare the differences on how mathematics is taught in China and the USA. Her findings were fascinating; even though US students go through more education to become a teacher than those in China, the Chinese teachers have a deeper understanding of mathematics and therefore are able to teach more efficiently. She found that American teachers taught more in a procedural way rather than using the logic of mathematics.

“A*bout 10% of those Chinese teachers, despite their lack of formal education, display a depth of understanding which is extraordinarily rare in the United States.”* (Liping Ma, 2010)

I was edger to find out more about Liping Ma’s discover; How do the chinese teachers teach more efficiently? and what can I learn from this for the future?

In Liping Ma’s book ‘*Knowing and Teaching Elementary Mathematics’ *she explains her theory and suggests how the Chinese teachers understanding how maths contributes to the students success. This is an important theory that i would consider while teaching children mathematics.

so why is it that Asian children consistently outperform American students? there are many factors that researchers have found that contribute to this “learning gap”;

- Difference in cultural (parential expectations)
- School organisation (time spent on maths)
- The content within the curricula.
- Teachers Knowledge.

Researcher Deborah Ball identified teachers knowledge and understanding of mathematics should be connecting ideas *of* and *about* the subject. The concept by the knowledge *of* mathematics meant; “comprehension of particular topics, procedures, and concepts, and the relationships among these topics, procedures, and concepts.” (Liping Ma, 2010). therefore, understanding all these things and making it clear to the students will assist them reaching success. The meaning behind the knowledge *about *mathematics is aiming at the comprehension of the nature and discourse of mathematics. Additionally teachers consistently thinking about the ‘substantive knowledge’; correctness, meaning and connectedness. Mathematics should always be open to more than one way solutions. Students who can solve a problem with a variety of methods will be able to achieve higher, as the skills can be applied to similar situations. I believe this is important for myself and teachers to consider while teaching because if we notice a child struggling to grasp a process, it may be beneficial to teach another method that they could use. Hopefully seeing another method will be the situation clearer for the child rather than becoming frustrated.

As Liping ma was researching she drew on how teachers taught; subtraction, multiplication, division by fractions and perimeter. I mainly looked into subtraction and found her way of teaching a lot more enlightening. She studied the American the method of borrowing or exchanging in subtraction, so for example, discussing that when subtracting 21-9 that they had to borrow unites from the tens column. she realised that teacher were expecting students to know, based on their knowledge, from a very procedural method of teaching.

Chinese teachers mainly use a regrouping method of subtraction and in contrast with US teachers, 35% of them demonstrate multiple ways to carry out regrouping. Liping Ma states that teachers address the standard algorithm as well as discussing other ways to solve a problem. The main method of regrouping is by **decomposing** a unit of higher value, so breaking down the hundreds, tens and units number. for example using 21 again, Chinese teachers would decompose the number rather than suggesting to borrow. This highlights that the language a teacher uses is crucial to help students understanding. Using ‘borrowing’ can confuse children as it acts as a metaphor whereas decomposing highlights that the higher digit can be broken down. Linking what happens when the children done addition is also important to help them understand how 10’s are formed and taken away.

An example of the regrouping by a Chinese teacher from Liping Ma’s (2010) book-** ****“How come there are not enough ones in 53 to subtract 6? Fifty-three is obviously bigger than 6. Where are the ones in 53? Students will say that the other ones in 53 have been composed into tens. Then I will ask them what can we do to get enough ones to subtract 7. I expect that they will come up with the idea of decomposing a 10. Otherwise, I will propose it. (Tr. P.)” **

An example of borrowing from An American teacher- ** “Where there is a number like 21−9, they would need to know that you cannot subtract 9 from 1, then in turn, you have to borrow a 10 from the tens space, and when you borrow that 1, it equals 10, you cross out the 2 that you had, you turn it into a 10, you now have 11−9, you do that subtraction problem then you have the 1 left and you bring it down.”**

Students that understand why higher value units need decomposed is more efficient than borrowing as they can also apply this knowledge when working with three digit equations. Once they’ve learned the facts and the procedure they an apply this to any situation they are in.

What I take away from Liping Ma and Deborah Balls’ theory is that teachers must be able to anticipate children’s response in order to encourage their way of working and not to simply restrict them to one method. Displaying multiple methods of solving a problem is essential as it promotes more independent learning and also a better variety as each child learns differently. I will also be more cautious of the language i use in the classroom to ensure I provide the best learning situation and avoid confusing the children.

**References **

Ma, L 2010, Knowing and Teaching Elementary Mathematics : Teachers’ Understanding of Fundamental Mathematics in China and the United States, Taylor and Francis, Abingdon, Oxon. Available from: ProQuest Ebook Central. [4 October 2017].

Cuarezma, A. (2013). Q & A with Liping Ma. *The New York Times*. [online] Available at: http://www.nytimes.com/2013/12/18/opinion/q-a-with-liping-ma.html [Accessed 4 Oct. 2017].