Liping Ma's Second Chapter Summary

Liping Ma’s second chapter about multi-digit multiplication states the issues that many U.S. teacher face when it comes to multi-digit multiplication. Just as the first chapter did, it showed the difference between an American education system and a Chinese education system. The main idea here is how teachers in these two different education systems deal with confusion within their classroom. The differences between these came down to conceptual versus procedural knowledge. Once again, Liping Ma’s analysis seems to put Chinese educators in the lead because they are promoting a deeper understanding for their students. One topic American teachers struggled with was the use of placeholders for the zeros to show that the zeros are still prevalent.

Kindergarten through first grade is often reserved for addition and subtraction, but starting in second grade, skip counting is added to the curriculum. Skip counting helps give students a better conceptual knowledge of multiplication. Common core also tries to make a strong connection between multiplication and division. In grade three students are given problems such as 8 x 5 = 40, so when it comes to 40 and dividing by 8 the answer should be very obvious to the students. These problems are elaborated on by the students and they are told to describe the conceptual knowledge of 35 equals 5 times 7 in different ways. For example, 35 is 7 times as many as 5. The Common Core acts as effectively for goals or objectives for classrooms to achieve. For instance, teachers are told that getting their students fluent in a specific number range will help the success of their academic success. For example, in third grade, students must have the ability to multiply and divide within the first 100 digits. The goal of Common Core to give teachers clearer and more explicit objectives. Another principle of the Common Core for math is the focus on conceptual knowledge. Properties such as communitive and distributive are emphasized to help students gain a deeper understanding of the subject. These students are also expected to know all the primes and composites within the first 100 digits and to also know the products of all singular digit multiplication involving two numbers. The common core also tries to emphasize the idea of place value in third grade, while when fourth grade starts emphasizing the rationale of said place values. For example, the example 700 divided by 70 is equal to 10 is given to students to help them to understand place