Over the past decades, Chinese students, particularly those from Shanghai, Hong Kong and Taiwan, have consistently excelled in a number of international comparisons of mathematics achievement. What are the significant characteristics of the Chinese learners that enable them to excel in many of the comparative mathematics achievement studies? What are the possible contributing factors? What can be learned from the Chinese way of mathematics teaching and learning so as to improve mathematics education? Indeed, these are questions that have attracted numerous mathematics educators and researchers, from both the West and the East?

Here are the findings.

*Strong collaborative culture among mathematics teachers*.

A significant characteristic of Shanghai mathematics teaching is that “teachers engage in continuous school-based collegial professional development through lesson study, and teaching research group”

*Strong coherence between the mathematics teachers’*

*teaching philosophy and the students’ beliefs about mathematics learning.*

Both Shanghai mathematics teachers and students view mathematics as an important tool for developing mathematical reasoning and mathematical thinking. They both strongly believe that it is not enough to simply practice answering questions. They both tended to believe that a variety of mathematical questions, at different levels and of different natures, were important to enhance mathematical understanding.

*Teacher-student rapport*.

Although the classroom atmosphere was observed to be serious and orderly most of the time, the rapport between educator and students appeared to be close and affirming.

Most of the Shanghai mathematics teachers often used inspiring and encouraging words during their teaching such as “Do continue with what you want to say”; “You must believe in yourself”; “Be brave and say what you think. If it is wrong, we can change”.

*Classroom discipline was always orderly and serious.*

Even in the primary school, when the students were given tasks to discuss with their peers, focused discussion, rather than off-task talk, predominated.

*Emphasis on the use of precise and elegant mathematical language*.

The teachers emphasize strict format of a proof or mathematical algorithm because “in the high school mathematics examination paper, if you do not write according to the mathematical format required, marks will be deducted. Every mark in the high school examination counts and it can change a student’s future.”

*Instructors stress logical reasoning, mathematical thinking and proof during teaching*.

This was evident from classroom observations where high level thinking skill questions such as ‘why?’, ‘how?’, ‘what if?’ were asked during lessons.

*The Shanghai mathematics teachers use procedural variation. *

This is evidenced in the use of multiple methods of solving a problem, and in the practice of giving classroom exercises as well as examination and test questions in a variety of formats and structures. Procedural variation provides students with ample opportunity for drill and practice. It is also used to diagnose students’ understanding of the concept at various levels and to test if they have mastered the requisite skills.

*Rote memorization is part of the process.*

Shanghai educators believe that not all knowledge can be discovered with manipulative exploration. Therefore explicit teaching and memorization is part of their paradigm.

*A final caveat is offered. *

Every culture is unique. Wholesale adoption of good teaching practice from one culture to another is not necessarily advisable. While it is important to reflect on and evaluate different cultural contexts and values, keeping in mind one’s own culture’s strengths and incorporating alterative ideas in the best way possible.

Reference:

Lim, C.S. (2010). http://www.merga.net.au/documents/MERJ_19_1_Lim.pdf

Teaching for mastery involves uncovering students’ individual learning needs and levels of comprehension. This strategy is simple but thorough. It involves a well-thought out pretest that covers previously learned material and general knowledge, a daily learning log sheet and a posttest that is identical to the pretest.

The pre- and posttests provide a means for discerning cognitive improvement. The daily learning logs offer an outlet for both student reflection as well as questions about the topic at hand.

The pretest helps the teacher learn what the students know and do not know. Their scores furnish a baseline measurement for their knowledge. Any prior understanding or misunderstanding is uncovered in this preliminary assessment. As a result, the educator can adjust the learning plan accordingly.

At the start of each class pupils receive a daily learning log sheet. This allows them to reflect on what they learned during the previous class and prepare for the new day’s lesson.

As part of the daily learning log, students are given a warm-up exercise that is based on the topic that was discussed in the previous day’s class. This warm up challenges the learners to use higher order thinking. This helps the instructor to determine if they are fully grasping the material.

During class, students are asked to write down in their daily lesson log any questions they might have on that day’s topic. Before beginning, the teacher addresses the previous warm-up question and discusses all the questions written on the previous daily learning logs. At the end of class, the students again reflect on what they have learned in their daily learning log. They connect prior knowledge to what they learn on a given day and are therefore able to see how the concepts are connected.

Reading the students’ reflections allows the instructor to adjust the next day’s lesson. This allows the options of addressing any misconceptions as well as tracking student learning as they perform learner centered activities.

As a final component, the students rate their confidence about the topic (one through four). This enables the teacher to assess the children’s confidence and adjust the pace of instruction accordingly.

The post test, which is identical to the pretest, is given at the conclusion of the unit. This tells the teacher how much each student has improved, whether there is a need to provide follow -up instruction and if adjustments need to be made for the following year.

This overall strategy enables the teacher to monitor student understanding throughout the unit and make sure that no student is left behind.

Reference**:
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Holzmiller, T. (2008). Changing misconceptions.

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