Dr. Su Ze received his bachelor's degree in chemistry from Massachusetts State College in bridgewater, his master's degree in educational arts from Harvard University and his doctorate from Rutgers University. He has teaching experience in all grades, taught high school science, served as the science director of K- 12, and served as the education supervisor in the school in West Orange, New Jersey. Later, he became the principal of New Providence Public School in New Jersey. He was also an adjunct professor at Sidon Hall University and a visiting lecturer at Rutgers University, and served as the chairman of the National Staff Development Committee from 65438 to 0992.
We often hear children shout "I can't do math", but never hear a child say "I can't talk!" Why is there such a difference?
Scholars explained this unremarkable achievement. Some people say that mathematics is difficult to learn because it is too abstract and needs more logical and organizational thinking; Some people say that using various symbols in mathematics is more like learning a foreign language. But educational critics insist that only a few students really lack the ability to solve mathematical problems, and those poor performances are mainly due to the lack of proper education. They believe that the so-called "mathematical war" has hindered the great progress in the development of mathematics curriculum, just as the "reading war" in the 1990 s had an impact on reading education.
In 2006, NCTM published Curriculum Focus, which set three important mathematics themes for each grade from kindergarten to eighth grade, called "Cohesive Block of Related Knowledge, Skills and Concepts", which laid the necessary foundation for understanding advanced mathematics concepts. This book is dedicated to unifying the different versions of mathematics textbooks currently used, and provides a framework for the development and design of mathematics curriculum from kindergarten to eighth grade in all States and regions, and for more targeted curriculum planning and teaching evaluation. Whether this new attempt can promote students' mathematics learning remains to be seen. At the same time, teachers should be prepared to help students build full confidence when they walk into the classroom every day, so as to master mathematical principles and operations. One thing seems certain: those students who didn't learn math well as children will still learn math badly in the future.
Chapter 1-Developing Digital Consciousness. Children's ability to determine quantity begins to form soon after birth. This chapter will analyze the components of this natural number sense and discuss how the natural number sense can guide children to count and perform basic calculation operations. This chapter will introduce the brain regions that work together and process calculations, and how language can help children learn to count faster.
Chapter 2-Learning to Calculate. Because calculating large numbers is not an essential skill for survival, the human brain must learn mathematical concepts and processes. This chapter deeply discusses the stages that the human brain must go through to understand the relationship and operation of numbers (for example, why the human brain regards learning multiplication as an unnatural behavior in the process of learning multiplication), and puts forward some methods that may make multiplication teaching easier.
Chapter 3-Review the basic elements of learning. This chapter introduces some discoveries of cognitive neuroscience in recent years, including the study of memory system, the nature and value of practice and retelling, the curriculum arrangement and the benefits of mathematics classroom writing.
Chapter 4-Children learn mathematics before teaching. Although children have a natural sense of numbers, certain teaching strategies can enhance this ability and prepare them for learning arithmetic better in the future. This chapter puts forward some suggestions on relevant strategies.
Chapter 5-Teaching pre-adolescent students to learn mathematics. Here, we observe the development and characteristics of adolescent brain before puberty and its influence on individual emotion and rational behavior. This chapter provides suggestions for teachers from primary school to middle school, and modifies the curriculum plan according to the characteristics of brain development at this stage, so that more students can learn mathematics successfully.
Chapter 6-Teaching young students to learn mathematics. Similar to the previous chapter, we reviewed the characteristics of teenagers' brains and put forward how to modify the curriculum according to the needs of the brain. This includes the discussion of mathematical reasoning and teaching choices, such as hierarchical curriculum and organization chart, which may be an effective strategy to make mathematics more relevant to today's students.
Chapter 7-Understanding and Solving Difficulties in Mathematics Learning. This chapter puts forward many suggestions, so that teachers can identify and help students overcome the difficulties in math learning, including math anxiety. This chapter discusses the main differences between environmental factors and development factors that may cause difficulties in mathematics learning. This chapter also puts forward some testing strategies, which can help teachers of all grades to help students with poor math scores understand numerical operations and form a more accurate and profound understanding of mathematical concepts.
Chapter 8-Summary: Mathematics Curriculum Planning from Preschool to Senior High School. What is mathematics? How can we apply the important findings discussed in the previous chapter to our daily practice? This chapter puts forward the suggestion of bringing this kind of research into the mathematics curriculum planning, and puts forward a four-step teaching model suitable for mathematics teaching from preschool to senior high school.
What keeps children from learning math? The answer is complicated, but at least two aspects should be paid attention to:
(1) We need to distinguish whether the unsatisfactory result is due to improper guidance or other environmental factors, or because of insufficient cognitive ability.
(2) How is mathematics taught? Teaching methods can completely determine whether a cognitive defect is really insufficient. For example, a teaching method emphasizes the understanding of concepts rather than the learning process and mathematical formulas (NCTM, 2000). Another teaching method, mentioned in the standard of California DX Part of Elucation (1999), emphasizes the process and formula. Under the first teaching method, a student who has difficulty in extracting mathematical formulas will not be considered as lacking in learning ability, because this method does not emphasize memorizing information. However, under the second teaching method, this difficulty will be considered as a serious lack of ability.
Students with mathematics learning difficulties can obviously benefit from various cases. They learn a concept at different cognitive levels. Mathematics educators have realized the essence revealed by research, and the best expression order of mathematical concepts is concrete-drawing-abstraction (CPA). This method is also called Concrete Description Abstraction (CRA) or Concrete Semi-Concrete Abstraction (CSA). No matter what kind of title it is, its teaching methods are essentially similar, all based on J. Bruner's work in the 1960s.
The details here mainly include demonstrations (for example, bars, foam sponge cakes and signs), measuring tools and other objects that students can operate in class. Painting includes pictures, processes, tables or charts drawn by students or provided for students to read and explain. Abstraction is symbolic presentation, such as numbers or letters written by students, to express understanding of tasks.
When using CPA method, the sequence of activities is the key. The first activity is to use concrete materials to make students understand that mathematical operations can be used to solve practical problems. The graphic relationship shows the intuitive presentation of specific operation objects and helps students visualize mathematical operations in the process of solving problems. Here, it is important for teachers to explain how graphic examples relate to concrete examples. Finally, the standardized representation of symbols is used to illustrate how symbols can express mathematical operations more concisely and effectively. Students need to skillfully use symbols on the basis of existing mathematical skills to reach the final abstract level. However, the meaning of these symbols must come from the operating experience of specific objects. Otherwise, their symbolic operations will be meaningless mechanical repetition of memory programs.
CPA method can benefit all students, but it is especially effective for students with learning difficulties in mathematics, mainly because it gradually changes from concrete operation objects to pictures and then symbols (Jordan, Miller &; Merccr，
1998)。 These students often feel depressed when the teacher states math problems abstractly. Mathematics teachers need to organize content and teaching according to concepts, so that students can learn new content in a meaningful and effective way.
Experimental research proves the effectiveness of this method. Witzel and his colleagues studied sixth and seventh grade students who were considered to have algebra learning difficulties. When solving algebraic transformation equations, students who adopt CPA method score higher in subsequent teaching and testing than those in the control group who receive conventional teaching. In addition, the procedural errors made by students who use CPA sequential teaching in solving algebraic variables are also reduced (Witzcl, MCRCER &; & Miller, 2003).
Primary school teachers have realized the importance of using concrete and drawing activities when introducing new concepts. However, although cognitive neuroscience has proved the effectiveness of CPA method through the latest research, it has not been widely used in middle schools and high schools. Perhaps junior and senior high school teachers think that using specific operation objects will make students feel too basic, or perhaps the requirements of the curriculum force teachers to go directly to the abstract level in order to save time.
The presentation of concrete objects and paintings should be used in all grades. By using cognitive strategies similar to CPA, teachers provide students with skills to deal with mathematical problems, rather than just seeking answers. The following is an example of presenting algebra application problems from three cognitive levels.
The reason why the process memory method is so effective for students with mathematical learning difficulties is that it is an effective memory means, which can make the brain actively participate in the basic processing of learning and memory. This method integrates meaning through metaphors related to students, which can not only attract students' attention, but also stimulate students' interest, and also help students to establish the connection between abstract symbols and concrete things by using visualization skills.
Suggestions on mathematics teaching;