Autumn in October, sweet-scented osmanthus fragrance. Thanks to the care and training of leaders at all levels, 10 year10.8, I embarked on a train to Xinxiang and started my learning journey.
The real learning began with the special report "Primary School Mathematics Core Literacy and Mathematical Thinking Methods" by Wang Yongchun, director of People's Education Publishing House, on the afternoon of June 54381October 9.
Professor Wang Yongchun starts with the curriculum concept and nature of "Mathematics Curriculum Standard for Ordinary Senior High Schools (20 17 Edition)", and then interprets "Senior High School Mathematics Core Literacy and Curriculum Objectives". Subsequently, he contacted the "four foundations", "four abilities" and ten core concepts in the Mathematics Curriculum Standard for Compulsory Education (20 1 1 Edition), and combined with the core literacy of high school mathematics, he refined the core literacy system of primary school mathematics.
As far as the source of constructing the core literacy system-the construction of students' cognitive structure is concerned, Professor Wang pointed out that in terms of the four levels of mathematical cognition (cognition, understanding, mastery and application) proposed by the curriculum standard, most students with learning difficulties "see the trees but not the forest", and there are obstacles in the specific application. The reason is mostly related to the mastery of mathematical concepts.
Professor Wang pointed out that mathematical concepts are the basis of mathematical propositions, mathematical thinking methods and cognitive structures. Common mathematical thinking includes concepts, judgments (propositions) and reasoning. In the process of learning mathematics, students often have the problems of "unclear concept, unclear judgment and invalid reasoning".
Professor Wang demonstrated the reasoning process that the sum of the internal angles of a quadrilateral is equal to 360 degrees, namely
? Proposition 1: The sum of the interior angles of the triangle is 180.
Proposition 2: A quadrilateral can be divided into two triangles.
Proposition 3: The sum of the internal angles of a quadrilateral is equal to the sum of the internal angles of two triangles.
Proposition 4: The sum of the internal angles of the quadrilateral is equal to 360.
With the help of this reasoning process, Professor Wang pointed out that this reasoning involves multiple propositions, and each proposition involves multiple concepts. Through the progressive and interlocking reasoning process, the transmission process of the proposition is completed.
Professor Wang pointed out that concepts need to be understood, memorized and structured, rather than rote learning. Concept learning requires two basic conditions: first, learners must be able to recognize or abstract their common features from numerous phenomena, events, things and situations in order to abstract; Secondly, learners must be able to distinguish between symbols related to concepts or not, so as to make different classifications. In other words, it is very important to have the ability to classify and distinguish through abstraction in the process of concept formation, which should also be the focus of teachers' teaching. Students acquire mathematical concepts by observing, operating, comparing, analyzing, synthesizing, abstracting and summarizing situations and mathematical objects.
Professor Wang pointed out that the level of students' mathematical concept representation is positively correlated with their mathematical achievements. There are five forms of expression, namely, objects, graphics, operation models, spoken and written symbols. The more excellent a student is, the more multiple representations can be made. Abstract mathematical definitions and abstract mathematical concepts are inseparable and cannot be instilled in students, but let students experience the formation process of mathematical concepts.
Professor Wang went on to distinguish the difference between mathematical achievements and mathematical cognitive structure. This is just to my taste as an earl. Because the mathematical knowledge structure belongs to mathematics, it is a universal objective existence, and it is not transferred by personal will, and it is the basis of mathematical thinking methods. Mathematical cognitive structure belongs to students and exists in their minds. It is a unique and personalized existence with strong subjectivity. It is the basis of students' mathematical thinking method and mathematical core literacy.
In the second half of the lecture, Professor Wang focused on introducing mathematical ideas. He pointed out that mathematical concepts, relationships and laws are the basis and carrier of mathematical thought. Regarding the idea of mathematical abstraction, Professor Wang pointed out that mathematical abstraction is a general extraction of mathematical attributes of quantities and their relationships, graphs and their relationships. Abstraction is always accompanied in the process of mathematics teaching and learning. Consciously abstracting is helpful to the development of students' thinking. The abstraction of numbers, the expansion, laws and relationships of the digital system (knowledge structure) are all the results of constant abstraction with the help of intuition.
Ideas about reasoning. Professor Wang takes the calculation of decimal addition and subtraction and fractional addition and subtraction as examples, and points out that calculation is concrete reasoning and reasoning is abstract. Today, with the rapid development of artificial intelligence, it is best to regard calculation as reasoning. Calculations that don't know arithmetic can only be arithmetic! In calculation, the calculation skills obtained by reasoning are more important than those obtained by rote learning!
About mathematical models. Professor Wang pointed out that mathematical models use the simplest and most important variables to express the relationship between things. Professor Wang emphasized the significance and value of the model idea from the aspects of equations, the quantitative relationship of travel problems, and finding laws in diagrams.
Finally, as far as the personal development of students' mathematics core literacy system is concerned, Professor Wang pointed out that mathematics needs thinking, and on the basis of independent learning and independent thinking, ask more "why"; Learn cooperative learning in cooperative communication; Form the ability of innovative practice in the process of hands-on operation, practical activities and problem solving.
How to implement the content of learning in the classroom and how to cultivate students' core literacy need to combine their own time in the future teaching and act to give a math-flavored classroom!
Erudition, unity of knowledge and action;
Easier said than done, facts speak louder than words;
Internalized in the heart, externalized in the line.