Reflection on the score multiplication score teaching

Part 1: Reflection on the score multiplication score teaching

This lesson, "Score Multiply Scores", is the second element of the sixth grade mathematics of the People's Education Edition. The focus is on consolidating and evolving the meaning of fractional multiplication and exploring the rules for calculating the score multiplication score.
In the teaching practice, I continue to use the mathematical method of “digital combination” to help students achieve the above two mathematical goals. There is no direct let go of the “inquiry activity” in the classroom. This is because the students’ understanding of the meaning of the score multiplication of “how many fractions is a few” is not deep enough, so the whole teaching process is divided into three levels. :
Guide the students to express the formula by graph, and then use the formula to represent the graph, deepen the meaning of the score multiplication of "seeking how many fractions of a number is", and the process of calculating the score multiplication score.
Taking 3/4×1/4 as an example, let the students explain the meaning of the formula first, then use the graph to represent the meaning. Finally, in the calculation process based on the graph representation, the purpose of this is to use the “number of arguments”. The process of “taking the number of forms” is the process of consolidating the score multiplication and the calculation process of the score multiplication score.
Students use the combination of number and shape to independently complete the test in the textbook, further achieve the above goals, and accumulate knowledge for the calculation method of summarizing the score multiplier. The overall teaching effect is very good.
Since students have a solid foundation for the meaning of integer multiplication, the exploration of the meaning and computational rules of exploring scores by integers can be done independently. In the exploration of the score multiplication score calculation process, since the students just know the meaning of the score multiplication of "how many fractions of a number is", and the calculation process of using the graph to represent the score multiplication score is more complicated, The strategy of helping and letting go is better.
Students can calculate the score multiplied by the calculation according to the calculation rule, but for the calculation process, some students are not aware of the difference, such as the multiple of 3, the multiple of 7, or even the multiple of the larger number, the student does not know. The scores are not the simplest, but also the training.

Part 2: Rethinking the score multiplier teaching

The meaning of fractional multiplication is the extension of the meaning of fractional multiplication. It is not difficult to remember the calculation method of fractional multiplication, but it is more difficult for students to understand the mathematics. The key point of this lesson is to consolidate and further understand the meaning of fractional multiplication and explore the rules for calculating score multiplication scores. In teaching, I mainly use the mathematical method of “digital combination” to let students intuitively understand the calculation method of score multiplication score in actual operation, and use their own language to summarize. First of all, in the review, through visual demonstration, the students are guided to fold 1/2 of the rectangular strips in turn, then take 1/4 of 1/4 and 3/4, and let the students use the multiplication formula to express the process. The meaning and calculation method of the multiplier, followed by 2/3×1/5, 2/3×4/5, let the students explain the meaning of the formula first, then graphically represent the meaning, and finally represent the formula according to the graph. The calculation process, the purpose of doing this is to pass the process of "single number theory" and "by number form" to students to consolidate the meaning of fractional multiplication and to understand the calculation process of score multiplication score. In teaching, I fully utilized the existing knowledge base of the students, through observation, experiment, operation, reasoning and other activities, through the intuitive operation of the examples, through the migration of knowledge to help students understand the meaning of the score multiplication score, and initially grasped the score multiplication score. Calculation method. In the inquiry activities, students can actively participate in the process of analysis, observation, conjecture, verification, comparison and induction, and further develop the students' initial deductive reasoning and reasoning ability.
Through the teaching of this lesson, I have the following thoughts:
Combine the number of the theory with the number of the form.
The meaning of the fractional multiplication and the principle of the calculation rule are more abstract. It is not easy for students to understand. Therefore, using graphics to visualize the abstract problem is particularly important in the teaching of this lesson. Throughout the textbook, the infiltration of the combination of numbers and shapes There are also different levels. For example, in the first two lessons of fractional multiplication, specific physical graphics are used to help students abstract mathematical problems from specific problems. In the third lesson of fractional multiplication, intuitive geometric figures are used to help students understand. The calculation of the score multiplied by the score; in the next fractional multiplication, we will also use the line graph to help students understand the problem of fractional multiplication. The process of combining numbers and shapes is not a simple abstraction that becomes an intuitive process, but an abstraction becomes intuitive, then from intuitive to abstract, that is, two aspects of "the number of shapes" and "the number of forms" The organic combination, only the complete "interaction" between the students and the number, can make them perceive the "digital combination", so that they can consciously apply the "digital combination" when solving the problem.
Experience the process of inquiry and optimize interaction generation.
"New Curriculum Standards" points out: "Mathematics teaching is the teaching of mathematics activities, the process of interaction and common development between teachers and students, students." This new concept shows that mathematics teaching activities will be students undergoing a mathematics The process of transformation is the activity of students to construct their own mathematical knowledge. Therefore, the teaching of this class tries to let the students personally experience the learning process. That is, let students experience the formation process of the “score multiplier” calculation process in a series of activities such as hands-on operation—exploration algorithm—example verification—communication evaluation—law integration. Here, we focus on letting students experience, experience, and feel and create. Learning is the child's own business. After the power of inquiry is truly returned to the students, the student's performance will surprise you. In the class of the two classes, there are different methods for verification and explanation about the score multiplication rule, which are far beyond the pre-class presupposition. The reason is that learning has become a matter of its own, learning is more active, and its potential has reached its utmost.

Part 3: Rethinking the Score Multiply Score Teaching

The content of this lesson is "score multiplication score", which is based on the students' understanding of the score multiplied by the meaning of the integer. The focus is on making students understand the meaning and calculation method of score multiplication score, which is also the difficulty of this unit. The teaching design mainly emphasizes the actual operation and graphic language, so that students can intuitively experience the calculation method of score multiplication score in actual operation, and can use their own language to summarize.
First, in the situation, let the students understand the meaning and calculation method of the score multiplied by the integer, and then through the visual demonstration, fold out one-half of the rectangular strip, one-half of the one-half, and let the students multiply The formula expresses this process, initially feels the meaning and calculation method of the score multiplication score, and then lets the students guess that since the student already has the basis of the score multiplied by the integer, it is not difficult to guess the result, and then let the students in the actual operation Graphic language, the meaning of score multiplication score, the feeling score multiplication score is the method of "molecular multiplication, denominator multiplication denominator", students in the process of origami, and then use the "discussion" in the textbook to encourage students to discuss calculations The relationship with the graphics, through a few similar questions, "folding, thinking, calculating," let students use their own language summary score multiplier method. In the discovery of the calculation rule, because a lot of pen and ink was spent in the front, when the law was formed, the students were asked to observe the numerator and denominator of the product and the denominator of the two factors according to the five formulas on the blackboard. What relationship?" Calculate the score multiplier.
Because this lesson is only for the students to feel the meaning and calculation method of the score multiplied by the origami activity, the whole time of the whole lesson is placed on the students' intuitive feeling of “folding off, painting one coat”, paying attention to the enthusiasm of the students. And initiative, giving students more opportunities for independent learning. The whole process of teaching is very clear. From reviewing to new teaching to practicing teachers, the teaching materials are well studied and very skilled in their own teaching programs.
Rethinking the teaching of this lesson, in the formation process of the calculation method, it is a bit of a conclusion that the light process is suspected. If you add the part of the student's own verification, it may reflect the penetration of the mathematical method. In addition, in normal teaching, if the student directly scores on the original topic, the student often has a relatively high error rate, so they are required to re-request. The transcripts are subdivided, so in the practice, when the first calculation is required, the students basically copy the questions first, and then make the points in the calculation process. In fact, this link can be carried out in the second lesson. Put it here to make the students feel a little confused.

Part 4: Rethinking the Score Multiply Score Teaching

In this lesson, we make full use of the existing knowledge base of the students, through observation, painting, comparison, induction and other activities, through the intuitive operation of the examples, through the migration of knowledge to help students understand the meaning of the score multiplication score, and initially grasp the score Multiply the calculation method of the score. In the teaching I paid attention to the following points;
First, create a situation, intuitive import
In order to break through the difficulty of teaching in the teaching, students can truly understand the arithmetic of the method of fractional multiplication. At the beginning, I asked the students to look at the rectangular paper attached to the blackboard. The coloring part indicates the fraction of the paper. ? This is a good way to reveal this by painting the rectangular paper. Combine abstract mathematics with intuitive schematics to combine abstract thinking with image thinking. In solving the arithmetic, the computational thinking is inspired by the correspondence and transformation between numbers and shapes. For example, one of the diagonal lines accounts for 1/4 of 1/2, and the unit "1" at this time is 1/2, but for the entire rectangle is 1/8, and the unit "1" at this time is a rectangle.
Second, pay attention to the deduction of arithmetic
"New Curriculum Standards" points out: "Mathematics teaching is the teaching of mathematics activities, the process of interaction and common development between teachers and students, students." This new concept shows that mathematics teaching activities will be students undergoing a mathematics The process of transformation is the activity of students to construct their own mathematical knowledge. Therefore, this lesson is intended to allow students to personally experience the learning process. That is, let students experience the formation process of the “score multiplier” calculation process in a series of activities such as hands-on operation—exploration algorithm—example verification—communication evaluation—law integration.
When I was teaching new knowledge, I showed "1/2 × 1/3" to guess what is the meaning of this formula? I am reminding students to think about the meaning of scores and integers. See if the scores are multiplied by the scores? Finally, the student concludes that “1/2×1/3” means one-third of the one-third. At this time, I told the students that this formula can also indicate how much one-third of the one-half. I want to be sure that some students can master it well, but certainly some students can't understand it, so I then ask the students to express the meaning of this formula in the form of drawing. This can help students understand the meaning of multiplying scores and scores autonomously and deepen students' understanding of the “multiplication of scores and scores” calculation rules.
When the students draw the meaning of this formula, I ask the students, can you see the result of “1/2×1/3” from the picture? The student immediately said the result 1/6, then I The calculation of several scores multiplied by the score requires the students to draw the map first and then count the number. After several hands-on operations, the students have a deep understanding of the calculation of the fractional multiplication.
Third, pay attention to the penetration of learning methods
In this class, from the overall design of the teaching, the "special" is used to trigger the students' conjectures, and then the examples are verified, and then summarized and summarized, trying to let the students experience the incomplete induction of ideas from special to general. First, let the students summarize the “score multiplier” as long as the “molecular constant, the denominator multiplication” or the “molecular multiplication, the denominator multiplication” calculation method, and then the student’s own use of drawing, origami, the meaning of the score, etc. The method is used to verify this calculation method, and the particularity of "score multiplication score, numerator invariant, and denominator multiplication" is found, and the universality of "score multiplication score, molecular multiplication, and denominator multiplication" is found. This infiltrated the scientific learning method and the scientific spirit of seeking truth from facts.
In this way, students pay attention to the independent inquiry of students in the calculation teaching, let the students do it themselves, enlighten, experience, experience, and create, which not only cultivates the sense of cooperation among students, enhances the autonomy of learning, but also enables students to understand the mastery method. At the same time, improve the ability to solve problems and form good mathematical emotions and values.

Part 5: Rethinking the Score Multiply Score Teaching

The meaning of fractional multiplication is the extension of the meaning of fractional multiplication. It is not difficult to remember the calculation method of fractional multiplication, but it is more difficult for students to understand the mathematics. Therefore, this part of the content is the focus of this lesson teaching, but also difficult. In teaching, I mainly highlight the actual operation and graphic language, so that students can intuitively experience the calculation of score multiplication scores in actual operation and can use their own language to summarize.
First of all, in the review, I first let the students understand the meaning and calculation method of the score multiplied by the integer, and then through the visual demonstration, fold out the 1/2 of the rectangular strip, then take 1/4 of 1/4 and 3/4, and Let students use the multiplication formula to represent this process, initially feel the meaning and calculation method of the score multiplication score, and summarize it with language, initially infiltrating the infinite thought; then let the students guess 1/2×1/4=? Since the student already has the basis of the score multiplied by the integer, it is not difficult to guess: 1/2×1/4=1/8, and then let the students use the graphical language to understand the meaning of the score multiplied by the score in the actual operation. Why is the score multiplication score used in the method of “molecular multiplication, denominator and denominator”, students experience the same result in the process of origami, and then use the “discussion” question in the textbook to encourage students to discuss the relationship between calculation and graphics. Relationships, through a similar number of questions, "folding, thinking, calculating," let students use their own language summary score multiplier method.
Through the observation, experiment, operation, reasoning and other activities, through the intuitive operation of the examples, the students can understand the meaning of the score multiplication score through the knowledge transfer, and grasp the calculation of the score multiplication score. method. In the inquiry activities, students are allowed to take the initiative to analyze, observe, guess, verify, compare, and summarize the process, and further develop students' initial deductive reasoning and reasoning ability.
There is a problem:
1. The class was very fast, so I was a little hurry and didn't make too much preparation. It took a lot of unnecessary time in the practice and the origami verification conjecture, which directly led to the rush in the practice and did not achieve the expected results.
2. The language is not refined enough, and the students are not well mobilized, resulting in a relatively small participation in the activities.
3. Discussing the results of 1/2×1/4, 1/2×3/4 is not well handled. Now I want to show whether the formula can be presented directly, and then let the students use different methods to discuss the results and then guess the algorithm.