Two-digit Multiplying Two-digit Problem-solving Activity

Answer 1

The following is a reflection on the two-digit by two-digit problem solving event:

** 1. Knowledge Understanding and Usage **

1. ** Mastery of Arithmetic **
- Arithmetic was the key to multiplying two digits by two digits. For example, splitting two-digit numbers into tens and one-digit numbers, multiplying and adding them, students might not understand the problem thoroughly when solving it. This could lead to calculation errors or incorrect formulas in practical applications. If the students found it difficult to understand mathematics during the activity, it might be because there were not enough examples in the teaching process for the students to explore the nature of mathematics.
2. ** Proficiency of calculation method **
- The calculation method of multiplying two digits by two digits included the steps of digit alignment, first multiplying by one digit, then multiplying by ten digits, and finally adding them up. When solving problems, students might spend too much time or make mistakes because they were not familiar with the calculation method. This reflected that there might be a lack of practice or targeted practice in the teaching before the event. For example, if a student was not familiar with rounding, it would be easy to make a mistake when solving a practical problem such as " a set of uniforms costs 32 yuan, and there are 45 students in the class. How much does it cost to buy a uniform?"

** 2. Ability to solve problems **

1. ** Problem analysis ability **
- When encountering practical problems related to multiplying two-digit numbers by two-digit numbers, students needed to accurately analyze the relationship between the numbers in the problem. Some students might rush to calculate the problem without thinking carefully about the meaning of each number. For example, in the question " There are 23 boxes, and there are 12 apples in each box. How many apples are there in total?" If the student could not correctly determine that 23 and 12 were the number of boxes and the number of apples in each box respectively, they would not be able to give the correct calculation. This might be due to the lack of specialized training in problem analysis in the usual teaching.
2. ** The variety of solution strategies **
- When solving the problem of multiplying two digits by two digits, in addition to the conventional calculation method, one could also use estimation and other strategies. However, students may only rely on pen calculations during the activity and will not flexibly use estimation to quickly determine the approximate range of the results. For example, if a student were to judge whether the product of 28×19 was greater than 500, they could quickly come to a conclusion if they could first estimate that 28 was close to 30, 19 was close to 20, and 30×20 = 600. However, many students might not have the awareness of this solution strategy. This showed that there was not enough emphasis on the variety of problem solving strategies in the teaching.

** 3. Teaching guidance **

1. ** The effectiveness of situation creation **
- If a relevant problem situation was set up in the activity, the rationality and effectiveness of the situation would have a great impact on the students 'solution to the problem. If the situation was too complicated or detached from the student's reality, it would increase the difficulty of the student's understanding of the problem. For example, creating a situation about two-digit multiplying two-digit numbers in ancient business transactions might be difficult for modern students to understand, but if they created a situation that was close to life such as shopping, class size, and item distribution, it would be easier for students to understand and solve the problem.
2. ** Guiding the students 'thinking **
- In the process of students solving problems, the teacher's guidance was crucial. If the teacher did not give appropriate hints and guidance when the student made a mistake or was stuck in thought, it might cause the student to be unable to solve the problem smoothly. For example, when a student was calculating 25×16, if it was difficult for the student to calculate it using conventional methods, the teacher could guide the student to split 16 into 4×4 and then use the special calculation of 25×4 = 100 to simplify the calculation. However, if the teacher did not have such a guiding consciousness, the student might go further and further on the wrong calculation method.

** 4. Students 'study habits **

1. ** Habit of seriously examining questions **
- Many students didn't have the habit of seriously examining the questions when they were solving the problem of multiplying two digits by two digits. They might ignore key information in the question, such as "about","how much more","how much less", etc., which would lead to mistakes in solving the question. For example, the question was " 18 school bags, each bag is 22 yuan, how much is it?" If the student did not pay attention to the " about " and did an accurate calculation, it would not meet the meaning of the question. This reflected that in the usual teaching and learning process, there was no emphasis on cultivating the habit of students to seriously examine questions.
2. ** Writing standards and checking habits **
- Two-digit multiplied by two-digit calculations required a standard writing format. During the activity, some students might be found to have irregular writing, which not only affected the accuracy of the calculations, but also was not conducive to subsequent checks. Moreover, many students did not have the habit of checking their calculations after they were done, so they could not find their mistakes in time. This might be because there was no strict requirement and continuous training for writing norms and checking habits in the teaching.
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