The decimal part of the dividend and the decimal part of the quotient have the same number of digits as the decimal part of the remainder . In your opinion, is the above rule correct or incorrect? Why?
At first, when this rule was introduced, students seemed excited because the rule for finding remainders in dividing decimals by decimals was something they had never known before. However, the situation required students to confirm the truth or falsity of the above statement. Therefore, students would find a way to check that statement. Students applied that rule to the calculation of the example 3.7:0.03, the result would be 123.3 (remainder 0.01). At this point, most students would try to re-calculate and quickly discover that the above statement was wrong. This created a motivation for students to mobilize their existing knowledge to find the answer: "So how is the rule correct? And what is the correct way to find remainders in these divisions?"
+ Point out student progress, help students adjust if not on the right track.
Maybe you are interested!
-
Measure 3: Building and Applying Self-Study Math Situations for Elementary Education University Students -
Content Two: Understanding the Current Situation of Training and Developing Math Self-Study Skills for Elementary Education University Students -
Developing Math self-study skills for students of universities training primary school teachers - 21 -
Process of Building an M-Learning System to Support 12th Grade Students in Self-Study Math -
The Problem of Cultivating Students' Self-Study Math Ability
+ Timely and specific comments on strengths and weaknesses in a tactful and skillful manner. Teachers promptly encourage students by giving scores.
+ In the classroom, students are usually divided into three groups: good and excellent students; average and poor students. Special attention should be paid to the third group by creating opportunities for them to successfully complete specific tasks. Then praise and encourage them to motivate them to actively participate in the next tasks.
+ During the teaching process, teachers should focus on the mistakes students often make and the types of exercises they often encounter in exams.
- Teachers need to find out and properly assess students' abilities and create opportunities for students to study and research by organizing seminars and self-study reports on course content.
Example 6: In the specialized subject: "Developing Mathematical Problem Solving Skills in Primary School" [32], there are 12 topics on Mathematical Problem Solving Methods in Primary School. In these topics, teachers can completely guide students to research in groups and individually, then organize seminars and reports by topic for discussion.
In basic subjects, lessons with content that is within the reach of the student include: "Operations on sets" [29, p.19], "Simple reasoning problems" [29, p.131], "Deduction and proof in teaching mathematics in primary school" [29, p.198]... with this content, teachers can completely guide and organize students to self-study and participate in seminars and reports on that self-study topic.
- Teachers need to closely combine their teaching methods with students' self-study methods.
- During the teaching process, teachers need to evaluate students' self-study results.
2.2.2. Measure 2: Organizing self-study Math activities for primary school pedagogical university students
2.2.2.1. Scientific basis of the measure
According to the synthesis of research from some countries such as England, France, Australia, ... and in reality in Vietnam, practical skills are one of the top 10 basic and important soft skills for workers in today's era. To have good practical skills, learners need to learn through experience, through practical activities. To be able to carry out practical activities proficiently and effectively, learners need to have practical activity skills such as: Learning planning skills; skills in preparing necessary knowledge as a premise for self-study of new Math knowledge; skills in reading Math documents; skills in taking notes in Math; skills in discovering - solving - proposing problems in Math; skills in working in groups; skills in self-assessing Math self-study results; skills in converting math problem solutions into elementary math language; skills in organizing situations to stimulate self-study activities in groups for elementary school students; Skills in applying information technology in teaching Mathematics in Primary School; Skills in applying mind maps in teaching Mathematics in Primary School. Especially in the current period, when Vietnam participates in the PISA assessment program (Programme for International Student Assessment) initiated and directed by OECD (Organization for Economic Cooperation and Development). Up to now, PISA is the only educational survey that assesses the knowledge and skills of students at the age of 15, the age at which compulsory education ends in most countries. Instead of testing the memorization of lessons according to specific educational programs, PISA considers the ability of students to apply knowledge
knowledge and skills in the basic professional field, the ability to analyze, explain and communicate effectively when they consider, interpret and solve problems [94]. Students cannot learn everything in school. To become effective lifelong learners, students must have self-study skills. For Mathematics, students must have good self-study skills, formed from the beginning of school. Therefore, equipping and developing skills to support self-study skills for students right at university is an important and necessary task. This task has a "double" impact: helping students develop their own self-study skills while studying at university and helping students after graduation have awareness, skills and methods to equip and develop self-study skills for primary school students.
2.2.2.2. Objectives of the measure
Help students understand the principles and methods of implementing the operational skills in the process of cooperative learning to help students have effective cooperative learning skills. From there, build a number of processes to help students develop their own cooperative learning skills during the learning process at home as well as in class.
2.2.2.3. Content and organization of implementation of measures
To develop cooperative learning skills, teachers need to help students equip themselves with some necessary skills during cooperative learning activities and at the same time build some processes to help students develop their own cooperative learning skills during their learning process at home as well as in class.
1) Equip yourself with some necessary skills for self-study of Math to meet university study requirements
a) Equip yourself with study planning skills
* Some basic principles when planning learning activities
To plan an effective Math study plan, students need to follow the following 5 principles:
Principle 1: The principle of combination. A self-study plan must combine one's own subjective conditions and external objective conditions that affect the implementation of the plan.
Principle 2: Specific goal principle. The self-study plan must outline small, specific goals for each activity that needs to be achieved.
Principle 3: Principle of ensuring duration. The self-study plan must ensure that the duration of the study is commensurate with the amount of information in the subject; reasonably alternating between forms of self-study, between subjects, between self-study hours and break times.
Principle 4: The principle of backward connection. The self-study plan must ensure the implementation of the backward connection which is regular and timely self-assessment so that students can take measures to adjust the self-study plan appropriately. The results of the backward connection are the basis for controlling and adjusting the plan.
Principle 5: Principle of perseverance and seriousness. Students need to have a sense of responsibility for themselves in self-study; seriously and persistently carry out their self-study plan goals, and constantly cultivate self-study skills.
* The process of guiding students to form skills in planning self-study activities.
Self-study activity plans can be divided into "long-term plans" (semesters, school years); "medium-term plans" (weeks, months) and "short-term plans" (days-work). Guiding students to form skills in planning learning activities is carried out according to the following general steps.
Step 1: Help students proactively grasp the program, plan of the semester, school year, each month, week and specific job requirements. Pay attention to listing the work according to the timeline (important milestones in the semester such as: starting time of studying the modules, testing time, finishing time of modules, exam time, internship time, internship end time, times to participate in group, social, family activities, . . .).
Step 2: Instruct students to arrange tasks in chronological order and in order of priority. Instruct students to plan and divide time for each task scientifically and reasonably; estimate the results to strive to achieve. Instruct students to write down a plan in chronological order. Pay attention to the expected results to be achieved.
Step 3: Students implement the proposed plan.
Step 4: Check the results achieved against the expected results, draw conclusions, and adjust subsequent plans.
Note that, although relatively independent, the medium-term (weekly, monthly) and short-term (daily-work) learning activity plans are an inseparable part of the long-term (semester, school year) plan. Therefore, when determining the medium-term (weekly, monthly) or short-term (daily-work) learning activity plan, it is necessary to regularly compare it with the "long-term plan" to avoid duplication and not let the "short-term plan" disrupt the "long-term plan".
With medium-term and short-term plans, it is necessary to guide students to visualize and list tasks; plan the implementation sequence and priority according to the importance and urgency of each task, clearly state the plan goals for the week and day, what results need to be achieved, what tasks need to be completed... record the expected results.
Self-assessment must be based on the plan and expected goals, drawing conclusions (lessons learned) to adjust subsequent plans. When implementing the plan, it is necessary to remind and encourage students to maintain the principles of operation in accordance with the plan, to be persistent, patient, and have the will to overcome difficulties. However, to avoid rigidity and dogmatism leading to failure, students must be flexible and creative when conditions and circumstances change. There must be reserve time to handle arising problems.
b) Equip yourself with the necessary knowledge preparation skills as a premise for self-study of new Math knowledge
* Some basic principles to prepare the necessary knowledge as a premise for self-study of new Math knowledge
Principle 1: Students understand their own abilities and knowledge and know the basic knowledge needed for the upcoming lesson, from there determine what knowledge they lack for the lesson they will learn.
Principle 2: Students know how to find and research new materials and review existing knowledge.
Principle 3: Students know how to apply existing knowledge, skills and experience in each specific lesson.
Principle 4: Students know how to identify their personal "gaps" in knowledge during the research process; must always be conscious of finding ways to supplement the missing knowledge.
Principle 5: Students use logical thinking to learn new knowledge based on existing knowledge compared with the learning objectives in the program (avoid forced, one-sided memorization).
Principle 6: Students take notes and sketch important knowledge learned and new knowledge acquired.
* The process of forming skills to prepare necessary knowledge as a premise for self-study of new mathematical knowledge
Step 1: Identify and gather the necessary knowledge and methods (minimum prerequisite knowledge). This prerequisite knowledge depends on the specific content of each lesson.
Step 2: Determine the requirements for the level of explicitness of the knowledge of the conditional method: The teacher asks students to review or study on their own under the guidance (direct or indirect) of the teacher.
Step 3: Build a situation with pedagogical intent (embed new methodological knowledge), through solving the situation, students can acquire new methodological knowledge.
Example 7: When teaching the lesson “Bernoulli's formula” [28, p.36].
C k p k (1 p) n
n
*, k
n,0
p 1
One of the key knowledge of the lesson is to form formulas for students.
Bernoulli is:
P n,k (A)
with
n, k
In which, event A in trial J appears with probability P(A) = p. When repeating that trial n times independently, the probability that in those n times there are k occurrences
event A is
P n,k (A). When surveyed, there are still teachers who often teach this lesson.
Provide Bernoulli's formula for students to comprehend and apply in specific situations. If teachers install lesson content in situations with pedagogical purposes for students to solve themselves, they will acquire new knowledge as a result of their actions. For students to be able to solve these situations themselves with their existing knowledge and experience, students must have the following knowledge:
- Knowledge of methods for performing common intellectual activities in Mathematics.
- Knowledge of methods for performing general intellectual activities (such as analysis, synthesis, etc.).
- Algorithmic knowledge
Example 8: Before studying the lesson “Bernoulli's formula” [28, p.36].
In the simplest way, teachers can ask students to prepare the lesson by reviewing the knowledge section "Finding the probability of independent random events". Give 3 situations in advance (in Example 7) for students to prepare at home.
Or in other words, teachers can create situations for students to review knowledge of conditional methods such as:
Situation 1: When rolling a dice 5 times. Find the probability that 1 of those 5 rolls will have a 6 dot face?
Situation 2: When rolling a dice 5 times. Find the probability that in those 5 rolls, 2 times the 6 dot side appears?
Situation 3: When rolling a dice 5 times. Find the probability that in those 5 rolls, the 6-dot side appears k times? (k = 1,2,3,4,5).
Situation 4: When rolling a dice n times. Find the probability that in n times
1, n
Toss that time has 1 face appear 6 dots? (k).
Situation 5: When rolling a dice n times. Find the probability that in n times
1, n
Toss that 2 times the 6 dot side appears? (k).
Situation 6: When rolling a dice n times. Find the probability that in n times
1, n
How many times does the 6-dot face appear? ( k ).
c) Equip yourself with the skills to read Math documents
after:
* Some basic principles when reading Math documents
To read Math documents effectively, students need to follow 10 principles.
Principle 1: When reading, take notes and mark important points or ideas you don't understand.
Rule 2: Follow the correct reading order: look at the table of contents; preview the review questions (if any); read the introduction or conclusion (if any); read all the headings and subheadings and then think about them.
Principle 3: Spend time studying illustrations such as charts, diagrams, and mathematical formulas if available.
Principle 4: Pay close attention when reading, read actively and diligently, maintain a state of alertness and clarity throughout the reading process; seek to absorb the knowledge and information in the documents.
Principle 5: Always ask questions and answer them yourself to deepen your understanding of the material you read.
Principle 6: Read and grasp the core information thoroughly.
Principle 7: Know how to choose the right reading method, at the right time and in the right place. Read at a variable speed.
Principle 8: Use what you have read to solve problems or practice exercises.
Principle 9: Review previously acquired knowledge before reading new material. Principle 10: Set yourself a standard of reading at least one article in the material every day.
Mathematics.
* Process of forming skills in reading Math documents
Step 1: Map out your reading path : Preview the table of contents; look at the review questions (if any); read the introduction or conclusion (if any); read all the headings and subheadings, then think about them.
Step 2: Determine the purpose of reading the document : Determine the problem and information you want to find (you can write down the reading goal on paper). You need to review related knowledge (if any) to serve the reading purpose and link old knowledge with new knowledge.
Step 3: Skim : Read continuously with the aim of grasping the general intention of the author. Mark the parts that you do not understand.