Consulting math tutor ∣ Lin Shoufu (math teacher of Xingya junior high school in Taipei, central curriculum and teaching counselor), Deng Jiajun (math teacher of Wufeng junior high school in New Taipei, math counseling group of New Taipei National Education Counseling Group as a counselor).
When Taipei announced the math literacy test, everyone's first reaction was: "It's so difficult!" "I don't want to force my children to go to cram school, and the pressure is getting bigger and bigger? 」
But a senior math teacher who is familiar with PISA test and has been teaching in junior high school for a long time said, "PISA test questions are really close to life." Students can take computers into the examination room without patience and care. I really hope that every student will try to learn to think and solve problems in life with mathematics.
What is a math literacy test? What is the biggest difference from the traditional math exam in school?
A: In the past, the examination method was "performance test". PISA math literacy test is closer to real life, which is very similar to what students may face after leaving society. The goal is to improve their ability to solve problems in daily life. The examination covers changes and relationships, space and shape, quantity, uncertainty and data analysis, such as election result prediction, exchange rate and time difference conversion, population growth rate estimation, etc.
In fact, the topic of PISA is not difficult, and there will be no complicated calculation. Students can bring computers with unlimited functions and types to take the exam. Therefore, it is enough to apply three years of junior high school plus elementary school mathematics knowledge.
For example, PISA has a problem to calculate the area of the Antarctic continent. Candidates can draw regular squares with the same size by using the concepts of proportion and area calculation taught in textbooks, and get the approximate value of irregular graphic area. Such a topic has actually appeared in the area unit of primary school mathematics textbooks, and it can also be said that it is actually a primary school mathematics examination question.
But the flexibility of PISA test lies in its scale of ○? Seven centimeters, not one centimeter or zero? Five centimeters, so many candidates think according to inertia and get the wrong scale from the beginning, which leads to the wrong answer.
PISA math problems are divided into multiple-choice questions, multiple true-false questions, closed questions and open questions, and there are clear scoring standards in the question-and-answer section.
For example, there is a chart title, which shows bar charts of the number of robberies in 1998 and 1999. The title asks: "TV anchors draw a conclusion from statistical charts that the number of robberies has increased sharply from 1998 to 1999. Is this reasonable? 」
People who only answer "no" can get partial points, and then they must be supported by data or statistical proportional relations and give reasons to get full marks.
The reason why many candidates can't get full marks is that the explanation is vague, even based on their own subjective judgment, and there is no mathematical point of view at all.
In addition, students in Taiwan Province Province are not used to using computers as auxiliary tools, and spend too much time or make mistakes in calculation in some places where actuarial calculations are needed, thus losing points.
In addition, the answers within the error value are acceptable, and small flaws such as misspelling or wrong use of units and punctuation marks, or long explanations of questions and answers can be ignored, so candidates need not be too nervous.
Can PISA math test questions be improved through repeated training or a large number of problem solving, and "math literacy" can be enhanced? Is tutoring useful?
Answer: Candidates can find some questions from PISA in the past to practice, and get familiar with life-oriented questions in advance, so it is unlikely that they will panic on the spot. Because this kind of examination takes a long time and combines reading comprehension and mathematical ability, candidates must find useful parts from a pile of materials, so the practice of "archaeological questions" is not perfect. As long as you use the right method, often reflect, and get used to reading longer questions, you don't need to go to cram school or ask a tutor.
Mainly because the life situation in the question is ever-changing, it is impossible to "guess the question before the exam." People with clear basic concepts are more likely to get high marks, so they should cultivate the habit of thinking and exploring problems actively on weekdays.
In the past, many teachers and parents used to "sea tactics", thinking that it would be effective to let students do as many questions as possible. But if you just repeat the problem and turn it into a formulaic intuitive response, you will not actually form your own problem-solving strategy, and you will panic if you encounter strange problems. Therefore, excessive practice or seeking help from a tutor may not achieve better results.
In fact, the so-called literacy comes from constant contact and observation, and then discover the correlation between mathematics and life, and solve problems through it. Therefore, instead of writing archaeological and simulation questions, it is better to make more use of the materials around you. For example, the service fee for going to the restaurant will increase by 10%, but the membership card will give you a 10% discount. Will this result be more expensive or save money?
Parents and teachers may wish to encourage their children to compare, analyze and discuss in interesting ways. Comments on figures and statistical charts in news reports are also good teaching materials.
Mathematics literacy is a characteristic entrance examination. Is it difficult for gifted students to learn?
A: Absolutely not. The problem of PISA's mathematical literacy mentioned above is not difficult. The basic knowledge of mathematics used may also be at the primary school level. When giving points, you will also judge your own understanding and logical analysis; Ugly or scrawled handwriting will not affect the score. Moreover, exams can also bring computers into the arena, and complicated calculations and drills are not the purpose of exams. More importantly, I hope to see what you have learned and whether you can use it, so that every student can effectively increase his ability in life by accumulating such literacy.
Do most junior high school teachers know how to improve students' mathematics literacy at present? What channels can help teachers learn?
A: Teachers can arouse students' interest in mathematics through appropriate situational arrangements, and then take the initiative to explore, study, review and reflect-this part of the ability is the most lacking of domestic students.
Of course, in the past, our teacher did too much for the students, always helping them clean up and solve their problems. Instead, it took away the opportunity for children to learn.
In the future, let them think independently and think more about problems: what are the possible solutions, whether there are multiple solutions to a problem, whether there are more streamlined solutions or different paths ... These are all things that teachers can guide students in time in the course. As long as it accumulates over time, it is helpful to improve students' mathematical literacy.
At present, junior high school teachers can participate in various PISA seminars or workshops to improve their professional knowledge as long as they are willing. Taking New Taipei City as an example, 9 large-scale seminars were held in 20 1210/month, and the counseling group will hold an advanced workshop in the winter vacation of 20 13 to discuss how to improve students' mathematics literacy in teaching.
How should junior high school students take into account the different proposition orientations of stage examination, examination and special examination at the same time in their study preparation?
A: The mid-term and mid-term exams still emphasize traditional questions, but at present, some schools have tried to include one or two PISA questions in each mid-term exam, which is the right direction. After all, the changes in the examination questions will attract the attention of teachers and students.
Because this kind of examination questions are lively and easy to arouse students' interest. As long as he is willing to think and answer, the teacher can ask questions and discuss further and encourage students to express their ideas.
Our mission is to try not to let students give up mathematics. Maybe one day they will fall in love with mathematics.
Many teachers are worried that the main course will not be finished, so they have no time to lead students to think about extra topics in class. In fact, the essence of teaching should be that quality is more important than quantity, and teachers may not need to teach all the topics in the textbook; It is an effective way to leave some time to strengthen your thinking ability.
Under the condition of normal placement, there is a big gap in mathematics among classmates. What should teachers do?
A: The ideal situation is to teach in groups randomly in class, just like Japanese "same-body learning". At first, two or four people can work in groups, listen and learn from each other. In the face of good students, the teacher throws some high-level thinking questions to let him challenge himself, while the students with relatively backward level should be encouraged to ask questions on their own initiative. In fact, math literacy problem is not the patent of gifted students, it can take care of high, medium and low level groups.
Are students with good reading literacy good at math even when the questions are generally long?
A: Generally speaking, yes, they are positively related. Students with good reading comprehension ability can not only understand various long articles, such as popular science, literature, art and so on. And you can express yourself well when answering questions, and you can clearly explain your ideas and concepts, which makes it easy to get high marks.