JOURNAL OF SCIENCE OF HNUE Interdisciplinary Science, 2014, Vol 59, No 5, pp 71 76 This paper is available online at http //stdb hnue edu vn A DIFFERENTIAL MATHEMATICS TEACHING METHOD FOR PRIMARY SCHO[.]
JOURNAL OF SCIENCE OF HNUE Interdisciplinary Science, 2014, Vol 59, No 5, pp 71-76 This paper is available online at http://stdb.hnue.edu.vn A DIFFERENTIAL MATHEMATICS TEACHING METHOD FOR PRIMARY SCHOOL STUDENTS IN THE SECOND SESSION OF DAY IN HANOI Chu Cam Tho Faculty of Mathematics and Informatics, Hanoi National University of Education Abstract An analysis shows that primary boarding school education is so ineffective that it does not meet Hanoi primary school requirements This study raises the questions: 1) How does one determine a student's mathematics learning competency? 2) Can teachers differentiate between students of varying ability? And 3) How can one teach differential mathematics to primary school students? Studies show that all of the above is possible if the teachers have the ability to observe and solve problems, and if they can classify students according to psychological manifestations Therefore, it is possible to create a suitable learning program for each student and group of students Keywords: Diversity teaching method, teaching in primary school, solving mathematics problems, boarding school, mathematics teaching method, learning demand Introduction It is the fact that the quaUty of stadents within a classroom is always unequal, some being stronger and some weaker in learning and competence [4] However, because all are taught under the same learning programs and targets, the curriculum used can not satisfy their learning needs According to Nguyen Ba Kim (2006, Mathematics teaching method), besides the normal formal training, curricular training is also needed in order to aid tiie less intelUgent stadents while challenging the best students In fact, almost every primary school in Hanoi teaches one group of students in the moming and another group in the afternoon This is done because there is a high number of students and this system makes best economic use of the school facilities and staff members However, the schools not make use of an individual orientation teaching metiiod due to the overcrowding and substandard infrastructure Received January 25, 2014 Accepted June 9, 2014 Contact Chu Cam Tho, e-mail address: camtho@ hnue.edu.vn 71 Chu Cam Tho Questions tiiat should be asked are: 1) How can one assess stadents' abUity to learning mathematics? 2) Can teachers appropriate teach both their slow and gifted stadents? and 3) How can teachers teach botii their slow and gifted primary school stadents? 2.1 Content Research results The research team did a survey in order to ask the first question, basing the results on the standard of mathematics knowledge and skills which is issued by the Vietiiam Ministiy of Education and Training, with the measurement derived from Bloom theory (1999) Because stadents can and repeat test which leads to most students receiving high scores, we tried to show both the depth and width of learning content in our survey Each exercise was looked at as a means to measure students' thinking capacity For instance, with reading and writing numbers, and stiucture of number content, students the exercises in the following order: reading and writing numbers (just foUow the rules, with measurement memory ability), understanding the values (the meaning of a number when its used in different positions, measurement of level of comprehension, analysis and summary) and applying what is to be learned (associating numbers and practical exercises) After that, each test was processed by Excel in order to assign a mark and also to put the data in graph form (Chart 1) which is to present stadents' mathematics ability To answer the second question, we suggested that teachers try to learn their stadents' psychology and needs by asking them With that information, teachers can divide stadents according to their mathematics ability and learning needs Creative Ih Inking Analvii^iVnl)*^!^ Loeital ih inking • aleorithms Problem solving Meaiuremenl • 80%-100% Pa Ice value •d6%-80% IndentiN geometric • 0W-45K Companion Fraction sen ie CalculaiionswiihinlDODO Read/wntD the number within 100000 AveitiBe J J I Chart I Summary of result of the survey given to 115 grade four students To answer tiie thkd question, we gave a test and suggested ways that teachers might improve their teaching techniquesand organize different teaching methods fortiiechildren in the second session 72 A diversity mathematics teaching method for Primary school students 2.2 2.2.1 Comments and a solution Rebuilding the content and learning process Human psychology is always subjective, everything outside being refracted through an individual's subjective prism Therefore, different stadents will have different attitades toward anything and everything An individual's learning abiUty is not the same because it depends on living standard, physical and mental condition, and genetic factors Consequently, individuals should have different learning targets, but these should still be based on the general educating target of the primary schools and Mathematic department Thus, teaching has to meet both the individual students' learning needs and the general teaching target This means that educators must always consider how much the children leam considering their age and internal development It is necessary to take a good look at the standard program and the textbooks used in primary education, and also the systems used outside Vietnam in order to provide topics which primary school students need and should be able to access A guiding document for teachers, students and parents should be composed for each topic which analyzes examples of case studies, presents teaching method recommendations and divides exercises into many encoded levels for easy stadent use The second session teaching needs to consider student weaknesses and support them For example, students identified in chart as being able to identify shapes, quick calculation and discover rules should be given word problems Teachers should teach to increase student potential and reduce student stress Second session lessons should be as follow: (1) Start: Use funny Mathematics activities, group exercises or folk games (2) Students the work assigned while teachers prepare teaching materials (3) Teachers check the work done by the students, help them their work and assign the next task (4) Teachers conclude and assess the lesson UnUke with mass teaching, individual oriented teaching needs good and regular assessment The teaching process can be seen in Graph Teachers should write a diary to monitor students' "learning emotion" and find solutions to problem promptly WiUi the individual oriented teaching method, die most important factor is to motivate stadents to want to learn and study Therefore, instead of having children exercises in a group, teaching must be oriented to make children understand, Uke and exercises on their own 2.2.2 Individual oriented teaching techniques Some teaching techniques we recommend are use of an attractive start, using suitable exercises and using an analysis technique with group distribution During our experiment, we found that the first moments of the class are very important to have an effective learning process This does not mean to start with a fun game, because makes it difficult for children to focus on learning Teachers can start by 73 Graph I A diversity teaching method talking about what they have learned, mathematical activities and games, the meaning of the lesson or some fun thing to For example: "Let divide this rectangle into four equal parts", and we give them some rectangular pieces of paper Students wiU passionately cut, spUt and connect We ten tell them about triangular symmetry Teaching theory in a constmctive way should be our interest Primary school stadents not have to learn many theories, but the imposition of formulas makes them lose their creativeness and flexibility, and children will feel fear and intense hatred (i.e 'I want to kiU') due to a lack of understanding To avoid this problem, we give the formula for the area of a triangle (many children not understand this and find it difficult to apply) We use the theory of conversion into units (the main theory of the integral) to create a habit of converting the rectangle into square units and then calculating ±e area of the rectangle by the length multiple with the width The area of triangle ABC is calculated as follow: After its split to 2rectangles,it is easy to find that SABC = - X (SAMBH + ^ANCM)1 ^ And stadents easily see that SABC -T^^ (-'^ ^ ^C) It also helps children apply the height and bottom edge in other cases Grouping individual technique helps stadents solve abstract exercises For example, a grade exercise: "In the sequence: 1,1,2,1,1,2,1,1,2 what is the 151th position?" It is a difficult exercise if we guide children to list or use a general term of the sequence (in fact, many teachers show such a guideline to the students) Now we group individual techniques to examine this exercise Fkst, we look for a rule for tiiis sequence, it is a group of (1, 1, 2) put together This sequence can be seen as a repetition of group (1, 1, 2) and we look to see how many groups tiiere are in a sequence of 151 numbers The answer is 74 A diversity mathematics teaching meUwdpr Primary school students 50 groups plus number This number must be the first number of the 51st group andso itis number To iUustrate the grouping individuals technique, we can look at this example: "Do the foUowing calculation: (2-:2) and (3-x2)" We saw lots of provided the fractions above then calculate as a formula (most of them need to use pen and paper) However, using the technique we are talking about, we don't need to use a pen and paper becuase it is easy to calculate mentaUy It is done as foUows: divide the mixed number into parts and mentaUy calculate with each part, then add 2resultstogether We can iUustrate the process with the foUowing: (2:2) + (i:2) = liand (3x2) + (ix2) = 6^ Teachers should use simple techniques to make the exercises real using the term "double" instead of (x 2), a half instead of (:2), number 10 conclude how many number (smdents can mentaUy calculate it) instead of (10:2) which stadents need to use pens, papers or calculators Therefore, grouping individual techniques is compared to the bunch of chopsticks tale,tiielession being that when an overaU problem is difficult, divide it into smaUer parts Not only doesthis help children carry out numerical thinking, it also makes them flexible 2.2.3 Diversify students' psychology who found difficult In order to diversify teaching methods to be more effective, teachers must be able to assess not only learning competency but also learning need and psychology After looking at more than ten teachers' abiUty to use a questionnaire and make observations to determine stadent needs, we found that they aU have difficulty with uninteUigent stadents and those who are unusual Such stadents can be divided as foUows: (1) Passive - fear ofrelationships.Expression: shy, almost never ask a question or answer a teacher's question; focus on an indefinite pointfora long time, not self-confident in communication This type of stadents is often unaware of his surroundings due to a lack of desire to communicate with an adult In order to help them, teachers should show kindness, be consistent and always encourage them (2) Passive - fear of failure Students usually show that t h ^ not like learning, tiiey rarely homework or it carelessly, giving unreaUsticreasonssuch as: T cannot it' and T don't know' With this type of stadent, teachers should emphasize that the stadent can succeed at a certain level and start giving them in easy chaUenges,tiienmedium, and upgrading the level graduaUy, always showing an absolute beUef (3) No focus - loss of focus, hyperactivity Students find it difficult to control their emotions, unable to work in silence, tend to say the answer out loud, constantiy cause trouble, intermpt others, not take care of details, rarely Usten to others, find it difficult to organize tasks, forgetful, and are distracted easily by external elements When interacting with such a stadent, teachers should specify what steps are needed to complete the required task To avoid freely asking questions, tasks can be Usted on paper then summarized This type of stadent needs psychological intervention, but teachers can 75 help them improve their sitaation (4) Perfectionist Stadents are self-critical, have low self-esteem and feel vulnerable They beUeve that being perfect is the only way to get love, respect and attention They also fear failure and usuaUy hesitate and delay, even finding reasons for not doing something Teachers should help them overcome theh mental barrier and be open with tiiemselves and others Teachers usuaUy guide them in social activities, and in class they usuaUy help then- mferiors We should t ^ to and advise these stadents to have a positive view of 'mistakes' With such diversity, teachers need to be able to understand the behaviors and provide suitable teaching metiiods when teaching math While stadents witii similar mental expression should be grouped, there should be some diversity Teachers could group more intelUgent stadents with less intelUgent stadents (1), (2) The students could then help each other when learning Conclusion More specific methods of assessing a stadent's learning ability and psychology are necessary We recommend that two-session teaching should be conducted to aUow for both psychology and subject speciaUzation, and enhance group coUaboration REFERENCES [1] Vietaam Ministry of Education and Training, 2012 Textbooks and Teachers' book class 1, 2, 3, 4, 5, Publisher [2] Hieu Do Trung (eds.), 2006 Mathematics Teaching methods in Primary school textbook PubUsher Hanoi National University of Education: Hanoi [3] Tho Chu Cam, 2012 Some discussions about building standard Mathematics competence in high school Vietaam National Education Seminar [4] http://www.pomath.vn.8 76 ... stadents'' psychology and needs by asking them With that information, teachers can divide stadents according to their mathematics ability and learning needs Creative Ih Inking Analvii^iVnl)*^!^... Primary school students 2.2 2.2.1 Comments and a solution Rebuilding the content and learning process Human psychology is always subjective, everything outside being refracted through an individual''s... and everything An individual''s learning abiUty is not the same because it depends on living standard, physical and mental condition, and genetic factors Consequently, individuals should have different