Experiental education in mathematics in order to develop linguistic intelligence at primary education

Chu Cam Tho and Nguyen Thuy Chung 84 HNUE JOURNAL OF SCIENCE DOI: 10.18173/2354-1075.2017-0178 Educational Sciences. 2017, Vol. 62, Iss. 12, pp. 84-94 This paper is available online at EXPERIENTAL EDUCATION IN MATHEMATICS IN ORDER TO DEVELOP LINGUISTIC INTELLIGENCE AT PRIMARY EDUCATION Chu Cam Tho 1 and Nguyen Thuy Chung 2 Vietnam Institute of Educational Sciences Faculty of Primary Education, Hanoi National University of Education Abstract. In this article, we present studies on linguistic intelligence and experiental education. Based on behavior of primary student on linguistic intelligence and characteristics of experiential education in mathematics, we design a number of contents and experiental education procedures for mathematic along with development of natural language and schematic language for primary students. Keywords: Experiential education, primary Maths, linguistic intelligence, natural language, mathematical language. 1. Introduction According to the psychologists - education has concluded that essence of intellectual development for students is to develop the ability to think and create. The first step is to recognize the “problem”, solve the “reality problem” at different levels [8]. Formation and development of intelligence must be made regularly, continuously, consistently and systematically, especially when children still study at lower and upper school. The formation and development of intelligence are not separate from the training of observational ability, development of memory, mode of mastering knowledge and some qualities of personality. According to theory of the latest development of Vygotsky, it is necessary to develop teaching content so that it does not “adapt” to available level of children, it should require children to have higher level and a more-complex method of method intellectual activity. All teachers are responsible for and can contribute to intellectual development of student by creating conditions so that students can take initiative in thinking, be independent in creation for suggestion and solution of awareness and practice “problem”, which need to be made regularly, continuously and systematically in all lessons. According to theory of multiple intelligences by Howard Gardner (1997), the intelligence is divided into specific abilities rather than combination of separate abilities of human. He set 8 criterias to define a type of intelligence, they are: may be lost due to brain damage; is placed in the history of human evolution; the presence of core activities; have a separate development process; identifiable; There is the appearance of special people who have these behaviors; be supported from experimental psychology; be supported by psychological findings. Based on these criteria, Howard Gardner has believed that there are 8 types of intelligence, including: Rhythm - music; space - visual; speech - language; logic - mathematics; body - movement; communication; inner feeling, natural, and now he Received: October 9, 2017. Revised: December 6, 2017. Accepted: December 8, 2017. Contact: Chu Cam Tho, e-mail address: chucamtho1911@gmail.com Experiental education in mathematics in order to develop linguistic intelligence at primary education 85 proposed 2 types of intelligence, they are: morality and ethics. Also according to Gardner, for origin of intelligence, he believed that it is a combination of congenital factor and impact of environmental factor through experiences. Therefore, we can teach to affect formation and development of intelligence for children [7]. Experiental education is proposed and researched by a number of philosophers, psychologists such as John Dewey, Kurt Lewin, Bruner. From the works of scientists above, David Akolb (1984) has completed and suggest learning model by experience which consists of 4 steps: 1) Step of “specific experience”: Students receive outside information (experience), record the awareness on those experiences. 2) Step of “reflecting the observation”: Students remember what they observed and think it in many different ways. 3) Step of “conceptualization”: Based on information from process of reflecting experience, the students get new lessons and knowledge for themselves. Step of “test operation”: Students carry out experiences in reality, observe and take lessons [9]. From the above studies, we will propose a content design and experiential education in mathematics process to develop linguistic intelligence for elementary students. 2. Content 2.1. Linguistic intelligence According to the dictionary “The American Heritage Dictionary of the English Language (edition 3), Boston: Houghton Mifflin Company (1992)”, “Language is a complex system that people use to contact or communicate and only human is able to use that system. Linguistic intelligence is mainly expressed by fluence of speech – which can represent for general ability on language of each person [2]. In addition, linguistic intelligence is also linked with ability of solving problem as well as ability of abstract argument [12]. We can detect the effect of linguistic lesions on the left brain (broca area). There are two most important areas: forehead lobes controls speech ability, temporal lobe controls understanding of language [14]. The basic operations of linguistic intelligence are: phonetics, syntax, semantics, and language practice. Howard Gardner considered linguisticcoi intelligence (and logical intelligence – math) as outstanding intelligences of human. From these perspectives above, it is possible to give some expressions of the linguistic intelligence of student at age of primary education as follows: Ability of using flexibly language in both spoken and written language (to be well-informed about vocabulary and master a rich vocabulary); Ability of using the language to memorize information (can remember event, data, numbers exactly); good ability of expression (can present a issue coherently, clearly, understandably to the listener); ability of arguing shrewdly (Can explain, argue, defend views by convincing arguments and words). Empirical evidence has shown that, when examining ability of fluent expression of children(dominant expression of linguistic intelligence), part of the cortex involved in this activity is greater than in adult. In order to explain this, scientists believed that it was associated with higher endurance of newly-developing brain than that of adults [3]. Thus, it is clear that linguistic intelligence should be done immediately and regularly for pre-adolescent children. Chu Cam Tho and Nguyen Thuy Chung 86 2.2. Experiental education in mathematics associated with language development activities Based on the theory of experiental education as well as the cycle of David Kolb on studying through experience, we can apply this model on teaching math at primary education. According to author Tuong Duy Hai (2016), concept of teaching through experiental activities: “is an organizational process which students directly seek by themselves, predict and discover new knowledge, form the initial skills of the subject based on the available experience, and then students gradually transform them into learning experience. From that, they can develop understanding, extend value system and change lifestyle” [11]. The author Nguyen Huu Tuyen pointed out the characteristics of experiental education in mathematics as "students are themselves and directly groping, anticipating to discover the knowledge and form mathematical skills, from which to develop mathematical capacities" [15]. Here we provide a teaching perspective in the form of experiences for mathematics at primary school “which can be understood as a way of organizing mathematical activities linked to reality or pure mathematical activities to help students based on experiences (available knowledge), actively participate in the exploration and discovery of new mathematical knowledge by reflecting and generalizing the experience gained from these activities”. Mathematics comes from reality and returns to serve for reality, from that i continuously develop and expand its application in life. Simulatenously, outstanding features for awareness of primary students is gradually to form the capacity of logical thinking and ability to generalize, abstractize through the operation of visual models. Based on these principles, we chose a approach for teaching math through experiental activities: Studying math through games; Studying math through mathematical situations that can be practiced; Studying math from a requirement of problem that contains practical content. The process of experiental education in math at primary school can take according to steps / activities as follows: - Step 1: Use existing mathematical knowledge to solve one or some problems (mathematical problems or problems that are associated with practice). - Step 2: Think, comment on how to solve the problems above. - Step 3: Generalize and draw new mathematical knowledge (methodological knowledge or content knowledge) - Step 4: Positively apply new knowledge to solve a situation associated with reality. In this article, we describe the relationship of experiental education in mathematics and linguistic intelligence in the following diagram: ↓ Fig 1. The diagram depicts the relationship of mathematical experiential learning and linguistic intelligence Mathematics Linguistic Intelligence Experiental education in Mathematics Linguistic Experiental education in mathematics in order to develop linguistic intelligence at primary education 87 2.3. Experiental education in Maths in order to develop linguistic intelligence at primary education 2.3.1. Experiental education in Maths to develop natural language Natural language here is understood as spoken or written language used to communicate in all areas of social life. In order to help student develop natural language through mathematical experience, we can use corpus expressed in form of folk puzzles, poem, “ve”, poemic formulas. How to use these corpuses of language development in teaching math at primary education: In activities of mathematical experience, in order to develop natural language, we can use some of the following ways: - Express formula in the form of poemry / ve. For example, when experiencing to formulate the formulas / rules for calculating the area of some figures, in the step of extracting new knowledge (step 3), students can express themselves in poemic form as follows: Want to find square area Side multiplies side that is always true (Rule for calculation of square area) I learned about perimeter Side multiplies four that never fail (Rule for calculation of square perimeter) Want to find area of circle Pi multiplies squared radius (Rule for calculation of circle area) To calculate trapezoidal area Small bottom plus large bottom Then multiply with height Then divide it by 2 to get result (Rules for calculation of trapezoidal area) - Express problems in the form of folk puzzles, poemry / ve, example: Problem 1: Both chickens and dogs Total is round There are 16 of both There are 100 legs. How many chickens are there? How many dogs are there? Problem 2: Big boat carries six people Small boat carries 4 people A group of boys and girls go across the river Ten small and big boats are loating Group has 100 people There are 48 people on bank who is waiting to across how many each type of boat are there on river? Problem 3: Love each other, six areca-nuts cut into 3. Chu Cam Tho and Nguyen Thuy Chung 88 Hate each other, six areca-nuts cut into 10 There are 80 people 15 area-nuts, how many lovers and haters are there?” Problem 4: A delicious tangerine is cut into 3 A delicious orange is cut into 10 Every people is equally provided 1 piece Cutting 17 fruits is enough for 100 people” How many oranges are there? How many tangerines are there? The above examples are used in step 1 of the process of experiental education. Students read and read each other problems in the form of poem, ve. Problems which are expressed in this form will be interesting for students, and motivate them to find solutions. In the next steps of the experience cycle, the teacher instructs the student to perform the activities described in item 2. - At a higher level, after the students are familiar with the formulas, problem in the form of puzzles, poems, ve as above, we can practice for self-learning problems (step 4 in the experience teaching cycle), self-expression of formulas (step 3) in the form of puzzles, poems, ve. The meaning of using corpus in the above forms: The way of using the language in the form of folk puzzles, poems and ve as above will help students feel excited with the content of mathematics that they are experiencing; They are feel interesting because there is a connection between mathematical language and natural language; It aslo help students easily understand the content of the problem, easy to follow the formula / rule; It helps students to be confident when they express the problems, formulas in the form of puzzles, poems, etc. Through these experiences, apart from formation of mathematical knowledge, the students are also trained, improved, and develop their own natural language. 2.3.2. Experiental education in Maths to develop mathematical language According to Tran Ngoc Bich, the mathematical language consists of symbols, terminology, symbols, and combinations that serve as a means of expressing mathematical content logically, accurate, clear. Signs include numbers, letters, alphabetic characters, mathematical operators, relational marks, and parentheses used in mathematics. A symbol consists of an image, a drawing, a diagram, or a model of a particular object [1]. To develop a schematic language for students, we use problems that use some types of diagrams: ven diagrams, line diagrams, tree diagrams, tables. The method used in teaching: - Organize mathematical experience to form and apply the method of solving problem by Venn diagram: Step 1: Students use the knowledge to perform the following requirements: The class has 20 students, including 15 students like to study Mathematics, 10 students like to study Vietnamese. Please show each student in the class with a round dot, and then use the pen to circle 15 students who like to study Math with a blue pen, 10 students like to study Vietnamese with a red pen. Step 2: Think about the picture you just created, about the dots that are in the blue circle and in the red circle. Which subject is presented by these dots students like to study, how many dots are there? Round dots are only in the red circle (or blue) for students who are represented for which subject, how many dots like that? Experiental education in mathematics in order to develop linguistic intelligence at primary education 89 Step 3: Find out the solution of the problem of the number of elements of the sets using the Venn diagram Look at the Venn diagram, the number of students who like learning Math and Vietnamese is: 15 + 10 - 5 = 5 (students) The number of students is only interested in learning Math is: 15 - 5 = 10 (students) The number of students is only interested in learning Vietnamese is: 10 - 5 = 5 (students) Step 4: Introduce a similar proposition and apply the solution to the solution. Fig 2. The Venn diagram shows the number of elements of the set - Organization of mathematical experiments to formulate the solution by tree map: Step 1: Your group has 5 students (the number of changes that are appropriate for the situation). Let's take a look at how many choices for 2 students as team leader and vice team leader you can. Students work in groups to select pairs of friends and record the results, for example: A and B, A and C, B and D,... Step 2: Review the pairs formed above and what comments? Suggestions: How many pairs are created? How many pairs have A? How many pairs have B without A? How many pairs have C without A and B. How many pairs in there is D without A, B, C. Step 3: Generalizing from the above comment in the tree diagram is as follows: Students who like to study Math Students who like to study Vietnamese Chu Cam Tho and Nguyen Thuy Chung 90 Fig 3. The problem solving tree finds the number of elements of the ordered pairs Look at the diagram above to see the number of pairs found is 10 pairs. Step 4: Each group gave the same proposition and then solved and exchanged with the other groups. - Organization of mathematical experiments to formulate solutions by tabulation: Step 1: There is a type of water fern, doubling every day. If the first day to put in the pond 1 water fern, then after 12 days drowned the surface of the lake. Please use the table to record the number of water fern each day. If the first day to put into the pond 2 water ferns, how many in the next days will be equal? After a few days, water fern covers the surface of the lake. (Students work in groups). Table 1. The data sheet shows the relationship between number of duckweed and number of days The order of the day Number of water fern 1 1 2 1 2 3 2 4 4 3 1 8 5 4 2 16 6 5 3 32 7 6 4 64 8 7 5 128 9 8 6 256 10 9 7 512 11 10 8 1024 12 11 9 2048 13 12 10 4096 A C B D A B C E D E Experiental education in mathematics in order to develop linguistic intelligence at primary education 91 If the first day to drop into the lake 2 seedlings, we marked the first day for the number of plants is 2, from which to see the number of plants in the next day (in the number red). Step 2: Comment: With the above table, if the first day of raindrops is 4 (or 8,...), we will mark the first day corresponding to the number of duck trees. Step 3: Generalization comes from reflections in activity 2. From the number of days corresponding to the number of water fern for the first, as we will find after a few days, water fern will cover the surface of the lake. For example, if the first day putting 02 water ferns in the pond, then after 12 days the water fern will cover the surface. If the first day to drop into the pond 8 water fern (in the column of the order of the day with blue dot), then after 10 days will cover the surface of the pond. If the first day to put into the pond 6 water ferns, after 11 days drowned the surface of the pond (because 6 < 8 so we take 10 days + 1 day = 11 days). Step 4: Ask the same questions to other groups on the basis of the rules outlined above. - Experimental organization using graphs (Number of flowers) 23 21 18 15 12 9 6 3 0 Group 1 Group 2 Group3 (Group) Fig 4. Chart of flower numbers of class 4A in week 20. A diagram is a form of expressive language that is highly visualized in statistics, which reflects the relationships and comparative relations of the objects to be studied. In teaching mathematics in general schools and in elementary schools in particular, the statistical knowledge flow is gradually being considered and appreciated for its wide application in life and in science. Elementary students are introduced to the types of charts: picture charts, column charts and fan charts. These are charts that are used quite commonly in all areas of social life. For example, we can organize the experiential Chu Cam Tho and Nguyen Thuy Chung 92 activity using the column diagram for the student as follows: During the week, every student of her