3.1. The implementation of CLIL in integrating Mathematics into English to primary school
3.1.2. Teachers‟ practices in CLIL class
The basic stages of four observed lessons are the following stages.
Stage 1: Warm-up. In this stage, teachers activate what students have already known about the topic to make associations of prior knowledge with new knowledge. Teachers ask the questions or let students listen to a song related to knowledge of Maths which they are going to learn in order to recall their previous knowledge.
Stage 2: Presentation. Teachers explain the knowledge of Maths in English as well as teaching new Maths vocabulary and related structures to help students master the knowledge.
Stage 3: Practice. This stage gives students opportunities for cooperative learning with their classmates to practice what they have learnt through a variety of activities.
Stage 4: Summary. Teachers help students revise vocabulary, structures and main content of the lessons.
To answer the question “How is CLIL program implemented in integrating Maths into English to primary school students”, the researcher has not focused on analyzing all stages in observed lessons, she has interpreted significant features in teaching process to gain the objective of contents and language learning including the use of the first language, the way of teaching new Maths vocabulary as well as grammar in context, Mathematic rules and the use of real-life examples in teaching process.
The use of mother tongue (L1)
The teachers started their lessons by activating prior knowledge of the students. The teachers want to find out what their learners already know about the topic in Vietnamese (L1) but students may have difficulties in explaining this knowledge in English (L2). When brainstorming ideas for new topic, students can use some Vietnamese and then teachers translate into English.
Through classroom observation, the researcher identifies that the use of the first language in CLIL may help students communicate more frequently.
In the lesson of Fraction divisions, T1 use Vietnamese to ask students about how to divide two fractions, then T1 guided students know how to read an expression of dividing two fractions and master the concept of reciprocal in English.T1 use L1 as an instrument to lead in new lesson so that all students know what they are going to learn.
Extract 1 from Fractions division lesson.
T1: Bây giờ chúng ta cùng điểm qua các phép toán phân số mà chúng ta đã học : + ; - ; x ;
T1: the first is……( T1 points these expressions ) Ss: addition; subtraction; multiplication
T1: Look at the expression: : = ……?
What‟s this? Who can guess? Come here and complete the expression?
Ss: ( go to the board and fill in the blank) : = x = T1: Bạn Tâm cho cả lớp biết con vừa làm phép toán gì?
Ss: Dạ thưa Cô, con làm phép toán chia 2 phân số ạ
T1: Và phép chia cũng chính là nội dung bài học hôm nay, chúng ta sẽ học về phép chia 2 phân số. Today, we learn about the division of fractions. Và khi cô muốn diễn đạt phép chia trên cô diễn đạt như sau: seven by three divided by three by five equals thirty- five by nine.
Và bây giờ cô muốn hỏi cả lớp, trong phép chia phân số, có 1 thuật ngữ rất đặc biệt, đó là gì ? Cô mời Phương Anh?
Ss: Dạ thưa cô, đó là phân số nghịch đảo ạ ?
T1: Và trong Tiếng Anh, phân số nghịch đảo được gọi là Reciprocal.
For example: four by five is reciprocal of five by four.
So, three is reciprocal of ……?
Ss: three is reciprocal of one by three.
The study shows that the teachers let students use L1 to encourage them talk about what they already know but they do not know how to express in L2.
Through classroom observation, the researcher shows that moving between Vietnamese and English, either mid-sentences or between sentences is used flexibly in CLIL class in order to allow all students to join in classroom interaction. Similarly, the use of L1 can help student feel more confident in the CLIL classroom.
Extract 2 from Ratios lesson
T1: How do you solve this problem?
Ss: um…uh ….con thưa cô con trả lời Tiếng Việt được không ạ?
T1: Ok.
S: Con tính tổng số phần là 7, sau đó con lấy tổng số học sinh chia cho tổng số phần , tìm ra được 1 phần con nhân với 3 thì ra số học sinh nam trong lớp.
T1: Thank you, Minh. Các con thấy bạn Minh làm đã đúng chưa. Vậy hôm nay cô sẽ hướng dẫn các con bài toán tìm 2 số khi biết tổng tỉ hoặc hiệu tỉ của hai số đó. Finding two unknown numbers when you know sum ratios or difference ratios.
In the lesson of percentage, T2 gave a new game named Hang man to check students‟ understanding about percentages. Because it was the first time, students have played Hang man game, T2 used L1 to explain the rules of game in order to make her instruction clearer and save time.
Extract 3 from Percentage lesson T2: Do you want to play game?
Ss: Yes…yes…
T2: I will divide the class into 2 teams: team A and team B. Have you ever played Hang Man game?
Ss: No…no
T2: Ở đây cô có 2 hình giá treo, mỗi đội sẽ chọn 1 số bất kỳ để trả lời một câu hỏi tương ứng. Mỗi câu trả lời đúng sẽ được 1 lần treo một bộ phận trên hình người của đội bạn, khi trò chơi kết thúc, đội nào bị treo ít bộ phận hơn sẽ giàng chiến thắng.
In short, the use of L1 is considered as a useful tool for teachers to examine prior knowledge of students, help students be more confidents and communicate more fluently in CLIL class. Also, L1 aids teachers simplify their instructions and save time.
Teaching new Maths vocabulary and grammar in context
After observing four classes, the researcher states that one of the most common way teachers use to teach new Maths vocabulary for primary school students is repetition. After giving new words, teachers asked students read words as whole class, groups, in pair and individual so that they could remember how to read and write new Maths vocabulary in the lesson.
Teacher T1 asked students take turn to read new words that helps all students have chance to read words and they are corrected their mistakes of pronunciation by teacher T1. Teachers also let students play games to review vocabularies they have learnt.
Extract 4 from Fraction division lesson T1: Now, whole class, look, listen and repeat.
Division; Reciprocal ; Divided by;
Ss: (whole class) repeat (three times) T1: take turn, repeat these words.
Ss: division, reciprocal, divided by………
The teacher T1 has taught students not only isolated words but also related structures to help students solve word problems. The structures: “The ratio of N1 to N2 is…, the number of N is …” were introduced at the beginning of the lesson and consolidated in teaching vocabulary part. The combination of teaching vocabulary and structures helps students know how to find the ratio of one value to the other and solve word problems involving ratios.
Extract 5 from Ratios lesson
T1: Students. Look, listen and repeat Ratio
The ratio of N1to N2 is….
The ratio of boys to girls is three over four The number of …is …
The number of girls is 30 girls
Ss: (listen and repeat) : ratio, the ratio of N1 to N2 is
T1: Open your notebook and write new words and structures.
Open your book and do exercises Page 13-14
Unlike teacher T1, teacher T2 has not taught new Maths vocabulary and structures at the presentation stage. She introduces new Maths vocabulary in the presentation stage, only when students have difficulties in solving word problems in the practice stage, T2 provides correlative structures for giving answers for word problems.
Extract 6 from Units of Mass lesson
T2: Open your notebook and write new words.
Tone : tấn Quintal: tạ
Kilogram: ki lô gam gram : gam
milligram : mi li gam
Ss: (write on their notebook) .
…….
T2: Open your book and do problem 2 and problem 3.
Ss: Dear teacher, I don‟t know how to write the answer for problem 2 and problem 3.
T2: Ok, with the question: “what is the mass of … or how heavy is it in …..
We use the following structure: The mass of something in tone/ quintal/
kilogram/ gram/ milligram is …
For example: The mass of car in tonne is 30 tonnes.
As the researcher see that teaching new Maths vocabulary and structure does not occur at the same stage, it depends on teacher‟s teaching styles and the objectives of the lesson so that teachers can combine the stages of lesson flexibly to achieve the aims of content and language learning.
Teaching Mathematics Rules
One of the objectives of integrating Maths into English program is that students can select and apply appropriate Maths rules to solve problems in English. However, it is not easy for students to memorize Mathematics rules in English. Through classroom observation, the researcher sees that teachers are excellent at teaching Mathematics rules by using word phrases instead of complete sentences.
Mathematics teachers often guide their students through three steps of dividing fractions. The first step is to turn the second fraction (the one you want to divide by) upside down, you have a reciprocal. The second step is to multiply the first fraction by that reciprocal. The last step is to simplify fraction. However, T1 did not instruct all the sentences which express the rule
of fractions division, she summarized three steps by three phrase verbs:
“leave me, change me, turn me over”. It is clear that students can memorize phrase verbs faster than complete sentences so the use of phrases instead of complete sentences is an effective strategy of teaching Maths rules in CLIL classroom.
Extract 7 from Fraction division lesson
T1: Để tóm lược lại 3 bước chia 2 phân số, Cô sẽ hướng dẫn lớp chúng mình 1 câu thần chú sẽ giúp các con hoàn thành được tất cả các phép chia phân số.
The key words are L, C , T So, L stands for …
Ss : love, like…
T1: love ?( laugh) …No.. LEAVE ME C stands for ….
Ss: Cook, Crack …
T1: ( laugh) … C stands for CHANGE ME And the last one , T sands for …what ? Ss : Ticktock …
T1: (laugh) TURN ME OVER.
Now, how to use LCT. I have two fractions : two by three divided by five by seven.
LEAVE ME means you don‟t change the first fraction CHANGE ME means change divided by into multiplied by
TURN ME OVER means change the second fraction into reciprocal And multiply , we get…..
Ss : fourteen by fifteen.
T1: very good. So, now listen, clap your hands and repeat: LEAVE ME, CHANGE ME, TURN ME OVER.
Ss: (clap their hands and repeat) LEAVE ME, CHANGE ME, TURN ME OVER.
Similarly, T1 combined the use of phrase verbs and diagram to find two unknown numbers when knowing the sum or the difference of two unknown numbers.
Extract 8 from Ratio and word problems lesson
T1: We have to find two unknown numbers when you know the sum or the difference of two numbers.
There are three steps:
Step 1: represent by boxes
Step 2: find the value of one box. We have thirty-five divided by seven equals five.
1 box = 35: 7 = 5 Step 3: Find the quantities.
Using real-life examples
Through classroom observation, real-life examples were usually used in CLIL classroom so that students not only master concepts of Maths but also understand the practical application of Mathematics in real life. The researcher shows that students were motivated to join in classroom activities when teachers used real-life examples.
To check students‟ understanding about fraction, T1 used three pens and divided for two students and ask about which fraction represents for the number of pens each student get from the teacher. Students responded to T1‟s question very quickly without any difficulties. It is clear that the use of real objects helps T1 simplify the concept of fraction to recall students‟
knowledge of Mathematic which students have learnt in the previous lesson.
Extract 9 from Fraction division lesson
T1: Now, I have some pens. Now, how many pens I have?
Ss: three pens.
T1: Yes, I have three pens. So, now I divide my pens for Minh, Tuan and this one, I keep for myself. So, firstly, I have three, how many parts do I have left?
Ss: one
T1: just one part, so the number of part do I have left?
Ss: one over three.
T1: How many parts do Minh and Tuan have?
Ss: they have two over three.
T1 also used real objects like candies or fruits to teach about the ratios in order to hold and attract students‟ attention to the lesson. First of all, teachers asked about the number of apples and oranges she had, and then she leaded in how to find the ratio. Through classroom, the researcher identifies that students master how to find the ratio of two things easily and they are motivated to join in learning activities when T1 use real objects in her lessons.
Extract 10 from Ratios lesson
T1: Look at apples and oranges on the table and answer my question: “How many apples and oranges are there?”
Ss: there are three apples and five oranges?
T1: How many times is the number of apples less than the number of oranges?
You can compare by division?
Ss: 3 divided by 5 equals 3 by 5
T1: Well done. Khi cô có 3 quả táo và 5 quả cam, Cô sẽ nói tỉ số giữa số táo và số cam là . Cô có thể viết ở dạng phân số hoặc cô viết là 3: 5. Vậy khi
cô biểu đạt tỉ số giữa số táo và số cam trên cô sẽ biểu đạt là : The ratio of apples to oranges is three over five or three by five.
Now, listen and repeat: The ratio of apples to oranges is three over five or three by five
Ss: (listen and repeat) The ratio of apples to oranges is three over five or three by five.
T1: Look at these candies, what is the ratio of red candies to green caddies?
Ss: the ratio of red candies to green caddies is three over two.
Or the ratio of red candies to green caddies is three by two.
To lead in the notion of percentages, T2 gave some pictures and says: “When you come to KFC store, you see the advertisement written 25% off. Or when you go shopping, you see the advertisement written 20%. Can you give more example of these notations?”. The notation of percentages is familiar with students because they can see everywhere such as advertisement boards on roads, restaurants, supermarket and so on. Therefore, it is not difficult for students to answer the T2‟s question and guess what they are going to learn in the lesson.
After students comprehend the concept of percentages, T2 continued with similar questions: “When your mother goes shopping, she wants to buy a dress which costs 1000000 VND, but the shop sales 20% off, how much does your mother have to pay if she buys the dress?” This context is very common in normal life, many students know the answer without calculation because they are often taken to the shop, supermarket with their mothers.
In brief, giving real-life examples in integrating Maths into English plays an important role to connect between the knowledge of Maths and real life so as to foster students participate in the lessons.
3.2. The opportunities and challenges of integrating Maths into English