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There is some evidence the teacher seems to test old knowledge. First of all, the students already knew how to read decimals (0.3 m) and fractions (2/5 m) in English! And also, I wonder how the students can read the title of lesson 1(Decimals and fractions) in English!
The ability to READ stuff you have never heard before is a good example of what we mean when we say that the word may be ready but the concept is not.
In our own class, I was very careful never to have my students do “presentations” or have them read aloud in any way. This is because I am aware of a large number of psychological studies that show that when people read aloud in a class they get only a VERY poor understanding of what they are saying.
Now, I very OCCASIONALLY have my students read data aloud in class. This is because I want my students to HEAR the data so we can discuss it. Even this doesn’t work very well!
Remember the Sound of Music. Maria says:
When you know the notes to sing
You can sing most anything!
It’s a beautiful song, but, as Brigitte points out in the movie, it doesn’t mean anything. The truth is that when we learn the notes, this is the BEGINNING of learning to sing, not the end. When I learn Hanggeul, this is only the BEGINNING of reading Korean, not the end. And, as Vygotsky says, when we learn the “carrier” of a concept, this is only the BEGINNING of concept formation and not the end.
The lesson is in the first Unit of 6th graders' text book! If the students had learned math in English before it can be possible. Or maybe they rehearsed the lesson.
Yes, good thinking. The lesson was certainly rehearsed. The curious thing is that although it was rehearsed the use of articles is really terrible. This strongly suggests to me that the children are not thinking, or at least not speaking, of the numbers 2/5 and .3 as actual INSTANCES of fractions and decimals; they are only thinking of the words that they read at the beginning of the lesson.
When the teacher asked the questions the students answered correctly. (Whose one is longer? Do you know the answer? -> 2/5). No, that’s not true. If you look at the data you will see only ONE student answered correctly. And there are many ways to come up with a correct answer that do not involve using the concepts (for example, comparing the ribbons visually).
May be someone say they just guessed. But some of the students already knew how to compare decimals and fractions! (They answered "To make fraction, make decimals!"). Then it means they already had the concept? ……
Careful! When you use rhetorical questions, make them into real questions:
Does this mean, then, that they already had the concept?
Did the children already, then, have the concept?
Can we say, then, that the children have the concept?
However, before you ask this question you might want to have a more careful look at the data. This isn’t a grammatical or comprehensible sentence in English. It’s not even a sentence. So it’s hard to say exactly what the child is saying.
But even if the child said it correctly (that is, even if the child had said “To compare the two numbers, make the fraction into a decimal” or “To compare the two numbers make the decimal into a fraction), that would not necessarily prove that the child knows HOW to do it.
Let’s remember what Vygotsky says that Tolstoy says: “The concept is not necessarily ready when the word is ready, but the word is almost always ready when the concept is ready”. It seems to me that the key word that needs to be ready when the concept is ready is “tenths”. But I don’t see that word in this data, do you?
If the students completely understood the kernel concept then it is not a lesson. It is only a test. But they did not.
Good point.
Although the students had some words (decimals, fractions etc.) they did not have complete concepts.
Right.
We can see the evidence they did not explain how to compare.
And they don’t in fact know how to say the correct sentence for what they want to do in English.
And there is some evidence the teacher formulates concepts. Look at the data below.
S1: To make fraction, oh! Make decimals!
T1: You mean 2/5, change 2/5 to decimals?
S2: (Nodding)
T2: Good idea. What else?
S3: Make 03 to fractions
At the first time none of the students could answer to the question. And the student’s answer is not clear (S1). Nobody mentioned about tenth (0.3=3/10, 2/5=4/10). These tell us the students have not mastered the concept yet. The teacher shows an example (T1) to make S1’s answer clear. And then another student (S3) could answer using teacher’s talk.
Good.
In this data we can see even if the word is ready the concept may not be ready. Vygotsky said
And so we see the most convincing proof of the probability and fruitfulness of our hypothesis, in the fact that the combined action of the experimental study and the theoretical hypothesis has produced results which are not only concordant but entirely identical. They have demonstrated that which constitutes the nucleus, fundamental axis and principal idea of all our work, namely that at the moment when a new word is acquired, the process of development of the corresponding concept does not end, but is only beginning. At the moment of the initial acquisition, the new word is not at the end, but at the start of its development. At that stage it is always an undeveloped word. The gradual internal development of its meaning also results in the maturing of the word itself. Tolstoy says that 'the word is almost always ready when the concept is ready'; whereas it was previously generally assumed that the concept is almost always ready when the word is ready. (1987: 241).
So, in conclusion, I will say like this.
On the one hand the teacher looks like testing but, on the other hand she teaches a new concept.
On the face of it, Jeongyi’s answer LOOKS LIKE equivocation, but if we look at it carefully we see that she says it LOOKS LIKE testing but it’s really new concept teaching.
I think we can’t really say. There are a number of other variables, for example the children, some of whom know this and some of whom don’t. There are also the numbers themselves: some are easy to convert (e.g. 2/5 and .3) and some are very difficult or even impossible (e.g. 1/3 or 3.14195…).
What we CAN do, though, is make a theoretical generalization. I think that IN GENERAL, new concepts are always built up on the foundations of old concepts; we cannot teach concepts directly, just by getting kids to repeat words. So IN GENERAL we need to organize the social environment in such a way that the children can reorganize their old knowledge as new concepts.
Now, in immersion teaching that can be particularly difficult! The “old knowledge” we are talking about is often native language word meaning, and that has to be “reorganized” into foreign language concepts. But the reorganization of native language word meanings into foreign language words offers a kind of COMPARISON, an understanding of the NATIVE LANGUAGE that isn’t really available any other way.
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