Phumy' teaching

Two main parts of the lesson. The first is called mental math, to practice computation needed for the new topic and second is to explain and practice about "multiplying fraction that include the squares, square roots, cube and cube roots."

In the first part, the teachers dictate the exercises (meaning verbally without symbolic form) for learners to write on their notebook under the title "mental maths"

There are 12 items and each item is about multiplying, adding, subtracting and dividing positive integers. Finding a square, a square root, a cube, a cube root of a number, adding and subtracting and multiplying decimal, adding, subtracting and multiplying fractions. Learners are asked to work on these for about 10 minutes.

The pattern of activity and interaction in this activity can be described below.

After learners wrote the items in their notebook and having chance to , the teacher asks all learners to answer number one and write it down on learner's white board (its size is about ...). Once the learner finish, he or she holds up the board to show the answer to the teacher. The teacher responded by saying "Yes", "good", "nice", "correct" or "beautiful" for the acceptable answer or saying "No" for unacceptable answer.

The difficulties faced by some learners are to write the items in symbolic form such as the square, the cube, the square root and the cube root. When learners are asked to write the square root of 9, a learner write 81=9. See p.6.

They also find it difficult to differentiate among them. For example, when learners are asked to write the cube root of 27, a learner write v27. In this phase, there is none explanation about the differences and the relationship between square and square root, also between cube and cube root. The only short explanation in relation to this is in the beginning of Part 2, by saying "square, having an exponent two" and "cube, having an exponent 3. See page 3.

Another clear issue for learner is to find 67 subtract 94. This is indicated by various answer offered by different learners such as 3, -33, 74, -30, -27, 73, (see page 4).
The teacher several times invite learners to show their answer in front of the class, but no students take this offer. Until a learner offer a correct answer, negative 27, and the teacher confirms, saying "that's the correct answer". In this event, the teacher doesn't explore learner's reasons of the correct and incorrect answer.

Despite many problems faced by learners, the teacher announces a new topic to be learned "Multiplying ....."

In this part, the teacher presents four examples and these require a fluency of dealing the items presented in Part 1.
The First example is multiplying fractions with all numerators and de numerators are exponent with the same bases.
The teacher instruct learners to expand all the exponents and telling about what to do. Quote "see p.11"
After that she invites learners to take turn to cancel one pair, until no more pair to cancel, and finally asking question:
"Are we left with any 2 on top? It means what do we have? Learners offer different answer: 4, 1, 1 over 4, which is the correct answer. Teacher that confirm the correct one.

The second example is similar with the first but the basis of the exponent are not the same. As a result, when it is expanded, no pairs to be cancelled. The teacher says, "We don't have pairs we can divide, so what do we do then?"... After expanding "you must multiply all of them"

Both examples are presenting "localized nature of the rule".
The rule of canceling cannot be applied in the second example. The rule of multiplying all the numbers in the numerators/denominator might be ineffective in another case. The teacher present her choices on procedure, without offering chance to get learners strategies or without reflecting on why is the certain ways works or doesn't works. Presenting particularly without acknowledging the generality or the principled ideas.

In the third examples, it contains square ..... In the numerator or denominator.
The teacher led learners to work on each.
See how learners responded.
The in fluency in the first part of the lesson seemed impact on the difficulties in working on this exercise.

Catatan:
Dari tulisan ini, saya telah menunjukkan localised. Bagaimana dengan explanation.

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3 August

Participants:
-------------
Sitti Maesuri, Jill Adler

Messages:
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Sitti Maesuri: I've just finished my interview Prof. Really hope to get this job.
Jill Adler: Me too. How did it go? Do you think u did ok? I saw tom at pme. He seemed v interested in having you. So I am hopeful.
Sitti Maesuri: It went well. I think I answered it well, mostly asking about what I have done in South Africa and Indonesia, what contributions I could bring. They often said My answers are great, excellent.:)
Sitti Maesuri: But at the end, Tom also said that they have some other candidates to interview. So need a longer time for final decision:(
Sitti Maesuri: Now, I should forget this and come back to my works, video analysis. I'll email you tomorrow before the meeting. Is it OK?
Jill Adler: Yes. We need to make time a little earlier. Can we do 4.00 SA time?
Sitti Maesuri: Ok
Jill Adler: Great thx. Speak then
Jill Adler: Just remembered, can u send the team all the papers on explanations
Sitti Maesuri: Ok. Last time I only sent to Moneoang and Craig. I will resend to all then. Tx
Jill Adler: Vasen, Ntsikin shadrack regina
Sitti Maesuri: Ok Prof
Sitti Maesuri: Prof, in our endnote, there's a group of explanation. So you can easily find them when you need them. I am still processing to send them to other. The internet con is quite slow now.
Jill Adler: I know. I have sent some. But it is not quick to find them in linked articles. So ithats why I wanted u to help :)
Sitti Maesuri: :)

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Pat teaching

There are 3 main episodes/activities/problems in this lesson.
The first problem is matching the word mono with an expression one term and an example: binomial with 2 terms and its example, trinomial with R terms with one example.

The opportunity for learners to see the link between the maths vocab (monomial, binomial, trinomial), an example, how many term in the first activity. So they can learn to associate, mono with one single term. It is not really about what makes 1 terms, 2 terms at this point. She does a little bit or partially about that. See .......

The main focus of the lesson is on like and unlike terms indicating by time spent in the second activity and the third is the extension of that, building up the pyramid, the opportunity to combine, to add the terms together in a pyramid and adding and combining in which require a recognition what is like terms and unlike terms.

Please check if there is an explanation, what make some thing like terms and unlike terms. They may do this before.

There are set of examples to introduce that. Learners get opportunity to name things with some examples. There is an interesting example to see why ........different. But most of the things are stated rather established. There is very little explanation around what things might mean?

It is interesting about how does she produce this activities, look like exploring things. BUt there is nothing really to explore. It is interesting her own interpretation about card activities are, in the sense the failure to understand the card activities.
It is interesting because we didn't focus on that, that the construction of the card is important. How to use the card to produce the activity is the most important thing. The card doesn't just arrive there.

It is really interesting, she tries to do this.

There are 3 main object. The way in which they way operated. There is not much goes wrong in them. But some of the key ideas, there are very little explanations. There are some. We need to look at that ......
....... She tried very hard.
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