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richardmullins44

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CELTA CHAPTERS 11-20 11. develop reading skills 12. develop presentation based on a text. 13. says that for a discussion, "there is no real outcome". But isn't the outcome (a) the fact that you have had the discussion (b) the fact that you found the discussion useful. 14. the book says that only interactive writing serves a communicative purpose. 15. brainstorm, collaborate on drafting. 16. leaners work in groups to devices questions using the pattern "what would you do if ..". 17. defining aims of a lesson. 18. approach to lesson design that prioritises communication and fluency. Tags: celta

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SOME POSTMODERN WRITING quoted by Julia Kristeva in Polylogue. "the unveiling is not reduction but passion. Logically the reader of the Comedy is Dante, in other words no one - he is also situated in 'love', and knowledge here is nothing but a metaphor of a much more radical experience: that of the word, where life, death, meaning and meaninglessness become inseparable. Love is meaning and meaninglessness, that which perhaps, allowing meaning to emerge from meaninglessness, makes the latter evident and readable... language emerges as the locus of totality, the path of infinity: who does not know his language slaves for idols, who sees his language sees his god". Philippe Sollers, "Dante and the Experience of Writing", 1965. Is this inspired by, or, indeed, the same thing, as the "abstract algebra" that has been widely promoted in university maths departments since the early 1960's? Tags: postmodern maths

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CELTA CHAPTER 10 LISTENING SKILLS. we can experiment with this, by playing back, listening to, and discussing, videos that were made in class. Tags: celta chapter error correction

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CELTA CHAPTER 9 error correction. this can be done, in the case of working a geometry problem, by showing the correct working from the point in the sequence where the working is wrong. From a functional point of view, from one person A's perspective, error could found in the behavour of another, B. Does A have the resources to vary its output in the aim of getting a better response from B. Another approach is for A to vary their evaluation of B. SUGGEST TRY OPTIONS: (1) handout at beginning of the lesson. Propose - handout this week, or next, in a block?? (2) hand out the assignment. Stress it (to myself) that itis my aim to get everyone to pass the assignment. However I should not say this to the students, as some will hear it as a false promise that is not kept. Tags: celta chapter error correction

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CELTA CHAPTER 8 practising new language. Why not use this as a prototype for a lesson maths or science also. (1) practice drills (2) written practice (3) produce larger stretches of language, with no single correct answer. (e.g. guessing the hardest question in a set of questions). activities where students can talk and listen the activity can be fun and playful knowing rules operating them under time pressure PLAN. at start of each class, a minimal test - a question to be solved. I can then supply the answer. building dialog from an item of language? e.g. generate dialog using a grammar, from an item of language. what is the grammar we need for the geometry class? CHECK MY YEAR 7 - 10 NOTES FROM 1990 for example questions. Tags: celta practising new language

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CELTA CHAPTER 7 presenting grammar (2) what did you enjoy doing in the past? find others with same interests. discuss different learning experiences. Tags: celta education

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CELTA CHAPTER 6 grammar. there are parallels between learning grammar and other skills. what are our future plans? grammar is a simplification. neighbouring grammars, not as good, would be needlessly complex. Perhaps having millions of words of text makes out a case for more complex grammar. Maybe if one has a vocabulary of 10K or 50K words they will very likely use complex grammar. So does learning vocabulary (e.g. by living) cause us to develop a more complex grammar? Or does having a complex grammar allow us to utilise a large vocabulary. Could the above questions be resolved? How? Tags: celta education

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CELTA CHAPTER 5 vocabulary. limited area: geometry. angles in a triangle add to 180 degrees. isosceles triangle. Tags: celta chapter vocabulary maths

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work junior high school Tags: junior high school

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CELTA CHAPTER 4 classroom management. small groups could write out their answer (or incomplete answer) to a geometry questions and then pass their sheet of paper to another group. The new group may write more on the sheet of paper. Why do we use the traditional classroom format? Is this because the rooms are too small to allow the number of students (up to 29 or so) to fit in a circle? We do not have cooking classes of 29. (The class I was recently had 15 or 16). Why do we imagine that 25 or 29 is suitable for a maths class? It will be impossible to continue the year 8 maths class, unless the problem of noise and disruption can be quickly resolved. I need to try something new - i cannot run YOUTUBE in class, but I could use a video camera and film presentations to be placed on youtube !!!! Prepare presentations for youtube!!! Tags: CELTA CHAPTER

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CELTA CHAPTER 3 30 minute lesson. give learners the opportunity to speak and to interact as far as possible. 1. ask students to talk in pairs and say what they like. 2. give reports 1 generated by 1, to class. could ask a student to choose an example for a small number of candidates. could ask a panel of students to choose some examples (e.g. from 2 pages of the book) which would then be used over the next 20 minutes. MAKE UP A WORKSHEET which is set out like an IQ test - we can make it easier to answer a question, by supplying part of the answer. We are doing geometry for another 2 weeks. Tags: celta chapter

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CELTA CHAPTER 2 how do you feel when your teacher corrects you? do you like maths? could we learn maths by watching youtube? do you like to learn by repetition? do you like to learn by interacting with others? do you want to be involved in making decisions about activities in class? Tags: celta chapter

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CELTA chapter 1 This is a meditation on ch 1, "who are the learners?". Since I am currently not teaching ESL, but teaching at a junior high school, I am trying to use my current work as a source of ideas to work with. Does youtube provide a source of ideas here? For example, let us take geometry as a topic - what is available on youtube. We could show a clip from youtube in class, and collect comments from each student. Currently, I do not have the capability to run youtube in class - is it possible to download clips from youtube and copy them to a DVD? Tags: CELTA chapter

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the star system - "only a few can do this" Jim McPherson, On the Nullity and Enclosure Genus of Wild Knots, American Mathematical Society, 1969. The fundamental group of the complement of a wild knot in a 3-sphere can be expressed as the colimit (direct limit) of a suitable family of groups and homomorphisms. To each group in the family we assign a Jacobian module - we prove that this assignment is functorial and preserves colimits. This is used to show that the nullity of the Alexander module of a knot with one wild point is bounded above by its enclosure genus. I have no idea what the above means. But after 40 years, it is no more unreadable to me than when I was studying maths. I am wondering if abstract algebra was promoted in 1960, by the same kind of people who are now promoting "performance indicators". I am wondering if maths was in fact an early adopter of postmodern notation. Why don't we demystify the writing by giving concrete examples? Is the hidden agenda to promote a version of maths that gets more difficult as you go. Why, in contrast, couldn't we promote a version of maths that never got any more difficult than junior high school geometry. Please understand that I am not questioning the value of McPherson's paper - I am only asking whether the same ideas can be presented in terms that are accessible to a high school graduate - or perhaps a junior high school student. Tags: maths postmodern education

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enneagram type 6: nitpicking I heard a talk on this last week. Maybe nitpicking is a strategy we can use to survive. Tags: enneagram type 6: nitpicking

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comment on "charter for australian education 2004" Education is not a matter of competition and choice, in which a few succeed by virtue of their capacity to compete with, and to beat, most of the others. Even if this is what drives the private sector, it certainly won't work for education. And there remains the all-important issue of underlying values. Education is a time and a place for nurturing, and of thinking. Applying the logic of competition to education is about as unproductive and destructive as it would be to set up a regime of competition and motivation based on the expectation of unequal outcomes amongst siblings within a family. Tags: comment on "charter for australian education 2004"

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postmodernism and maths Why is maths unreadable (for the non-specialist)? Does it have to be this way? I said in the post that it was not a question of English grammar. But I was wrong. The syntax is clear, but the semantics is not. Is it possible to give a simpler treatment by translating the English in some way? Or can we use formal methods, already developed for computer languages, to implement a model giving the semantics of the English we need. Is the unreadability of maths a result of the way it is presented? Could it be presented instead, as, say, an interactive discussion? Can we develop an automated tool which translates the text into something readable - for example a game with actors. This question emerges. A maths paper is written in a dialect of English. Is a maths paper solving, in a coded form, problems that we will need to solve in order to provide a (more complete) grammar of English. A (more complete) grammar of English will be able to derive the meaning of a particular text. Perhaps the tools we need to derive the meaning of text are being built as we speak, by people writing maths papers. From a paper by Joseph Goguen: "understanding natural language can ... be seen as solving equations in substitution systems". My take on this is that maths is hard to read because it is trying to deal with problems that are equivalent to studying the grammar of natural language. However, it is still possible that the presentation of maths can be greatly simplified, and that current presentations are difficult to read (1) because no one has found the time to improve them, or (2) society is currently organised so that a lot of knowledge is coded and therefore unavailable to the non-specialist Tags: postmodernism and maths

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speech interface Reading from a web page which suggested that developers develop a voice application in 12 "programmer hours", with a client sign-off of 30 minutes or more. In the sign-off, "Try to sit down with your client face-to-face and observe them going through all the nooks and crannies of your VoiceXML interface". Write down the client's answers to the following questions: * How useful do you think the voice interface that you just tried will be? * What extra information should we make available via voice? * What are the most crucial tasks that users would like to be able to accomplish from a standard phone using only touch tones and voice? I think the above is problematic. If you have not already been paid for your work, how will you get the client to sign off before you have completed the (never ending?) list of new things you have invited him to suggest. -------------- If the work can be done in "12 programmer hours", why not work on developing tools which can reduce this time so that the client can do the work themselves in 12 minutes rather than 12 hours. In the same way, it is possible to go to an internet kiosk and design one's own business cards or birthday invitation cards, in five minutes, without needing to call on "developers". Tags: speech interface

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chart of accounts chart of accounts is an "accounting concept" accounts are presented in a tree structure, so that an account can have 0 or more sub accounts, and each sub account can have zero or more sub accounts. The hierarchy may be limited to, say, 5 levels. However, it is probably just as easy, or easier, to write code which works for any number of levels. C.J. Date in his books on SQL, discussed using an SQL table to represent arbitrary tree structures. We could also have MULTIPLE charts of accounts. In traditional accounting, the cost of the accounting system itself did not need to be cost-justified. This can hardly be the case for computerised systems, where the cost of the system could be very high. The question arises: is the "chart of accounts" sufficiently general to be of use in other areas, such as theory of computing, and grammar of natural languages? In fact, tree structures are very widely used in theory of computing, and grammar. For example the VDL interpreter model for formal languages used trees. Tags: chart of accounts

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maths in high school what does maths offer us? suggest using the class as a platform for discussion. The teacher can introduce some examples to look at, every couple of weeks. However, students can propose alternatives. Let us assume there are 19 students in the class, and that classes go for 50 minutes, and that there are 4 classes a week. This would give the average person in the class (20 people) up to 10 minutes talking time per week). But the teacher will be more familiar with the material and hence tend to dominate all discussion. If we want students to be able to speak more, and speak withat least minimal fluency, we might try small group discussion as a way of developing their ideas before putting them to the class. IN FACT, the syllabus is cyclical, each year building on what has been done before - this means that some students will know the material well, and be able to solve problems as well as the teacher can (and perhaps faster than the teacher can). We want all students to be able to contribute, but it is ok to have a system which allows the more advanced students and the teacher, to talk more than the less advanced students. But equally, we could use socratic dialogue where we elicit ideas from the less advanced students, so that they do much of the talking. Whatever examples we do, we can adopt this approach: use a minimal example to illustrate a point. (elicit the method from a student, or give our own explanation). The audience can ask questions. Let other students do similar examples. The audience can ask questions. We then note what examples have been covered. As a record of this, we might get students to write up a sample answer in their book. WHEREVER POSSIBLE, relate the above to past exam paper. (The only reason for not doing this is if I don't have past exam papers, and haven't had time to get them from the school). Tags: maths in high school

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Why do maths in high school? There are too many maths books for us to read them all. This doesn't mean that we should read nothing. Even reading half a page per week of a maths book, and doing exercises, will give immense benefits. Everything in the maths syllabus could appear in other courses. For example, maths is part of oour cultural heritage, and could be learnt by learning the history of particular maths problems. Classical: Euclid, Archimedes. Pythagoras' theorem. A new approach in more modern times: Cardano found the formula to solve a cubic equation in about 1300. Descartes solved the quartic equation in about 1640. Fermat's last theorem remained unsolved for more than 300 years. Many people thought that perhaps it was true but could not be proved. Then it was proved in about 1993. "In about 1820, Galois proved that there was no general solution to the quintic equation". This is not quite correct. Reading Encyclopedia Britannica, someone used elliptic functions to give a solution to the quintic equation, and then "Fuchsian" functions were used to solutions to the general equation of order n. WIth computers (e.g. the pocket calculator contains a computer) we can more easily find answers that are not practical to solve by hand. (e.g. adding and multiplying millions of numbers). We don't need to know maths to operate a camera, but we could use maths in designing a camera. mp3 is a code - it stores pictures and sound using numbers. We don't need to know this code in order to use it. A virtual reality world on a computer screen - maths is used to calculate every point in the pictures we see on the screen. High school maths gives us a cultural background. It gives us tools to think about concepts in all areas, not just in a subject called "maths". What is a "canon" of mathematics that we need to know in high school? Don't try to do all the examples in the book. Instead, why not aim to look at say 20% of the examples in 20% of the book. This would mean we only need to look at 1/25 of the examples. By doing exercises, we learn the subject. Tags: Why do maths in high school?

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SUSPEND ACTIVITIES Work on PHP and STAGE2 is suspended. My immediate goal is to be ready for classes which I start to teach in two weeks. I might read some toastmaster notes for some ideas on how to conduct meetings. I hope the classes can consist of discussion between stakeholders, and nothing else. (e.g. any requirement to demonstrate a sample worked answer for a problem, can be handled as part of a meeting). Students can decide on what will be looked at in the next 2 weeks. Perhaps after 2 weeks, SOME people could give a little demonstration. Tags: stage2 PHP

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REPORTS A report is a document created using a database of information. The report could be the same as information that is presented on a computer screen. Assuming that the computer screen is too small to show the whole report at once, we could use scrolling or other means, to view parts of the report. The user may wish to generate a report by selecting values in certain fields. These fields could be in the report itself, or could be also appear as fields in a data entry window outside the report. A "macro" language appears to be suitable for the above. We could for example have a code #xyz which appears in the report. The system interprets this to prompt the system for the value of a field called "xyz" - this value could be obtained from a database, or possibly supplied by the user. Since HTML is a standard (or XML or whatever it is called today) we could arrange for our screen designs to be automatically translated to and from HTML. Perhaps we could define a MACHINE consisting of an arbitrary number of software processes, and use this machine to implement a particular screen or report as a network of connected subsystems. Perhaps what what we should be doing is talking about our needs for screens, and allowing this discussion to continue until usable methods emerge? ---------------------------- Suggest we implement a grammar processor as a theorem prover. Perhaps an approach to a general method for designing a user interface, is to use a theorem prover. Perhaps a theorem can be such as: If we type something new into field a, then within .1 s the system will react. Here I need to add more statements to define whatis meant by react. IS IT POSSIBLE that the problem of building a user interface is the same as the problem of discovering English grammar. Isn't a practical example of discovering English grammar involved in interpreting a phrase Or sentence. By interpreting the systems, we discover what the meaning is, i.e. isn't this close to "discovering the grammar"? We can make statements about a user interface, as a way of defining it Can we easily state a TG grammar, using a suitable theorem prover. For example, couldn't we set up the theorem prover to accept TG rules. Is it possible to define a theorem prover by using TG rules. By this I mean, can I write down a particular set of TG rules so this grammar operates as a theorem prover. How do we define a grammar so that it operates as a theorem prover. COMMENT. The grammar, if run, will tell us if an utterance is in the grammar or not. So this means it can prove theorems (at least theorems of the form Utterance 156 is in the grammar). A tool to create the trees we need. A tool to build screens with XML. AT last, my justification for using HTML and XML - it is a Pidgin (simplified) form of English. Build up a library of pre-used screens. How will we translate between "operating systems". Perhaps ultimately, we need a system that will run from spoken natural language - our system will need to be able to handle the grammar of (at least a fragment of) English. Tags: forms data entry hoare turing award emperor's clothes

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Hogg and Craig Q. 1.64 (c) A bowl contains 16 chips - 6 red, 7 white, 3 blue. If 4 chips are taken at random and without replacement, find the prob. that there is at least one chip of each colour. This could be solved by running simulation experiments and then inspecting the results. I am too bored to do this. But I also too bored to work out the problem manually. here is an attempt: The answer = P(2 red + 1 white + 1 blue) + P(1 red + 2 white + 1 blue) + P(1 red + 1 white + 2 blue) 6C2 * 7C1 * 3C1 + 6C1*7C2*3C1 + 6C1*7C1*3C2, all divided by 16C4 (This is the method explained on page 42) = 9/20 (I don't know if this is right - the book does not give an answer for this question). It would be more interesting to have a system where we could run experiments easily and observe the results. Any computer language would allow us to device and run experiments of this nature. But for ease of use, we would like to interact with the system using natural language. This could allow us to handle a much wider range of problems, but it could cost millions or even billions to set up such a system. Tags: mathematical statistics

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KAFKA on semantics To derive the semantics of English, do we need computation to work out things that might happen? "The meaning of life is that it ends" - this has been attributed to Kafka. Maybe we can expand this idea a bit. One way to define something is to say how it is used. From Kafka's definition, I take the idea that we can include in the meaning, how something might be used. This could include, for example, how something might be used as a metaphor. This suggests that for a more complete semantics, we need to be able to prove theorems (or otherwise do calculations, e.g. by simulation experiements) about what might happen in the world, including how a particular concept might be used. In fact, I think all this has been looked at before, e.g. by writers on possible world theory. Tags: KAFKA on semantics

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HOGG AND CRAIG q 1.60 this is a question about limits and a cumulative distribution fn. I can't work it out, and am too bored to try. It would be nice however, to derive the answer, automatically, from a database of definitions and theorems This a problem from a book on mathematical statistics. My approach to solving it would be to treat it as a question about the semantics of English, and to discuss the problem until the semantics were apparent. F(x) is an increasing function, and it can be discontinuous. We are asked to show that lim as h goes to 0 of F(b-h) exists. I can't see at present how we can be sure that lim as h goes to 0 of F(b-h) exists. Why will a limit exist if F(b) is chosen to be discontinous at b? At present I am stuck on this point. Tags: mathematical statistics

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HOGG AND CRAIG Q 1.19 The mathematical problem can be expressed in English. Do we have a method for deriving the answer from the "semantics" of the problem statement? Tags: introduction to mathematical statistics

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back to HOGG AND CRAIG Might suspend work on HSC examples. Hogg and Craig examples are probably difficult than the HSC examples - they will serve as good revision for the HSC work also. Looking at Ch1, there are 108 exercises. I have not completed about 14 of these, because I found them too hard. Having a computer means that we could obtain answers experimentally to some of the questions. However, I am probably too bored to attempt this. My current plan is to reread chapter 1, and then check to see if I can do some of the questions I could not do. 2.07.2008. I'm working in a high school from 14.7.2008, so I have no free time to continue looking at Hogg and Craig. Tags: Hogg and Craig introduction to mathematical statistics

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Waite's STAGE2 system Waite's book arrived in the mail, from Amazon. The copy was formerly in the Berkeley library. Maybe I will do more with this, maybe not. Does this work have much relevance today, or are we better off working with some other tool? - if so, which one - there are so many to choose from? STAGE2 has been used to install many compilers - but the details of this are not in Waite's book - in fact this work would have been done in most cases after the book was published. As Harvey Cohen pointed out later, a macroprocessor of sufficient power can be used to implement a compiler. Do we in fact need to define some further tools? is it too difficult to expect to write a compiler using STAGE2, without developing a lot of infrastructure? Can all this be done in STAGE2. Suggested case to work: implement a processor for a grammar (for English, or for a pidgin version of English). It is obviously a lot safer to promise to deliver a processor for a pidgin version of English (such as SQL?) than for full English. A slightly different idea is to implement a processor for a "transformational grammar". We don't then need to be concerned with a particular language such as English. Hopefully we can then copy a grammar someone has already written. What notation for TG will we use? Akmajian and Heny gave a notation that was documented in a book. Perhaps LISP also provides a suitable notation for defining a TG grammar. OF course, all this has been done already. Joyce Friedman and her team wrote a TG processor in 10K lines of PL/I in the 1960's. Since 1980's there are many books with grammar programs written in Prolog. Tags: Waite's STAGE2 system

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NSW 2006 HSC mathematics Q 1(d) Question 1(d). A triangle has two sides with length 5 and 9. The angle opposite the side length 9 is 33 degrees. What is the angle opposite the side with length 5? There is a formula which gives us 9 / sin 33 degrees = 5 / sin theta. i.e. sin theta /5 = sin 33 degrees / 9 i.e. theta = sin to the minus 1 of ( (5/9) * sin 33 degrees) We are not required to prove the formula. It turns out that the formula is easy to prove. If we drop a perpendicular from the point C, this length can be written as B sin a, but also as A sin b. hence we have B sin a = A sin b. i.e. A / (sin a) = B / (sin b). Obviously I did not work this out for myself. I must have been shown it. Looking at the problem again has re-activated this memory. Tags: NSW 2006 HSC mathematics

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