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**learn2teach****Member**- Registered: 2010-08-28
- Posts: 11

Hi everyone,

I am new here. I know math, but have trouble teaching math at K-9 to K-12 level.

The problem is that my students on average do well on my tests, but do terribly on the tests given by other teachers or the state exams. Can anyone help me?

Thanks.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

Hi learn2teach;

Welcome to the forum. Would you consider posting one of your tests. Maybe it can be made more challenging.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**learn2teach****Member**- Registered: 2010-08-28
- Posts: 11

I make tests based on what the students already learned in class. If I give a little different, but I don't think more challenging, just the same problems with different wordings or numbers, they quickly give me bad looks. I am a little worried about my job.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

Hi;

Where are you teaching?

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**learn2teach****Member**- Registered: 2010-08-28
- Posts: 11

Hi bobbym,

Some of my colleagues may be in the forum, but people can search easily on the internet anyway, so I'd prefer not to disclose my school. In that way, people can tell their true thoughts without being worried about their jobs. In any event, I am in the state of New York, where deficits are huge, taxes are high, private new jobs are scarce, and school budgets are being cut.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

Hi learn2teach;

I respect your desire to remain hidden. Trust me none of your colleagues are members of this forum.

In any event, I am in the state of New York, where deficits are huge, taxes are high, private new jobs are scarce, and school budgets are being cut.

I know that state well, I was born, raised and uneducated there. I am from Brooklyn. I can only say it is a good place to be from, emphasis on the from. While I was there I saw the change in education that toppled the US from number 1 in math and science to around number 28 th. I saw teachers and curriculum turned ineffective. I had to fight daily to even attend classes.

I hope you do not lose your job. Did your first post indicate that you felt that your tests were not tough enough? Maybe I can help you beef them up?

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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**learn2teach****Member**- Registered: 2010-08-28
- Posts: 11

Do you mean that there are not many teachers in the forum? Well, the state is ranked one of the worst states to do business, so it is a good place to be from.

If you teach longer enough, you know what kinds of test questions your students can do well. You can easily make a test so the class average is around 90 and make another test the average is 80.

The problem is not that I don't know how to beef up the test, but if I beef up the tests a little, my students are not happy, their parents, who are powerful than I, are not happy. That's why I am worried about my job, because to them, I am not a good teacher.

My tests are easy, so everyone is happy and I become a good teacher and make a good living. The problem is, the students do not do well in the state tests.

So one question I want to ask everyone is: how do you teach students to solve one problem so that they can solve another one -- the same problem but with diferent numbers plugged in after a few weeks?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

Do you mean that there are not many teachers in the forum?

Usually teachers and I don't get along very well. I don't like the way they teach. So we tend to clash. Not on this forum, we have teachers here and they are good, in my opinion.

The problem is not that I don't know how to beef up the test, but if I beef up the tests a little, my students are not happy, their parents, who are powerful than I, are not happy. That's why I am worried about my job, because to them, I am not a good teacher.

You are faced with the toughest problem in the world. The choice between doing what is right or at least doing what you think is right and doing what pleases others. I can not really make that choice for you, just let me say I have made both decisions and both were painful. When you do what you think is right you risk termination from irate parents. That is painful. When you do what they want you to do, you will keep your job but find it difficult to look in the mirror.

Also, and this really sickens me, when you compromise in their favor they will not appreciate it. They will

criticize you and call you cowardly. Their parents will blame you for their future failures.

So one question I want to ask everyone is: how do you teach students to solve one problem so that they can solve another one -- the same problem but with diferent numbers plugged in after a few weeks?

The students I have seen are typically geared up to forget everything in a day or so. It is difficult to defeat todays programming that it is cool to be an idiot. One thing is certain, memorization will not get the job done. I think you must stress concepts and lots of problems. Try to impart your enthusiasm for the subject into your students. Explain to them that they need more preparation to do well in state tests. If they still insist on not working hard then your conscience is clear and so is your path, if so consider keeping your job, give them easy tests and do not worry about how they are going to do later.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,122

Hi learn2teach,

Welcome to the forum. But what a shame that you've landed up here because you're scared to do what is right.

I'm a teacher (actually retired, but I'm still proud to declare myself one!) in the UK. When I started out there was lots more freedom to educate ( and I choose that word deliberately) but then the government started to interfere and introduced tests that are, I think, like your state tests, a 'National Curriculum' and much more inspection. So I'm familiar with the pressures you're under.

I also have been torn between doing what I thought was important and what the state and parents thought was needed to 'pass exams' and 'get a good job'.

Like bobbym I think your students need to understand the concepts, not just memorise how to get the right answer. But it'll be tricky to find a way that keeps all happy.

Here's a suggestion. When you've taught a topic and set your questions, try to dream up a concept tester too. Sneak it in as a challenge and gives lots of praise to any who meet it, because the class need to see that it's what you, personally, value. If you get asked, by parents or your principal (is that the right term?) what you're up to, the answer to give is that you are encourging them to THINK and that's a valuable life skill. They cannot argue with that!

I'm not sure what topics you're doing but here's a little example that will show what I mean.

Let's say you've 'done' Pythagoras and they have learnt to square the sides, add or subtract, and square root the result. So they 'know' how to do Pythagoras. (?maybe?). So then the challenge:

**Here are some sides of triangles. Which ones have a right angle and why?**

**(a) 3, 7, 8 (b) 13, 5, 12 (c) 9, 40, 41 (d) 27, 33, 35 (e) 7, 21, 43.**

And spend some class time letting the students discuss their answers and justifying them.

Then throw in this supplementary question for the triangles that haven't got a right angle:

**Has this triangle got 3 acute angles or 2 acute and 1 obuse angle.**

And what will they make of (e) ? And if you've got time, **can anyone make a triangle with 2 obtuse angles?**

Many years ago I had to set an exam that was used for all the different ability groups in one year group. For one question I asked:

**What comes next ? 0.6, 0.7, 0.8, 0.9, .......**

The question turned out to be a 'perfect discriminator' for grade E. By that I mean that when the marks were given, added and grades awarded every student who got grade E or better got this question right and every student who got a lower grade got it wrong. The usual wrong answer was 0.10

Those students had got the other decimal questions right, but they clearly hadn't got the fundamental concept of what a decimal is. From then on, I have used that question as a concept tester for weaker students. And used their responses to gauge how much time needed to be given to getting the concept sorted out in their minds. Hopefully, their understanding improved.

If you want to try what I've suggested, post me a topic and I'll make a suggestion as to how you can challenge their understanding. (They might even start to like math!)

Good luck,

Bob

*Last edited by bob bundy (2010-08-28 22:30:41)*

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**learn2teach****Member**- Registered: 2010-08-28
- Posts: 11

Hi Bob,

Thanks for your detailed reply. You are in the Uranus Kingdom, we are on the Earth. There are a few top public high schools in each state may teach the Pythagoras the way you do. For most of us, no. First of all, you make more than one correct choice, which is much harder than only one correct choice question. Once you do that, the kids easily figure out your intention --- not helping them to pass the test by making the question harder than it is. They immediately hate you.

In my example, after I show the students how to solve

2x +3 = 7

In the test, I mistakenly put 7 = 2x + 3, some of them could not write anything. They said nobody taught them how to do it.

Second, many teachers cannot do the problem you gave themselves, not to mention to teach it. Teachers on our Earth planet are not really qualified to teach. You can see the links below:

http://www.guardian.co.uk/education/201 … aths-tests

http://www.boston.com/news/education/k_ … t_on_math/

The good news is: people are smart enough to survive any harsh reality. These are what our Earth people do:

Oregon will test 11th-graders using 10th-grade tests, so more students can do well.

http://www.oregonlive.com/education/ind … ost_6.html

"States have dumbed down their tests to make it appear that more students are passing".

http://beta.wnyc.org/articles/wnyc-news … ate-exams/

We are united to make our education look good.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

Hi learn2teach;

I've read your links. There is a lot there to think about. Let's look at some of it and what you have said.

not helping them to pass the test by making the question harder than it is. They immediately hate you.

I think you are forgetting what it means to be a kid. Kids by definition are not fit for society. Kids hate everybody that has authority over them, teachers, parents, police, all adults actually. I was like that too, and I turned out sort of okay. Okay bad example. Bet you were on the rebellious side too when you were there age.

2x +3 = 7 and 7 = 2x + 3. This may look pathetic when you know what to do but everyone has been in that spot at one time or another. As Doron Zeilberger says, "Humanity has always consisted of just 5 % pulling it along." So I guess to a Newton or a Gauss our thought patterns would appear just as pathetic. Adrian Oldknow relates how he taught a class of bright mathematics students where they were asked to solve (x - 1)^2 = 0. They all expanded it and used the quadratic formula.

Is that pathetic? No, just part of the learning process. I've done worse.

Your students don't hate you. Later in life they will think of you and actually admit you were right. Some will think of you for the rest of their life. Meantime do the best job you can do. Yes, even in bad surroundings you are still required to get the job done. In life, you and I are students and the adversity you are facing now is no different then 2x +3 = 7 and 7 = 2x + 3. It is the same problem humanity has faced since the beginning, it just is in a different form.

Maybe those articles are true. Maybe the quality of teachers and students has dropped. Maybe that has occurred in general for all mankind. One thing is for certain, teachers and students today have computers and the internet. This is a huge advantage over my time. They have forums like this one where they can ask a question. Some of your students, yes yours, will get through.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,122

Hi learn2teach,

Please, not Uranus. It is the same here, with the same pressures, the media jumping on any chance to bash teachers and kids hating math.

But, that's not a reason for giving up on trying. Your equation example, and bobbym's quadratic both show that the students were just trying to apply a 'parrot fashion' technique, not thinking about the problem and what it is actually asking. I've had that too.

eg. Kid: "And so the man earns £30 000 a week." Me: " Doesn't that seem a bit high for cleaning windows? Do you think there might be a decimal point in there somewhere?"

It sounded to me like your own tests were close to what you'd done in class ... and hence they could do them; ..... and then they get someone else's test, where the questions are a bit different, and their brains cease up. That's why I advocate trying to get them to think. You won't find it easy; I've had kids saying 'Just tell me what to do; I don't want to know why!' But I've got more determination than they have, so gradually I wear down their resistence.

Can you afford lollipops? That's to reward good thinking. "And today's lollipop for good thinking goes to Bill for ......."

Or little rubber stamps that print a happy message like "Skate boarding Joe (+picture) says well done" or "A+ from the Smart Cat". I've had tough, street-wise, 16 year olds begging for a stamp.

Or postcards that you send home to their parents, saying how great their kid was today.

If thinking is not what they're used to then it's an uphill battle. But that's what you're paid for isn't it?

Hope you find a way forward, best wishes,

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**learn2teach****Member**- Registered: 2010-08-28
- Posts: 11

Hi bobbym and Bob,

Thanks. bobbym's arguments are quite convincing. The root cause of 'parrot fashion' is people's laziness nature. People always want to achieve something with the least efforts. When you say "There is a lot there to think about", that must be true to many of us reading the postings. Yet only two of you responded, so teachers are lazy too.

Bob, when I say Uranus, you can take it as a compliment. Your teaching style is way above ours. On youtube, I have watched a lot of math videos from many teachers, who claim they are really good. Yet, none of the teachers I watched reach your level of pedagogical sophistication and soundness, with only one exception. Please take a look at the video to see if that teacher is doing the similar things as you do.

Here is the Youtube video at http://www.youtube.com/watch?v=FC2JtUFt-jE

*Last edited by learn2teach (2010-08-31 04:12:24)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

Hi;

The root cause of 'parrot fashion' is people's laziness nature. People always want to achieve something with the least efforts. When you say "There is a lot there to think about"

You are absolutely right. Generally I am lazy too. If I thought math were work I would be ducking it too. But I really like and enjoy math problems.

that must be true to many of us reading the postings. Yet only two of you responded, so teachers are lazy too.

Not necessarily true, the people here are phenomenally good at math and certainly not lazy.

I just have a lot more free time than most of them so I can respond more.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**learn2teach****Member**- Registered: 2010-08-28
- Posts: 11

Hi,

As I dig into the topics of our discussions, I found an article talking about exactly what we have discussed here. It discusses essentially the same problem, but at a higher level, of solving "a new different word problem using the knowledge of old problem when the two problems are involving the same mathematical equation." The way to do it, it says, is to "teach students to connect the surface structure (distance of travelling, the speed, and time travelled) with the deep structure (algebra equation)".

Therefore, it claims that contrary to decades of cognitive research, critical thinking can actually be taught. I do not quite understand this and how that kind of teaching works. Would anyone enlighten me on this?

The article can be found at http://www.ftlmath.com/research.html

Thanks a lot.

*Last edited by learn2teach (2010-09-01 02:19:52)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

Hi learn2teach;

My favorite thing. Partial credit!!!!!!!

After all, on the state tests in New York, students can get half-credit if they answer 15 cents instead of 18 cents by subtracting 57 cents from three quarters.

Nothing has done more to erode todays education then the horrible notion of partial credit. When a student gets into the real world, he is crippled. When you are working on a real problem and you do 5 pages of great math and on the last line say 75 - 57 = 15. You are not given any partial credit. The rocket still explodes even though you did 99.99% great work.

If your student gives me 15 cents I am going punch your student in the nose. Whamo!

I don't care that his school system congratulates him for being close.

Close is for hand grenades and spit fights.

Sorry, when I went to school and you said 75 - 57 = 15 you were marked wrong.

Now that didn't help me any that's true. I still make all kinds of mistakes.

At least my instructors were being honest with me marking it wrong.

Worse is telling the student 75 - 57 = 15 is partially correct.

And what nimrod came up with the figure of giving that answer 50%. Why not 47% or 38%?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**learn2teach****Member**- Registered: 2010-08-28
- Posts: 11

Q: Thomas buys a stkateboard that is 2 feet long. What is the length, in inches, of the skateboard?

Show your work.

A: 24 + 24 = 48. The anser is 48 inches.

NY State gives half of the credit.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

Only half, how chintzy! Out here we have people who cannot make correct change.

But I notice they always try to under pay me. Hmmm, I figure they are business majors.

http://www.nypost.com/p/news/local/how_ … kO5SoPYWRI

students got "partial credit" for wrong answers after failing to correctly add, subtract, multiply and divide.

Some got credit for no answer at all.

I don't like that "some," give everyone full credit for not even showing up. Heck, why can't I retest?

It is unfair and smacks of prejudice against older idiots. Alan Dershowitz where are you when we need you?

Setting up a division problem to find one-fifth of $400, but not solving the problem

-- and leaving the answer blank -- gets half-credit.

I want her/him as my loan officer. It is much fairer to let the borrower do the calculations.

Despite flubbing the answer, students can get 1 point on a 2-point problem

and 1 or 2 points on a 3-pointer.

Sounds like a basketball game.

holistic rubrics,

What the heck is that. I thought it was the new Dan Brown book.

Scorers joked about giving points to kids who wrote their names, brought a pencil or shared gum.

Heck, if they brought food for me, I would give them full credit!

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

Here are some of the comments about the material in the above posts.

http://www.nypost.com/p/news/local/how_ … kO5SoPYWRI

Centrist wrote:

Society needs people of all intelligence levels to staff the different jobs required. Not everyone can be a cardiac surgeon. These "tests" weed out the less intelligent so they can focus on working in the least desirable jobs requiring little or no knowledge.

And we walk around thinking that all the nazis are dead.

sdchanman wrote:

They got close and participated. That is how schools are run these days. Everyone is special and a winner. Ha Ha It is going to be fun taking their welfare check one day.

Well, we know the nazis are not all dead but the humanitarians are.

HealingMindN wrote:

"holistic rubrics," require that points be given if a kid's attempt at an answer reflects a "partial understanding" of the math concept, "addresses some element of the task correctly," or uses the "appropriate process" to arrive at a wrong solution... Since this same concept applies to the Gulf Oil Disaster, should we be giving BP partial credit?

Of course they should get partial credit, they had the right method, did they not? They were close to getting the oil up. I say throw them a couple of hundred billion. We can raise taxes to get the money.

Katharine Beals wrote:

Partial credit for wrong answers where work is shown, combined with partial credit for *correct* answers were work is *not* shown, combined with the low mathematical level (and and low ceiling) seen in these tests, collectively reverse who does well. The math buff who does problems automatically in his or her head and has no work to show ends up doing worse than his or her less capable classmates.

Katharine Beals

Author of "Raising a Left-Brain Child in a Right-Brain World"

Ahhh, left brain, right brain, isn't that special. Like the way she threw a plug in for her book. On sale, only $179.95 - 50.00 = 125.00 , get it now!

nostudme wrote:

The dumb educating the ignorant, BEAUTIFUL!

How about the beautiful educating the ignorant, while the dumb head to politics.

buzz wrote:

Hey, the USA elected a man as Vice-President who couldn't spell: "POTATO"!!!!!

Why does he need to spell potatto, wait I mean, patato? Why should we insist that he spell whatever that

word is correctly. He doesn't like them. I respect his right to proclaim his individuality and not like those things.

Probably someone who lives in a country that is supposed to be our ally. One question, how about your leaders?

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**learn2teach****Member**- Registered: 2010-08-28
- Posts: 11

Hi bobbym and Bob,

Did you want to modify the advices you gave me after you read the articles? Essentially, my original question can be stated in another way: how to teach 10th grade math to 5th grade students?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

Hi learn2teach;

The reality is that the system is in far worse shape than it has ever been, and this is just one of the multitude of problems facing our schools. Other issues in the waiting are kids passing classes when they have rarely showed up, schools using credit recovery (which is a total joke)to make sure students are getting their credits, teachers and administrators outright cheating on Regents scores and results, and the dangereous environment created when schools don't suspend or discipline students because it will negatively affect their report card grade.

Oregon students will be able to use spell check to pass state writing test.

Degrees in lap-dancing?

Those articles paint a dreary picture of your educational system. Those students cannot add, subtract multiply or divide at the the fourth grade level. They do not know how many inches are in a foot. I don't think you can push 10th grade material on students at that level. They are only as strong as their fundamentals. I think the system needs to go backwards and teach them the basics.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**learn2teach****Member**- Registered: 2010-08-28
- Posts: 11

Dear Katharine Beals,

Your left brain, right brain theory is intrigue. I was wondering if the visualized math tools can help half-Brain Children learn math. The best 3-D animated math tools I found is at

http://www.ftlmath.com

Look forward to your explainations. Thanks.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 81,718

Hi learn2teach;

Sorry, I copied her response from one of the pages you provided, she is not a member here so she will not see your question. Try going to that page and posting it there.

I have the result, but I do not yet know how to get it.

All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,122

hi learn2teach,

I think my response is unchanged. Afterall, it's what you do that's important; not what the rest of the profession do!

So, to provide a good education, I would recommend you teach them to think.

To help them to pass the tests, proceed as follows.

(i) Get as many old test papers as you can to use as practice tests.

(ii) Give them a test and mark it.

(iii) Based on the 'failed' questions and areas that you identify as causing a problem, make a hints sheet that helps them towards an answer without actually giving the answer.

(iv) Give the class a limited amount of time to do corrections using your hints. Circulate to encourage and give additional help if the hint isn't enough. TARGET: to improve their mark by 15%.

(v) Repeat the process with the next paper.

I have done this for years with SATs pupils (UK age 13/14) and GCSE students (UK age 15/16)

You will find examples of hints sheets on my website www.bundy.demon.co.uk/lessons

These are based on questions that you haven't seen of course but, it'll give you an idea what I mean. Mostly they are WORD documents so you are welcome to download any you like and extract bits that might be useful to you. The same goes for any others on the site. I did these over many years; some are lesson plans and refer to specific text books so will be less useful; but others are there to provide help on topics that might be useful to others.

Now I'm retired, I've got time to sort out these pages and take off the stuff that's not really much help to make room for new stuff by request so any feedback would be welcome.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**learn2teach****Member**- Registered: 2010-08-28
- Posts: 11

Hi,

BoB, what grade in the U.S. is equivalent to Year 10 in the U.K? You have this question:

(16) I buy a magazine for 56p.

I give the shopkeeper 80p.

How much change should I get?

similar to the particial credit one in the previous post.

bobbym, one thing you need to know is that in our our educational system, we are increasely spend more money on whereever you can find excuses. We have the best technologies in the classrooms. The still high tech flat creen big TVs are being replaced with more expensive Whiteboards. We bought Wii for high schools. We have the highest expenses per student in the world.

Of cause, schools always ask for higher pays for their teachers in order to find better teachers.

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