Memory

This year I was asked to assist the yr 11/12 students with life skills once a fortnight. The idea is to give the students some understanding of the skills required to succeed post school. Last week was a course on memory.

I started out by asking the students to listen to 15 two and three digit numbers. I then waited ten seconds and asked them to write down as many as they could remember. The frist time varied between 4 numbers and seven numbers.

We then talked about different ways of remembering things

a) chunking (eg it is easier to remember 9456 1426 than 9 4 5 6 1 4 2 6)
b) rhyming (During the depression I felt fine, back in old '29. or creating concentration cards)
c) acronym (NATO - North Atlantic Treaty Organisation)
d) pictorial (see below)
e) Look Cover Write Check
f) multi-modal delivery (Hearing, Writing, Reading)

The pictorial one was interesting as it struck a chord with many students. I drew a picture with a guy jumping off a waterfall, a Teddy bear, some stick figures lying on the ground, a guy jumping out of a three story window, an arrow pointing down. Then I asked students to complete the picture with other images of the great depression. They could see how interesting pictures could help them remember.

We then talked about how getting information into STM was not enough, STM information decays rapidly. For information to be recalled from long term memory reliably it has to be input many times to prevent decay. We discussed that we could apply the number test to learning.. If you hear 15 points in a class but don't attempt to remember them your brain will just forget them! If you spend some time trying to learn and recall the information you will have less decay of information and better recall. Revision of the same topic multiple times over multiple days is important. (I really like Saddler's miscellaneous exercises for this in mathematics!)

Over learning was also discussed. I often say to students we go through three phases when learning.

...duh?.............I get it!.............. I know it!
..............trying............practising

When students are in the 'duh?' phase they don't have a clue and nothing makes sense. If they try, they may enter the 'I get it!' phase where they can follow the teachers and do some work independently. To reach the 'I know it!' phase they have to practice and experience a range of examples and scenarios integrating their knowledge with other areas of discipline.

Overlearning a topic comes after this when knowing when to implement skill or knowledge occurs to the point of automaticity (instant recall without thinking). This can only happen when a student learns the skill and then actively seeks deep understanding of the topic, mastering the skill to the point where they will never forget through constant practice well after the 'I know it!' phase.

Interference was discussed and how Ipods and the like can be beneficial if used to block out background noise (eg with a song that is well loved but does not require active listening) as opposed to a new song that would "interfere" with the learning process.

I then asked the student to listen to the 15 numbers again. After the ten second wait they again wrote down the numbers.

I was astounded, 5 students had all 15 numbers correct. I've run this test a number of times to test transferral of information from working memory to short term memory(STM) but never with these results.

Some clever cookies here!

Here is another article on the topic.

Alternatives to chess club

Chess club has always been a good way to get students (typically boys) to think ahead before making a decision or committing to a particular path of investigation. Unfortunately it is seen as the forefront of nerddom. With some students nerdiness is seen as a badge of pride, but students today are very socially conscious and if we seek to capture students with ability in lower years we need alternatives to foster this skill.

There are a range of alternate games, not as elegant as Chess, but have similar outcomes. The ones that I have been investigating are Caracasonne, Ticket to Ride, Portabello market, BattleLore and Small World.

The last two BattleLore by FFG and Small World by DoW seem to have the most promise as they are infinitely replayable (like Chess) but have a different level of appeal. The main issue I am having is that they require a permanent home as a game tends to take longer than 45 mins.

BattleLore is a fantasy war game that takes about 30 mins to learn and up to two hours to play. It runs through different missions and lends itself well to a leader board type scenario. The downside is that it is only played by two players at a time. This is the main factor I rejected it as a possibility for the entry point game.

Small World is different in that it has up to 5 players and takes between 40 minutes and 80 minutes to complete a game. Its humorous and requires thinking ahead and is quick to learn (less than 5 minutes)

We have created a web server and found six desktop machines. We aim to create a mathematics lab for key senior school topics. One of the kids is formatting the boxes. Maybe we could even use my personal cals for AOE or RON to increase a session size to 10-15 students!

3A Mathematics Specialist Course

Well I sat down today and finished my worked solutions for the 3A MAS course for Saddler's text. The most difficult part seems to be the Vectors component as the other areas are quite simple in their delivery.

I suggest to students to get a hold of the OT Lee text and do extra examples of these vectors questions. A couple of examination preparation books are also available from Academic associates and Academic task force. I was lucky to have been given the West One 3A CD that also has some great material to supplement the standard text.

A problem that I have seen in the class is getting students to understand the nature of vectors, especially the idea of magnitude and components. I even have to think twice when wind problems are involved. I need to amend the programme and structure it more to vectors and away from logarithms.

My advice for all starting out teachers is to do the hard yards and complete any exercises set for students before asking students to complete them. This is especially true for mature age teachers with long gaps between completing high school maths and teaching it.

One useful thing I did was mark stop points against the work where I felt I'd had enough before starting again. Although I completed the text in a couple of days, it was in multiple sittings. I'll use these stop points as indicators where I can slow the programme down.

The TDC assignments to date have been well received by students. They have been able to complete the assignments and have been positive in their feedback. If the TDC can keep supplying quality assessment then that will reduce the assessment problem for teachers starting to teach yr 11/12 specialist courses. It is daunting for starting teachers to identify good assignments/investigations.

The MAT course on the other hand so far is a bit of a doddle given the work we did with students last year.

Fractions

Primary parents are always asking about ways of teaching fractions. The main thing I tell them is to spend time with their kids and work through their own thinking. One of their main concerns is that they do it differently to the teacher and don't want to get their child confused.

I relate to this as many times as teachers we have to think if we have broken it down far enough to promote thinking. Sometimes having a framework is handy with steps to teaching a concept or skill. Here's an ebook that does that (it's not perfect but it could help).

There are many other ebooks on mathematics found here

Four days to go...

The countdown is on to the next break.. four days to go.

The last week of term is a time of wind down, with students in upper school focusing on their ball on Thursday and those in year ten disappearing on holidays before the end of term.

I'll gather in the last of the test results from this term and celebrate getting through another week eight of term. For me, week eight is always a milestone, each week eight signals getting through the goals of a term and getting that much better at teaching.

One interesting experience last week was a student that despised my teaching method last year actually sitting for two hours with me conquering a topic - at her request. Hopefully she can keep this up - it would be wonderful if she could, the re-engagement of a student into education is something that should be celebrated, too often students are lost in year 10, on the verge of starting a run at university. It signalled what we all know deep down, that a student should never be given up on, you need to be on the lookout for ways and means to repair damaged rapports.

The last week was a good one, with many signs of students understanding what senior school is all about, smiles and students seeing success in their progress.

I'm really looking forward to the break.. and some baby time. She's growing up so fast. Now that we've figured out that the expressed bottle is causing the colic.. she's another baby (and a wee bit quieter and happier!)

We reached a few milestones with the blog too, 1100 visitors this year (the same amount as the whole of last year) and over 3300 pages read. Many thanks to those that have left words of encouragement.

:-)

Three steps forward...

There are times when I wonder, 'what have we been doing for the last two weeks?' My year tens are at this stage right now. We've been going through linear algebra for two weeks and it's clearly beyond a good dose of my students.

There are a number of issues:
a) They have weak self esteem and give up before trying
b) They have a low work ethic
c) Their algebra skills are weak-non existent (transposing to find c in y=mx+c is heartbreaking)
d) Their operations are weak (explaining gradient in terms of rise/run leads to all sorts of issues)
e) Their understanding of negative numbers is suspect

So I have two choices, teach them the topic and hope that the students get something from it to help them on their next iteration of learning or try and fill the gaps that 9 teachers before me have tried to fill with limited success.

Current thinking would say cater to individual differences and backtrack. I'm not sure that this is the right thing to do. By teaching the topic it gives the students an opportunity to 'get the gist' of what is being achieved (associate linear algebra with lines and equations, learn about gradient and slope, be able to find the y intercept and the like) and then hope that when they do 1B or 2A next year they can use this knowledge to properly participate in class.

I don't know.

Variables on the classpad

There has been some confusion about how to define variables on the classpad in my class. Here is what we have discovered.

If we use a variable found under the mth tab -> var on the soft keyboard (the variables that are italicised) it is treated as a normal pronumeral in algebraic equations (multiplication is assumed with adjacent pronumerals). The x,y,z on the keypad is also treated this way.

eg x = 10, y=20; therefore xy=200

The multiplication sign is automatically added.

If we name a variable using the abc tab in the soft keyboard(the variables that are not italicised) then we are naming a variable that has multiple letters.

eg xy =10; x & y are undefined.
m = rise ÷ run



Potential Gotcha!

We have to be careful not to confuse functions defined under the mth tab (eg. trig ratios) and variables that we have created when using NumSolve. One of my students entered this on their calculator.

Cosθ=adj÷hyp

It would return the fractional value adj÷hyp rather than the value for theta. This is because the student had defined a variable "Cosθ" by typing Cos via the soft keyboard rather than entering the function Cos via mth->trig->Cos.


Superscripts and Subscripts

Later on students will want to use subscripted characters when creating variable names. One example is the gradient formula.

m=(Y2-Y1)÷(X2-X1)

The subscripts are found in the soft keyboard under abc->math at the bottom of the screen. Superscripts are on the line above it. Only numbers at this stage (more will be possible as more fonts are released) can be superscripted or subscripted as far as I can see.



Here is a link to other CAS calculator posts.

Trigonometric equations and the CAS calculator

There are lots of ways of solving trigonometric equations on the Classpad but I have avoided using Trisolve as it takes away the thinking aspect of trigonometric equations. Instead I focussed on setting up equations in eActivities with the intent to complement them with the Geometry section later.

eActivities are a great place to store frequently used equations. In this instance, I wanted to keep all of the trigonometric and circle equations in one place ie sine, cosine & tan ratios, sine rule, cosine rule, sector, segment equations, circumference, area.

To do this I opened an eActivity from the main menu.

Then I started a new eActivity by going File -> New. Then I saved it by going File->Save. I called it Trig Formulae.

So then I inserted a Numsolve strip to hold my equation.

Once the strip was added I used the soft keyboard to name it the Sine ratio. Then I pressed solve to put the equation in.

Using the mth tab in the soft keyboard and then selecting the Trig option at the base of the soft keyboard I entered 'sin('. Directly below the mth tab, the theta button can be found and then closed the bracket. Don't type the word 's' 'i' 'n' using the soft keyboard as it won't work - it will treat it as s x i x n.

Then using the 2D tab, I created a fraction and using the var option entered o ÷ h. I hit exe, then closed the equation using the x at the top left hand corner of the window.

I then tried it out using the example opp=7, hyp=14, theta = ? I left theta blank, made sure the angle was selected (with the dot next to it coloured in) and pressed solve in the toolbar. Viola, theta = 30°. If you get some weird answers check that the calculator is set in degrees mode. If the answer is still weird, reset the calculator and it seems to work.

Update (25/3/09): After using this with the class for a few days (especially with radians) I noticed a few strange results where the calculator would return unexpected answers (eg for the above example -330°). To fix this, set the Lower bound to 0 and the upper bound to 180 (for degrees) or pi/3.14159 (for radians) and the results will appear as expected.

I then set about putting in the cosine ratio.

It's a great tool for things like the cosine rule where students find it hard to transpose equations and forget negative signs or for circle, segment and sector equations that are commonly forgotten.

Here is a link to other CAS calculator posts.

Escalating issues with students.

Some teachers are really good at identifying a potential behaviour issue with a student and bopping it on the head. Occassionally a student just gets a bee in their bonnet and won't let it go. What starts as a shoosh directed at a student when I start my lesson, ends with the student on in-school suspension for multiple misdemeaners during the lesson and ongoing issues for months thereafter.

There's a knack for diffusing students and when I'm concentrating usually I can pick the student and prevent them from doing stupid things. My favourite list of things to prevent these events is as follows:

Sleep well: If I'm tired I'm bound to miss the signs of a student ready to blow and probably respond with less patience than I normally would.
Maintain firm class rules: Respect, responsibility, doing your best.
Look for storm clouds: Student body language on entering the room can give an indication to their mood.
Use of humour: Sometimes a simple laugh can turn a student around.
Check their understanding of the topic: If a student feels hopeless they may compensate with poor behaviour to hide the issue.
Low key responses: Have a range of responses that don't draw attention to the student (eg. hand signals, proximity, diversion, interacting with nearby students, sending on an errand.)
Backup responses: Moving students, talking to them out of class, preventing students sitting near disruptive influences, extra homework, class detention.

If all these fail (and the student continues to disrupt the class) or a critical incident occurs (abuse of teacher/student, uncontrollable anger, damage to school equipment, visibly upset/crying) then upline referral is required - probably resulting in suspension. This of course causes further issues (my estimate) is that it takes 4 days to catch up for every day missed in senior school. The quality of the upline support will dictate how easy it is to re-introduce the student to class and resolve the issue.

When suspension occurs I see this as my failure - albeit sometimes I wish I knew some of the 'confidential' information within the school so that I could modify my responses to errant behaviour accordingly.

Absolute value and the 3A MAT course

Ok. Absolute value - easy enough, to take the absolute value of a number, make it positive if it wasn't already. easy peasy...

... until you start to look at IyI=IxI and ask students to graph it..

... then ask them to find the intersection of Ix-3I=I2x+4I algebraically
... then ask them to find Ix-3I<=I2x+4I

Students really bogged down when they reached inequalities. The approach I used was similar to that by Sadler in his 3A book for MAS. The problem was that I really wasn't sure they understood what they were doing.. they could follow the algorithm but understanding was eluding them.

I started by looking at absolute numbers and explained models for solving using number lines, graphing and algebraically. Then I used a composite approach to assist students visualise what it was they were doing with problems like:

Ix-3I<=I2x+4I

I started by displaying the graph on the board using the overhead gadget for the Classpad.

I entered Graph&Tab from the menu workpane (using the menu icon at the base of the workpane).

I selected Graph&Tab and entered Ix-3I for y1 and I2x+4I for y2. For some reason the graph workpane doesn't allow you to use the 2d tab absolute value option - so use the abs() function under the cat tab in the soft keyboard. When you hit enter it will restore the absolute value notation.

Make sure both y1 and y2 are ticked (if they are not place the cursor on the line using your stylus and hit exe). Hit the graph button in the toolbar (the first icon with the top formula pane selected). The following graph should appear:

We then looked at the original inequality again and I asked what did it really mean?

Ix-3I<=I2x+4I

One way of thinking about it was, "when is the graph y=Ix-3I less than or equal to the graph of y=I2x+4I?"

We looked at the graph and found that the part marked red on the line y=Ix-3I satisfied the inequality.

Using the intersect function under analysis in the menu bar we know that the two lines intersect at -1/3 and -7 therefore the interval is x<=-7, x>=-1/3.

We had discussed that we could also do this algebraically by using the property if IxI=IyI then x=y or x=-y to find the points of intersection.

Eg.

Ix-3I<=I2x+4I

x-3 = 2x+4

-x = 7

x=-7

x-3 = -(2x+4)

x-3=-2x-4

3x=-1

x=-1/3

I then asked students to draw a number line with the intervals marked and substitute the values back into the original inequality. We numbered the three intervals. The first interval represented x<=-7, the second -7<=x<=-1/3 and the last x>=-1/3.

We then selected a value within each of the intervals and substituted them into the inequality. If they were true then this indicated values of x that satisfied the inequality.

Ix-3I<=I2x+4I

Interval 1 (x=-8)

I-8-3I<=I2(-8)+4I

I-11I<=I-12I

11<=-12 (true)

Therefore x<=-7 is a valid interval.

Interval 2 (x=-5)

I-5-3I<=I2(-5)+4I

I-8I<=I-6I

8<=-6 (false)

Therefore -7<=x<=-1/3 is not a valid interval.

Interval 3 (x=0)
I-0-3I<=I2(-0)+4I

I-3I<=I6I

3<=6 (true)

Therefore x>=-1/3 is a valid interval.

The inequality Ix-3I<=I2x+4I is valid over x<=-7, x>=-1/3

Drawing students attention from the graph and back to the algebraic representation released the tension in the room, the screwed up faces and suddenly lights went back on.

Thank goodness!

Here is a link to other CAS calculator posts.

Eureka.. one problem solved!

Teaching students to solve equations with the balancing method can be difficult as many different skills are required. Collecting like terms, fractions, multiplying pronumerals, dealing with coefficients and the like. When adding all the complexities together students can really struggle.

Surfing around yesterday I found the following link using a classpad calculator to assist students check their understanding of how to use the balancing method. It has worked fabulously well and yr10 students that typically hate algebra (and maths) are all smiles...

Here's the sequence of lessons up to this point (first week of term one)..

1. review of algebraic terminology
2. review of collecting like terms
3. review of multiplying algebraic terms
4. solving simple equations

Students were shown x + 5 =7 and asked what was a possible value for x. They responded 2 and we discussed how the observation method is often a good method for solving equations. We discussed how this was good for simple cases but with more complicated examples it became too difficult.

I then introduced the balancing method saying we could get to the same result by making x the subject of the equation by examining the LHS and thinking what operation could we do to isolate the x value.

A student suggested that we subtract 5 and I said great.

Then I said to students that the crux of the balancing method was that anything we did on the LHS of the equation has to be done to the RHS. I wrote on the board

x + 5 = 7
x + 5 -5 = 7 - 5
x = 2

and asked how did that compare with our original answer. We then did the following example:

5x + 5 = 20

A student offered the following step:
5x + 5 - 5 = 20 -5
5x = 15

Typically students get stuck at this stage as 5÷5 =1 is not an intuitive step. For once I told them that I would divide by five and showed them how it works.

5x ÷ 5 = 15 ÷ 5 (please excuse the division symbol, I actually used fractions but it is too hard in html)

x = 3

And here's the real magic.. I then took out CAS calculators borrowed from the senior school and they did a number of examples with them. For the following example:

2x - 2 = 15

Their brains started making connections and they actually were using the calculators to check that their logic was correct rather than to give them just answers.

You can see from the example that each step in the calculator mimics the steps to answer the problem on paper. It is easy to see how after each operation (+2, ÷2) x becomes the subject of the equation and ultimately becomes solved with x=8.5









Common errors become obvious earlier. Students decide what operation needs to be done and see what that operation would do. Take this common case:

The student has multiplied by 2 before they have subtracted. They can instantly see their mistake (the LHS of the equation looks more complex rather than simpler so the student starts again. The second attempt subtracting 5 gets them closer to making x the subject of the equation.

For many of us, this is how we learnt to transpose equations - a little trial and error. Lots of practice. Lots of heartache. Lots of looking at the back of the book.






The students found using the calculator fun... and the calculator only gave them guidance - not just solving the answer. It was a mix between the old inverse operations method (change the sign/change the sign that causes all sorts of difficulties when fractional terms/multiple terms are introduced) and the balancing method. To be honest, I've never found the 'scales' explanation that typically accompanies the balancing method useful - but the CAS introduction way I think may have real promise.

The other great thing is that they were recording their answers really well on paper.

For the above example I would see (with equals signs aligned):

2x-2=15
2x-2+2=15+2
2x=17
2x÷2=17÷2
x=8.5

To see mid tier students lay out work like this rather than
1) 8.5
was fantastic.

Here is a link to other CAS calculator posts.

Maths backgrounds for worksheets and Powerpoint

As an upper school teacher, we sometimes ignore the requirements of appearance of our materials and focus on presenting quality content. This is evident in the material available on the web.

When I get a moment I like to (in the words of my wife) make things pretty and spend the time to ensure there is a background on worksheets, a powerpoint slide with a coloured background and the like.

One site I like to use is http://www.brainybetty.com/. There are some great free backgrounds there for Powerpoint. I really like the orange one and have used it a lot.

Here is a background I made for a recent certificate for the summer school using the MSWord 2003 equation editor.

Have no fear the image is bigger. Just click on it, right click the image and save it. Here's a simple way to make it a watermark in Word 2003.

1. Open up a Word document.
2. Go Format->Background->Printed Watermark
3. Select the Picture Watermark option
4. Click Select Picture
5. Find where the background is saved and select it
6. Change the scale to 200% (or to whatever works for your image unless you want a tiled image)
7. Ensure the washout checkbox is selected
8. Click apply

Voila. A professional background for your MSWord 2003 document.

Sometimes you will find the washout selection too light for your printer. In that case you need to insert the picture, send it to behind the text and increase the brightness of the picture to a printable level that doesn't interfere with the readability of the text. This is the way I usually do it as my printer is temperamental but it makes it a bit of a cow to work with the page.

Here's how it turned out.

Getting fired up about the start of term.

Yes, another PD session today . The time left for planning was great and I am feeling ready to start the new term. The work done at the end of last term has made this easier than expected thus far. Our TIC provided input on the course and directed worthwhile changes. Programmes and daily plans are written for the three year 10 streams my yr 11 1B/C classes, 3A/B MAT, 3A/B MAS and yr 12 Modelling with Mathematics. Yay!

We're all pretty keen to get started and even the most cynical of us are looking forward to what the year can bring without last year's threats of industrial action. Let's get on with the job of teaching.

The PD material was of dubious standard with a part time presenter condensing a week long course into 1.5 hrs to a group of 60 teachers from different learning areas. The topic of course was literacy, which meant another rehash of primary strategies, collaborative learning and.. you guessed it.. graphical organisers.

We were asked 'how we knew that students were engaged?' with a range of answers from 'if a student is looking at you (culturally inappropriate in many cases)' to 'actively answering questions (disposition/culturally inappropriate)'. No answer was given by the presenter (I think her answer was discredited before she had a chance to supply it). Doodling notes on the page was deemed a valid method of note taking. We again were informed that the 2 squillion genre's were a necessary part of learning and teaching.. a focus on breadth of learning over depth again. The change in emphasis from version 1 to version 2 of First Steps is a shame as the original First steps had focus and is still a valuable teaching tool as it gave students a foundation to learn other genres. Despite being a Maths teacher I own copies of both the first and second editions of First Steps.

The presenter put us in a lineup and instructed us to stand from engaged to not engaged. She then asked us 'Did we feel engaged by PD opportunities? and to position ourselves accordingly in the lineup. I stayed where I was which was on the disengaged side. As I had been critical of earlier answers (and was sitting under the presenters nose) she asked me why I felt disengaged from PD sessions. I said that I rarely encountered worthwhile PD (to which I embarassingly received a clap from staff). Yep.. that's me.. survival skills of a bunny on a freeway.

More seriously I would add to that PD's are rarely well prepared as they inadequately take into account prior learning (no more bloody graphical organisers!), show little awareness of the requirements of staff (we had staff from every learning area), have no follow up or action points (this may be more of a management issue), take too long to tell too little and generally are just not good value for money. She rightly guessed I was a maths teacher as I was critically evaluating the value of PD sessions.

On just the value for money point.. 1.5hrs x 60 people at an average of $70,000 per year conservatively cost the school $3,000 in lost wages. That's a projector installed for each of the teachers in Maths which would benefit 150 students every year or a new set of text books for a classroom. It has an opportunity cost of our students having a more cohesive programme that could have been developed. I would be interested to know how many graphic organisers are actually used in classes or how many teachers use the text supplied.

I don't accept that we should be grateful for any PD given and accept mediocre presentations. If we waste 90 man hours of training time, it is a criminal waste. We cannot stay professionals and not continue to learn our craft. Without good PD opportunities we cannot grow at our optimum rate.

I took away one point from the PD, an interesting example on the use of questions to promote discussion on a subject. It was ok but explicit teaching would have imparted the same knowledge (drink water if in the desert) in 1 minute rather than through a round of discussion. I can see how it could be useful and is another tool to use in the kit bag. It also explains why a number of my alternate lessons work..

The materials presented by the principal were great in that they allowed teachers a chance to vent concerns in a healthy environment. In another session it was interesting to hear that 360° reviews were contemplated and rejected (where teachers review performance of management and vice-versa). It's difficult to see the benefit of inexperienced management staff reviewing inexperienced staff. It's all a bit silly really when experienced staff exist to perform the teaching review within the school.

It was raised that we needed to communicate better with like schools and embrace some of their successful strategies. This is a great idea - unfortunately one rarely possible. It would be good to see long term strategies that lead to teachers on loan to adjacent schools for terms, semesters or for the year, further developing our abilities and bringing back learning to our schools.

It was nice to hear that many teachers thought our mathematics summer school was a worthwhile first attempt. It will be interesting to hear the anonymized results when they are handed to admin by students on the first day back. These trailblazing year 11 3A MAS and MAT students are the bleeding edge of our new maths students and for them to succeed would be great for them and the school.

Only time will tell.

Classpad 330 and Normal Distribution

Normal distribution problems can be done quite simply on the Classpad 330, but the method seems a little weird.. perhaps I haven't found a menu yet, or completed an update.. but here's how I did it for the following problem.

"A packet of mince contains 500g of mince. Suppose the actual weight (x) of
these packets is normally distributed with a mean of 512 grams and a standard
deviation of 8 grams. What is the probability of picking a packet between 504
and 520g?"

Firstly open the main window and add the list editor from the toolbar.

Opening the list editor should make the Calc menu appear in the menubar at the top of the window.

Select Calc->Distribution. This will make a popup appear with some options

The Type dropdown needs to say Distribution.

The second dropdown should say Normal CD. After that is selected tap Next. A new dialog box will appear.

For our problem the lower bound is 504, the upper bound is 520, the standard deviation is 8 and the mean is 512. Tap Next when this has been entered. The answer will appear with a probability of 0.683

Tap the graph icon in the toolbar to view the distribution.

Viola!

Here is a link to other CAS calculator posts.

Keeping it real

I suppose it's not the catch phrase it once was, but students like you keeping it real. When you speak to them they like to know your opinion, what you think and what you are doing outside of school. Much of the time we are frozen by protocol and have to keep professional distance but sometimes it is a good idea to let them see some of your opinion.

Case in point, an A student taking a traineeship - no apparent reason for doing so other than she "hates" school. She's one of the few that actually smile now and again. Rather than telling her - look you're on the hump, hang in there, the PC response is "you need to do what you think is best" or "evaluate your options and see where it takes you". BS, stay in school or you'll join the 10% without an education you bloody dill!

After all it's sooo much better to tell a kid they're doing well, feed them success and then let them find out that they are unable to pursue their chosen occupation because they've been a lazy blob. Teenagers are moody, emotional, need to fire up from time to time, will do at little as possible to get by, have little vision of the future past 5 minutes from now but they're also fairly resilient and need a dose of failure from time to time to ensure that they get back on the right track.

Keeping it real is about helping them see the bigger picture and find school an enabling influence on their lives rather than a drag. Our summer school for high ability yr 10 maths students entering year 11 is about connecting students with the real world. We improve their minds, feed them motivating experiences and they see that public and private companies are willing to support our efforts through a certificate where the school logo is not front and centre. Many thanks to the companies that are supporting our little event. More importantly - there is no cash prize for attending, no sponsorship money, no reward other than self improvement. What a fabulous lesson for these kids to learn and appreciate at 15 years old.

Lost hope

Two years ago I spoke to one of my colleagues whilst I was teaching at another school. He spoke of the amazing progress his students were making. It was a deciding factor in moving to his school later that year.

Moving to a government school was something that I had contemplated but after a woeful experience trying to enter the system, I had not anticipated trying again until I had more experience to offer. Once I was given an opportunity and a taste of it, I didn't look back.

The feeling that I have received from others in the government system though (whilst on PD or in the community) is that of lost hope. If I hear one more teacher saying "we haven't the clientele to do it" or "we are going to do the course through SIDE (via remote access) because we lack numbers" I'll jam a pick axe under their fingernails.

Can I make something very clear - in some schools, teachers have had to work very hard to get students to a high standard. Students in low socio-economic areas typically have the ability but lack environmental support. Students are nurtured into performing well above their weight level. I suppose, coming through a low socio-economic system I remember what teachers did for me, without some of them taking a personal interest I would have slipped through the cracks.

In high performing schools (the "leafy greens"), teachers have to work very hard to get students to perform to a high level - public or private. If they don't succeed, parents complain and they get turfed out or nerfed to a lesser course. If we get complacent in challenging students within public schools and let excuses get in the way of trying and not do at least as much as private schools... then these kids have little hope. That means the before/after school classes, the extension work, the calls home, extra homework, the lecture for poor performance, doing corrections, study skills, ensuring test preparation is done and fostering of an academic environment is not optional in our schools. Who pays for the extra work is a different issue. I leave that to academics, advocates and DET.

Parity between public and private needs to be found or public schooling will become more of a sub-par alternative. I don't know many teachers that would send their child to a government school (behaviour not academic standards is the most common reason given) and that is a sad inditement on the system. We need to recognise this as an indicator and institute change.

I hope we have achieved something special this year in our academic programme and in 2009 we hope to be able to demonstrate our model as an example of what can be done. Something needed to be done to rescue our TEE programme (DET teachers are getting worn down by the fight). We could have become another school without a TEE programme.

Relief Classes

In the last weeks of term, senior school teachers tend to do a lot of relief. I don't actually mind doing a little relief as it is a chance to meet students in the lower school.

What gets my goat is when I am asked to come down to senior school and I'm not needed. If I am needed to teach, great, give me a class and a lesson and away I will go.

Ask me to come down when all you want me to do is be present in the room while a teacher runs a general knowledge quiz and watch my blood boil. We had a team leader, team assistant and two teachers in the room and a quiz running with about sixty kids. If you can't run that without extra help split them into three classes of twenty and do it. Put the team assistant with the most difficult class.

I have work to do people!

You are saying to the senior school teacher, "my need for behaviour management assistance is more precious than your preparation time for 2009". I know the general belief is that because senior school teachers have fewer classes in term 4 then they should be available to assist in lower school tasks and I agree with this, but the best use of their time is not as babysitters, use their expertise to improve curriculum.

Don't think because you see them more often in the staff room it's because they have nothing to do - they may just be getting a breather after working on the course for a couple of hours. Creating new material in preparation for new year 12 courses is difficult.

Don't underestimate their need to prepare for the following year - the pressure is on for performance as the public image of the school rides of school league tables (for better or worse). Today I was writing outlines for 2009 3A courses and preparing materials for the summer school we are running for year 11 level 3 students. This would have been a far better use of my time.

Grrr...

Last two weeks of school

When I was a lad, the last day of school was a day for cleaning the place up. After 12 pm we started cleaning and after cleaning was complete we had a goodbye party last period on the floor with the desks and chairs piled up at the back. Until then, we completed classwork.

Today, this does not happen. During term students drift out of school thinking that taking a week out here and there is ok, that it is their right to have personal tuition to catch up when they return and that teachers must prepare material for them (that will not be done) whilst they are on holidays.

My favourite thing now is to ask students that have been absent (even for a day) if they have found a friend and caught up during form class (form is usually 20 mins of dolittle time each day where students rock up 2 seconds before the bell and get their names ticked off whilst talking through the notices). If they haven't caught up, I direct them to get their notes complete and until they have I help others first that have done the right thing (..after all once students have made an attempt to catch up they probably won't need the help).

Programmes seem to wrap up in week 8 term 4, as reports and all assessment have to be in. Student absenteeism starts to increase by week nine as students get sick of watching videos. Fun days start to appear to keep students busy. By week 10 absenteeism is at an all time high.

Students get roped into tasks to help get things done around the school. The sad fact is that it is usually the reliable kids that have the most to lose. They get taken out of class and valuable learning time is lost not to mention the disruption of reteaching when they return.

Unfortunately all of these things also occur in week 10 of every other term. That means we potentially lose 5 weeks out of 40 for the year to these cool down periods. Couple this to ramp up time, assemblies, exams, excursions, PD days and public holidays we can easily lose another 3 weeks. That means a clear 20% of programme time is lost over the year.

Teachers that run their programmes through to week 10 are put under pressure to stop by students (and teachers) as their class is the only one doing any work and it is not fair.

Last year in year 9, I had my practice of getting kids to work to the end of term questioned and I caved in and stopped the programme on the last day. This year for my year 10 class I was not so kind. Any of my kids that were being roped into alternate activities were found and returned to class. They worked until their last period practising trinomial factorisation... And do you know what.. they seemed to respect that their programme of learning was being protected. I don't get to see them until the last day next week (one period lost to a school assembly, one to a whole of school fun day, one to finishing on a Thursday), effectively making it a nine week term and that too needs looking at.

I can't complain about student knowledge if I'm not willing to do anything about it. This is an area that can be improved especially for my high ability students.

Exam review

We were reviewing the exam results and I pointed out to students the importance of exams and a different way of looking at the whole process.

Before the exam

• Use class time effectively
  There is no substitute for working well in class if you want good results. If you know the content, have practiced hard, retention is higher and understanding deeper. Muck about and the consequences follow.
• Identify content
  It is important to try and identify content that may be in the exam. Check notes and chapters covered and have a good look at material at the end of chapters.
• Identify proficiencies
  Do a few questions from the end of each chapter and see how well you understand the content. The more you are able to do, the better your exam results.
• Make good notes
  Any areas that you need to refer to the book make notes of. Where notes are not allowed in the exam, use them as quick review to memorise key material in the days leading up to the exam. Where notes are allowed, to not have them is a recipe for disaster.
• Find a study buddy
  Check what others are finding hard and things they think might be in the exam. They may have picked up on a hint that you haven't.
• Ask the teacher for more information
  Ask the teacher stuff. Who knows what they might give away? You have nothing to lose.
• Quarantine impossible material
  Some stuff you just can't learn in time. If this is the case focus on what you do know or can learn before the test.
• Sleep well
  You can't expect to retain anything without sleep. Your anxiety levels will rise to the point where you will be unable to function. Little anxiety good. Lots of anxiety bad.

On the day of the exam

• Be prepared
  Nothing is more likely to unhinge your confidence than losing your notes, calculator, pens running out, no ruler.
• Focus
  Find that point of calm within yourself. Don't Panic. Grab your notes (regardless of whether you can use them inside or not) and review what you know. I find it easier to go sit on my own than sit with friends that may hype you up.
• Wear comfortable clothes
  If that means you need to wash your most comfortable trousers or skirt the night before, find that shirt that is just the right size, make sure you have on your favourite socks (as long as you are still in uniform) then do it the night before.
• Be punctual
  Be prompt. Having the examiner yell at you for being late is not a good way to get into an exam frame of mind.

In the exam

• Seating
  Listen to the examiner and find a nice quiet place to sit. Settle your material just where you want it. Make sure that you only have material out that you need for the exam
• Remember your exam technique
  Spend two minutes reading the paper before starting. Identify the hard questions so that you mind can start working on them in the background - allow yourself multiple 'aha' moments as the answers come to mind. Find the easy questions. Number them. Start from the easiest and work to the hardest. Make sure you get all the marks you can before you start the doubtful ones. Identify how many minutes per question and how far you need to be at different times to complete the exam.

After the exam

• Reflect
  It is important to reflect (I didn't say beat yourself up) on how you did, identify your strengths and weaknesses and then use this knowledge for indicators how and when to really concentrate in class. It will help you at that moment of "Please shut up so I can listen to what the teacher is saying" as you will know when you need to listen and ignore the friend with that bit of gossip about the weekend. There's a reason some some students can ask good questions and others always ask questions that are irrelevant. Reflection is a key area of development for many students.
• Natural Ability vs Good work ethic
  We have all seen the students that coast along until year 11 and then hit the wall. These students are not prepared for failure and typically fall apart blaming all and sundry. A good work ethic is necessary for success in academia and in the work force.

Despite what many may say, good students do these things and somewhere along the line someone has taught them.

Sometimes unfortunately it ends up being me in year 10.

Links to other articles on exams:

• Exam preparation
• To do list before an exam
• Graduate teachers and preparation for TEE exams

Another week 8 gone

Well, with the help of a few friends I have made it through another week 8. True to form it is coupled with a bit of tiredness but was managed well by those around me.

I suppose in week 8 especially in term 4 we all suffer a little doubt. Have we done enough? Are they ready for next year? I suppose only time will tell.

I know that we're at least achieving in little things. There's a programme of work in place, resources have been gathered and evaluated, there are changes in assessment policy, we have established some diagnostics for cohorts. The team is coming together and is expressing interest in meetings next year. People are starting to see that these gatherings (I hate to call them meetings as it has that connotation of useless waste of time) as something useful and needed to make that whole of school approach work.

It's been a horrible year in terms of individual events happening to kids and of things happening here at home. Let's hope that next year, with the new baby arriving things change for the better (although I don't know how I will manage with fewer hours of sleep). It's good to know that even with a little trouble going on outside of school, things held together in school.

It's getting to the end of the cycle, time to close off this year and start preparing for next year. Another year, another new course, more new kids. Next stop material for summer school and then into the school year. I think we'll concentrate at the summer school on linear algebra, quadratics, problem solving/investigations, probability and 'other stuff' on the last day.

Soon I'll be in my third year of teaching.

Yay!