Evidence Based Education

Evidence based education is the new buzzword in education. It shares an acronym similar to OBE but is remarkably different in its approach to teaching. We need to be careful in engaging in more edubabble.

At face value it sounds much like common sense. From what I have read it can be summed up as following: "Systemic change in education should only occur with valid, statistically supported evidence." Today, where information is so easily shared there is no excuse for implementing blanket change without scientifically verified support (note that I don't say pseudo-scientific).

You can imagine some resistance from teachers as this sounds that it might take any chance of introducing new ideas/methods into the classroom. To my mind it is hard to argue against a process that ensures that the majority of what teachers do is tried and tested (if it fails, it is easier to detect why) and new ideas are limited to a small portion of the curriculum/pedagogy.

The prescribed evidence based methods would be imbued at teacher training programmes. This ensures that the majority of teachers perform at least at a minimum standard by being educated in tried and true methods. Higher risk alternative strategies or optimisation strategies would only be used as an adjunct to the tried methods.

As a parent you would not want your child subject to scientifically unsound/unproven educational methods. But.. with proof comes a necessity for time to find proof and judge what level of proof is required. This is not conducive to the immediate political needs for success in education. The issue it brings to mind is, "can the need for evidence march at the pace required for results?" ..and will the need for results and commercial lobbying compromise any findings made to the point of irrelevancy. I suggest this irrelevancy and bastardisation of results is exactly what will happen.

Change of this type would take at least 15 years to develop content, rotate in new teachers, start new students on their 12 year journey and develop change management processes to effectively monitor progress. Can you imagine a minister standing up and saying we will start the process now and if a subsequent government doesn't mess with it, we will have a good educational results in 2024? The long term nature of education is a good reason to divorce it from political imperatives and place it into a vehicle responsible to government via regulated requirements. I imagine this was first intended with the Curriculum council or SEA.

OBE was an opportunity for teaching to become a true profession again with each teacher becoming a curriculum expert for a given range of students. For those trained in the concept and with the necessary horsepower and support to use it, OBE is a wonderful curriculum development tool. Unfortunately the poor implementation of OBE, the tangling of cooperative learning with OBE and issues with assessment/levelling made it an unmitigated disaster in WA.
Despite this it still would be a mistake to throw the baby out with the bathwater.

EBE is the pendulum swinging and brings a new range of opportunities with the pressure of performance on teachers falling back to professional curriculum writers and systemic decision makers. It too needs to be taken with care until any evidence of success justifies the hype.

Driving school curriculum

The connection between middle school (yr 8-9) and senior school (yr 10-12) in the absence of a prescribed syllabus is cause for concern. When a teacher is limited by timetabling to only teach middle school classes they can lack the perspective gained by teaching senior school classes.

Similarly teachers only teaching in senior school that never teach lower school classes can lack an understanding of the difficulties in teaching younger students.

Where there are middle schooling practices, we have to be ever so careful to ensure that the "developmental" curriculum in middle school is dovetailed into the prescribed and effectively "streamed" curriculum of senior school... or else we end up with cream puffs with little resilience and disparate understanding/skills.. that when faced with pressure of performance they sadly crumble.

To not have cooperation between the middle and senior school is a real recipe for disaster. By not pushing hard enough in middle school, students find it difficult to adjust to the rigor of senior school. By pushing too hard, students become disengaged and arrive at senior school unable to enter effectively into more demanding subjects.

I believe that the only way forward is with strong leadership and it has to come from the staff that have taught and have an understanding of the needs of all five years. As staff with courses of study experience only exist in the senior school, under normal circumstances, this is where you would normally find that person. Typically they are well respected and driven individuals, although recently they may be feeling disempowered and ill used.

Once that person is identified they need to be empowered with the ability to make change such that the transition of students through middle to senior school promotes the highest outcomes from students. Being part of performance management and hiring processes for learning area staff may be a good idea.

Secondly they need to identify areas of intervention that will improve results across all five years at school, in assessment practices, student motivation, ICT implementation, curriculum development, statistical analysis of results and pedagogy ideas.

Thirdly they need to be a conduit to other learning areas to measure the amount of transference of information, examining opportunities for application of mathematical concepts effectively.

Lastly these leaders need to be recognised for their achievements and clear measurables need to be defined to show them any progress that is made. This needs to be a positive process with focus on success and examining failures for better ways to achieve desired outcomes.

With the dogs breakfast that currently exists with the lack of a current syllabus and the imminent failure of the development of a national curriculum, the opportunity exists to enhance state schools through effective identification of issues and the subsequent change management. State schools that face this challenge head on will avoid the catastrophe that is approaching post the disaster of the OBE implementation.

Baby Week

We're all prepped and ready for the arrival of our first new family member..

nursery finished... tick
house tidy... tick
bag packed ... tick
classes prepped for next week... tick

baby?? late of course.. just like it's mother.

My wife had a dream that she was having a Labrador. We checked on the ultrasound and it definitely is a baby.

I'll take a day off when it's due and then another four days when they come home. It's all very exciting and we're both looking forward to meeting our new family member. I've been telling my students that we'll name the baby Eunice or Eugene to make sure they grow up a maths dork, study hard, don't get boyfriends/girlfriends until they are at least 40 and make lots of money.

I'm finding the 3A MAT Trig test difficult to construct as my first attempt was too easy. I'll have to beef it up again later.

:-)

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.

Rewarding effort of teachers

Today I received a certificate from the Principal in recognition of the summer school run for our 3A maths students and a letter of appreciation from the school. It acknowledged the engagement of students in the summer school programme and recognised the planning required for such an undertaking. Our other two mathematics teachers in the senior school received similar commendations. This is really positive performance management (albeit in normal business it would be accompanied with pay rises or condition benefits). One really negative thing about teaching is that career progression requires entry into management roles and lateral "teaching students" advancement is not really catered to (level 3CT is the one exception and IMHO I haven't met a worthy recipient).

It is nice to put another letter/certificate in my Portfolio!

Now for planning next year's summer school with involvement from schools and students in adjacent areas. It would be great to be able to get some publicity/media attention and for participating students to be able to choose lecture/tutorials based on student needs and interests.

On another front, in the senior school we have a rolling class strategy in year 10 math, where each of the three senior school math teachers take turns following a top year ten class through to year 12. The middle school maths programme (developed last year by the senior school) has made a difference already, with the current year 10 coordinator already noticing that our top students have made solid gains in algebra compared to last year. Our middle school teacher has done well by these kids implementing the programme - a real achievement for the school.

The year 11 3A course is moving along swimmingly thus far. Yay!

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.

Talented students and self confidence

If a talented student at the start of year 11 wants to leave your class what do you do?

It's a question I don't know the answer to and is a difficult one.

Paths I've taken in the past have included:
a) Discuss their choices and investigate their motivation for leaving
b) Direct them to school counsellors
c) Do nothing

Invariably before now I have been sucked into option a). This last time I've decided to do c). Whether it is peer pressure, lack of support from parents, lack of confidence in your abilities, interference from other learning areas to bolster numbers, laziness or poor work ethic; students feel compelled to make changes at the start of year 11. It will be interesting to see what they will do. I know though that I can't in all honesty tell them that they will pass if they think the grass is greener elsewhere. I'd much rather have those students that are enjoying themselves in the new courses.

The pall cast by students wishing to leave really dampens my enjoyment of classes as I was really looking forward to working positively with them. I suppose it's just the ups and downs of working with adolescents.

The main course affected seems to be the year 11 3ab MAS course. The introduction of new content seems to have spooked a few students. I am concerned that the MAT only students this year will struggle in 3C MAT next year without the additional practice provided by 3AB MAS. It is only guesswork at this stage.

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.

Understanding reports in WA

I am often asked to interpret reports of friends children and explain to parents what the report really means. I am no expert on writing primary reports but I am critical of the lack of transparency in school documents and the degree of technical literacy required to understand them.

Reports are one of those things that have been bastardised by bureaucracy and politics. To be honest their usefulness is limited in their current form unless you are a teacher or bureaucrat. Even as a teacher, the variance of grading between one teacher and the next is too great making the data unreliable and thus is rarely referred to. Here are two cases that recently presented themselves.

Scenario A
Student is in year 7, has been given an excellent report. He has a level three in Maths and English and is finding school boring and too easy.

Q: Is my student doing ok?
A: Probably not. If they are level 3 and finding school easy then they are not being extended enough. Asked student to record what they did today in paragraph form (not dot points). Spelling accuracy was limited. Student was writing without an understanding of conjunctions, limited punctuation and was writing very slowly. Student could not recall last book longer than 10 pages read. Student could not recite 4 or six times tables. Student had limited understanding of order of operations.
Remedy: Indicated that parent needed to take greater interest in performance of student. Suggested student complete homework at kitchen table each night with parent assisting and providing additional examples to complete. Indicated a few books that the student may like and indicated that parents reading with them would be a good idea. Suggested methodology for learning tables and order of operations.

Level 3 is the minimum level a student should be getting in year 7. You would expect students to be completing a variety of level 4 tasks in year 7. Sadly many teachers are only teaching level 3 material. This is very evident when talking to primary teachers at PD through their lack of understanding of level 4 tasks in mathematics.

Scenario B
Student is in year 4. He is the top of their class in mathematics and performed well in NAPLAN testing. He has been given a B. The student is distressed as they expected an A.

Q:Huh? How can this be?
A:Back in the day when we were students, results for a class were scaled to a normal distribution - each class had a few A's, a few more B's, lots of C's, a few D's and a student or two earmarked for being held back. Sadly this is no longer the case. If a teacher does not teach the 'A' material (for whatever reason defined by that abomination smartie chart), an A will not be given, the same goes for B's, C's, D's & E's. In this case this is what has happened. NAPLAN testing at this level is more IQ testing than progress testing which is why this result was consistent with student and parent expectations.
Remedy: I supplied printed copies of progress maps and pointers for mathematics and links to sample items for the next NAPLAN test. Suggested parents consider looking at level of student and work at assisting student understand material at the next level.

It may sound ok to define 'A' material and provide an 'A' consistent with students across the state until you consider that in some low socioeconomic schools if grading was done consistently with curriculum framework directives, no student would get higher than a C for the first years of schools whilst they caught up to their contemporaries in more affluent schools. Even gifted students (but lacking environmental support) get discouraged as they try to overcome their lack of support at home and get C's despite making large jumps in knowledge and applying themselves. Although the idea of A-E grading was good, the application was poor. For low ability students in lower classes - they may never get higher than a D despite a great work ethic and working at a level consistent with their peers.



The solution? Provide normalised results for each class on reports (allowing students to get grades in relation to their peers) and use NAPLAN tests to show progress in relation to other schools with expected ranges for university and TAFE entry. Duh!

(Addendum 30/1/2008: It is interesting to note that the West had an informative article on just this topic today.. details of the article can be found here (half way down the page) by Bethany Hiatt titled "Parents need lessons on the grading system". Yes I am being positive about a media article - must be the optimism and endorphin spike associated with the start of a new year.)

Trigonometry and CAS calculator I

During exams last year we noticed that those who had CAS calculators were not using them for Trigonometry problems. During summer school we sought to rectify this. To start with we looked at properties of triangles.

Students stated that the calculator would give no solution when solutions existed. This sounded doubtful but I had a good idea where they were going wrong.

I started with the following. Take three lines, 4cm, 2cm, 1cm. Now obviously this can't make a triangle. Right?




No matter how we change the angles at A & B they cannot form a triangle. This was to inform students that a no solution result in their calculator had meaning.

So now we had a look at a problem that they were having difficulty with.

In their work pads they had written A=x, a=5cm, B=72°, b=72 and labelled the triangle correctly. So far so good.

They could tell it was a sine rule problem but had difficulty entering it into the calculator. Where did the sin, cos, tan buttons go from the calculator?

The first thing to do is find the sine function. Open the soft keyboard, select the mth tab and press the Trig button at the bottom of the keyboard.



Next enter the sine equation with the substituted values. They needed the fraction template inside the soft keyboard under 2D






Hitting execute at this point gives no solution. Huh?

Well.. we still have to solve for x. So highlight the equation and go to the interactive menu (in the menu bar at the top of the work pane), select Advanced and then solve. The Equation should be there and the variable listed should be x.



After a rather long wait a huge expression appeared with a strange looking answer.

I'll rekey it here as the whole answer does not appear on the work pane on the calculator.

{x=360.00.constn(1)+137.209, x=360.00.constn(2)+42.791}

The answers are the two bits in red (at this point we had a bit of a chat about the ambiguous case with the sine rule). To get to the answer you have to navigate with the style and the left/right arrows at the edges of the equation.



So the answer is x=137° or x=43° (0 d.p.)

We then drew these triangles to give students a better understanding of the ambiguous case.

In the next example we'll look at the perils of rounding and go back to the case above with the impossible triangle.


Here is a link to other CAS calculator posts.

Solving Simultaneous Equations using the Classpad 330

There are a number of ways of finding where two lines intersect. Let's solve this example.

"Where do the equations y=x and y=-2x+3 intersect?"

One way to find the solution is to solve the two equations algebraically using simultaneous equations.

First open and clear the main work pane.



Press the blue Keyboard button and bring up the soft keyboard. Select the 2D tab.

You should be able to see a button with a bracket and two small boxes (circled below in red). Press it.

You should see the simultaneous equation template in the main pane.
(Update 1/6/2010: Press it twice to add a third equation line!)

Click on the first box and type y=x

Click on the box below it and type y=-2x+3

In the third box to the right of the vertical line type x,y (the variables we wish to solve).

Hit the exe button.

The answer (x=1, y=1) should appear.

Here is a link to other CAS calculator posts.

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.

Middle school & end of year reflection

After a year of trying to establish rapport with middle school I think the obvious is as follows:
Without teaching upper school classes and being involved with NCOS, middle school teachers have disconnected from upper school requirements through no fault of their own.

Added to the traditional "it's an issue at primary level - but we have five years to rectify it" we also now have "it's an issue with middle school, how can we possibly fix it in two years".

Students wrapped in cotton wool, unable to connect success with working hard find senior school difficult.

Assessment changes and alteration to pedagogical methodology in middle school has reduced the rigor required for TEE subjects especially in those with little discipline at home.

Without a detailed syllabus, critical topics can be deferred to later years causing irreparable damage.

Responsibility for subject performance should be left in the hands of those that understand the subject area.

Graduation should not be automatic. Pastoral needs of the individual should not be placed above the academic needs of the student and group as a whole.

Students can be entertained and placed with friends to stay in school but when once the demands of TEE level education arrives, it gives students too little time to adjust to the requirements of real study. The adjustment needs to occur in year nine - especially for the gifted kids.

General observations from 2008:
Streaming in mathematics is required where more than four levels exist across a cohort.

Intervention time is limited to less than 1 minute per student in homogeneous classes greater than thirty and puts teachers at risk with the current defer intervention actions BMIS discipline policy. Intervention time is greatly increased in a streamed class as peer assistance, direct instruction and modelled lessons become more effective.

Collaborative lessons can work when consequences for non-performance are correctly administered (peer pressure is a fantastic tool in this case).

The most reward comes from success with students with the least demonstrated ability.

Any student (without a learning difficulty) can learn any topic given an adequate amount of time (Kevin Casey).

Male students are not getting the results in mathematics in line with their ability levels.

It is possible to make a difference. Bring on 2009.

Intuitive Teachers

I wonder if there is a connection between those that deal with a lot of people and their ability to be intuitive towards their needs. As teachers we need to be able to "read" students as many times their articulated response may not reflect their needs.

I've found that since teaching it is easier to read what people mean compared to what they say. Is this a common finding? Do occupations that deal with a lot of people on an ongoing basis develop the same ability? Does frequency of interaction hone the ability further? Is this a trait we should be looking for in new teachers in the same way we look for bedside manner in doctors?

Making schools a part of the social system

Many attribute social behaviours to treatment within schools.

Children under the age of 18 are arbitrarily required to attend school or seek gainful employment. Yet many of the children in our justice system are no longer attending school or seeking gainful employment.

Similarly, many children in schools are not students, but young adults actively being impediments to the learning of other students. They have little or no interest in schooling and have no interest in seeking gainful employment.

If students have no interest in schooling or are not in gainful employment I suggest that we strip them of their rights as children and call them adults... any illegal activities get tried as adults, protections given to children are removed and sentences roll into the adult system as they turn age. After all not in school, not acting like a child, demanding adult responsibility and treatment - grant their wish.

Similarly if a child is not contributing in school, not valuing their education, being an impediment to the learning of others (with no feasible solution available to get the child performing as a student) .. whoosh - out they go either into an alternate programme off campus or into the real world as an adult and lose their privileges as a child.

With one proviso - any government payments for children are instantly stripped if they stop attending school and adult payments for these children are not available until they turn 21 if school is not finished (a very simple process that could be completely handled electronically). Exceptions would be handled on a case by case basis with very strict criteria after testing for learning disabilities and available environmental supports.

Whoa! I hear you say.. that's a bit radical... but nobody values what is given on a plate - only when there is a risk of loss is it valued. For schools to be a part of the social system, it needs to be recognised that schools cannot be held account for all social ills, they can though be a filter for recognising them and helping the borderline cases back into the mainstream. Stuffing extreme cases into an already taxed system and hoping all will be ok runs the risk of dragging many more real students down with it. Schools should be centres of learning filled with students and families that value education... not a young adult minding service.

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.

Milestones

Milestones:
2000 hits since July (started site 22 July)
600 individual people visiting for the quarter
500 hits in a month (November)
120 individuals in a week, 180 hits (week 46)

From the little map it's good to see people from all over the place... Hello!!!

Most visited pages
CAS Calculator help index (by far)
Mathematics pathways 2009

On an excursion today.. probably the last post until the new year. Soo... from Benjamin bunny and educationWA have a very Merry Christmas and I'll see you in 2009!!

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!

Mathematics Pathways 2009

On paper the new courses next year look to be improvements on the existing 2008 MIPS/Foundations/Intro Calculus/G&T combinations. In 2008 MIPS was for weaker students, Foundations for mid tier students and Intro Calculus/G&T was for the capable students (think Maths 2/3 if you're from my era). In Year 12 MIPS lead to Modelling, Foundations lead to Discrete, Intro Calculus/G&T lead to Calculus/Applicable mathematics.

There were definite issues with the old structure. First MIPS was very language oriented which caused serious difficulties for low literacy students. The Foundations course was more difficult than the year 12 Discrete Mathematics course that it lead to. Many capable students opted to take the easier option (Foundations/Discrete) rather than Intro Calculus/G&T students as the scaling was never quite right for(although Intro Calculus/G&T students did get the benefit of satisfying many pre-requisites in university and avoided bridging courses)

The new courses for 2009 on paper better cater to a range of students. These courses are semesterised and labelled 1B-3D (eg. 2C in semester 1 and 2D in semester 2 year 11, and 3A in semester 1, 3B in semester 2 year 12). Each year 11 course (if necessary) can be sat again in year 12 (eg. if a student failed 2c/2D in year 11 and repeated 2C/2D in year 12). There are lower courses aimed at students with learning difficulties (PA/PB/1A).

Weaker students have a more traditional year 9/10 type course in 1B/1C/1D/1E or 1D/1E/2A/2B (replacing MIPS/Modelling)
Weak mid tier students now have 2A/2B/2C/2D (replacing Foundations/Discrete)
Strong mid tier type students now have 2C/2D/3A/3B (replacing Foundations/Discrete)
Capable students have 3A/3B/3C/3D & 3A/3B/3C/3D specialist (replacing IC/G&T/Calc/Applic)

The strong/capable students are typically university bound, weak mid tier students may use their score for low requirement university courses or TAFE. Level 1 courses are generally for vocational students.

The real benefits are for mid tier and capable students that now have real options in selecting 2A-3A as a starting point in year 11. Students that sit higher end mathematics are now promised a more equitable scaling factor than was in place under the old system. The general opinion is also that the new courses are easier (in general) than the courses they replace. Only time will tell.

Fight Club & media beat up

RE: http://www.abc.net.au/news/stories/2008/11/25/2428740.htm

Here we go again. Another beat up by the media of a topic that will waste immense amounts of time within schools. Here's a forum post on the topic.

Amount of research done by media? Positive outcome for the community? None.

I feel for John Forrest SHS as they were just the poor school that was focused on this time. Morley kids in fight after school - hardly headline news..

I wonder if the genius that suggested keeping all students in school until the end of year 12 (especially those students too lazy to get a job) thought through the consequences properly. Couple this to increased scrutiny on suspension rates and we end up with the situation of dangerous students being kept within schools and encouraging/bullying students into situations like the 'Fight club' scenario. How long before we have metal detectors looking for knives, police required on school grounds, security guards patrolling a regular occurrence and schools feeling bullied with little support, with blame pointed squarely at schools? Oh that's right - it's already happening.

We (parents, media, community, government) need to support schools not finger point. We need solutions (exclusion of troubled students is a starting point) not blame. That means parents taking responsibility for their children, programmes that empower social workers with real consequences (such as removal of welfare payments), society taking responsibility for ill prepared parents (like removal of the baby bonus), support for academic students (whether aimed at low or high ability students with grading on progress rather than state based comparison - abolish the smartie chart and myschool!), and no in-school baby sitting programmes (students, not clients/customers).

Senior school is now effectively many things: pathway to university, pathway to vocational studies, home of unsure students and a dumping ground for kids that don't wish for a job nor to study further. There is no pressure on these latter students to perform away from home and little leverage to ensure that they enhance the school environment by contributing to the school. They are disenfranchised, lack enthusiasm, see little in their future beyond today. They need babysitting to prevent them from causing social ill. This is a social problem, not an academic one; worse still it only defers the problem by two years and has significant negative impact on schools. Children that cannot be directed into contributing students (despite all attempts) of the school community need to be directed out of school so that they either come back wanting to be a student or find a new pathway.

Teachers are not social workers, entertainers or babysitters, they are academics there to guide the learning of students and should be valued as such. Schooling is a privilege and a responsibility offered to all but should never be seen as a right. If a student brings a school into disrepute - they should be looking for a new school with fairly tight restrictions placed before re-entry into the school system. If we want better schools we need desperately to make schools academic centres of learning with spotless reputations, place clear boundaries around students, provide power to principals to act; and empower teachers effectively as tools of learning.

Class load next year

I don't know if I like or dislike my proposed timetable for 2009.

It looks like I will have 3 dot periods in a row next year (on a Thursday) which will make life a little difficult. The saving grace is that most of my class sizes are around 15 with taking the level three year 11 classes, modelling in year 12 and some of the alternate eduation kids. Only my year 10 class bodes to be larger than 17.

This time only 3 of my five classes are first timers rather than all five (I've taught year 10's and modelling before). The level 3 classes and the alternate education kids have the potential to draw a lot of time.

So far I'm one period down, which will make me a lightening rod for reliefs too. At least I'm not teaching out of area!

Upper 10's and exam preparation

My upper tens have begun revision for their exam. I've pushed them over the last week, getting them to complete twice as much work as my normal expectation per class as a prelude to expectations in year 11. Next I wanted them to experience the expectation of exams and model how to study in year 11. I set aside four days for them to revise and they did the following:

Day 1: Identification of material that could be in the exam
Day 2: Finding of resources (where in texts, portfolios) and identification of areas of weakness
Day 3: Preparation of notes / judging detail required via marks allocated
Day 4: Review and identification of material to study over weekend

Key findings
Students tend not to use contents pages in texts very well. Even when given words to find (solve, substitute, trigonometry) they can't find where in the text to examine. Students also need to consider that higher order questions are more likely to be in the exam therefore they should make sure they can answer questions at the end of exercises.

It was interesting to note levels of anxiety from the beginning (a couple of students with high levels) and the anxiety decreasing as they realised that they had mastered most of the content already. I look forward to next year when I can show them the progress made from year 9 to 10 by showing them their own year 9 exams and comparing it to their year 10 exam.

Students can now produce notes quite well and after a year of reinforcement they can see how to both use and benefit from them.

Students are starting to see that exam hints can be used to improve marks and how necessary it is to follow up and fix any areas of weakness.

Probability & statistics

I have running battle with my lower tens getting them started but found that a game of craypots generally helped. I've bought some foam cubes from Clark rubber (2 for $3.50) 125cm x 125cm x 125cm.

I've labelled the sides storm, storm, last, fine, fine, fine in red marker so that the students can see what the weather is and decide how to play their craypots to maximise the chance of profit.

It's been great to see students find the maximum possible value, the quickest way to get out of the game (eg. the riskiest route), see their mental mathematics in action and their ability to follow a process. It's a game that's easy to set up (it needs a worksheet and a teacher with dice) and one where the class highscore can be kept to be aimed for. Here's a copy of the online version. When I remember I'll bring home my worksheet for upload.

A fair few other dice games can be found here.

It's also a bit of fun to throw the foam cubes around the room near students not paying attention.

Milestones

For the first time we reached 500 hits for the month and already have over 500 unique visitors this quarter - well up on last quarter and we still have a month to go. I attribute all this success to the rabbit banner and his joke.

Most popular topics this month were:
CAS Calculators (by far)
EBA4
Performance pay

Yay!

Diagnostics

Sometimes teaching year 10's you get so caught up in your lesson you miss the bloody obvious.

Today we were looking at distance from origin, Perth to Meekatharra, Perth to Newman and so forth using trip counters and odometers. My students were finding it hard to find the distance between two locations (I forget the real distances so please excuse my made up ones)..

They could understand that the 259km and the 1600km indicated distances from Perth but could not understand how to determine the distance between Meekatharra and Newman. So I tried something similar but with smaller numbers.

When asked the distance between Mary's house and the shops, this time students were able to say 1km. I asked them how they did that and they gave me the answer 9+1=10. I asked if they could think of another way. A sea of blank looks from the new kids in the class. I think to myself OMG. No wonder these kids couldn't do the previous problem. I showed them that subtraction could work and they were able to complete the exercise finding distances between various destinations. By the end it was obvious that they could learn the pattern for solving the problems but did not have an understanding of the underlying maths - thus had forgotten the method by the next problem.

So I went a bit further and used my favourite diagnostic tool. I wrote the following on their page.

10
99
109
119
1109
1229

And asked them to add one to each number. Thankfully only one student couldn't do this. Then I write 10526 and 52679 at the end of the list and moved to each asking them to say the numbers quietly to me. This was not as successful. This was the trigger to split the class (again) and start these kids on a different programme of work.

The integration of low ability or underschooled students into the mainstream and removal of dedicated remedial classes has meant that many students are falling through the cracks. It is no wonder that some of these kids can be disruptive, disheartened and are having confidence issues. Students that cannot read numbers above 100, can't identify simple operations or understand place value have little chance in mainstream classes. It's enough to make you physically upset and reminds me why I originally intended teaching year 7 rather than senior secondary. The impact of intervention is greater at an earlier age than now.

I have many of these kids next year and have identified areas of focus, we're designing entry tests for new students and aim to improve numeracy with low performing students. It's frustrating the amount of time that it takes to find these issues and detect the underlying factors behind avoidant behaviour. Time will only tell how much success can be made of it.

Building a better future for our kids

Getting kids to see opportunity rather than negativity is a key objective for 2009. As times get more difficult and unemployment rises, it is ever so important for kids to use their education for a new start in life and bring hope not only into their lives but into their families.

There are inspirations in every year group, the child with a terminal illness that strives for A's, the child that works every spare second to send money home to parents in Africa, the student that couldn't read two years before and now is able to contribute to mainstream classes.

Once an opportunity is presented to a student we get limited opportunities to demonstrate that effort leads to success. Any success with some kids needs to be celebrated, even staged to ensure that they get on the right road. If they are going to fail at a task (and they must learn how to cope with failure) they need to be supported, prepared and lead by the ear to see the achievement gained in failure. The learning of resilience is important beyond any skill.

We need to believe that they can do things. They have enough doubt in themselves, it does not need to be reinforced. Push them hard, see what they can do - it will always surprise you. Work to drive them to a better place - a good work ethic is an an achievement in itself.

The little darlings need to learn that boundaries are ok and are there to protect them. The world may not be fair or cheering them on, but generally it's not against them. All of us old folk fight for a better future for them. Learning the rules is a precursor to learning how to interact with others and the community - simply modelling polite language can save them from being instantly judged the minute they open their mouths.

Value systems now that religion is no longer impressed on kids are lacking. Without a value system kids lack a knowledge of right and wrong. In a world where everything moves so fast and knowledge is valued over experience, it is hard for them to see that there is wisdom in older folks. This is of course every generations fate - but with the rapid pace of the information age it is being exacerbated. They don't believe in our values (what would we know!) and lack a better system themselves.

Parents, rather than argue at the end of a hard day at work, just give in to an argument - kids do not understand no as an answer being used to the last word. At least until they do something that has a consequence that cannot be overlooked. When this happens, the gentle leading of them to their errors is a hard task that requires patience that I need to develop further.

We need to protect students that have good qualities from students that are developing them. Once an academic student is identified they need to be driven forward. Students developing good qualities need to have champions that mentor them through and help them through difficult times.