Creating inspirational students

Students aren't born inspirational. They're born rather podgy blobs that whinge a lot... Some never change...

This week I spent a bit of time reminding my year 10's that they are inspirational. Lower school students look to them for cues on how to behave, on determining what is important and setting the tone within the school. If they want a happy school - be happy. If they want a school with a million rules - do stupid things. If they want a school based on success of students, show the lower years that our school can perform at a high level.

For this I think it is important that we create opportunities for them to be successful and protect those that foster these activities. It might be taking an interest in a student that is doing an afterschool ESL class, or not getting grumpy with the dance teacher that is taking students out of class for a recital, being supportive of the physical education staff and their events, supporting SOSE excursions by providing extra supervisor bodies or helping out with relief classes.

I think it also means looking for information that might help inspire kids. I recently found two books by the actress that played Winnie on the Wonder Years (Kevin's girlfriend for those of you ancient enough to remember). One is called 'Math doesn't suck' and the other is 'Kiss my Math'. The books themselves may be just the thing to get a student going and get them to believe that you care about how they think. The maths is a bit dodgy in places ('Highest common factor' becomes 'greatest crush factor') but it has a go at making maths pop culture ready and that's a good thing.

Another bit of success I've had is to let them into my life a little. Last class we created tally tables on the best baby name that we had selected. Next time I'll have a silent poll as it was a case of many just following the leader. Maybe this is a discussion in itself. We've also used my history to investigate stocks, examine salary ranges and evaluate priorities on what is important in life.

Another opportunity has been with my guitar. I am worse than hopeless, but the kids see that I am still learning well beyond school.

Lastly whenever a leadership event occurs I draw their attention to it and suggest that they pay heed to things done well or poorly as they will soon be in that position. If they can learn good leadership habits now, they will be in better stead going forward.

Year 12 leaving ceremony

It was interesting to watch the leaving ceremony for the year 12's. It gives you a lot to think about for times where you are helping set up such an event and things that kids really need to do to make these events successful.

Firstly all kids need to feel included in the ceremony - not just the popular kids. Photo montages need to include everyone, memorable events need to cover the full spectrum of students academic, sporting, VET; dominant personalities need to celebrate and value the achievements of all, not just the popular few.

Perhaps we need to consider how we could create photo libraries for all years, mini yearbooks documenting events as they occur as part of the various handshaking ceremonies throughout the year.

There was a clear lack of thanks from the current year group. There was a brief thanks to all our teachers and then a celebration of all the events where misbehaviour had occurred and had perhaps caused embarrassment to students, the school or disrupted classes. This left a sour taste in the mouths of the senior teachers as a lot of effort had gone into getting this cohort over the line. Many have decided to give the graduation ceremony and dinner a miss. Maybe this is an indication that we need to focus on those that appreciate our efforts and that the efforts at 'inclusive' education have gone too far. Maybe students beliefs are right and we are not doing enough! I don't know but somehow I doubt that our efforts are best spent on students that perform at a very low level (even with all the help in the world) and take away time from students that could really use extra help. There needs to be further authority given to schools to move students that will not respond to learning opportunities to free up time for those ready. Perhaps it is just my utilitarian tendencies showing through.

When all graduate there is a clear diminishing of value placed on secondary graduation. With graduation rates of 80-100% and all students needing to continue school to year 12, graduation for many has limited worth. Many leave with little more knowledge than they had at year 10. It has diminished the achievements of those attempting TEE courses, there is little recognition of the difference in effort required. I feel for those that attempt TEE courses and get fails on their certificates due to external circumstance instead of taking the easy option and doing VET or alternate education courses.

Another clear transformation is the knowledge that these kids will probably communicate with their cohort for some time unlike any cohort from my time. The advent of Facebook and mySpace will mean that they can have instant communication with their cohort and an instant network to resolve issues and celebrate success. I don't know if this is a good thing as coming of age was about new times and new people, the removal of negative reinforcers and a new beginning.

The lack of concern of students for their TEE exams and the haphazard attitude to study borne through portfolio entry and low TEE scores is definitely to their detriment. The baptism of fire is now more dip in a warm pool. These students have managed to leave school without any anxiety of security and self worth - how will I support myself, what occupation can I do, how will I be worthy of my life partner, how will I be a valid contributor to society? Resilience is something borne of experience and these students lack any real concept of the difficulty of gaining true independence.

Casio Classpad 330, Finding the mean and missing values

I posed the following question to my year 10's in order to continue our learning of the new calculator. It is an example of solving a problem where the mean is known but a value in the sample is not.

"Q: A class had 5 students. Student results in the last test was {50,56,64,72,81}. Isabella joined the class and the new mean became 68. Did Isabella score higher than the old mean and what was her score?"

H: If the mean of {50,56,64,72,81} is less than 68 then Isabella has scored higher as a higher score by Isabella will raise the mean. Since we know the new mean (68) we can work out Isabella's score by working backwards.

Set up a working pane with a main application and a list editor. Title a column 'list1'. Add the 5 student results to the list editor.

Click in the main application and type mean(list1) using the soft keyboard. Hit the blue exe button. The answer is 64.6 .
A: The old mean 64.6 is less than 68 therefore Isabella has scored higher.

To find Isabella's score click in the list editor and tap the next empty cell in list1. Press the x button. Click in the main application pane on the line that says mean(list1). Press the blue exe button.

This will return a sum to work out the mean of the list for values of and value of x i.e. (x+323)/6.

As we know the new mean alter the first line to read mean(list1)=68. Highlight the solution sum and tap Edit in the menu bar and then Copy. Paste the sum on the next line in the main application pane. Highlight the sum, tap Interactive on the menu bar, then tap Advanced on the sub menu and then tap solve. Tap ok at the base of the dialog box. The answer is x=85.

A: Isabella's test score was 85.

Click here for other CAS calculator articles

Revisiting fractions

My 10D class has revisited fractions over the last week. For many fractions is like another language others have managed it in the past but have forgotten basic principles. The sequence I have used leading up to percentages of amounts is as follows

Drawing and identifying numerators and denominators
First exercise was identifying a variety of numerical fractions from pictorial form and then constructing pictorial fractions from numerical forms. We spent a lot of time looking at mixed numerals and converting between mixed numerals and improper fractions using pictorial means.
eg. for 3 2/3: draw 3 lots of 3 boxes with all boxes coloured and 1 lot of 3 boxes with two boxes coloured. When students counted the coloured boxes they had 11/3.

Investigating fractions of amounts
It seemed strange to do this here, but funnily enough it worked well as it established relevancy of the topic for many students. We started with a problem 3/4 of $24 is to be given to John and 1/4 to Mary.
I explained it as:
3/4 of 24 is: $6 per part (24/4)
I drew a box and split it into 4 equal parts (drawing attention to the denominator)
I put $6 in each box.
I coloured in three sections that represented John's portion
then counted $6 x 3 parts = $18 for John

I then repeated the same steps for Mary
1/4 of 24 is: $6 per part (24/4) then $6 x 1 part = $6 for Mary

We checked our answer to ensure all the money had been accounted for ($18+$6=$24). Students then completed a number of examples.

Investigating multiples and factors & Equivalent fractions
Next day we looked at multiples and factors. I explained this through examples, showing them examples of multiples and factors, then getting them to find the first five multiples for 2,3,4,7 and then the first five multiples for 2,3,5,7 over 100. After this they found factors of 10, 15, 24 and 42. We investigated patterns in factors (none greater than 1/2 the original valure other than itself, how it helped knowing your tables, factor pairs, 2 is always a factor for even numbers)

Students were then given a fraction wall and identified equivalent fractions in preparation for adding and subtracting fractions. The idea was put forward that fractions rely on parts to be equal otherwise the idea of equivalency would not be able to be used.

Adding and subtracting fractions
In the third lesson we looked at the problem of 1/3 + 1/2 using paper strips. The aim was to establish why equal parts is essential to an understanding of fractions. We used our fraction wall to look for equivalent fractions that allow us to add equal parts. After a few pictorial examples I started to show students how to use multiples and factors to assist in finding common denominators.

Next lesson we look at multiplying fractions...

Recharging students for success in mathematics

Being in a low socio-economic school sometimes is disheartening. The students don't believe that they are able to achieve academically. This is reinforced by parents, teachers and the school in subtle ways throughout the year.

A parent complains that the student is only doing lower maths and does not need a $175 calculator. The timetable allows many non-TEE subject to run, but only a few TEE subject selections are available. Portfolio entry is seen as a primary pathway to university rather than a backdoor entry for extreme cases. Lower school programmes lack the rigour of programmes in more academic schools. A single student or groups of students can disrupt classrooms for an entire year, but little coordinated effort can be made to limit the damage being caused. The idea of secondary graduation is diminished by the idea that 'anyone' can graduate. Cohorts of students are labelled challenging and good students lose opportunities as classes are aimed to manage the lower students and keep them engaged to detriment of academic achievement by top students.

Charging academic students for success is a mentality that must be driven - it doesn't just happen. Kids need to be told that they have the ability to succeed, shown possible outcomes, be given opportunity to try/fail/succeed and be mentored as they go along. Setting clear standards sets the groundwork for success.

Things that I consider serious issues in my A class:

• Not being quiet and ready to start work within 2 minutes of entering the room
• Being late for class and not entering the room quietly
• Complaining, whining and whinging before attempting work
• Not paying attention when instruction is given
• Relying on friends or personal attention of the teacher for instruction rather than some level of personal investigation
• Not attempting homework
• Failing a test or assignment ( lower than 1 standard deviation from mean)
• Not seeking assistance when required

Students that continuously fall into these issues risk demotion to BCD classes. For some, demotion is the right option, for others the motivation to be moved down is enough for them to alter negative behaviours. For a relative few, it identifies students with ability but are unlikely to succeed at TEE level. This year, boys in particular have been a real issue and a focus for the course next year (I think this is the most significant issue at our school).

Things that I do to promote positive attitudes towards mathematics and address issues:

• Look for opportunities to congratulate students on achievement
• Attempt to talk to each student each class
• Allow friendship groups to remain together only when learning is occurring
• Ensure that new topics include new material
• Promote the A class as being a privilege and a responsibility
• Reinforce that attitude is as important as aptitude
• Change the difficulty level regularly to allow for opportunities for success/failure and stretching of the mind.
• Question their own beliefs of their ability and remind them of progress made
• Use personal experiences to enhance class material
• Focus the basis of enjoyment in mathematics in achievement rather than entertainment by the teacher (though the converse may be more important in lower classes)
• Encourage students to self monitor behaviour and provide peer feedback
• Create opportunities for students to see the different rapport with yr 11/12 TEE students than with yr 10 students

Casio Classpad 330, Creating a Histogram

Today in class we looked at how to produce a Histogram using the list editor. A Histogram is used when data is continuous (there is no gap between intervals).

Class interval (Frequency)
0 <= x <>=80 (1)

Tap in the list editor. Tap Edit in the menu bar. Tap Clear All. and tap Ok in the dialog box. If a graph is open tap the StatGraph pane to select it. Tap the cross in the top corner of the window to remove the graph.

Name a column in the list editor ‘classmid’using the soft keyboard. Put the midpoint of each class into the classmid column. eg. {5,15, 25, .., 85} (make sure you name the column before putting the data in!).

Name a column in the list editor ‘freq’ using the soft keyboard. Add each corresponding frequency into the freq column. eg. {3,10,16,..,1}.

Tap SetGraph in the menu bar. Tap Setting. Select Histogram in the Type dropdown, select classmid in the XList dropdown and freq in the Freq dropdown. Make sure the Draw option is on. Tap Set at the base of the dialog box.

Tap the StatGraph icon in the icon bar to display the graph. Make HStart 5 (midpoint of first interval) and HStep 10(size of intervals).

A Histogram will appear. Tap the StatGraph pane and then tap Analysis in the menu bar. Tap Trace in the menu.

A flashing crosshair should appear above the first column of the graph. Use the blue cursor key to navigate column values in the graph. You can use these values to create your histogram on graph paper. The xc at the base of the graph are horizontal axis values and the Fc are your vertical axis values.

viola!

Other educationWA articles on CAS calculators
How to navigate through menus (what's a menu bar?) Click here
How to create a list (what's a list editor??) Click here

Here's a link to an index of other CAS calculator posts.

Casio Classpad, day 1 with students

As I play with the calculator things become a little more obvious. It was good fun with my year 10's showing them how to find the mean of

S:{10,12,13,14,15}

with the CAS calculator during p5 on a 35°C day and then set Maths for WA3 10C with 50 items in the sample. I was upfront in saying to my students that learning all the new content next year and learning how to use the calculator was a bad idea (lights went on... ahh, that's why I need to get one this year!!). For those students still unsure, I made them find the mean of a 50 item sample with their scientific calculators. They promised to buy a CAS calculator tomorrow.

Anyhow.. this is one way of finding the mean with the CAS calculator. There are many better ways but the idea was to learn how the calculator works (the picture is the end result).

Open a main application in the work pane.

1. The last icon in the tool bar should be a graph. Click the dropdown to the right of the graph. Tap the icon that looks like three columns in the sub menu. The list editor will open in the bottom pane below the main application.
2. We need to give our list a name. Tap the top of the first column. “list =” should appear at the base of the list editor.
3. Press the blue Keyboard button. The list editor will temporarily move to the top pane. The soft keyboard will appear in the bottom work pane.
4. There are four tabs in the soft keyboard. Tap the abc tab with the stylus. A qwerty keyboard should appear. Name the first column in the list editor ‘list1’ if it is not already. You may need to click again in the list editor list= textbox first.
5. Press blue Keyboard to get rid of the soft keyboard. The main application should reappear in the top pane and the list editor in the bottom pane
6. Use the stylus, tap the first cell in list1.
7. Using the number keys press 10 then exe (bottom right hand corner of the keypad). This should put the first number in the list. Not that the cursor has dropped to the next item in the list without having to use the stylus. Now enter 12 then exe. Your list should now have two entries. Add the remaining entries.
8. Click in the main application. Raise the soft keyboard with the blue Keyboard button. Open the abc tab and type list1 and press exe. {10,12,13,14,15} should appear.
9. Click Action in the menu bar and tap List-Calculation. Tap mean from the options provided. 'mean(' should appear in the main application.
10. Complete the action by typing ‘list1’ using the soft keyboard and the button ‘)’. You should now have ‘mean(list1)’ displayed. Press exe. The answer 64/5 will appear. To get a decimal representation, highlight ‘64/5’ with the stylus and click the first icon in the icon bar.

viola. You should be able to finish the tutorial by finding the median yourself. (An alternate way is to type list1, highlight it, tap the Interactive item in the menu bar, tap list calculation in the sub menu and then median and then select ok at the base of the dialog box.) You could also use statistics mode (tap Main on the icon bar, then tap Statistics.) The Statistics application is very similar in structure to the stats mode on the fx graphics calculator).

Here's a link to my last article on learning how to use a CAS calculator.
Here's a link to an index of other CAS calculator posts.

My Casio Classpad 330 Journey

Second weekend playing with the calculator.

When I was doing phone support often I could not see what the person on the other end was doing. I became quite adept at directing customers on quite difficult tasks blind. The most important thing to do was to adequately define things up front.

With the CAS calculator the windowing system can be quite confusing at first. It is important to name things in such a way that students can listen to your direction and follow it, rather than needing snapshots all of the time.



In the worksheets I have created, the calculator is divided into the screen and the buttons. The screen in divided into the menu bar, the tool bar, the work pane, the status bar and the icon panel. The buttons are blue, grey and black.

i.e.
The Edit, Action, Interactive text at the top is the menu bar
The icons underneath the menu bar is the tool bar
The area underneath is the work pane, it can be split into the top pane and the bottom pane. The work pane is currently filled with the main application.
The bit beneath the work pane (eg. Alg, Standard, Real, Deg, battery indicator) is the status bar.
The stylus and buttons are used to enter data and operations into the calculator.

Here's a link to the "How do I.. ???? on a Casio Classpad" book that I have been using.
Here's a link back to my first article on CAS calculators
Here's a link to an index of other CAS calculator posts.