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.