Saturday 19 December 2015

OPINION: The third option

At the end of a lesson after having given back a class test one of my students confronted me, telling me, "You should not push students into aiming for University, there is another option you know. Students might want to just go and get a job!"

I waited before I gave my reply, "so those are the only two options?"

To put the situation in context, she had just received a sub-standard grade; not below the class standard, but below her own and she wanted someone to beat in an argument to regain some lost pride. My response was not what she anticipated.

She assumed that teachers generally moved from school to further education and then just returned to school as a teacher. Thereby through a self serving bias (https://en.wikipedia.org/wiki/Self-serving_bias) teachers rank further education as the superior option upon the completion of school education. Over recent years there has been increasing push, particularly in Australia, for vocational options typically through an apprenticeship programs or some entry level employment. 

This student was expecting to argue with me regarding academic versus vocational options. Given her favorable grades I suspect teachers, parents and even other students must be pushing, or at least assuming she would tend towards academic endeavours where she would surely succeed. 

Her critical and insightful mind (with a pinch of adolescent rebellion and surging hormones) was conflicting with this pressure. She often came up with creative ways to solve mathematics problems, surely she can find an interesting method to solve life problems, rather than follow the clear path ahead of her.

Finally she responded, "What do you mean, Sir?"

"Well, is there an option outside of further education or employment?"

"Are you suggesting I should drop out and live off of social benefits?"

"I don't really see that as an option, as much as a delay"

We discussed for quite some time as she guessed all of the various other options, generally falling under either further education (e.g. TAFE, community college, MOOCs) or employment (defence force, office work, volunteering).  Her obtuse brain also put some interesting ideas, such as marrying into money or turning to a life of crime.

The length of the discussion pushed well into lunch before it got close to what I was thinking of.

She was becoming exacerbated when she dropped a throw away line, "perhaps I just need to discover my own Facebook, or something"

"Now you are getting close... but Facebook has already been invented."

I could see the look in her eye change as she saw my face brighten. 

So I told my student about my friend, Chris who was passionate about pets. She hadn't got the grades (and she didn't have the composure) to study veterinary science at university. While Chris was considering what to do with her life she decided to print off 200 flyers offering to walk local dogs and put the flyers at the local vet. 

After a month, she had 3 clients with dogs which she walked every week. Chris would always arrive early, bring toys for the dogs and send the owners picture of the dogs having fun at the park or beach. Her passion was obvious and her client base kept growing. 

One day an existing client was going away for a weekend, and asked if my friend could drop by, feed her dogs and check that they were okay. My friend accepted, and quickly found many more people looking for dog and house minding. 

In less than 2 years, this attempt to make a little money walking dogs had expanded to a young lady in her early 20's converting a shop into a Doggie Day Care, and employing a group of casual dog walkers and house sitters.  

So I asked my student, "What was the point of this story?"

She immediately said "Follow your passion."

"That is part of it," I replied "and an important part, but the underlying point is that there is a third option, outside of academic or vocational. You can choose an Entrepreneurial path. Start your own business. It is a high risk option and it is hard to teach for, but it may be the most rewarding"

The student didn't say much else after that. She left with a polite, "Thank you, sir" and went to lunch (or what was left of it). That was the last week before a month and a half of summer holidays, so I will need to wait to hear her update from our discussion.

Meanwhile I am left to consider what school can and do provide for students interested in the third paths after school. Core subjects give students the communication and logical skills, and the business and accounting courses that many school run, give some insight into business side also I am increasingly hearing of entrepreneurial topics being explored at various schools (including my own). 

Perhaps the last piece is a cultural shift, for teachers and parents to value the option for students whom seek to start up their own businesses. These students generate the jobs and develop solutions for all of us to enjoy.


Saturday 5 December 2015

Interactive online revision tool

For some time now I have felt that revision has too often been assigning students piles of practice questions. For a change, in addition to the assigned revision questions I produced an Interactive online revision page using Sway (My original post on this is here)

The student results spiked. It seems that when students are reviewing a maths topic it is better for them to have visual and interactive tools to explore and extend the concepts they are preparing for.

This is one of my favorite examples with interactive cards plus videos and pictures.


I have also loaded it for others to see at:
https://sway.uservoice.com/forums/266643-show-us-your-sway/suggestions/10975671-revision-canvas-for-year-8-mathematics-students

From a maths point of view I have found the ability to embed Geogebra materials into the Sway are valuable and easily found at https://tube.geogebra.org

The process is quite simple as follows:

1) Find the activity you want to include in your sway.

2) Click on the share button in the top right of the window.




3) Then copy the embed code to your clipboard.


4) In your Sway, Select "Cards" from the top and scroll down to "Embed"



5)  Then simply Paste from the clipboard, into the description (it even says to tap here are paste)



6) Click on Play or Preview, to see the embedded content in action.

I found it quite rewarding and so did the students when they were playing with these carefully selected activities.

Let me know how you go using Sway and embedding content in the comments.



Friday 4 December 2015

Box Optimisation

This was my penultimate lesson with my Year 11's Maths Methods class, it was perhaps my favorite lesson with them (accidentally left the best for last).

Inspired by a Question from the Sadler Mathematics Methods Text book and some photos Mr Woo shared recently, I undertook an activity with my class. I broke the students in to groups. Each received

  • 1 set of scissors,
  • 1 glue stick,
  • 1 ruler,
  • 6 pieces of colourful A4 paper.

and kindly lent from the Science Dept:

  • 1 set of digital scales and
  • 1 bottle of plastic fragments (but could use sand, rice or grains)



The first task was for students to convert the 6 pieces of A4 paper into 6 different sized boxes/baskets. This involved cutting squares of various sizes from the four corners (with the students measuring each square to be a set number of centimeters. (The larger the square the deeper the box.)


Students then put their boxes one by one on top of a set of scales and poured in plastic fragments. Once the students had documented the weight of the bits that each box could hold, they plotted these coordinates (with x being the size of the corner squares in cm, and y being the weight in grams)



Above is the points plotted by the students (different colours for different groups) As the examples above shows, after ~4cm the capacity of the box is reducing for any increase in size of the corner squares. This was good, but the real learning was yet to come.

Next we looked at the formula for the volume of each box. Students were able to recall the volume of a rectangular prism (from Year 8) is equal to length by width by height. We took one side of the corner square and labelled it "x", given A4 page is 21cm x 30cm, they identified that volume must be:

Height: x
Length: 30 - 2x
Width: 21 - 2x

Volume: x(30-2x)(21-2x)

Students graphed this function on top of the plotted points, and found that they didn't match. Why?
Much discussion, starting with students blaming the tools, then blaming each other and even blaming the graphing software. Until one pointed out that they were graphing different things.
The coordinates are the weight, and the function is volume.

As students realised this I asked how could we convert from volume to weight (covered in Year 9).

"We never learnt the formula to change between Weight and Volume" Really? Did anyone?
"I think that 1 litre weighs 1 kilogram" Does it? For all substances?
"We could weight a 1 litre jug?" Sounds good.

After a few measurements the students worked out that the plastic bits we used, weigh around 0.3 grams per cubic cm. Can we can transform this graph to approximate our findings (as we did in Year 11)?

What do we need to do? Translate or Dilate? Vertical or Horizontal?




(Dilate Vertically, by multiply 0.3)
https://www.desmos.com/calculator/ykreaoty9d

Finally my challenge was to find and create the maximum sized container. Using calculus techniques, the students found the stationary point at around 4cm. 

The lesson covered geometry, graphing, transformation of functions, calculus and problem solving using both hands on and ICT tools as part of group work. Although it required considerable teacher direction, this lesson was demonstrated every aspect of a lesson I try to include in my lessons and it was a wonderful success.