A Rather Cruel Problem...

Higher Education Seminar

A few weeks ago I attended a High Education Seminar run by the University of Oxford. Although heavily geared towards Oxbridge entrance, a few points of note were raised.

New Curriculum

August 2013: publication of final version of framework

September 2014: first implementation of the new syllabus

UCAS Applications

• UCAS.tv on youtube - advice on many matters
• unistats: statistical information on previous applications to universities
• prepare students well for HE fairs: give them guidance on what questions to ask and what to look for
• speak to local universities about people coming in to give talks about higher education
• prospectus grades are now often used as a marketing tool; students believe universities asking for AAB are better than ABB so universities are changing prospectu grades but may well accept lower
• HEI are unaware of where else students have applied
• all students for Oxbridge, Medical, Dentistry and Veterinaray are interviewed prior to offer
• not all universities operate a gathered field - when a good application comes in, they will get a place
• find out in advance if an interview is for selection or recruitment
• adjustment process on results day: be aware of students making snap decisions
• reference is very important: make HEI aware of any extenuating circumstances
• inform university immediately if a student faces difficulty between application and exams
• subject reading makes the most difference: talking about 1 or 2 texts in detail is much better than skim reading 10 or 15

Oxford Focus

• reduced grade offers are given to pupils from low income postcode and first student from a family etc.
• Oxford offers a unique week-long subject specific summer school to introduce pupils to the style of Oxbridge learning
• recent reduction in application of "working class" boys
• marked drop in part-time and mature student application since the fee increase
• Oxford is looking for pupils with "super-curricular" activities, ie. subject specific; they are not looking for all rounders
• want "intellectually brilliant" people
• consideration of pre-U qualification

Think ... Notice ... Wonder

This post comes as a culmination of many blogs that I've read this week, on the wondrous app that is flipboard (I'm not plugging, I promise).

Epsilon-Delta wrote a fantastic post on Noticing and Wondering, taking any article, commenting on what they noticed and the further questions they wanted to ask about it.
Inspired by Dan Meyer's Maths Curriculum Makeover, I aim to get students to think about what it is they need to know, rather than simply plucking the available (and often only available) information out of the textbook question.

Caloric Quandry
With this in mind, and Geoff's post on Caloric Quandry, the following problem could be posed.

Which coke can is higher in calories?

I expect some of the following 'notices' to appear:

Notices
- one coke can is taller than the other
- one coke can is fatter than the other
- coke cans have a cylinder shape
.... etc.

Students would then move onto the questions they wanted to ask...

Constructions

 In an observed lesson on the construction of triangles, the following question was posed:

What do you need to know in order to produce an exact copy of this triangle?

I liked that the students then had to consider the angles and lengths of sides of the triangle rather than simply beginning with "this is how you construct an SAS triangle..."

Perhaps beginning with a less leading questions such as:

"Copy this triangle onto the paper in front of you"

Would encourage pupils to ask themselves the question "what do I need to know" rather than it being presented to them.

Once a large collection of different pieces of information had been gathered, the more focussed question of

"What is the smallest number of pieces of information you need to be sure you had it correct?"

Then later on...

"Are there 3 pieces of information that you could be given and still not be able to construct the triangle?"



Update 20/05/2013

Mr. Taylor used the Notice / Wonder technique fantastically with a Year 7 class last week - he puts its success down to the careful structuring and explanation of the technique, and reminding students when they didn't use "I notice" or "I wonder" at the start of their statements.

An Insight from Canada

During the Easter Department week, we were graced by John Mason, who shared a wealth of ideas and thoughts with us on attention - here are just some of the few I managed to jot down.

Our first task of the morning was this:

We all initially considered it individually, then discussed our thought processes as a group. One person started looking at the overview first before focusing down, another looked for a particular corner first before the rest of the shape, and another was mesmorised by a certain part of the diagram!

When we were given the answer, it was noted that a variety of emotions: delighted / satisfied / depressed / cheated were felt, depending upon how far through the problem a person had worked.

Parking

One of the key ideas of the session was to develop pupils' ability to park an idea; when they had a good idea, temporarily put it to one side and see if there is a more efficient way of doing it, rather than just ploughing on through.

Just

Having said I'd aim not to use this word, I realise I've written it in the sentence above. "Just" implies a simple step, in the eyes of the speaker, but it may not be so in the eye of the listener, so should be avoided.

If a student is attending to a problem in a different way, they may not be able to hear what you're saying, unless you give sufficient detail to show how you are attending to it prior to any further development.

Group Discussion

Throughout this session, John elicited ideas from us and exemplified classroom techniques. The two I have taken away from this are:

Please

In PDP sessions in my S1 school, we were advised to use thank you rather than please as a behavioural technique. However, although this is effective in terms of showing pupils that a behavioural pattern is expected, I had almost forgotten where please could be used to equal effect/

As John called upon us to offer our opinion, he said please, inviting us to talk and demonstrating that he was interested in our comments.

I think I want to modify my conjecture

A helpful alternative to "bummer, that doesn't make any sense"

Say What You See (SWUC)

Possibly stolen from catchphrase this was really helpful in allowing pupils of all abilities to participate, such that everyone can succeed - it lowers the threshold. This was implemented with the image below.

Update 22/05/2013: Used this with a Year 9 class who weren't particularly vocal but came out with some good ideas, particularly when we allowed the large blue block to be worth £300 and determined how much each of the other blocks would be worth.

However, one comment: "I notice it's a fraction wall cos I did it in Year 8" was followed by further discussion, where the student in question knew it was a fraction wall but couldn't tell me any fraction that the wall could represent. Perhaps not so memorable, or not enough discussion in Year 8?

A Selection of Activities

Without time to comment on further, here are some of the other ideas that appeared in the session...

Snowballs

I've previously used snowballs as an icebreaker - given each student a piece of paper to write their name, something about themselves and the hardest maths question they can answer.

Recently it was suggested that it could be used to creating polished answers, by posing a question for each student on a card, then they throw them across the room and add to each others' answers. A possible (maybe ideal?) way it would be play out is shown below...

The ideas could then be shared with the class, as the person with the snowball would not be "responsible" for the ideas, merely sharing someone else's.

Packs and Packets

No comment needed!

Guess the Objective

With a bit of time of my hands this weekend, I've revisited an idea sent in the faculty newsletter, on a dingbat-style lesson objective.

Inspired by this, I've started to create a collection - can you guess which topics these are? Suggestions greatly appreciated!

Assessment

We have all struggled to find effective formal and informal assessment methods, both for and of learning. The brainstorm session in the morning was a discussion of those ideas which we have found to be successful, which covered the following:

- using proformas to give feedback to pupils

- putting books in coloured boxes depending on progress at end of lesson

- 5 minute "snapshot" test at the start of a lesson with immediate feedback

- using a betting system on whiteboards, so you can see how confident students are of their answers

- having a google form mini-test on laptops at the back of the room that students take it in turns to do throughout the lesson: particularly useful for assessing prior knowledge before starting a topic

Working with Groups

Yesterday we took part on a fantastic session on working in groups (note: categorically NOT group work.) The emphasis of this session was on using the activities in a pastoral setting, but many could be equally applied to a curriculum lesson.

Fruit Salad
This initially activity was an icebreaker, where each person stated their name, their hero and a reason for their choice. The catch was, as we went around the circle, each person had to say the names and heroes / heroines of those that had previously introduced themselves. (N.B. The reasons for the choices do not have to be remembered) By the leader of the group positioning themselves at the end, this gives a good amount of time to learn names.
A further development for this is to have one person standing in the middle stating 2 heroes / heroines, who then have to move to another seat. The goal of the person in the middle is to get to the free seat before the movers can. If the person in the middle prefers, they can call "heroes" and everyone has to change seat.

Mathematical Adaptation
Substituting favourite number for heroes and heroines would also be a good icebreaker, as students often have interesting stories for their preferred numbers. In the latter part of the activity, mathematical sums could be given to arrive at possible favourite numbers, ranging from clues such 7+1 to sin(pi/2).

Chair Numbers
In this activity, each chair in the circle was assigned a number. Adapted from the zoomy-zoomy drinking game, each player states their chair number, then another number, e.g 4 - 1. The catch here is that you cannot send it back to the chair you had before.
This activity can be developed to use different labels for the chairs, for example emotions then if the group is ready for it, they can then discuss which chair they think they should be on today and which chair they would least like to be on.
The final version was very effective in getting the members to be more comfortable with certain vocabulary, in the context of sex education.

Mathematical Adaptation
Each chair could be named by a mathematical keyword.

Teddy's 5
A chance for people to show their knowledge on a particular topic, those around the outside challenge the person in the middle to list 5 of a category, for example 5 football teams in the premiership. The person in the middle then has to list these before the teddy bear gets back around to the challenger.
Mathematical Adaptation
5 things associated with right-angled triangles. To ensure good topics were being selected, it might be useful to start with a card to be given to each person, from which they can select a topic. This would give a better idea of the style, then the group could move onto choosing their own.

I imagine...
Here the aim is to get out any preconceptions about a personand give the person in the spotlight the opportunity to coounter these, where in other situations they might not have had the opportunity.
When introducing this exercise it is important to give a mixture of superficial and meaningful examples, e.g.
- I imagine that you prefer cornflakes to rice krispies
- I imagine that you get on better with your Mum than your Dad
It must be stressed that you cannot say anything that you know to be true, only things that you imagine about a person.

Differences
Here, the person in the hotseat can only get out of it if they say somehting about themselves that isn't true of anyone else. If it is true of someone else, they must say so, and the person remains in the hotseat.

Positives
One person becomes the guesser, and faces  outside the circle. By silent pointing, the group decides who is going to be described. Each person in the circle then has to describe the person with a postive thing, e.g. "This person has really nice blue eyes." Afterwards, the guesser can turn around before making a guess.
It is very important that no-one is able to pass, as this sets a precident. Instead, go back to that person at the end,  to avoid slowling the pace.

Interactive Pythagoras

In an attempt to implement Dan Meyer's style of finding out which information is required to solve a problem, I inroduced strings, spiders and flies to my revision lesson on Pythagoras and Trigonometry.

Excuse the Perspective Please! Open-ended cuboid with string diagonally across, requiring 3D Pythagoras.

3 cuboids with one open end were constructed, with a piece of string running diagonally from the bottom left corner in the diagram to the nearmost top right hand corner. Students were then challenged to find the length of the string. At the end of the exercise, they were quite excited to rip the boxes open and check whether they were correct!

For the second activity, a spider was placed on one side of the room and a fly on the other side. They were asked to find the shortest distance that spider could travel to get to eat the fly.

A combination of 7 boys each holding metre rulers across the room as they were unconvinced that the room didn't have exactly parallel walls and ceiling/floor. Shortening of the route by going diagonally across the ceiling came quickly, but going diagonally across the whole route became a little more difficult. This practical is based upon the following worksheet question:

My hate of fizzy drinks meant that I didn't do this question today, but it might also be a good investigation for the future.