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Saturday 28 December 2013

Information is Beautiful

Thoroughly engrossed in my new TEDTalks podcast, I came across David McCandless's talk on "The Beauty of Data Visualization"




And later on Google nGrams, which graphs over 200 years of data in books and is searchable by keywords. With certain terms, there is an awful lot of fruitful discussion that could come from them, click here to have a go.

Coupled with some great infograms on iPads, there's plenty of thought provoking material to go around.

Estimation

While tutoring a new students last week, I was surprised, but perhaps shouldn't have been, that they didn't have any appreciation for how much a gram was, or a kilogram, or how many pens would fit in my pencil case. Time for some research of how to best to engage and educate... I came across the game above and although it's a leap too far right now, it could be easily adapted to a range of objects that the student would be more aware of, and perhaps even things they could round up in the home after doing the task to check their answer.

Meanwhile for whole classes as well as tutoring, Andrew Stadel has created a fantastic website called Estimation 180 where you input your estimation into a google form, can see other peoples' responses and also get an answer, for all those that require a sense of resolution. In his blog he suggests using it as a start of lesson activity with students recording their guess and confidence level in the back of their book.


Sunday 10 November 2013

Ofsted

Just read this fantastic quote about Ofsted inspections from Cazzy Pots.

"In preparing for lesson observations, what is actually happening to many teachers in an awful lot of schools is more reminiscent of what Michael Jackson ultimately did to his face. He kept picking and messing to the point of ugly ruin. So obsessed was he with achieving the perfect nose, that the whole thing eventually collapsed onto his face and he had to use tape to hold it together."

Inspired by Dyslexia Series: A Fraction

To me, a fraction is a specified number of pieces, where the pieces are equal segments of a whole (I'll probably revise this many times during my career). 

So the equal segments part of the meaning is represented by this:

But to show the specified number of pieces part, I feel a video might be required. Also the picture, does not define but does imply, that a fraction must be less than one. Hmm.

Saturday 9 November 2013

The Gift of Dyslexia

This morning I went to a fascinating talk by Sue Hall on the Gift of Dyslexia. Three hours of dyslexia lectures, many hours and papers of reading and I hadn't learnt anything. In one hour with Sue, my mind's eye was opened and I'm starting to understand how it all fits together.
"everybody is capable of learning, just not necessarily the way they are being taught"
Sue defines dyslexia as a natural ability to alter perception (which I don't possess to any real degree).

Exercise 1: Picture a dog in your mind, and have it looking at you face on. Now walk around it, so you can see it side on. Now walk behind and look at it from the tail. Finally walk round, looking at the final side and again face the front.

Dyslexic people find this incredibly easy, whereas for myself I was just able to turn the dog around, almost as though it was stood on a lazy susan, but I wasn't able to move myself around the dog. This ability to alter perception is incredibly useful for athletes, for example Wayne Gretzkey is able to view the whole hockey game from above so can easily decide where he needs to be or where to hit the puck.

But out of the 3D real-life world and into the 2D world of print, this gift can be a hindrance. When looking at a lower case d when your mind's eye is wandering around it, there's no guarantee that it will come up as a d, or a p, or even a sticking out tongue. Our education system is established for auditory learners, so phonetic instruction is used for learning to read, which doesn't work for dyslexic learners. Instead they need to visualise the whole word and connect it with an image. Instead, students are often given 'band aid' techniques, such as big elephants can always understand small elephants which helps to spell 'because' , but this doesn't directly relate to the word, it's like third party learning.


Exercise 2: Picture a bicycle in your mind. What colour is it? Now get rid of the bicycle and think of a pencil. Now picture the meaning of tree. Now picture the meaning of the.

In this second exercise, I was surprised by how unimaginative I was when I realised that my image of a bicycle was a pencil sketch in 2D. I used my imagination for the next few, picturing a beautiful oak tree, with the reds and oranges of autumn. But 'the' and I was completely stumped. As was everyone else. For a dyslexic that is creating their own internal film from reading, the screen is suddenly blank. It turns out we have 217 of these 'filler' words.
If the movie screen is blank would you stay in the theatre?
A simplistic image of
multiplication.
So for maths we need to come up with images to represent our concepts, our vocabulary, our meaning and our purpose. What's the image for an integer? What's the image for multiplying?

Now initially for multiplying it seemed easy to consider it as bags containing sweets, and having multiple lots of these sweet bags. But what happens when we multiply fractions? It seems that if we are able to come out with a satisfactory image to represent multiplication, we will have completely defined it, not only for dyslexic pupils but for the understanding of all students.

Exercise 3: Imagine the house that you live in. Now get rid of it. Now imagine your house again. And get rid of it. Now imagine it again. And get rid of it. Now imagine it again.

Repetition is dull. Once you have an image in your mind, you don't need to repeat it over and over again. In fact, after a while, I started doubting whether I was truly picturing my house properly. If this is done with a mathematical concept, the student might start doubting whether they truly understood it in the first place.

Exercise 4: Calculate 137 + 19 in your head and write down the answer. Now, without a single word entering your head, and with no internal dialogue of what you are doing, calculate 293 + 18.

I couldn't it. I literally couldn't stop my brain from talking me through what I was doing and what the result was. For some dyslexics at the extreme end of the spectrum, they have never heard a voice inside their head. They must be working in some other way!

Exercise 5: You can only watch the video below once. As it is running, write about it. Stop writing when the video stops.

If you didn't make it to the end don't worry! Most movies are 24 frames per second. Dyslexics think at 32 frames per second. Imagine being asked to write about a concept, when the video is running even faster than what you just watched. I gave up and now I understand why they might too.

Instead, Sue recommends drawing a picture mind map. Once that's done, number the pictures. Then the student has a framework, taking each picture in turn and writing about what each picture means.



Now to begin to find images for all of mathematics... in the world...
Sue's website can be found here.

Monday 24 June 2013

Twitter!

So... twitter is like everyone's reflective blogs... straight into your phone, your laptop, your tablet. GENIUS. And I am VERY late on the seen.

However, better late than never, this is what I found for assessment today:

Wednesday 12 June 2013

Wednesday 5 June 2013

Making the Most of your NQT Year

Today's PDP session was run by 2 NQT's, who got us thinking about the things that would really improve our management skills as teachers. The session was run fantastically; here are some of the key pieces of advice that came out.


"The pre-RAG"




A cunning idea to cut down on marking time: get students to RAG their own work prior to handing it in.


GREEN: for something they are proud of

PINK: for something they want more help with.


This then means that you have something to praise, and something to work on immediately, and can give personalised feedback without it taking too long.





Additionally, using a routine colour scheme, for example purple for teacher feedback and green for pupils response will mean it is quick to check understanding in response to the questions that have been set.






Lesson Moulds & Templates
Have some pre-made powerpoint and lesson templates that encompass most of the different styles of lesson you will teach and share these with the pupils, for example:
"this is a jigsaw lesson" - and the pupils will know they will be slotting lots of mathematics together.

Other styles could be: exploratory, consolidation, practice etc.



Here's a video of the prompters we were using in the session:
Use the pause button to view prompters for longer.



Other Useful Pointers

  • don't try and fix everything when marking
  • plan term first, then the week
  • if you can do it in the next 5 minutes, do it in the next 5 minutes
  • make routines simple enough for students to explain to each other
  • use the same system for every class
  • "eat the frog"
  • keep a walk with me remembering device
  • reply to mass irrelevant emails with a "this isn't meant for me" style of email

Monday 3 June 2013

"Feel Good Friday" Phone Call

Choose three students who have really impressed you that week and call home - be specific to start but then expand to more general behaviour.

"What's the least amount I have to do and the most amount they get to do?"

Today's CT meeting focussed on marking and assessment. We read an extract from "The Lazy Teacher's Handbook" by Jim Smith, which began by defining the difference between marking and assessment.

Assessment: is any form of feedback - verbal, written text from the teacher or any other student
Marking: feedback that includes justification of a grade of some description

In advance of the ideas below, it is advised to use these as part of a learning routine rather than a special one-off occasion.

"Assessment and marking must surely be a two-way activity"

  • students respond to feedback
  • communicate the focus of the marking and assessment to the students
  • ask the students to identify something for you to focus on, such as where they have improved their spelling, presentations or explanation points
  • students keep learning blogs: teacher can comment on it
  • students write the comment they think you should write and justify why by writing comments in the margins of really good pieces of work that meet the success criteria
  • ask students to mark the marking : students mark feedback in terms of how it helps them learn.
Other Assessment Ideas
  • exhibitions to showcase work: "comments on this one please"
  • 'guest marker': mayor, math professor etc.
  • film group presentations with 2 groups at a time, post on VLE & in IT room get students to complete thought cards from presentations
  • presenting to colleague's classes
  • checking time in class: but the checker gets the penalty rather than the person who's work it is

Wednesday 22 May 2013

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

Monday 20 May 2013

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.

Sunday 12 May 2013

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!

Saturday 11 May 2013

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

Tuesday 7 May 2013

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.

Thursday 2 May 2013

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.




Wednesday 24 April 2013

Sequence Zoo

In preparing for a Year 8 revision lesson for a SATS paper, I came across the following questions:


This is a great example of the requirement for proof and reasoning: any of the nth term expressions would fit the first three terms of 1, 2 and 4, yet depending on the situation it is likely that some of the expressions would be inappropriate.


It is also reminded me of an idea of Lucia Handley, using cubes to investigate sequences.


The Sequence Zoo

The lesson began with an arrangement of animals: giraffes, pigs and cows/zebras. Pupils could then be challenged to work out what the baby of each animal looked like, or to work out whether they could give the number of bricks required to make a species, given its height.

Alternatively, the animals in the image above could be used and pupils had to find out which animal had grown out of sequence.

The cow/zebra is particularly interesting, as you could look either at total number of blocks, or the white / black components.

Thanks Lucia!

Tuesday 23 April 2013

Maths is Just Another Language

Inspired by the video of the 10 year old maths teacher, I want to increase my focus on maths as a language.

For example,

Translate these sentences into mathematish



These could be adapted to suit each topic but overall should help students to understand how expressions are formed and therefore also to interpret them. This falls in line with Anne Watson's thinking that students should be taught to read algebraic sentences out loud to give them meaning.

UPDATE: 28/05/2013
For algebra specific translations, translating english to algebrese

When you take a real-world situation and translate it into math, you are actually 'expressing' it; hence the mathematical term 'expression'.

Monday 22 April 2013

The Lesson Planning Mountain

A strong focus of the department week has been on lesson planning.

Within our small groups, we analysed our own lesson plans to look for evidence of Learners' Mathematical Development, in terms of the following structure:
see - do - record

see - experience  - master

We were particularly sceptical of the latter of these structures, as experience didn't necessarily imply investigating, doing or analysing, before the pupil was expected to have reached the master phase.


The Lesson Planning Mountain
Instead, we began to consider the lessons using the analogy of a mountain climb of two peaks, as shown below.




  • The lesson begins with the class consolidating prior knowledge together, at base camp.
  • The climb begins with everyone walking together up the mountain, as new material is introduced. During this stage, pupils will begin to acclimatise to the higher altitude.
  • By the time the summit is reached, it is time for the pupils to part ways on their descent and continue as individuals.
  • Depending on how comfortable the students feel, they can sled, ski or abseil down (in increasing speed order). This gives the first opportunity for differentiation of activity.
  • At the point at which the second mountain comes into view, pupils can make the decision whether to climb higher to explore the subject in more detail or whether to continue practising as they head down the mountain.


Having previously seen the model of the tree where pupils label which person they think they are [insert link here], this mountain analogy could also be used, where pupils label where on the ascent they think they are at any stage in the lesson.

Tuesday 5 March 2013

Big Picture Learning Objectives

Giving Pupils the BIG PICTURE  in the LOs:

Room Layout:
continue to change table arrangement to tables of 4 for Year 9 to encourage group work

Monday 4 March 2013

That's a Genius Idea!

I've come to a stage where I've heard of and thought of lots of great ideas for teaching maths, but had no real way of sorting them, remembering them, or being able to search for them when re-teaching a topic.

So I've created a quick document which should give enough information to kick-start my memory and point me in the right direction to the resources on TES. The template is a work in progress... but essentially consists of:

  • main topic
  • sub-topic
  • key words (also helpful for when searching)
  • 4 real-life images relating to the topic (or something else if not yet thought of!)
  • main idea
  • links to TES resources



On the real-version (found here) all TES links are active. Hopefully a much better system than my brain!

Tuesday 26 February 2013

Beer - Guinness - Gordon's ... a pattern?

Professional Tutor's opinion of the belief in young people, from the QISA website.



A lot of today's session comes from Teacher's Toolkit, by Paul Ginnis. One lesson this week, I will use the Lesson Planning Audit against one of my lessons.

We were also pointed again to Jackie Beere's book, the Perfect Oftsed Lesson.

Learning Objectives
  • 2BA2 - to be able to
  • bridging between previous lesson to today and beyond
  • put 'previous lesson' section on 5 mins Lesson Plan
  • think about 'purpose' column in terms of impact on learning
  • could put double-sided sticky tape on the back of printed learning objectives so they can be stuck in... messy?
Lesson Planning
  • higher level questions: Bloom
  • think about time frame for teaching this area
  • laminated mobile phones, write a text to their mum? ... might be problems with recording in book
  • SA extension: smart arse!
Key Terms
  • glossary stuck into back of book at the start - highlight as each word is covered?
  • "key word" spotter: record in a class key words book

Plenary Idea
  • "I am an expert at..." "To do this you need to..."
  • "I need an expert for..."
  • make sure there is a space for names!

Active Lessons
Negative Numbers
Giant number line in sports hall, get them to start at different places and then give sums, gives opportunity for some pupils to walk along the number line but some to have to work it out straight away - possibly in a different area?

Multiplication
Make giant multiplication grid, students in each 'box' of grid with a whiteboard, give sums so have to work as team to get final answer as each person has a job - differentiate by putting certain students in different spaces, then progress by moving around.



Tuesday 19 February 2013

Delphi Method

Wikipedia

The Delphi method (pron.: /ˈdÉ›lfaɪ/ del-fy) is a structured communication technique, originally developed as a systematic, interactive forecasting method which relies on a panel of experts.[1]
In the standard version, the experts answer questionnaires in two or more rounds. After each round, a facilitator provides an anonymous summary of the experts’ forecasts from the previous round as well as the reasons they provided for their judgments. Thus, experts are encouraged to revise their earlier answers in light of the replies of other members of their panel. It is believed that during this process the range of the answers will decrease and the group will converge towards the "correct" answer. Finally, the process is stopped after a pre-defined stop criterion (e.g. number of rounds, achievement of consensus, stability of results) and the mean or median scores of the final rounds determine the results.[2]

As I am about to move onto area and perimeter, words with which many pupils seem to struggle, I thought it might be an idea to use this Delphi method as a way to elicit meaning from the pupils, highlighting misconceptions then attempting to narrow down to a definition that all pupils agree with and can understand.

Possible Implementation: in silence each student writes down their own definition, then discuss to find best definition in groups of 4 - read out to class inc. any that they discarded because they thought it wasn't correct.

Friday 8 February 2013

Autograph Session

Pentagons, Hexagons and Airports

We were shown to use Flash Earth for a whole variety of uses!

  • Reagen Airport - bearings, what do the runway numbers mean
  • Hexagon on the North Western tip of Australia
  • Pentagon in Washington
  • Parabola in Dungeness


Jing - download here.

For more info on everything... go to Douglas Butler's Blog





word_test_jing

Thursday 7 February 2013

Mathematical Language Idea

A fab find on Mr. Collins' blog - Mathematical Concepts Wall! This idea ties in nicely with the week's focus on mathematical language.


For more info, see his blog post here.

Too Exciting Problems!

Classroom Management
This morning began with a continuation of the classroom management discussion from yesterday.

  • Benchmarking: draw a line in pupils books to help them see how much work they've done in 5 minutes  - possible photocopy and send home?
  • Quiet Word: avoids giving pupils the attention they may be craving with their behaviour
  • Orders not Requests: removing the "can do" option makes it non-negotiable; adding "thank you" at the end compels them to follow instructions
Seating Plans
  • seating plans for instruction, then can work with whoever they want providing they remain on task; bring back to seating plan if not
  • study buddies: get students to decide who they work well with
  • seat pupils with a friend but not in friendship groups
How Important is Proof?
Proof was the main part of our discussion today. Initially we all had varying definition of proof, so described it as:
Proof: a valid argument that logically builds on knowledge that the students already have to get to the next step.
 We then looked at a progression of problems given in a lesson aimed at motivating proof..



Motivation
The above is an example of motivation for the study of proof, in the same way that the algebraic magic triangle is motivation for the study of algebra.

Individual task motivation could also be achieved by having codes, padlocks and prizes.

The full article written by Andreas Stylianides can be found here.



Polynomial Division
On a total sidenote to the whole session, I learnt synthetic division today (RH working):
As it's very removed from what you're actually doing with polynomial division, I'd be reluctant to teach it this way, but use it myself to check pupils' answers quickly and/or teach to Year 13s if I feel they have a full understanding of the concept and therefore would just be giving them an alternative method.

Proof of Adding +ve and -ve



Tuesday 5 February 2013

Blonde Hair ... tis a problem.

Language
The session began as a follow on to yesterday's EAL focus; discussing language in mathematics.

Common confusion with words came up:

  • minus & negative
  • trials & events
  • alternative and alternate angles
  • random & strage
  • area & perimeter
In order to combat this, a possible idea is to use games such as Taboo (or Oobat, as pupils are encouraged rather than not allowed to use the words on the cards) and Articulate (or Mathiculate, link here.)

Definitions
So it turns out that none of us can define anything - on being asked to draw a diagram, we nearly all drew something with 4 sides and a rectangle - a very particular case! Instead, a much more open example such as:
We were encouraged to focus on the meaning of words rather than their definitions; especially in considering the context in which the word was used.

One possible ideas was to split the class in half, having them each working on different things, e.g.
  • multipling and adding fractions
  • adding and multipling negative numbers
  • intercept and gradient
  • a squared and 2a

A Level Teaching
Nick's session on A level teaching followed, with a match-up activity of graphs, their derivatives and stationary points.
We then created our own activity for a topic we may be teaching.

Our activity was on momentum and is most definitely a work in progress...
The first steps involve matching the worded problem with initial and final diagrams:


then sorting these sets into one of the boxes in the table below:

Conservation of energy and momentum are both considerations here!

Problem Solving
Gabriel's session began with a blonde problem (I really did feel blonde after failing to answer it!)

A discussion followed on the importance of giving us time to first read and think about the question, before group discussion was allowed. We were also given a task to step out of problem solving to write down what we felt about the task, and again at the end - a great way to consider emotions with problem solving.

Resources Extra Session

Here are the links to (hopefully) everything you may need to access during this evening's session.

TES
To see resources that each other have made, search for the person and use People as the drop down box, the click Follow.

Wordle
Words are scaled according to prominence in the text, blogs etc.
Useful to do at the beginning of a chapter and get pupils to highlight in yellow when they hear a word for the first time and highlight green when they feel comfortable with that word.


A helpful app created by a teacher which allows you to enter your classes, your timetable and your students name and overlay this random name generator on top of your powerpoint presentation.

Downloadable emulator for sharp calculators - requires ZIP unpacker.


MJMT's Resources

´        New Zealand maths, nzmaths [http://nzmaths.co.nz/]
´        Centre for Innovation in Mathematics Teaching, mepcimt [http://www.cimt.plymouth.ac.uk/projects/mep/default.htm]
´        Mr Barton Maths [http://www.mrbartonmaths.com/]
´        Waldo maths [http://www.waldomaths.com/]. Equation solver is recommended.
´        Risps [http://www.risps.co.uk/]