Building firmer maths foundations

Ever wonder why young people struggle with mathematics? Some say it's too abstract. But very practical users of maths like accountants and store clerks would probably disagree. Others say it's too disconnected from real life, but most tradesmen would point out you cant build a house, lay bricks or make furniture without it. Some think its because we teach maths as technique. But architects, engineers and physicists rely on  routines to make numerous calculations simple.

Another view is that unless your teacher knows their mathematics, neither will you. But as any teacher will tell you, neophyte teachers often learn more about a subject by teaching it. That's how I learned to love maths.

The biggest problem maths teachers face - especially in secondary schools - is the poor foundations on which they are having to lay more complex concepts in algebra and geometry. It's like trying to stand a skyscraper on tree stumps.

The problem begins in primary school. If you can't understand numbers, fractions and decimals and the four basic functions - add, sutract, multiply and divide - you are not in the race. Or if you can't tell the difference between a circle and an ellipse, or a square and a rectangle, or comprehend angles, you are also in trouble.

Most primary teachers have very little confidence is their own maths ability and even less in their ability to help young people learn the basics. The last time most primary students in the UK studied maths was towards the end of secondary school. Now the UK government is spending million of pounds to hire 13,000 maths specialists to coach students and teachers. The USA has similar problems. Just 27 per cent of 600 Massachusetts teachers who took a teaching licensing exam passed the maths part of the test, although most of those who failed, went on to become teachers.

But simply knowing your maths may not be enough. How you learn maths could be much more than important, such as learning to discuss mathematical ideas, in addition to knowing how to use mathematical techniques/operations.

I have had the pleasure of working with some gifted mathematics teachers such as Ian from Middlesborough in the north of England. They are gifted because they inspire young people to fall in love with mathematics. It's not only because they know their mathematics but because they know how to engage young people in exploring the patterns and the mysteries.

Middlesborough Ian helps "feral" secondary students become capable mathematicians in less than 12 months. He uses an approach which is more akin to the "change management" tactics employed in big corporations. Very few of the techniques are specific to mathematics. But every primary school teacher would recognize the teaching techniques he applies as the fundamental principles of "co-operative learning".

The students practise working/learning in groups. They give leadership to their peers, helping each other achieve their goals, resolving conflicts and communicating ideas. They value their own opinions and the opinions of others. Along the way, they play with mathematical ideas and begin to think, act and and feel like a community of mathematicians. They could be just as easily be learning to think and act like geographers, scientists or writers.

The class is organised into three groups. A demonstration team guides other groups through whole-of-class learning activities using a team learning system. A resource team searches the internet for images, videos, simulations and sounds that can be used with questions and question sequences used to explore mathematical topics. Activity builder teams, which includes everyone in the class, design and create the questions and methods and decide which to trial.

Most class activities begin with a ten minutes-long engaging, fun activity that reflects on previous learning, not necessarily about mathematics, but often about general student literacy or a mental oral activity.

Six months into the school year, the culture of the class begins to change. The teacher is no longer "the enemy" but is valued as a mentor and challenger. The students begin to see themselves as "risk takers", willing to explore any new ideas to which they are exposed. They take full ownership of their activities and the bad behaviour evaporates.

There is a good explanation for this change, and it is provided by Complexity Theory, which predicts how systems change state, like the shift from ice to liquid water. A group of students is just another system. New order emerges in the group "auto-catalytically" when the discussion cross-fertiilizes other discussion. This occurs when the ideas provoke so many new ideas, that the process becomes, self-sustaining.

Like a contagious disease!

Here's an example of a workshop designed to help students create their own learning activities:

1. Search the internet for an image, simulation or website that would help you learn about the names of the parts of a circle, and how to calculate the diameter and circumference. Make a list of the sites, images etc.you have discovered and what each explains.

2. Design an activity/sequence of questions to a) describe all the parts of a circle and b) how they relate or connect to each other.

3. Describe a technique for calculating the circumference of a circle if you know the radius. Give an example

4. If you know the diameter, how could you go about calculating the circumferene of the circle. What's a really simple trick/technique to remember?

5. Describe a technique for measuring the area of a circle if you know the radius? If you know the diameter?

6. Explain the number Pi to a five year old.

Fitzgerald, R.N., & Findlay, J. (2006). Transforming a mathematics classroom with new roles, rules and tools. Presentation at Transformational Tools for 21^st Century Minds conference, Rockhampton, October 25-27, Queensland. Download this article.

Creative writing with constraints

Fancy yourself as a poet? It's actually quite easy if you practice the arcane literary art of constraint-based writing. Leave out a letter. Use only certain letters. Use only some words.

Imagine the havoc that missing "a"s or "e"s would have on Shakespeare's Macbeth, Chaucer's Canterbury Tales or Charles Dickens A Tale of Two Cities. Gibberish perhaps.

But not when you deliberately write that way.

Christian Bok, author of Eunioa, which literally means beautiful thinking, is a master of the art. Eunoia has five chapters - A, E, I, O and U. The words in Chapter A contains only "a"s such as all, ball, bat, chat and abracadabra. Each chapter follows the same rule.

Australian teen author John Marsden teaches young people to write great stories using sets of rules, which implement some of these constraints. Rules such as "Don't let language bully you", "Capture the voice of the character" and "Show, don't tell a story."

When he asks you to "Write a story about the ocean without using the letter "e", all that rolls of your ball-point sounds like poetry. It's a form of constraint-based writing.

Some of the people in our network use these kinds of fun activities to warm up the conference crowd before we get down to the strategizing and decision making. Here are some examples of what some people collectively contribute. My favorite is the pirate talk, achieved by breaking the lipogram rules and using words containing "e", but simply omitting the letter:

• Crabs fly through big salty H2O. Happily nibbling on all and sundry. 
• Swimming cold. Trusting cool liquid to quickly coat my throat. I spang to my fins, arms thrashing in windy rolling mountains of foam.
• Da c is big and runs from wall to wall. Its long and high and if you fall in you will want to dry off. My mum says that it was not so high as it is now, that it is low at night.  I think gravity has a tug and that this is why it slops about.
• In aqua crystals. Starfish, sand, and a pail of clams. I go for it, baby!
• Oshorn ar to b sailin d ruddy o's'n aaaaarrrrrgh @ d nd to b shor ma 'arty splis d bldin main bras i'll b skutlin yr buttlin on d mount of yi (splash splash splash) undr d oishin hoit da joli rogr o giv mi a 'ome v'r d mrmaids doz roam aayh.
• An old man took a boat out far into a vast and wild mass. His craft was still and placid. It could not align with fish nor fowl.
• Foam. Flotsam. Rolling loud crashing fluid. A shark fish swam in coral again.
• An old man's rod knocks against boat in a tidal pool whilst fish, stingrays and crabs swam in salt flats.

So here's a workshop to practice your skills using various kinds of constraints:

1. Write a story about the ocean without using the letter "e"

2. Write a story about your life using ONLY the letters a,e,t,h,m,n,r,s,w.

3. Write an anthem for Africa, America, Australia or Asia using ONLY words that begin with the letter "a". e.g. Artists and artisans are attracted as Africa arises. Ascendant.

4. Write a story on any subject using ONLY or ALL the first 100 most frequently used words in English.

5. Write a story using words with no vowels using this list. You might have to use a dictionary to see what the words mean:

6. Write some snazzy words for a song to celebrate what your class, school, team, group or organization is going to do next year. Use alliteration, so most/all of the words start with the same letter. Choose any letter you like. e.g. Smart Students Sing Scintillating Songs.
7. EUNOIA means beautiful thinking and contains all the vowels - a, e, i, o and u.  Make a list of words containing ONLY the vowel “e” for example, men get.

8. Brainstorm words with ONLY the vowel "a". 1 vowel = 1 point, 2 vowels = 2, 3 vowels = 5, 4 vowels = 10, 5 vowels = 50, e.g. abracadabra = 50 points

9. Write a story using words that only contain the vowel "a", such as lava, cat.

10. Brainstorm words with ONLY the vowel "e”. . 1 vowel = 1 point, 2 vowels = 2, 3 vowels = 5, 4 vowels = 10, 5 vowels = 50, e.g. abracadabra = 50 points

11. Write a story using words that only contain the vowel "e", such as better, lever, me.

12. Brainstorm words with ONLY the vowel "i”. . 1 vowel = 1 point, 2 vowels = 2, 3 vowels = 5, 4 vowels = 10, 5 vowels = 50, e.g. abracadabra = 50 points

13. Write a story using words that only contain the vowel "i", such as sit, bit, wilt.

14. Brainstorm words with ONLY the vowel "o”. . 1 vowel = 1 point, 2 vowels = 2, 3 vowels = 5, 4 vowels = 10, 5 vowels = 50, e.g. abracadabra = 50 points

15. Write a story using words that only contain the vowel "o", such as moon, pot, soon.

16. Brainstorm words with ONLY the vowel "u”. . 1 vowel = 1 point, 2 vowels = 2, 3 vowels = 5, 4 vowels = 10, 5 vowels = 50, e.g. abracadabra = 50 points

17. Write a story using words that only contain the vowel "u", such as cut, mutt, bus.

Preparing for the school inspection

A sudden visit from the school inspection service (OFSTED in the UK) can bring terror to the heart of even the best and most experienced Head Teacher.

These days, not only do teachers have to demonstrate their pedagogical competence but they also have to show how well they work alongside parents, carers and other agencies such as the police and health services in the interests of the children.

OFSTED is the acronym for the Office for Standards in Children's Education and Skills which one Catholic School wag once described as standing for "Our Father Send Thee Eternal Damnation" which somewhat summarizes the general feeling of many head teachers.

The inspection process is a combination of self-evaluation, visitation/observation and a review of the records of your students' performances.

Prevention is better than cure. If you take positive steps to make improvements to your school ahead of inspection, the chances are you will be judged well, despite the difficulties you may encounter such as chronic absenteeism, bullying, racism, mass disengagement - 60 per cent of students in OECD countries are bored by school - or the 1-in-6 who leave school unable to read, write or count properly.

UK schools are judged on:

* Student performance (attainment, progress, dealing with disabilities/learning difficulties, whether they feel safe, adopt healthy lifestyles, contribute to the school or wider community. develop workplace skills that help them be successful in life ad whether how well they are catered for morally, socially, culturally and spiritually)

* Teacher performance (quality of teaching, assessment to help learning, whether the curriculum meets student's needs, and the care guidance and support that teachers give students).

* Leadership effectiveness (how well the leadership team drives improvement of teaching and learning, the role of the govering body in tackling issues, engagement with parents and carers, partnerships with others, promoting community cohesion and spending the budget well).

Parents also get to have a say about your performance and so do the students.

If you are taking positive steps towards improvements in all critical areas you will earn brownie points. If the parents think you are performing wonders, even though the changes are snail's pace incremental, then that will help your case. If you address individual learning styles, student safety and enjoyment and the special needs of students you will be rewarded.

The four ratings you can be given are Outstanding, Good, Satisfactory and Inadequate.

There are 25,000 schools in the United Kingdom and at any one time 40% of those schools are judged Satisfactory. That's 10,000 Head Teachers who live in constant fear of a downgrade to Inadequate or in the earnest hope their efforts will be judged Good.

Here's a check list of what schools can do to make life easier for themselves:

* Self-evaluation: Regularly and collectively complete the school self-evaluation against the "schedule of judgments". Develop develop strategies and action plans to deal promptly with every issue where the school has shortcomings. Expand the programs that work well. Involve the board of governors in planning for the future.

* Parent and carer engagement: Regularly conduct workshops with parents to get on top of their concerns about student progress, safety and wellbeing. Set up mini task forces so parents/carers can take some responsibility for resolving generic issues.

* Other agencies: Conduct regular meetings with other agencies to deal strategically with issues that cross agency boundaries e.g. crime, truancy or violence.

* Student voice: Conduct workshops with a large sample of students to learn how to better meet their specific learning needs, what captures their attention, what they like and don't like about their lessons and which kinds of pedagogical approaches work best.

* Professional and leadership development: Use the student voice outcomes as a basis for individual professional development.

Here's some workshops from the School Futures and Children Matter software applications from the Zing range of education titles that can help schools prepare for inspection and elevate their performance:

* A self-evaluation workshop to report on the effectiveness of the provision. There are six workshops which help staff collectively prepare for inspection:

1. Quality of teaching: How does teaching promote learning, progress and enjoyment for all pupils? e.g. range of teaching styles/activities, use of time, appropriate use of technology, builds on what students know, lesson planning etc.
2. Quality of teaching: How is assessment used to meet the needs of all pupils? e.g. the pupils know how they are doing, personalised learning, effective questioning, alert to errors/misconceptions.
3. Curriculum: How is the curriculum relevant to the needs of individual and groups of pupils and its impact on outcomes? e.g. memorable experience, rich opportunities, designed/modified to meet individual/group needs, extended/improved, etc.
4. Care, guidance and support: How is care and support provided to promote learning, personal development and well being? e.g. making use of parent and pupil views, welcoming environment, transition from nursery, between years and to secondary. vulnerable groups. challemging behaviour and to promote attenance.
5. Care, guidance and support: Write a story/case study about a potentially vulnerable child and show how you school provides effective, care guidance and support.

* Student voice workshops. See the blog: What young people want from school.

* School development: A professional development planning workshop to follow on from a student voice review of what students enjoy/dont enjoy about their school experience:

1. In 20 years time, what skills, capabilities and knowledge will our current students need to be successful in the world?
2. Describe the current problems that teachers experience in the classroom and how this affects teaching and learning. Respond like this (problem: impact).
3. Describe the current successes that we have in the classroom and how this benefits our students or society. Respond like this (successful activity: benefit)
4. If you had the task of remodelling/creating the ideal school, how would it be structured differently/the same? (classrooms, facilities, furniture, equipment, play areas, style).
5. What approaches to teaching and learning should we ideally retain or further develop to help equip our students for the future?
6. What aspects of our current approaches to teaching and learning will be need to eliminate if we are to be more successful in the future?
7. If we were to create a model of the ideal teacher, what would he/she be?
8. If we were to create a model of the ideal principal and senior staff, what role and management style should they have?
9. What should we do to cater for different learning styles?
10. What should we do to deal with current learner dissatisfiers with school, especially boredom and anxiety?
11. What should we do to deal with learners with disabilities?
12. What should we do to deal with learners who learn at differential rates.
13. What models of teaching and learning should we apply and in what contexts?
14. What should we do better manage the transition from primary to secondary schools?
15. What should we do to ensure that students at risk of non-completion are identified early and assisted?
16. What new/emerging pedagogical methods should we be aware of and be experimenting with in our school?
17. What should we do to deal with/capitalise on the differences between teacher and learner technological competence?
18. What should we be doing to satisfy or manage the expectations of parents, employers etc.
19. What models of teaching and learning around the world are we aware of that we could either emulate or surpass?
20. What should we be doing to cater for differing career paths, especially the vocational and academic divide?

* Engaging with parents: Here's the Staying safe workshop from the Children Matter workshop series. The six workshops are designed to achieve desirable health, enjoyment, achievement, positive contribution and economic well-being goals for young people.

1. How can we ensure children & young people and their carers are informed about key risks and how to deal with them?
2. What steps should be taken to provide children and young people with a safe environment?
3. What steps should be taken to minimise the incidence of child abuse and neglect?
4. What child protection arrangements should be put in place to meet the requirements of "Working Together to Safeguard Children"?
5. What should we do to ensure children and young people who are looked after are helped to stay safe?
6. What should we do to ensure children and young people with learning difficulties and disabilities are helped to stay safe?
7. How can we ensure that children affected by repeat domestic violence are identified, protected and supported?
8. What guidance and training should we provide to staff, carers and the public on how to recognise and raise child protection concerns?
9. How should we ensure there are secure arrangements for the recording and sharing of information on children and young people at risk, especially those crossing council boundaries and countries?

Talk like a scientist or expert

Although most of us can list the big inventions of the last century, very few of us can explain the theories. Think electromagnetism, nanotechnology, quantum dynamics, thermodynamics, nuclear fission or fluid dynamics.

Now, thanks to on-line encyclopedias such as Wikipedia and websites with interactive models, most of us can go on-line and learn about the theories for ourselves.

Knowledge that took centuries for the best brains in the world to discover and turn into well-tested theories can now be acquired in an afternoon by almost anyone.

But the act of observing a colorful, interactive model all on your own, may be just as ineffective as trying to memorize the old paper-based models they replace. Medical students, motor car mechanics and computer programmers can attest to the complexity/difficulty of rote learning new families of concepts, what they mean and how they connect to each other.

But there is a more effective way.

When you discuss a model/theory with others, the concepts become associated with concepts we already know. Over time, as we use the words, we strengthen the neuronal connections associated with the concepts, and so our own personal Google - our frontal lobes - has less trouble finding stuff when we need it.

In this way, learning shifts from being a left brain/hippocampus activity to a right brain problem solving/sensemaking approach.

By playing with and talking about any of the tens of thousands of models that your will find on-line you can start to think/act/talk like a scientist, mathematician, geographer, writer or the expert you would like to be. For example, How Stuff Works is a treasure trove of working models which you can link to and explore with others as shown in this image

Theories and models have come to have a life of their own. We often treat them as the real thing. The computer simulation, the town plan, the business spreadsheet, the script for a play, an orchestral piece, the steps for a dance, a shopping list, the cargo manifest or an airline ticket with its destinations and flights. They all represent something else.

What begins as a vague concept can grow up into a theory or a model and become a psychological tool that can be used initially by a handful of experts or professional few, but at a later stage of development by novices who learn the specialized language. At the same time a lexicon is developed. We name the parts of the technologies/tools to explain the ideas/methods to the novices which contributes to the further development and the spread of the language associated with the tool.


Here's an example of a method to discuss how an engine works:

1. Go to How Stuff Works and look at the engine simulation
2. Make a list of all the parts of the engine, e.g. piston, valve
3. Choose one engine part. Name the part and describe what you think it does.
4. Choose another engine part. Name the part and describe what it does. Improve on other people's ideas.
5. You are a mechanic and you have to explain how an engine works to an apprentice. In 30 words or less describe how an engine works.
6. What improvements do we need to make to our descriptions of how an engine works?
7. Use the best descriptions of how an engine works to improve your description of how an engine works.
8. What did you discover/learn today?

Collecting-connecting words via "language games"

Philosopher Ludwig Wittgenstein showed that concepts are part of a language game. They live in wondrous webs (or families) of meaning, connected by how similar or different they are to other concepts.

Brains remember by association. The memory of a concept can deliver up its' friends. They are autocatalytic and catalyze other concepts. When our own personal Google - our frontal lobes - goes out to search for associated ideas, it links to stuff we have experienced, read, seen, heard or felt before.

We get to know the concepts at the periphery of our memory by using them more frequently, especially if we use them in the context of other words. The synapses between the neurons in our brains are strengthened and recall becomes easier/faster/more automatic.

We can use this knowledge to design learning activities which develop new and strong associations with new or unfamiliar concepts.

Most often we know what we experience by the labels we give to events, things and how the events occur. And once we label something, the label sets it apart from ideas that are similar. Or its' opposites. The word "yes" can easily recall its' opposite "no", or indeterminate, "maybe". Or be connected into different kinds of categories.


If you ask people to perform a word association activity the words come tumbling out. Think vegetable and you immediately get carrot, potatoes, peas, lettuce and tomatoes and dozens more. We know these words because we consume them frequently. If we ask people to list the parts of a plant the words may be recalled more slowly, but if we direct their attention to the various aspects of the plant and stages of development with prompts e.g. petals,... or e.g. seed,... the task is made easier. By using the words frequently we become familiar with their meaning and their links to other words.....think roots, stem, branches, leaves, flowers, fruit, stamen etc.

Acquiring new words maybe slow to start but over time it becomes an avalanche, especially if you read and talk about stuff, often. Generally around 5 to 10 new words every day. A child of three has a vocabulary of 500 and 1000 words developed via 200,000 and 500,000 lifetime interactions. The more interactions, the more words and connections.

Over time this is how we progress:

3-year old: 500-1000
5-year old: 5,000
13-year old: 20,000
College student: 50,000-60,000 words

Here's the 100 most frequently used words in the English language. We learned most of these when we were very young. It's a whole bunch of basic verbs (doing words, e.g do, make), pronouns (that define who/what we are talking about, e.g. the, I, you, me), prepositions (that tell give a sense of direction/place/space, e.g. in, on, over, into) a handful of nouns (the what words, e.g. year, day, house, John), adverbs (that describe the verbs e.g. ran quickly, spoke clearly) and adjectives (that describe the nouns e.g. blue sky, happy boy).

"the, be, to, of, and, a, in, that, have, I, it, for, not, on, with, he, as, you, do, at, this, but, his, by, from, they, we, say, her, she, or, an, will, my, one, all, would, there, their, what, so, up, out, if, about, who, get, which, go, me, when, make, can, like, time, no, just, him, know, take, people, into, year, your, good, some, could, them, see, other, than, then, now, look, only, come, its, over, think, also, back, after, use, two, how, our, work, first, well, way, even, new, want, because, any, these, give, day, most, us."

Australian teen author John Marsden has a wonderful workshop exercise to teach young people how to write brilliant prose. To practice the rule, "Don't let language bully you" he asks you to "Respond to the calling of the class roll", with "Yes, Present, Here Miss....etc." In a few minutes a group of students will generate a list of 30-40 variations on the theme.

So here's an example of workshop where we practise the use of new concepts in a way which helps us remember their connections to words we already know. You can use a visual thesaurus to access words you don't know.




1. Make a lists of all the different kinds of relationships you have e.g. friends, etc.
2. Brainstorm a list of different kinds of emotions/feelings you experience e.g. happy, angry.
3. Choose one emotion from this list and explain what causes you to feel that way. Angry, happy, sad, bored, lonely, excited, nervous, stressed.
4. Based on your personal experience, what are the best ways to make and keep good friends?
5. Based on your personal experience, what are the best ways to have a bad relationship with other people?
6. From this list of aspects of personal relationship issues, choose one and describe what it is - trust, support, meanness, dishonesty, friendship, empathy, sympathy.
7. Make a list of all the events in your life where you feel a sense of gain/improvement.
8. Here are some positive relationships events. Empathy, sympathy, concern, congratulations, hugs, hand shake, caress. Choose one and describe how this could contribute to a feeling of wellbeing.
9. Make a list of all the events in the life of a person where there might be a sense of loss.
10. Here are some serious relationships problems or events; bullying, racism, fight, theft, assault, revenge, criticism. Choose one and explain how this could contribute to a sense of loss.
11. Make a list of words about relationships and feelings you discovered/played with today or better understand their meaning by linking it to other words you know. e.g. miserable - sad, unhappy etc.

Learning faster with gestures

If you are a teacher who organizes small group conversations or uses new tools in the classroom it is really important to give clear instructions to orchestrate the group activity.

Fluff your lines and the participants will not be sure what to do. Make a mess of using a tool and you might appear incompetent, and so destroy your carefully cultivated professional image.

But there is a faster and more certain way to remember and fluently give instructions to your students or participants.


It's all connected to how we "program" our brains using language and gesture. It's the way we learned to do new stuff when we were very young.

At a certain stage in their development, children talk silently to themselves to sequence and organize new actions. Older people occasionally do the same. We think aloud when faced with a complex/difficult task, when under pressure or when we feel tired. If we are a teacher or presenter, our external "inner speech" can quickly become a muddle with hard-to-remember precise instructions, old speech routines that belong to another topic and the authority speech we use to keep the group under behavioral control.

But if we associate gestures with the instructions, magically we remember the correct sequence, a kind of spatial or kinesthetic memory. Memories of the words and gestures point to each other in memory and reinforce each other.

Gestures and speech go literally hand-in-hand. They fit like a glove. Sometime gestures complete what we say, or explain with a flourish what we mean, develop a life of their own or even become independent languages. Emblems are gestures with special meanings such as thumbs-up for "Yes!" Signs are a language in their own right, such as pointing to yourself to indicate "me". And pantomimes are complete stories using gestures of various kinds.

The orchestration of speech and gesture occurs in Broca's area, a part of the brain where the sequencing of motor and speech actions are side-by-side. The same mirror neurons fire when we see others performing an action as when we do it ourselves. What begins in young children as pointing and grasping becomes a veritable avalanche of gestures at about age three co-expressed with the sequencing of words.

Here's a workshop to practice gestures, emblems, pantomimes and signs:

1. Brainstorm a list of all the different kinds of GESTURES you have seen people use when they communicate with others e.g. OK sign where the thumb and pointer finger make an “O”.
2. Take turns to explain to your partner, “what Life’s like at my house”. Make notes of the GESTURES that each person uses and what they were saying at the time. Then capture a list of the gestures: what people were saying.
3. As a group, play two rounds of Charades. After each turn, from memory name the mystery activity and describe the GESTURES each person used to offer clues.
4. EMBLEMS are gesticulations which have developed their own special meanings e.g. V for victory. Describe as many emblems as you can.
5. SIGNS are a complete language in themselves. Design a language using a mixture of signs for common concepts as such as me, you, come, go, up, down, into, through, house, car,
6. PANTOMIMES are sequences of gestures that tell a story. Craft a description of some gestures and the story that they tell.. e.g. you and I will drink tea...(points to other person, then points to self, then holds thumb and first finger together and lifts to mouth).
7. Propose a hypothesis for how gestures, emblems, pantomines and signs might develop in childhood. Consider these points in your theory. Brain cells represent cells. Speech and gesture are co-expressive. The orchestration of motor and speech actions are side by side in Broca's area of of frontal lobe. The same mirror neurons in Broca's area fire off when people watch others perform an action and when they perform the action themselves.
8. Design a learning activity which makes use of the features of mirror neurons and the co-expression of gesture and speech.

Out of control

The lecture is a very persistent "meme" that refuses to go away. This curious form of "knowledge telling" is the main way teachers and lecturers communicate with students.

The word "lecture" comes from the Latin lectus, which is the past participle of legere "to read" which is what some people do when they simply read aloud the words crammed onto their Powerpoint slides or the text of their lecture notes.

At first glance, the lecture seems to give a speaker considerable control over the audience. People sit quietly/respectfully in their seats. They listen. Some make notes. Others ask questions at the appointed time. Most remain in their seats until the lecture is over. Then they leave.


But the reality can be quite different. Unless the audience is so entertained by the topic or so enthralled by the speaker their minds may be somewhere else. Thinking about sex, shopping, what to buy for dinner or the hot guy in the first row. Some snooze. One or two snore.

My friend Professor Emeritus Sean O'Connor conducts a workshop to demonstrate the difference between the lecture and the workshop. He shows how workshops allow the facilitator to exert remote control over the learning experience.

He divides the session into two half hour activities. The participants are invited to use a sequence of questions to guide their discussion about a poem, such as Samuel Coleridge Taylor's poem..."In Xanadu did Kubla Khan, a stately pleasure dome decree...." Then he asks the participants to critique their discussion.

Most groups report that the process was very democratic, everyone had a say, they were very creative and it was fun. They also conclude the process gave them control over their own learning.

Sean begs to differ about the issue of "control".

He begins by asking "who gave you the task?

"You did," they tentatively reply

"Who gave you the process to explore the topic?"

"You did." they say.

"Who performed the task as requested?"

"We did." they chorus.

"So who was in control?"

"......You were." they reluctantly acknowledge.

You too can regain control over the learning process by combining the "information" elements of the lecture and the "interactive" elements of the workshop...even if the audience is seated in rows like a lecture hall or classroom.

In doing so you can become a challenging Interactor - an inspirer, provocateur, orchestrator and facilitator of knowledge creation - who asserts power and influence by helping people engage with each other in new and interesting ways. They will never forget you, the experience or what they learned during the process.

Here's a workshop to help you achieve the best of both worlds:

1. Briefly describe a topic and the main points you would like to communicate to an audience about a theory, method, concept, idea or issue.
2. Choose a topic other than your own (from question 1), and brainstorm an open-ended discussible question that you could ask the audience to discuss in pairs for 2-3 minutes.
3. Choose a different topic (from question 1) other than your own, and brainstorm an activity, experiment, exercise, you could ask two people to perform in pairs (and the results shared with another pair in front or behind them). e.g. draw something, act something out, observe a set of actions.
4. Design an interesting way that a large number of ideas could be collected from an audience and recorded and displayed for all to see.
5. Thinking about all the Multiple Intelligences, brainstorm an idea for an audience participation activity that could tap into two or more of the different learning types. Bodily-kinesthetic. Interpersonal. Verbal-linguistic. Logical-mathematical. Naturalistic. Intrapersonal. Visual-spatial. Musical.
6. Describe a method you could use to get an audience to find the patterns in some data collection activity e.g. the colour of people's eyes, favourite pastime, most dangerous experience.
7. Describe an amazing activity you could design which gets the whole of your audience on its' feet at the end of your "interactive lecture" that resonates with your big idea. e.g. a Gregorian chant of slogans for next year.
8. Imagine yourself as an Interactor. Describe how you might deliver a 30-minute "interactive lecture" in which you have three activities interspersed through the process that engage your audience interactively, perhaps with a resounding finale.