Imagine a Classroom teaching maths like this.

                                          It is a Multiage Classroom.

 

There are two teachers about to walk into their classroom for the after recess Maths lesson but with quite a different philosophy in their minds.  We won't spend much time on teacher one as we often run into her as she rushes down the hallway several minutes behind the bell with a cup of hot coffee in one hand and seven sets of duplicated sheets balanced on a box of maths resources and a text book that will be used if there is time.  The maths topic is Time because that's what it says on the planning calendar and there's never enough hours in the day to teach maths properly let alone get groups organised and teach Time.

 

There are twenty-three copies of each sheet for she has twenty three children in her class, or up to yesterday she did but there was a new enrolment this morning which will create a little more chaos as each carefully chosen activity will need to be explained a little differently.  “I know you don't want to share with Robert but just for today as we have a new class member who will feel very left out if she doesn't have her own worksheet.  What do you mean you'll feel left out ?”   Anyway you get the drift as these teachers will eventually make a nonsense of whatever they teach and the rest pay for their incompetence.  

 

Mathematics in five interrelated boxes:

1. Pre-test,

2. Needs Grouping,

3. Games and Activities,

4. Drill and Practice 

5. Extension/Enrichment

 

Teacher two carries in her mind five boxes labelled Pre-test, Needs Grouping, Games and Activities, Drill and Practice and Extension/Enrichment and into these five boxes fit all of her maths planning.  She metaphorically wraps a ribbon around all the boxes and today's ribbon is  'Time' and it will stay there for as long as interest and excitement continues.  She has carefully linked the Science syllabus and objectives with her total maths curriculum and the Time section of Maths is going to be driven by several major science topics.  There is also a literacy link with the writing of reports genre and an imaginative literacy story on time travel and time machines.  None of this is new to multiage teachers for they instinctively integrate and cross fertilise wherever the opportunity exists for they know there is just not enough time in the day to teach any other way.  The needs of their Copycats, Stickybeaks and Scallywags are always to the fore in their planning.

 

The first thing that strikes us when we enter her room is the Junk Table which now holds a wide array of time devices, from fob watches to egg timers, from notched time sticks to the innards if an old clock and so on.  The challenge a week ago was to bring along anything that has any connection with Time and this is a good start.  The last topic saw the table covered to overflowing with money and currency and cash registers and calculators for the math's theme was 'Money' and the excursion to the shopping centre was a real and integrating activity, with a cafeteria luncheon.  The class shop and the social studies topic on trade export and colonisation is still continuing for a small group who are investigating E-trade and how you can buy and sell on the internet, but back to 'Time'. 

 

The walls of the room are saturated with calendars and time tables of every description.  There are tide charts and seasonal gardening planting guides, there are clock faces with numerals and dots and Roman Numerals (for this is where Roman Numeral study is done), twenty-four hour clocks, a poster of Stonehenge and a display of  photos of dated gravestones of the most famous people in the cemetery.  And so the classroom has taken on a new twist but the Money resources of coins and currency dated from the beginning of trade will remain and be added to as they will be useful again, this time in relation to 'Time'. A number of time lines on different aspects of history and inventions has been hinted to on broad outline charts for these will be an important aspect of the concept and study of Time. 

 

The music playing in the background is Peter Allan's  “Time is a traveller, Tenterfield Saddler, ride away” and together with “My Grandfather's Clock” will be enough to spark a search into songs that relate to 'Time'.  Everyone is encouraged to bring along songs that can be added to a  tape, or burnt to the class CD of all of the relevant music for background listening pleasure at times in the day.  A metronome keeps a steady beat so beat and rhythm will be given an extra boost as the topic continues. Two children take an interest in heart beats and branch into a physiology strand which fascinates the whole class at feedback time when the class heart beat data is shared.  A stethoscope is added to the junk table. There is as much more as the children will suggest and ask and explore to the topic’s endless limits. 

 

“What about teaching Maths?” you might ask.  Going back to the five organisational boxes which the teacher carries for all of her maths topics, one is not more important than the others for a balanced learning diet.  All children need to take from all boxes, some more from one box than another or other children.  The pre-test activities may consist of a simple written test or an observation on a task.  They may be a personal written or spoken statement which discloses what the learner knows about time, what the learner would like to know about time and how they would propose finding that out.  The use of simple tests may be quick and easy but beware the learning truth in the two statements “I don't know what to teach you because I don't know what you know,” is quite different to “I know what I have to teach you so I will find out what you don't know,” and pre-tests should focus on finding what the learner knows and build from that base.  Surely it is the concept of 'Time' that one must focus upon not simply teaching children to read the time and convert hours to minutes and all the related busy page tasks.

 

The first teacher has finally got the message through to the teacher aides that yes she knows that it is school policy to not do more copying after 9 o'clock but she only needed one extra copy of each of the seven sheets, not seven of the one that Robert evidently told her and anyway how was she to know there was a new child to start today as she can't be expected to remember everything.  She hasn't got the time!  

 

The Needs Grouping box is exactly for that purpose and these are specific short sharp lessons or Clinics, like getting a measles injection.  They work best with no more than five or six children at a time and are followed by a reinforcing game or activity, maybe a drill and practice or at a later time another brief test.  For all learners the extension or enrichment box must offer that extra challenge and many cards in the box at this stage are blank for they will be designed and devised by the children themselves and then offered as tasks to their classmates.  In the Time topic there may be several dozen Clinic topics which will arise, from basic number facts of adding or multiplying, writing the time from a clock face into a statement or converting twenty-four hour time to twelve hour format, all depending on the level of maturity of the learner.  In a multiage classroom the older or more able learners will push the limits higher and drag the others along with them.  The teacher has the role of facilitator and knowledge navigator and judiciously uses the talents and expertise of the more able learners to explain and persuade those who are still coming to the understanding.  Note that the 'more able learners' need not be the older learners in the class!  The Drill and Practice box is used more frequently by some than others and uses many novel ways to tempt the intellect of all learners.

 

Mental maths is a regular feature of every day for a few minutes, as is quick recall of number facts using a 20/20 club format.  Only five mental maths questions constitute a mental session and they all relate to the same aspect or operation in Time.  This facilitates easy analysis of the children’s learning  and serves as  a valuable measure of progress for needs grouping. The most important aspect of the oral maths sessions is problem solving with the emphasis on Number Sense or Short Cut Maths.  If a child has to do any mental computation to find the answer to 4 times 3 minutes 59 seconds other than saying four times four is  sixteen, less four seconds, then Maths is not being properly taught.  Approximate answers are all that need to be supplied in these sessions initially till children see number relationships and patterns.  It all begins much earlier with scissors and cardboard and blocks and counters, or it did till the school bought the new photocopier and the expensive text books to which everyone is now obligated to use as they were on the book list.  A child's mind is a far greater resource than any black line master, text book or maths program.  It is common for teachers to substitute source books, text books and the like for the syllabus documents.  Big mistake!  It is the role of every teacher to know the content and intent of the syllabus implicitly and then to work with the learners to create meaningful and exciting learning episodes through which the child will come to understand more about how his/her world works.  

 

The Games and Activities box is the excitement end where true understanding takes place, often in the form of play, for play is the work of the child.  It is where true concept development is tested and proven and much of what is on offer is the result of other children’s work, such as making a board game or a crossword.  The social activity and all that goes with it when learning how to play a game with a group of other players is seen as important as getting a successful conclusion to the activity.  The creative talents of all learners are especially addressed in the Games and Activities box as each year the older children delve back into the previous year’s box and develop new and novel ways of learning.  

 

Back to the first teacher's class where the activities are used as a reward for the better children or those who finish their work first.  Everything is very competitive.  There are lots of sums on the board, seven worksheets to be completed by everyone. The teacher finally has the photocopying sorted out but now has forty two surplus sheets that have been added to the pile of surplus photocopied sheets in the cupboard that may be useful, but in reality will end up in the rubbish skip at the Christmas clean up, about three reams of accumulated and expensive resources,  But it's covered in the budget, and the new photocopier arriving in the holidays can copy twice as fast so that is going to save a lot of Time.

​

“Now that we have that worked out and the test on Friday to find out what you don't know, we can all go through it together again next week.  I know you got all of this right last week, Robert, but it will be good revision for you.  How dare you yawn when I am talking to you, young Man!”

 

“Of course I do group work and activities, every Friday morning from recess till lunch and each group of six children has fifteen minutes on each rotating activity then I ring the little bell so they change to the next activity.  Frankly I find group work very stressful as the children talk and argue a lot and don't seem to value all of the time I have put into the activities that take me almost the whole weekend to prepare.”

 

Let some time pass and we can now observe how the second class is using their Time. 

 

Teacher two's classroom certainly uses the photocopier but never for the purpose of giving all children the same sheet.  Even if she had a single year level class this wouldn’t change for she knows their learning needs are spread across at least a three year and more level in anything she might choose to measure.  But all teachers know that, it's just easier to ignore than to address, some would say.

 

It's a bit hard to see the classroom now as a Maths classroom for the activities and tasks in which children are engaged are diverse and complicated.  Many of them would fit Education Queensland's description of Rich Tasks as per the New Basics Frameworks Project which was abandoned years ago.  However there is certainly evidence of Time being the carrier in most of the activity and the loaned Grandfather Clock which takes pride of place beside the door, chimes the quarter hours with melodious regularity.  The teacher next door hasn’t been told that it is possible to mute the chimes.   No one thought to tell her.

 

The teacher is currently conferencing a child with a piece of writing which is nearing publication stage, for the classroom follows the guidelines of 'Let Them Write Before They Read' and the class book on Time has contributions from all children, several from some, and ranges in scope from adventure narratives along the lines of Back to the Future/ Past, some mind bending problems and number puzzles devised by children and not copied from other busy books, some timely poetry, several articles of a factual historic nature, a very comprehensive time line on the history of the school, a couple of biographies of key people at times of great change.  The recordings of the interviews with the grandparents have been transcribed into print as anecdotal snippets of history.  Several were students when the school was a one teacher school so the decision to make a time capsule, as well as studying a lot about the history of them is made and a group is busily putting the final arrangements towards what it should contain, what it should be made of, where it should be buried and when it should be opened.  A letter to the local councillor asks that she be present at the forthcoming Time Capsule ceremony and the parent body has given approval for a plaque to mark the spot be funded.

 

There is a life sized model of a time machine constructed from cardboard boxes resplendent in bright paint and real motorbike gauges and handles that spin and levers that squeeze, complete with every form of time measuring device all calibrated to the same second.  The Time Machine has become the focus of all of the Time measuring devices the class has discussed and all children ride in it and explain the purpose of each piece of equipment.  There is a photo in the local newspaper with several professor type characters in white jackets explaining the machine’s functions to a reporter.  A group is putting the final touches towards their mouse trap racing mobiles and the racecourse is being cleared, graph paper readied and the three time keepers are considering how they can most accurately record both the time taken and the distance travelled as there is a challenge that arose from the same activity a year ago when  some of the children were younger as they wanted to know the actual speed of each racer.  Another small group is rehearsing the play they will perform at the end of year concert, a comedy about missing a time cue because someone couldn't read the time properly which creates a bizarre set of circumstances.  There are overloads of puns on the Time terms and measures and the play has a basic tuned percussion accompaniment with a chorus the audience is to sing along with at the appropriate times.  

 

Several very educational board games have been added to the games area and the standard of construction and durability has improved greatly, as has the depth of knowledge and understanding on the questions and the Chance cards, a bit of a cross this game between Monopoly and Trivial Pursuits.  Time crosswords have also been added to the crosswords which reside in the computer and are also printed out for personal use.  The teacher has used the crossword format to reinforce terms and facts related to Time and these serve as a simple and effective post test analyses, followed by further Clinic sessions.

 

The computer is seen very much as a tool in this teacher's classroom and it is in constant use in searching for Time information, printing final drafts of writing tasks for the Time Book, together with scanned photos.  The Time web page is also taking shape with the added expertise of two of the pupils from the senior class overseeing the project, for they mastered the task several years before.  There are several computer driven projects which relate to Time in some way including graphs, a spreadsheet and a data base exercise. The computer is used to enter the individual progress each child is making for all of the expected outcomes as per Maths Gateways which are clearly listed and individual children enter their own assessment comments into the appropriate spaces.  The teacher recognises excellence by writing a comment to that effect onto a card which the child enters into his/her individual file, the teacher's copy being pinned onto the Wall of Excellence for all to see. If they choose they can print out their personal performance reports on the Time project and add their own comment.  Their parents would be invited to also add a comment.  

 

There is a lot more that is taking place almost without any teacher direction for this was done so carefully last year and the year before so older pupils pass on the expectations to the new and that is the way this multiage teacher works.  She maximises the talents of her Copycats, Stickybeaks and Scallywags in all that the class does.  She has carefully modelled the current activities and some of the children from last year also model the way they went about Time tasks a year ago and will be available as Time tutors if needed.  The teacher believes this is how children learn best, by co-operating and sharing, by challenging each other's clarity of thinking, by creating and engaging in activities and games, using the teacher as a reference point when necessary.

 

Imagine such a classroom and then imagine two teachers working as a team with all of the benefits that children receive when they have two teachers who model relationship education as the priority of the four Rs.  Now that is indeed an extremely powerful model of learning and teaching. 

 

The first teacher? Well she has finally lodged a complaint with the Principal about the grandfather clock chimes and how it has disrupted her entire class for the past week and it is little wonder that her class has learnt virtually nothing in all of that Time. The chimes are now muted, actually they had been cut back to on the hour after two days but who is counting?  One of the big problems now is that the children in the multiage classroom seem to be having too much fun in their learning and those next door are telling them that they aren't learning proper maths and doing sums off the board and text books and worksheets and tests.  “Would one of you mind taking Robert next year as I’ve had enough of his smart behaviour and increasing disengagement from learning.”

 

Several parents have also picked up on the same theme, kids having too much fun and not enough proper learning, especially as they have had to purchase several quite expensive text books, so it looks like at the next staff meeting teacher two will once again have to defend her strategies and philosophy and try to persuade the computer guru that she gets better value from having her computer in her room rather than gathering them all into a computer lab in the library.  The budget is now so tight with the impending purchase of the new photocopier that the only solution to make it more equitable for all is to put the computer guru in charge of all technology and that will ease the load on the teachers having problems with technology, even though the whole staff has been accredited at level ???

 

There is no happy end to the story for mediocrity is easy, you don't have to plan for it.

PS  I have seen all of the above and much more in child centred multiage classrooms but I have never seen a grandfather clock in any classroom.  Now  that would be something to see.