What To Do With The Others?

Many of us have been encouraged to have groups within our Maths Classes, in fact it has been a basic organisation since the 60’s when I started teaching.  These groups were originally based on ability(much research says this is not the best way of grouping) now we can have all sorts of groups, 

•         Interest
•         Social
•         Groups of 2 or 4 etc
•         Small groups for interacting with the teacher, rather than a large class 
•         Groups of one
  

 

How ever we organise the issue is about the groups that are not under "Direct Supervision" so we here the catch cry

             “What Do I Do With The Others?”

For successful 2 or 3 group organisations to work then the most important thing is that the groups/children, not with the teacher, know what to do!!  

One organisation that has been used for a number of years is Groups of Four.  The class has a common open ended activity and groups of four work together to solve/attempt the activity.  After a period of time the groups report back their findings to the whole class. Sometimes roles are assigned to each child (with the roles changed for each new task)

• Reporter
• Recorder
• Gopher
  

For any groups/small group teaching we have to make sure that the students, not with the teacher, are generally on task and know what to do!!

This means:

• They can work Independently or in pairs, small groups, without supervision
• They know the organisation of the classroom:
• They know how to work quietly,
• They know what to do when they have completed the task,
• They knowwhere to get another activity,equipment and tidy up
  
• They know where to place completed work,
• They can Self Mark, as appropriate without cheating
  

They also need to Know the Mathematics, and I believe this is where most of us fall down: 

We teach something today/yesterday and then go and ask them to practise it.  

        In many cases students need teacher supervision to become masters of the skill/process. 

In the immediate aftermath of teaching a process/skill: 

        they may not know what to do or how to complete the worksheet etc.  

 

Please take time teaching repeatable Thinking type activities so that all students know what to do,

• Have repeatable activities printed on card and laminated, if possible, so students can write on them with Dry Erase and then wipe clean
• Have the activities organised by group, or content.  possible coded for topic/strand
• Some teachers have these in Plastic Bags-but if a die is missing someone has to check- so I advise that no equipment is with the activity but in a place where students can go and get the dice or pen or paper clips(organisation) 
• The equipment needed for an activity should be listed on the Card(see my examples)

I have advised all teachers to take time teaching and practising Independent activities and routines as a class, before trying to introduce groups.  The children’s knowledge of these routines and behaviours make your maths' teaching so much easier.

This time, organising students to work independently,  could be anything up to 3-4 weeks (a whole term) depending on the group of students.  We cant rush these things if we wish to enjoy the teaching as well as the kids learning the maths.  Remember KISS.

When ready have two groups and get those working before starting with 3 groups(and no more)

Without the appropriate activities, and behaviours by the children, we do make our work hard for ourselves.

Marking

Traditionally the teacher has used the Red and Green pens to say which one is correct or which is not.

• I prefer teachers and myself not to stand in judgement,( be the Policeman) but to ask the Groups/individuals to report back with reasons and explanations as to why they think they have ended up with the result. Other groups/children may wish to dispute the result so we should be asking the children and groups to JUSTIFY their answers.
• I can remember a situation in a classroom where a child gave an answer, say 4, and was told that it was wrong.  This upset the child so I went and said, “can you explain what you did?” During the explanation the answer was 4-for what the child did

Questions

In my time working with Teachers and Students, I often did not know the “answer/s” to particular questions, problems that I presented  This meant I could not “lead” the kids to what I thought was the answer, I used questions such as:

•     Did you try this?
•     Can you explain how you got that answer?
•     Can you show me what you did?
•     Would you like to teach /explain this to a group?
•      What does the problem tell you?
•      What do you have to find?
•      What Strategy approach will you/did you use?

 I like this approach that one school uses for getting students to explain how they tackled a problem.

 

Balloons Over The Wairarapa

 This is a great NIM type activity for all ages.

Can be played One to One or pairs (Two vs Two): I prefer the latter in a classroom and two places are more likely to discuss the moves before making a decision.

Dont emphasize the competition but after a few times get the students to think about patterns or special numbers of toothpicks etc.

A worthwhile quote for every classroom wall, OR Do, Say, Write

 Might need to put the "s" in.

I must admit I am a   Do, Say, Write Proponent

                        Do                explore learn through doing, using, drawing 

                                            when Proficient at doing

                        Say                explain in your own words what you have been doing

                                            when proficient and explaining orally

                        Write            first in long hand and then if appropriate in maths language

All for Maths and Maths for All

I have just received the Wilkie Way Newsletter and Charlotte's comments made me get on to my hobby horse:  I will copy her comments below)

Why is acceptable to say "I cant do maths, yet not socially acceptable to say I cant read!" 

Recently I wrote to "Seven Sharp" because both of their presenters said that couldn't do maths, which is perpetuating Society's attitude to maths. Needless to say I did not get a response and soon after stopped watching it.

Many years ago about 20 maths and science specialists were invited to a Learning Media Conference to discuss writing articles for the new Maths/Science Journals.  We were welcomed by the CEO who said to us all that, "he was amazed at us all with out interest in these topics as he could not do maths!"

At morning tea I was standing next to him and asked, (Paraphrased)

    "Why did you say you were no good at maths?"

        "Because I cant do it?" 

    " In your position to you set financial targets? Budgets? and try and meet or exceed these?"

        "Yes all of those"

    "Isn't this maths? What was your job before this one?"

        "I was an accountant!"

To me, this shows how many in society do not connect "Real World Maths" with "School Maths"

This is not a fault of the person/people it is the result of the education system that does not have a connect between the real world use of maths and what we are teaching in the classroom.  In the 80's an 90's there was a huge push for Problem Solving and Investigations to be part of the classroom curriculum, and I am pleased to reflect and say I was part of this push, after meeting and working with, the late, Murray Britt Auckland College of Education (writer of the NZ Maths Curriculum)

We need to make all our maths teaching and student learning Real and Connected.

All for Maths and Maths for All

Can you create an artistic masterpiece or are you happy to dabble, know about artwork, give it a go without a fear of failure? Can you appreciate art in the environment and the world around you without a negative attitude?

So why is it considered acceptable to have a negative attitude to mathematics?

Our New Zealand culture has allowed mathematics to become something completely separate from everyday life - something that is hard and fearful, that only a special few are allowed into the ‘Maths Club”It is a total myth that you are born either mathematically inclined or literacy inclined. This is actually a choice that you are making and perpetuating the myth.

Every human is born with a mathematical brain. Without it you would not survive. Within a few hours of birth, a baby can distinguish between same and different - the most fundamental mathematical concept. Most actions a child makes in their first year of life are grounded in mathematical concepts:

•   same/different - visual, auditory, tactile, pattern and rhythm
•   judging distances
•   exploring objects - for shape, size (length, area, volume), mass, temperature,

Through distinguishing between same and different, auditory, pattern and rhythm they learn the language of words to communicate by being spoken to. Their ability to distinguish between the patterns and rhythms of different languages means they are able to learn multiple languages at the same time. At no other time in a human’s life is this ability so strong.

The spoken word becomes a communication tool to enhance the ability for more conscious thought and more deliberate acts of discovery about the world around them. They learn to ask questions and seek information rather than having to find out everything for themselves. “Why?” is a word asked frequently by young children in their quest to learn.

The same/different concepts begin to be quantified as young children begin to use words of one and two to distinguish between these small quantities by subitising. Anything more is just more (one student in my class on entry to school recognised one, two, heaps.)

In a purely playbased environment students are likely to develop sound foundations in the fundamental mathematical concepts through opportunities to explore and experiment. However if these experiences are not verbalised and mathematical language acquired by the students to communicate, describe, explain and reason with these concepts, they will remain unusable foundations for building further knowledge and therefore developing the concepts to deeper understanding.
These foundations are very important and while schools are trying to compensating for development opportunities often missed in our rushed modern world, schools cannot ignore their essential role in teaching the knowledge required for developing the man made created mathematics. The mathematics we use in our daily lives did not just happen - it was invented to be used, it shapes the world in which we live

Counting is the first concept that requires direct teaching, it involves

•the learning of the words,
•the assigning of a word name to a collection of objects and understanding the last word said tells you how many. (Cardinal aspect of number)
•the understanding that the next counting number is the result of adding one more
•the numbers form a sequence where each number has a set position (ordinal aspect of number)
•recognising the number symbols (0 - 9)
•recognising the symbols are repeated in particular positions to represent other numbers

Do not underestimate learning to understand counting:

Achieved Level 1 Patterns and Relationships is when a student has generalised the concept of counting

•Generalised that the next counting number gives the result of adding one object to a set and that counting the number of objects in a set tells how many

Most adults see mathematics as about numbers - while it could be argued to be true, I would define mathematics as about mankind’s ability to use numbers to describe and model situations that already exist in the real word (using and applying) or to use the patterns and relations in the known mathematics to predict and create what could exist.
Much mathematics is created and never used, like an art canvas that has been abandoned. Much mathematics is created and then put to one side and picked up by someone else and reworked - like an art canvas that has been painted over.
Whatever mathematics is created, it is mostly built onto an existing body of knowledge - explored and experimented with just as humans do with those fundamental concepts. A new idea can be created from something already known that can revolutionise mathematics. An historical example is the idea that nothing is not nothing. If numbers represent something then what if you had nothing of something? Zero can now be classified as a number - from that idea a complete new number system was created.

I am not creater of mathematics in the same way I am not a creater of artistic masterpieces. However I like designing very nice quilts and I use and apply mathematics to do it.

Most people use and apply mathematics in their everyday lives so why do people perpetuate the myth that mathematics is something separate, that is hard, is not accessible to all, is to be feared and is allowed to generate so many negative emotions.

Listening to a speaker at a conference last week, she probably didn’t even realise she was separating mathematics from real life when she could not see how mathematics could be included in a Christian view of education when collaborating in PE was given as an example.   I hear public figures say they were no good at maths as if it is something to celebrate.

What do people mean when they say I am no good at maths?
If being good at art means being able to create artistic pieces, then being good at mathematics must mean being able to create new mathematics.

Most people do not create fantastic artistic pieces likewise most people do not create new mathematics.

We need to change the culture about mathematics - change your words

I am good at using and applying mathematics. I have the ability and inclination to use mathematics, at home, at work and in the community. I am numerate.

 
If you put your mathematics lenses on you will see how much you use and apply mathematics and how much mathematics surrounds you in your world.
Enjoy and appreciate it as if it were a masterpiece.

Charlotte Wilkinson  www.wilkieway.co.nz

Please check out Charlotte's website.

    

DIFFY - A subtraction Investigation

 Instead of regular worksheets, it is often more exciting for students if the activity has an investigative or a surprise result.

Diffy, from Nimble With Numbers is one of these activities.

Four In A Row Multiplication

 Recent FB Posts have been asking for ideas on how to help students memorise (and use) multiplication facts.

There are many game type activities that help with this and one of my favourites is the one that follows.

The beauty of this one is it requires thinking and strategy development to win, which in my view is better than more worksheets that do not require this sort of thinking, problem solving.

This game could be played with two teams(pairs). Encouraging teams to play means students will need to discuss the possibilities for placing the paper clips, perhaps blocking opponents etc.  Communication in maths is very important.

The Temple of Gloom

 I have just been asked for this activity.  It was one I used extensively while working with teachers in an endeavour to use more investigations and problem solving in the maths classroom.

With the recent pronouncements by the Govt about our declining Math's abilities at year 8-10 perhaps it is time for more of these to be included in our programs.

The beauty of this activity is that:

1. it can be used with individuals, pairs, small groups.
2. it can be acted out with children, and hoops, in the playgound
3. it can be modelled using stones and circles.
4. it can be done with pencil and paper (and lots of crossings out!!!
   
5. it may not have one unique answer
6. it lends itself to students to create similar problems(work backwards etc

 

Please post some of the ways your students solve the problem.  Teachers-not too much direction please.