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.

A couple of activities for Christmas

 For those who do not get the Wilkie Way Newsletter, Wilkie Way Numeracy Resources it is worth considering, Charlotte usually has something challenging to say and there are always some thought provoking activities for the students 

(note: I am neither endorsing nor promoting the Wilkie Way Resources, each teacher/school needs to review them themselves)

This could be sent as a Holiday Project   hahaha

 

 

And if you are looking for a party trick!!

 

 

 

I always liked this one when active in classrooms and preparing problems to solve 

 

What is the true cost of the 12 days of Christmas now?

Go to: Costs of "The 12 Days" since 1984

 

[Verse 1]
On the first day of Christmas, my true love sent to me
A partridge in a pear tree

[Verse 2]
On the second day of Christmas, my true love sent to me
Two turtle doves, and
A partridge in a pear tree

[Verse 3]
On the third day of Christmas, my true love sent to me
Three french hens
Two turtle doves, and
A partridge in a pear tree

[Verse 4]
On the fourth day of Christmas, my true love sent to me
Four calling birds
Three french hens
Two turtle doves, and
A partridge in a pear tree

[Verse 5]
On the fifth day of Christmas, my true love sent to me
Five golden rings
Four calling birds
Three french hens
Two turtle doves, and
A partridge in a pear tree

[Verse 6]
On the sixth day of Christmas, my true love sent to me
Six geese a-laying
Five golden rings
Four calling birds
Three french hens
Two turtle doves, and
A partridge in a pear tree

[Verse 7]
On the seventh day of Christmas, my true love sent to me
Seven swans a-swimming
Six geese a-laying
Five golden rings
Four calling birds
Three french hens
Two turtle doves, and
A partridge in a pear tree

[Verse 8]
On the eighth day of Christmas, my true love sent to me
Eight maids a-milking
Seven swans a-swimming
Six geese a-laying
Five golden rings
Four calling birds
Three french hens
Two turtle doves, and
A partridge in a pear tree

[Verse 9]
On the ninth day of Christmas, my true love sent to me
Nine ladies dancing
Eight maids a-milking
Seven swans a-swimming
Six geese a-laying
Five golden rings
Four calling birds
Three french hens
Two turtle doves, and
A partridge in a pear tree

[Verse 10]
On the tenth day of Christmas, my true love sent to me
Ten lords a-leaping
Nine ladies dancing
Eight maids a-milking
Seven swans a-swimming
Six geese a-laying
Five golden rings
Four calling birds
Three french hens
Two turtle doves, and
A partridge in a pear tree

[Verse 11]
On the eleventh day of Christmas, my true love sent to me
Eleven pipers piping
Ten lords a-leaping
Nine ladies dancing
Eight maids a-milking
Seven swans a-swimming
Six geese a-laying
Five golden rings
Four calling birds
Three french hens
Two turtle doves, and
A partridge in a pear tree

[Verse 12]
On the twelfth day of Christmas, my true love sent to me
Twelve drummers drumming
Eleven pipers piping
Ten lords a-leaping
Nine ladies dancing
Eight maids a-milking
Seven swans a-swimming
Six geese a-laying
Five golden rings
Four calling birds
Three french hens
Two turtle doves, and
A partridge in a pear tree

 

Another activity with this song is:  How Many Presents are given in Total?

 

May I take this opportunity of wishing you all a very Happy Christmas and a great 2021.  

 

My apologies for the tardiness of pasts during 2020. I cant blame Covid-19, but I have shifted house and district some 500kms from where I used to live!!😀😀  

Students must know their Facts before Practice!

Recently on a social media platform I noticed a post along the lines of:

"I have students in my class who are still doing repeated addition and other approaches to do their tables!  What are some good practice activities both to help these children with their tables?"

The concern I have with this question is that if students do not know their tables giving them practice examples will not help them learn them, they will just keep using the method that they know.

We as teachers need to make sure that students "know" the tables before asking them to practice them.

Imagine a Sports Coach who says, "I know I have not taught you how to pass the ball correctly but just go and practice the correct way anyway. I will call you back in 5"

As a Mathematics Adviser years ago we talked about:

New Learning

Practice

Maintenance

New Learning as the label suggests is the new skills, methods, procedures that a student has not previously learnt
Practice is the activities used to  help ensure New Learning is committed to memory etc
Maintenance is the long term practice of previously learnt skills concepts etc.

I can remember being corrected after using the oft quoted phrase, "Practice Makes Perfect". I believe it may have been a Physical Education Adviser who said, "NO! it has to be Correct Practice Makes Perfect"

To me this must be at the back of our minds as we set activities for students to do, 

is it the correct practice they are doing? 

(I used this regularly when working with teachers from the 80's to 20's)

Mastery of a fact is indicated by the students’ ability to: 

•Show it with materials, talk about it and write or draw about it
    This demonstrate, record and explain stage is vital for the initial development of understanding.              This is done by presenting the fact in a meaningful context and having the  student model it with a variety of materials and record in a way appropriate to their level.

•Have instant recall
    Students need to have memorisation routines to achieve instant recall.  This is not rote                 learning, rote learning implies a lack of understanding.
    The goal is for the students to internalise the facts so that the recall is quick and effortless.      

This can only happen once the concepts behind the facts are understood.
    Explore possible strategies for helping to organise information in a 

table to make memorising easier

    • Practice is needed to make the facts automatic “PRACTICE IS ESSENTIAL”

 
    • Allow time each day/week for it to happen.
    The routines suggested below will have two purposes a) self assessment and by finding a     method         that works for them.
Routines you might choose to use with the students to help them memorise a basic fact.....

1.    Identify the fact to be learned
    Correctly record the fact
    Look at it say it, write it with your finger 5 times
    Look at it say it write with your pencil 5 times
    Cover it, write it, check that it is correct
    Repeat the routine if necessary

2.    Write the fact in big numbers on a piece of paper
    Trace it with your finger saying it out loud
    Close you eyes and say it
    Turn the paper over and see if you can write it
    Check it, give your self a pat on the back if you were correct.

3.    With older students explore how they can best    
    memorise the basic facts, let them try their method
    and test a partner to see if it is successful

Expect/demand that the students learn their facts.  

They are capable of it-just look at the way they memorise moves in computer games

• Use facts when solving problems
    Can be done through a variety of activities such as mental problems, games and quizzes

Knowledge of single digit number facts is essential, mental arithmetic is a 

valuable skill and both enhance “NUMBER SENSE”


TO COMMIT BASIC FACTS OR TABLES TO MEMORY STUDENTS SHOULD:
•    begin to memorise basic arithmetic facts soon after they have
    demonstrated an understanding of symbolic statements
    students should be able to demonstrate their understanding of the 

mathematical concept with equipment, verbally and in writing.
•    participate in practice activities with intent to memorise
    using fingers, tally marks etc as aids is not practicing memorisation
•    practice during practice sessions
    short and snappy, not time for explaining or teaching.  

Give instant feedback of correct fact.
•    be involved in short practice sessions every day when possible
    5-10 minutes is long enough. Keep students enthusiastic
•    try to memorise only one fact each session
    keep the task realistic and manageable
•    constantly review previously memorised facts
    we all forget!!! especially add/subt once students move on to mult/div

•     be praised and reminded of what they already know, by the teacher
    express confidence in the students ability to memorise.  

Capitalise on the pleasure they feel with success

•    be involved in verbal practice activities and receive immediate    
    feedback use full class response drills cautiously.  

It is difficult to tell what individual students are saying or    

 whether they are participating.
•    be exposed to a variety of activities
    have a pool of activities and change frequently to maintain interest
•    be praised for good efforts and keep a record of their progress
    be enthusiastic, praise students ability to memorise rather than ‘clever practices’.

DON’T CONFUSE TESTING WITH TEACHINGTimed tests emphasise speed where the emphasis should be on persistence and understanding.  Those students who do well under time pressure get to show off their skills and they are the ones who DON’T need the practice.  The students who have difficulty, work more slowly and run the risk of reinforcing wrong practices under pressure and develop fearful and negative attitudes to math’s learning.
    Prior to ‘Tomorrow’s Schools’ (1989) the School Inspectorate noted that they found a great deal of testing of tables and very little teaching of tables.

I leave you with this thought, 

"Is the anguish and energy over Basic Facts Learning and Memorisation 

as important as we think it needs to be?

Should we be helping students to explore processes and thinking?"

It is interesting to note that many Mathematicians, and Leading Math's Educators 

(Jo Boaler included) do not know all of their Basic Facts yet have succeeded mathematical
 

 

Inequality here in New Zealand is alive and active as well.

This arrived in my inbox this morning, from YouCubed (Jo Boaler)  I felt that I had to post as we have similar disparity in New Zealand, in Education, in Society.  We all need to look into our hearts and see how we can change to create equality in our own small worlds.

Hello youcubians,

We at youcubed extend our support for educators fighting the structural racism in the US daily. We have all witnessed the horrific murders of George Floyd, Breonna Taylor, and Ahmaud Arbery. We also have all watched video of how Amy Cooper weaponized the police against a black man. Our hearts grieve for their families and the Black community. We acknowledge that for people of color in our nation, this violence is not new, but ongoing.

At this time, we are strengthening our commitment to fight for a more just society. To us, good teaching that is inclusive of all students, with high expectations for all, is central to an equity-focused teaching approach. Moving forward we commit to our community that we will:

• Seek out districts and schools with predominant population of black students and other oppressed groups, and faculty to participate in research
• Highlight the work of black mathematicians and educators throughout the world
• Develop a webpage for the site that shares activities and teaching practices built on culturally sustaining pedagogies
• Continue to fight for education legislation that disrupts the systemic oppression of black, brown, and low-income people

All educators have the power to make a tremendous impact in the pursuit of equity, and mathematics educators probably have more than most, as mathematics is such an inequitable subject. Here are some actions moving forward:

• An important initiative is de-tracking and offering high level content to all students to help end the racial disparities we currently see. 
• A more specific action that is important for tackling racism in the classroom is teaching students to value each other’s ideas, and to respect each other.

We mention these ideas to remind us all that we can make a difference through our teaching and leading practices. We also want you to know that whatever route you want to take, we are here to help; equity is our first and most important mission.

Viva La Revolution!
The youcubed team