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

NCETM: Mixed Ability Vs Ability Groups

 Sorry if I am repeating myself, but I know there is still ability grouping happening in some classrooms.  Many of us may have suffered under this structure-if we were not in the "top group" we considered ourselves dum!!! 

In real life we don't group we work cooperatively with all types of people, ethnicities and so called "academic achievements"

We really need to  re-think our classroom organisations to create better learning environments to encourage enjoyment and achievement.  If we reflect on what is happening in homes all around the world at the moment there are all levels of ability, interest, age working together on maths activities and investigations (hopefully all happily!)

'Not working in ability groups has been a revelation'

One of the first things Year 4 teacher Tracey Baruah tried when her school joined the Mastery Readiness Programme was abandoning the practice of putting children in different groups according to their perceived ability.
But Tracey, maths lead at Spring Bank Primary School in Leeds, with over 25 years' teaching behind her, quickly saw the benefits:

Not working in ability groups has been quite a revelation, she enthuses.

Watching Tracey lead a class discussion with Year 4, it is striking that all the children are involved, and that the discussion she’s leading is only possible because the children have all been working on the same, open-ended question.

Sarah Hawes, the headteacher, notes the high level of engagement from all children:

…and that speaks volumes about how children rise to the challenge. Regardless of what their ability is deemed to be, if you give them an equal opportunity at something, they rise to it. They will have a go.

Sarah explains that they now often use the format of question we have seen in the Year 4 lesson: asking children what they know, and what they can find out. It has really helped pupil confidence because it removes the feeling of ‘I can’t do it’.
Spring Bank Primary School is a one-form entry school in the Headingley area of Leeds. Following an Ofsted judgement of Requires Improvement (RI), the school joined the Mastery Readiness Programme with the West Yorkshire Maths Hub. They took the decision to remove ‘ability’ groups early on, hoping to increase all children’s success in maths.
Pupil confidence is one of the things that has been improved by removing ability-groupings, says Tracey:

Some of my children came into Year 3, last year, thinking ‘That work’s not for me’. And now they would never say that.

Sarah agrees:

Children will still say ‘Yes, I find maths tricky, but I know what to do to help me, I know who I can talk to, I know what I can use’. I think historically, when we did do that three-way, five-way differentiation, we were labelling. I really do feel it labels children. And children aren’t daft – they know when they’re not getting the hard work.

So, how does giving the whole class the same problem help build all children’s confidence? Sarah explains that those children who might previously have been given work for ‘lower ability’ pupils would never get the opportunity to see or hear the most difficult maths being done in the class and to engage with it. She says, ‘Now all children are seeing the best possible (mathematical) outcomes (from the problems set)’. Not only that, Tracey points out, but their contributions are being valued by others in the class:

They are also getting someone saying to them, ‘Oh right, actually that’s a really good way, I’d not thought about doing that,’ or, ‘Show me how you did it, oh right, that’s a really good way to do it’.

Furthermore, Sarah points out that ability-grouping was crude and didn’t allow for times when children found a topic easier or harder than usual:

We’ve also talked about how one size doesn’t fit all. All children have different skills, different areas of expertise, different understanding. You can have a child that really struggles with calculations and problem-solving but is a complete whizz when it comes to time or money. They bring those skills to the table.

And what about those children that might previously have been on the ‘top table’ or doing ‘harder’ work? Tracey says that children can still be challenged, but by deepening their understanding rather than racing on to the next topic with only a procedural understanding of the previous one:

At the other end of the spectrum, the ‘more able’ children, they’re still engaged in what you want them to do. And they’re able to share their expertise. There are lots of very subtle ways that you can extend them. It doesn’t have to be a different activity. It can be through your questioning. When children are busy, there’s lots of scope to go and ask individual questions.

Sarah adds:

It’s not just about ‘they are very good at that, let’s see what’s harder, or more challenging or a bigger number’ – the old style of looking at challenging maths. The staff collectively really do understand that going deeper is about the reasoning, the explanation, the ‘how can you show this?’ I think the children have really embraced that as well – they understand that it’s not just about harder maths and bigger numbers, it’s about truly understanding.

Removing ability-grouping is just one aspect of how things have changed at Spring Bank Primary School. To hear the whole story of how the school has thrived as part of the NCETM Mastery Readiness Programme, supported by West Yorkshire Maths Hub, listen to Tracey and Sarah in this NCETM podcast. It’s an inspiring story.