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.
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
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.
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.
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.
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:
Please post some of the ways your students solve the problem. Teachers-not too much direction please.
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
Go to: Costs of "The 12 Days" since 1984
