The NZ Maths Curriculum states:
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to: (then lists the Achievement Objectives)
What are Meaningful Contexts?
Is the usual Maths Text (work sheet) activities meaningful for most students? whether it be 4 + 5 = ? or use Pythagoras to find the length of the 3rd side of the triangle. Apart from doing as they are told or pleasing me the teacher, is there a real reason for the students to answer?
To me a meaningful context is something that appeals to students whether it be cultural, imaginative, a challenge, a real life situation, something that really engages the learning and they see a reason for finding the answer/solution.
In a previous post "TwentyOne" I suggest the "Challenge to beat me" was a meaningful contect for many of the students I worked with.
Over the years I have seen so much "busy work' in maths that no wonder we produce so many people who dislike or "cant do Maths"
At one mini conference I attended the Manager of a large printing company, welcomed us and said "I admire you people with your interest in maths and science... I just cant do maths!!" At morning tea I challenged him and asked why he said that. In the discussion he revealed that he was an accountant and did budgets and kept records etc. HE DID NOT EQUATE ACCOUNTANCY TO MATHEMATICS. I suggest that is because he did not explore maths through meaningful or real life contexts!!!
I suggest that many of the measurement activities that we get students to do are often not motivating for them and they therefore do not learn the required objectives we had hoped.
Is there a need for students to be measuring the netball court, when it is already marked out?
Why do we ask students to measure the height of the door to the classroom?
I suggest that we need to look for activities that have a “realness” to them so that the students can see a reason for investigating and completing the activity and hence developing the skills of measurement.
Perhaps we need to rephrase the netball court in a different way,
“There is a limited budget available for spending on court markings.
To help the BOT decide how much money is available we need to know how much it will cost to repaint the netball court lines”
We now have a situation where there is richness to the activity rather than just taking the trundle wheel and measuring the lengths of the lines.
As a School Committee member, before ‘Tomorrows Schools’ I was asked to estimate the cost of repainting the school swimming pool.
I felt that this was better done by the senior children as a ‘practical measuring activity.
We, the School Committee, told the students the cost of the paint was and what area a litre could be expected to cover.
The students had to work out the surface area and then decide on how many litres of paint and consequently the cost.
The important outcome was that their maths was used to assist the Committee and the students actual saw the pool being painted!!!!!
The challenge for each of us is to find, WITH THE HELP OF OUR STUDENTS, interesting tasks that will help them achieve the desired learning outcomes.
Have you considered reading books like "Counting on Frank" as a starting point for a maths investigation: (Is Frank's investigation about Ball Point Pens still true?)
How many students in the class have attached ear lobes? and how many have unattached?
In Gulliver's Travels Gulliver's thumb was measured and from this one measurement the Little People made him a coat. Would this be true today, How could we find out?
How much pocket money does each child get in the class?
What can you tell me about Kowhaiwhai Patterns?
In the Bible Goliath was described as being "6 cubits and a span". Would he fit through the classroom door without banging his head?
In the song "Twelve Days of Christmas" many things are mentioned. How much would all these things costs? check out this link 12 Days of Christmas
New class in 2020 (Year 4+) check in with me for an interesting "Trait" investigation with a Circular Graph
Monday, 16 December 2019
Saturday, 7 December 2019
We Learn Maths By DOING
I often wonder if we play lip service to the way children learn. If we spend time with pre-schoolers we see them constantly playing and through their play and questioning and interaction with the teachers the learn various skills and concepts.
Yet when we look at primary maths' learning there is often an emphasis on numbers and numerals. Yet these are quite abstract concepts. I am sure we would not just a put a book of words in front of students and expect them to learn.
As a Maths Adviser to schools/teachers and then as a private consultant I encouraged teachers to use the following:
When fluent with "Do" ask the students to explain what they were "Doing", When fluent with "Doing" then "Write" about what you said and did!! This then leads to mastery of the concepts.
A couple of years ago I saw a FB post in response to request for feedback about a Measurement Activity created by a Canadian Maths Teacher. The response:
"This is a great measurement activity but we are an iPad school so it would be great if it could be created for the iPad"
To suggest that I saw RED was a bit of an under statement ! How does a children learn what a metre a cm, a gram, a kilogram, a litre etc through manipulating abstract concepts of electronic screens. They need to measure length, estimate mass if they are going to understand the concepts of measurement.
You probably are thinking, what brought this on Len? This post on FB originally from Jo Boaler
It could be a great poster in every maths class and teachers staffroom
Yet when we look at primary maths' learning there is often an emphasis on numbers and numerals. Yet these are quite abstract concepts. I am sure we would not just a put a book of words in front of students and expect them to learn.
As a Maths Adviser to schools/teachers and then as a private consultant I encouraged teachers to use the following:
Do
Say
Write
When fluent with "Do" ask the students to explain what they were "Doing", When fluent with "Doing" then "Write" about what you said and did!! This then leads to mastery of the concepts.
A couple of years ago I saw a FB post in response to request for feedback about a Measurement Activity created by a Canadian Maths Teacher. The response:
"This is a great measurement activity but we are an iPad school so it would be great if it could be created for the iPad"
To suggest that I saw RED was a bit of an under statement ! How does a children learn what a metre a cm, a gram, a kilogram, a litre etc through manipulating abstract concepts of electronic screens. They need to measure length, estimate mass if they are going to understand the concepts of measurement.
You probably are thinking, what brought this on Len? This post on FB originally from Jo Boaler
It could be a great poster in every maths class and teachers staffroom
Some activities to get you started.
These could be arranged as Stations around the room for students to explore and complete.
Thursday, 28 November 2019
Twenty One
Another Nim activity.
As an adviser/consultant I had this activity at hand(in my head as it does not need counters or pens and pencils)Objective: To be the last person to take away either 3 or 2 or 1 to leave zero
Players: Two or two teams. (when introducing the activity I would always play the "Class" or Group, so I was one team and the class was the other. This of course made it easier for me to win as a class would try numbers at random, with no clear strategy)
How: First player starts by verbalising ("I will take away 1 and leave 20")
Second player takes away 1, 2, or 3 ("I will take away 2 leaving 18)
First player takes away 1, 2, or 3 verbalising and leaving the remainder
Continue until one player takes away 1, 2, or 3 to leave zero
Encourage: The students(and yourself to find a strategy that will allow you to always win.
Does the first player always win?
Does the second player always win?
What is the last number that you must leave to always win?
Adaptation: Start at Zero and be the first to reach 21
Take away a different set of numbers, e.g. 1, 2, 3, or 4?
Please Dont: Share your strategy, encourage the students to come up with their own. This is the basis of Creativity, Investigations, Becoming Stuck and moving through, Problem Solving.
As soon as two players know a strategy then whoever starts will control the game this is whn you use an adaptation.
When I was working in classes and schools as an adviser/consultant/teacher I would often use this activity as by doing it mentally as explained above helps mental agility with students.
At any break time of the next visit there would be queues of students wanting to play against me so that they "could win" It often took a number of days before I came a cross a student who knew the strategy.
Yes: We could show the working on the board, but this takes away the mental aspects and the strategy is much easier to see!
We could use a pile of 21 counters
Sunday, 24 November 2019
Encourage Creativity and Investigations: STOP USING WALTS etc
This photo is self explanatory. Whoever thought we should write WALT's, Specific Objectives on the board, screen, before students working, must have been more interested in Test results than student's real learning.
See below for another post about Writing Objectives before a lesson:
Thanks to the person who shared this on FaceBook.
Writing Objectives A waste of time
See below for another post about Writing Objectives before a lesson:
Thanks to the person who shared this on FaceBook.
Writing Objectives A waste of time
Friday, 8 November 2019
Struggle/Being Stuck with Maths
I can remember seeing in a lecture room, at Auckland College of Education some years back, a wall poster along the lines of: STUCK, congratulations. I just wish I could remember the rest but it nwas along the lines of "this is when the learning starts"
When I read the article below, by Jo Boaler, I thought I should share, because often as teachers we often try and make everything so easy we break math's learning into small steps, each step taking us towards the big goal. Is this really the way children learn best? (Most Text Books and Programs do just this!)
In the real world, outside the classroom, most of us learn best when we become STUCK, figure a way through and achieve what we wanted.
I would like to encourage all teachers to have activities available for all students to become STUCK and perhaps FRUSTRATED, so that REAL Learning can take place, and the student can feel real achievement in what they have done.
Feel free to share this article and perhaps join Jo Boaler's You Cubed email list.
Why Struggle Is Essential for the Brain — and Our Lives
As parents and teachers, we do just about everything we can to make sure that children don’t struggle. It turns out we are making a terrible mistake. Research shows that struggling is absolutely critical to mastery and that the highest achieving people in the world are those who have struggled the most. The more I communicate this message to parents and teachers the more stories I hear of complete personal transformation.
Neuroscientists have found that mistakes are helpful for brain growth and connectivity and if we are not struggling, we are not learning. Not only is struggle good for our brains but people who know about the value of struggle improve their learning potential. This knowledge would not be earth shattering if it was not for the fact that we in the Western world are trained to jump in and prevent learners from experiencing struggle.
“When students look at me and say: “This is hard,” I say, “That is fantastic.”
An international study of mathematics teaching found that teachers in Japan put their students in places of struggle 44 percent of the time in classrooms—they saw this less than 1 percent of the time in U.S. classrooms. What do we parents and teachers do instead? We jump in and show the way, offering steps to a solution to help save our students from struggle. This is in large part because this new science is not widely available and we are culturally trained to feel bad, and to rush in and help, when this is probably the last thing we should do.
The research on the impact of struggle turns out to help adults too—in all sorts of jobs. I interviewed sixty-two people for my new book, “Limitless Mind.” Many of them shared similar accounts of how they used to go into meetings afraid they would be found out for not knowing something. After learning about the importance of not knowing and of engaging in struggle they now proudly show up and say “I don’t know, but I will find out.” They display a mindset of discovery and curiosity, which has helped their lives in many ways.
Once we stop the charade of knowing everything, and embrace knowing less, with a willingness to sit with uncertainty, unexpected things happen.
When I was teaching middle schoolers in a research math camp a few years ago one girl stood out to me; she was nearly always wrong in her thinking, but she was always engaged, arguing her case, pushing to understand better. An observer of the class would have described her as a low achiever, but she improved more than any other of the 84 students we taught that summer. Her standardized test score in mathematics improved by 450 percent after 18 struggle filled lessons. Our messages to the students—that struggle would be valued and mistakes are productive—had helped her feel good about struggle and embrace it.
When I tell young learners that struggle and mistakes are the best times for our brains it is freeing. Students no longer give up on problems when they find them hard—they push through the struggle to the wonderful places on the other side. When students look at me with a puppy dog face and say: “This is hard,” I say, “That is fantastic. That feeling of ‘hard’ is the feeling of your brain developing, strengthening and growing”.
“We cannot achieve anything creative without being comfortable with mistakes and struggle”
In 2016, two young computer scientists rocked the world of mathematics by solving a previously unsolved math problem, an event that many described as audacious. The two young men reflected that it was knowing less that allowed them to solve the difficult problem. It freed their mind to think in better ways.
I am not arguing that knowledge is bad or knowing answers is not helpful. What I am saying is that knowledge is less important than a mindset of discovery and curiosity. We cannot achieve anything creative without being comfortable with mistakes and struggle—and we should all embrace times of struggle, knowing they are helping our brains. When we adopt a limitless perspective, approaching different jobs and conversations with a comfort with uncertainty and struggle, with a willingness to learn from others and with a flexible approach to problems, outcomes improve—in learning and in life.
Millions of students start the school year each year excited for all they will learn, but as soon as they struggle or see someone solve a problem with ease, they start to doubt themselves and mentally shut down. This starts a less productive learning pathway for them. Instead they should value the time of struggle and know that they are on their way to being better, wiser and equipped with a stronger brain. Getting answers right is OK, being stuck and finding them hard is fantastic.
Jo Boaler is the Nomellini-Olivier Professor of Education at Stanford, co-founder of youcubed.org and author of the new book “Limitless Mind: Learn, Lead & Live without Barriers.”
When I read the article below, by Jo Boaler, I thought I should share, because often as teachers we often try and make everything so easy we break math's learning into small steps, each step taking us towards the big goal. Is this really the way children learn best? (Most Text Books and Programs do just this!)
In the real world, outside the classroom, most of us learn best when we become STUCK, figure a way through and achieve what we wanted.
I would like to encourage all teachers to have activities available for all students to become STUCK and perhaps FRUSTRATED, so that REAL Learning can take place, and the student can feel real achievement in what they have done.
Feel free to share this article and perhaps join Jo Boaler's You Cubed email list.
Why Struggle Is Essential for the Brain — and Our Lives
As parents and teachers, we do just about everything we can to make sure that children don’t struggle. It turns out we are making a terrible mistake. Research shows that struggling is absolutely critical to mastery and that the highest achieving people in the world are those who have struggled the most. The more I communicate this message to parents and teachers the more stories I hear of complete personal transformation.
Neuroscientists have found that mistakes are helpful for brain growth and connectivity and if we are not struggling, we are not learning. Not only is struggle good for our brains but people who know about the value of struggle improve their learning potential. This knowledge would not be earth shattering if it was not for the fact that we in the Western world are trained to jump in and prevent learners from experiencing struggle.
“When students look at me and say: “This is hard,” I say, “That is fantastic.”
An international study of mathematics teaching found that teachers in Japan put their students in places of struggle 44 percent of the time in classrooms—they saw this less than 1 percent of the time in U.S. classrooms. What do we parents and teachers do instead? We jump in and show the way, offering steps to a solution to help save our students from struggle. This is in large part because this new science is not widely available and we are culturally trained to feel bad, and to rush in and help, when this is probably the last thing we should do.
The research on the impact of struggle turns out to help adults too—in all sorts of jobs. I interviewed sixty-two people for my new book, “Limitless Mind.” Many of them shared similar accounts of how they used to go into meetings afraid they would be found out for not knowing something. After learning about the importance of not knowing and of engaging in struggle they now proudly show up and say “I don’t know, but I will find out.” They display a mindset of discovery and curiosity, which has helped their lives in many ways.
Once we stop the charade of knowing everything, and embrace knowing less, with a willingness to sit with uncertainty, unexpected things happen.
When I was teaching middle schoolers in a research math camp a few years ago one girl stood out to me; she was nearly always wrong in her thinking, but she was always engaged, arguing her case, pushing to understand better. An observer of the class would have described her as a low achiever, but she improved more than any other of the 84 students we taught that summer. Her standardized test score in mathematics improved by 450 percent after 18 struggle filled lessons. Our messages to the students—that struggle would be valued and mistakes are productive—had helped her feel good about struggle and embrace it.
When I tell young learners that struggle and mistakes are the best times for our brains it is freeing. Students no longer give up on problems when they find them hard—they push through the struggle to the wonderful places on the other side. When students look at me with a puppy dog face and say: “This is hard,” I say, “That is fantastic. That feeling of ‘hard’ is the feeling of your brain developing, strengthening and growing”.
“We cannot achieve anything creative without being comfortable with mistakes and struggle”
In 2016, two young computer scientists rocked the world of mathematics by solving a previously unsolved math problem, an event that many described as audacious. The two young men reflected that it was knowing less that allowed them to solve the difficult problem. It freed their mind to think in better ways.
I am not arguing that knowledge is bad or knowing answers is not helpful. What I am saying is that knowledge is less important than a mindset of discovery and curiosity. We cannot achieve anything creative without being comfortable with mistakes and struggle—and we should all embrace times of struggle, knowing they are helping our brains. When we adopt a limitless perspective, approaching different jobs and conversations with a comfort with uncertainty and struggle, with a willingness to learn from others and with a flexible approach to problems, outcomes improve—in learning and in life.
Millions of students start the school year each year excited for all they will learn, but as soon as they struggle or see someone solve a problem with ease, they start to doubt themselves and mentally shut down. This starts a less productive learning pathway for them. Instead they should value the time of struggle and know that they are on their way to being better, wiser and equipped with a stronger brain. Getting answers right is OK, being stuck and finding them hard is fantastic.
Jo Boaler is the Nomellini-Olivier Professor of Education at Stanford, co-founder of youcubed.org and author of the new book “Limitless Mind: Learn, Lead & Live without Barriers.”
Tuesday, 22 October 2019
Homework is damaging our children
Admittedly this is from the USA but similar feelings and understandings can be found in NZ. As a father, Grandfather and working in Education for 54 years I believe we are not allowing kids to be kids and setting homework is often not justifiable, as it can be:
I wonder what has happened to all the Family Math books schools and teachers bought? Along with the monthly activity newsletters the Trust published?
“There is no evidence that any amount of homework improves the academic performance of elementary students.”
This statement, by homework research guru Harris Cooper, of Duke University, is startling to hear, no matter which side of the homework debate you’re on. Can it be true that the hours of lost playtime, power struggles and tears are all for naught? That millions of families go through a nightly ritual that doesn’t help? Homework is such an accepted practice, it’s hard for most adults to even question its value.
When you look at the facts, however, here’s what you find: Homework has benefits, but its benefits are age dependent.
For elementary-aged children, research suggests that studying in class gets superior learning results, while extra schoolwork at home is just . . . extra work. Even in middle school, the relationship between homework and academic success is minimal at best. By the time kids reach high school, homework provides academic benefit, but only in moderation. More than two hours per night is the limit. After that amount, the benefits taper off. “The research is very clear,” agrees Etta Kralovec, education professor at the University of Arizona. “There’s no benefit at the elementary school level.”
Before going further, let’s dispel the myth that these research results are due to a handful of poorly constructed studies. In fact, it’s the opposite. Cooper compiled 120 studies in 1989 and another 60 studies in 2006. This comprehensive analysis of multiple research studies found no evidence of academic benefit at the elementary level. It did, however, find a negative impact on children’s attitudes toward school.
This is what’s worrying. Homework does have an impact on young students, but it’s not a good one. A child just beginning school deserves the chance to develop a love of learning. Instead, homework at a young age causes many kids to turn against school, future homework and academic learning. And it’s a long road. A child in kindergarten is facing 13 years of homework ahead of her.
Then there’s the damage to personal relationships. In thousands of homes across the country, families battle over homework nightly. Parents nag and cajole. Overtired children protest and cry. Instead of connecting and supporting each other at the end of the day, too many families find themselves locked in the “did you do your homework?” cycle.
When homework comes prematurely, it’s hard for children to cope with assignments independently—they need adult help to remember assignments and figure out how to do the work. Kids slide into the habit of relying on adults to help with homework or, in many cases, do their homework. Parents often assume the role of Homework Patrol Cop. Being chief nag is a nasty, unwanted job, but this role frequently lingers through the high school years. Besides the constant conflict, having a Homework Patrol Cop in the house undermines one of the purported purposes of homework: responsibility.
Homework supporters say homework teaches responsibility, reinforces lessons taught in school, and creates a home-school link with parents. However, involved parents can see what’s coming home in a child’s backpack and initiate sharing about school work--they don’t need to monitor their child’s progress with assigned homework. Responsibility is taught daily in multiple ways; that’s what pets and chores are for. It takes responsibility for a 6-year-old to remember to bring her hat and lunchbox home. It takes responsibility for an 8-year-old to get dressed, make his bed and get out the door every morning. As for reinforcement, that’s an important factor, but it’s only one factor in learning. Non-academic priorities (good sleep, family relationships and active playtime) are vital for balance and well-being. They also directly impact a child’s memory, focus, behavior and learning potential. Elementary lessons are reinforced every day in school. After-school time is precious for the rest of the child.
What works better than traditional homework at the elementary level is simply reading at home. This can mean parents reading aloud to children as well as children reading. The key is to make sure it’s joyous. If a child doesn’t want to practice her reading skills after a long school day, let her listen instead. Any other projects that come home should be optional and occasional. If the assignment does not promote greater love of school and interest in learning, then it has no place in an elementary school-aged child’s day.
Elementary school kids deserve a ban on homework. This can be achieved at the family, classroom or school level. Families can opt out, teachers can set a culture of no homework (or rare, optional homework), and schools can take time to read the research and rekindle joy in learning.
Homework has no place in a young child’s life. With no academic benefit, there are simply better uses for after-school hours.
Heather Shumaker’s new book It’s OK to Go Up the Slide (Tarcher/Penguin Random House) was published on March 8, 2016.
- Just busy work (As we have to set homework)
- Not practise of already learnt ideas
- Set as punishment for behaviour or other reasons
I wonder what has happened to all the Family Math books schools and teachers bought? Along with the monthly activity newsletters the Trust published?
Homework is wrecking our kids: The research is clear, let's ban elementary homework
Heather Shumaker March 6, 2016 4:00AM (UTC)
This statement, by homework research guru Harris Cooper, of Duke University, is startling to hear, no matter which side of the homework debate you’re on. Can it be true that the hours of lost playtime, power struggles and tears are all for naught? That millions of families go through a nightly ritual that doesn’t help? Homework is such an accepted practice, it’s hard for most adults to even question its value.
When you look at the facts, however, here’s what you find: Homework has benefits, but its benefits are age dependent.
For elementary-aged children, research suggests that studying in class gets superior learning results, while extra schoolwork at home is just . . . extra work. Even in middle school, the relationship between homework and academic success is minimal at best. By the time kids reach high school, homework provides academic benefit, but only in moderation. More than two hours per night is the limit. After that amount, the benefits taper off. “The research is very clear,” agrees Etta Kralovec, education professor at the University of Arizona. “There’s no benefit at the elementary school level.”
Before going further, let’s dispel the myth that these research results are due to a handful of poorly constructed studies. In fact, it’s the opposite. Cooper compiled 120 studies in 1989 and another 60 studies in 2006. This comprehensive analysis of multiple research studies found no evidence of academic benefit at the elementary level. It did, however, find a negative impact on children’s attitudes toward school.
This is what’s worrying. Homework does have an impact on young students, but it’s not a good one. A child just beginning school deserves the chance to develop a love of learning. Instead, homework at a young age causes many kids to turn against school, future homework and academic learning. And it’s a long road. A child in kindergarten is facing 13 years of homework ahead of her.
Then there’s the damage to personal relationships. In thousands of homes across the country, families battle over homework nightly. Parents nag and cajole. Overtired children protest and cry. Instead of connecting and supporting each other at the end of the day, too many families find themselves locked in the “did you do your homework?” cycle.
When homework comes prematurely, it’s hard for children to cope with assignments independently—they need adult help to remember assignments and figure out how to do the work. Kids slide into the habit of relying on adults to help with homework or, in many cases, do their homework. Parents often assume the role of Homework Patrol Cop. Being chief nag is a nasty, unwanted job, but this role frequently lingers through the high school years. Besides the constant conflict, having a Homework Patrol Cop in the house undermines one of the purported purposes of homework: responsibility.
Homework supporters say homework teaches responsibility, reinforces lessons taught in school, and creates a home-school link with parents. However, involved parents can see what’s coming home in a child’s backpack and initiate sharing about school work--they don’t need to monitor their child’s progress with assigned homework. Responsibility is taught daily in multiple ways; that’s what pets and chores are for. It takes responsibility for a 6-year-old to remember to bring her hat and lunchbox home. It takes responsibility for an 8-year-old to get dressed, make his bed and get out the door every morning. As for reinforcement, that’s an important factor, but it’s only one factor in learning. Non-academic priorities (good sleep, family relationships and active playtime) are vital for balance and well-being. They also directly impact a child’s memory, focus, behavior and learning potential. Elementary lessons are reinforced every day in school. After-school time is precious for the rest of the child.
What works better than traditional homework at the elementary level is simply reading at home. This can mean parents reading aloud to children as well as children reading. The key is to make sure it’s joyous. If a child doesn’t want to practice her reading skills after a long school day, let her listen instead. Any other projects that come home should be optional and occasional. If the assignment does not promote greater love of school and interest in learning, then it has no place in an elementary school-aged child’s day.
Elementary school kids deserve a ban on homework. This can be achieved at the family, classroom or school level. Families can opt out, teachers can set a culture of no homework (or rare, optional homework), and schools can take time to read the research and rekindle joy in learning.
Homework has no place in a young child’s life. With no academic benefit, there are simply better uses for after-school hours.
Heather Shumaker’s new book It’s OK to Go Up the Slide (Tarcher/Penguin Random House) was published on March 8, 2016.
Circular Nim
Here is another NIM activity that is different from the usual type. It encourages players to think about spatial(geometry) issues rather than just number as in the traditional.
The activity could be approached, through a class/group demonstration and then assigned as an independent activity.
Once students have found a strategy for winning encourage them to tweak the rules to create a new/similar activity.
As usual I do not share answers or strategies, as I believe that this takes away the investigation, thinking and creativity of learning. If we as teachers know the answers we can subconsciously encourage students to look for the answer, strategy we have when there could be others as well.
Enjoy the exploring
The activity could be approached, through a class/group demonstration and then assigned as an independent activity.
Once students have found a strategy for winning encourage them to tweak the rules to create a new/similar activity.
As usual I do not share answers or strategies, as I believe that this takes away the investigation, thinking and creativity of learning. If we as teachers know the answers we can subconsciously encourage students to look for the answer, strategy we have when there could be others as well.
Enjoy the exploring
Sunday, 20 October 2019
2 D Nim
In the last post we had a single dimension Nim game, this post introduces a Second Dimension.
Nim is a mathematical game of strategy in which two players take turns removing (i.e., nimming) objects from distinct heaps or piles. ...
Nim is typically played as a misère game, in which the player to take the last object loses.
Nim can also be played as a normal play game, where the player taking the last object wins.
After playing one way, it is great to change the rules so that the opposite is the winning. Teachers and parents should observe studenst to see if they can transfer the knowledge into a new situation.
I look forward to hearing how you use the Nim Games with family or class. As well as, of course, how the students enjoy the activities!
Nim is a mathematical game of strategy in which two players take turns removing (i.e., nimming) objects from distinct heaps or piles. ...
Nim is typically played as a misère game, in which the player to take the last object loses.
Nim can also be played as a normal play game, where the player taking the last object wins.
After playing one way, it is great to change the rules so that the opposite is the winning. Teachers and parents should observe studenst to see if they can transfer the knowledge into a new situation.
I look forward to hearing how you use the Nim Games with family or class. As well as, of course, how the students enjoy the activities!
Sunday, 13 October 2019
Party Balloons
Many mathematics curricula encourage problem solving, investigations, logical thinking, but we seem to focus on on developing skills through following directions all the time.
There are many great activities that can be used as whole class starters, Math's Table activities, enrichment and the Chinese NIM Type games fit nicely into this area.
Students once they have mastered the strategy want to then challenge others including teachers and parents.
When working with teachers and Students I regularly had a "Nim" type activity up my sleeve, and would finish the period with it. On my next school visit I would be accosted by students "trying to beat me" Some did but often they would because I might suggest that we play it in reverse-as a way of seeing if they could adapt their thinking/strategy. I really enjoyed leaving the students(and teachers) the challenge and interacting with them on a return visit.
At NO stage would I would give the rule/strategy, but would play the game and acknowledge those students who appeared to have a winning strategy.
This activity, adapted from Family Math's Balloon Ride can be introduced to quite young students but do not force them to look for strategies, but to just play and see their excitement.
There are many great activities that can be used as whole class starters, Math's Table activities, enrichment and the Chinese NIM Type games fit nicely into this area.
Students once they have mastered the strategy want to then challenge others including teachers and parents.
When working with teachers and Students I regularly had a "Nim" type activity up my sleeve, and would finish the period with it. On my next school visit I would be accosted by students "trying to beat me" Some did but often they would because I might suggest that we play it in reverse-as a way of seeing if they could adapt their thinking/strategy. I really enjoyed leaving the students(and teachers) the challenge and interacting with them on a return visit.
At NO stage would I would give the rule/strategy, but would play the game and acknowledge those students who appeared to have a winning strategy.
This activity, adapted from Family Math's Balloon Ride can be introduced to quite young students but do not force them to look for strategies, but to just play and see their excitement.
Thursday, 1 August 2019
Supermarket Checkouts
After finding I had to queue at a DIY Checkout this week, it reminded me of this activity we used to do with students. A number of customers with no employee at the one "open checkout"
A good activity for Practical Probability and predictions. It also gives a reson for rolling dice and seeing the outcomes.
I would love to hear how the kids enjoyed the investigation
A good activity for Practical Probability and predictions. It also gives a reson for rolling dice and seeing the outcomes.
I would love to hear how the kids enjoyed the investigation
Saturday, 20 July 2019
Hopscotch Goats
I believe this activity, in this format, was originally published by NCTM. I have seen it with frogs on lily pads, and I have used the principle in the classroom with seats and children.
It is important in our math's classrooms that we incorporate more problems/investigations like this where students can not just say, "I know the answer!" These types of activities encourage lateral thinking, investigation and blockages which students need to get used to.
I hope it proves successful in your math's class
For further information and extensions look at this site: https://nzmaths.co.nz/frogs-teachers-notes?fbclid=IwAR15UV2ujnpSmNqAT6eJ-5z3Faq_ExmhI-G7rq1C8rusHFc_SS-t5CszVOA
It is important in our math's classrooms that we incorporate more problems/investigations like this where students can not just say, "I know the answer!" These types of activities encourage lateral thinking, investigation and blockages which students need to get used to.
I hope it proves successful in your math's class
For further information and extensions look at this site: https://nzmaths.co.nz/frogs-teachers-notes?fbclid=IwAR15UV2ujnpSmNqAT6eJ-5z3Faq_ExmhI-G7rq1C8rusHFc_SS-t5CszVOA
Monday, 8 July 2019
Why are we still fixated on teacher computation to the detriment of MATHEMATICS?
“Mathematics is the alphabet with which God has written the universe” Galileo Galilei.
I have believed for a number of years that, the traditional approach to teaching has been incorrect. It was based on the need for “Tally Clerks” during the Industrial Revolution and it has hardly changed since.
Think about the way maths was taught to you, now how about your parents? and your grandparents?
My grandparents and father never flew on an aeroplane, none of them had a cellphone, tablet or a computer, how the world has changed in one short generation, because now my grandchildren have tablets, interactive TV etc
We are told that we have a “Child-Centred” Education system (Be damned we have not) We are told we are educating for the future (Be damned we are not)
Where is the creativity in Maths Teaching? The Thinking? The Cooperation? The open-ended questions? the child-centred investigations?
When was the last time you brought a flower, some fruit, into the classroom and asked the question “where is the maths? or, What can you see in the object?
When was the last time you asked the class, what do you want to know about: fractions, or, measurement, or, geometry, or, art and maths?
Len Cooper, retired maths adviser/consultant and teacher:
https://mathslen.blogspot.com/
Charlotte Wilkinson, “The Wilkie Way” (NZ) in her last newsletter asks similar questions so I share her thoughts and questions.
In making maths modern - mental strategies were the new way of solving - these quickly became more procedures for students to memorise (or not).
Why does school maths have such an unhealthy fixation with procedural knowledge?
The era of human computers has passed, so many of the arbitary skills promoted by school maths are also archaic - long multipication and long division, adding and subtracting fractions to name just a few.
We are presented with acronyms STEM and now STEAM which implies Maths is separate to Science, Technology and Engineering and now Art too.
While it is relatively easy to dismiss the stupidity of thinking mathematics is unrelated to science, technology and engineering let us now consider Mathematics and the Arts.
Bertrand Russell (Nobel Laureate, Philosopher, Mathematician) once said: “Mathematics, rightly viewed, possess not only truth, but supreme beauty - a beauty cold and austere...sublimely pure, and capable of stern perfection such as only the greatest art can show.”
GH Hardy Another famous mathematian in the earlier part of the 20th century known for being a harden purist advocating for rigour and abstraction, ultimately declared that: “I am interested in mathematics only as a creative art.”
If mathematics is an art form, what are mathematicians. Hardy called them “makers of patterns”. The late Maryam Mirzakhani, the only female recipient of the Fields Medal (the highest accolade in mathematics) was often mistaken by her daughter for an artist.
To mathematicians, school maths is something of a desecration of their subject. There is no doubt the rise of numeracy has crowded out more conventional arts subjects but it has also concealed the true nature of mathematics.
Paul Lockhart (American school maths teacher and research mathematician) wrote in his book A Mathematicians Lament - “No society would ever reduce such a beautiful and meaningful art form to something so mindless and trivial.”
Even where calculation has its place, the mathematican seeks rich representations that illuminate the procedures they call upon.
Do you see times tables as just a matter of memorising number facts (learn them by rote) or do you spend time exploring the myriad of patterns within a multiplication table and between the multiplication tables.
We spend alot of time talking about 21st century education - I see modern learning environments, I see school maths curriculums as completing workbooks. I see students working on laptops and maths apps but the mathematics I see them doing is still archaic, procedural and not the kind of mathematics our students need.
The kind of mathematics that our students need, that our world is increasingly dependent on, is much more aligned to its artistic tenent. I think this is why STEM has become STEAM. Skills like curiosity, persistence and resilience are not divorced from mathematics, they are the very traits that mathematicians through the ages have brought to their problems.
As with any art, there is a subjective element to deciding what should go into a mathematics curriculum, or how to assess these broader skills. However that is no excuse for persisting with an outdated brand of the subject that brings joy to so few and value to fewer still.
The history of mathematics is entwined with the history of technology. Humans have precedent for updating their ways of doing mathematics based on the tools available to them. (OK the complete change from using Roman numerals to the base 10 system took about 200 years). With the technologies now available at our fingertips, we can put calculation in its rightful place as the footnote to mathematical thinking power.
Calculation is simply the price we once paid to do mathematics.
When maths anxiety is a real issue for many people, and so many others show an indifference to a subject that promises such immense power and beauty, the price to continue with a fixation on procedural calculation as the backbone to school mathematics is too high.
Samantha, a year 5 student once said to me: “ I love doing sums (calculations) because you don’t have to think.”
How true - once a procedure is memorised no thinking is required.
While the content is the curriculum, how you choose to teach it to your students is dependent on your own creative flair and knowledge of the subject matter.
My own daughter’s advice to Primary school teachers given 5 years ago was
“Calculate less, estimate more”
Mathematics will never be replaced by the Arts.
Mathematics is an art, and it is time we embraced it as one.
©Copyright N C Wilkinsons Ltd 2019
I have believed for a number of years that, the traditional approach to teaching has been incorrect. It was based on the need for “Tally Clerks” during the Industrial Revolution and it has hardly changed since.
Think about the way maths was taught to you, now how about your parents? and your grandparents?
My grandparents and father never flew on an aeroplane, none of them had a cellphone, tablet or a computer, how the world has changed in one short generation, because now my grandchildren have tablets, interactive TV etc
We are told that we have a “Child-Centred” Education system (Be damned we have not) We are told we are educating for the future (Be damned we are not)
Where is the creativity in Maths Teaching? The Thinking? The Cooperation? The open-ended questions? the child-centred investigations?
When was the last time you brought a flower, some fruit, into the classroom and asked the question “where is the maths? or, What can you see in the object?
When was the last time you asked the class, what do you want to know about: fractions, or, measurement, or, geometry, or, art and maths?
Len Cooper, retired maths adviser/consultant and teacher:
https://mathslen.blogspot.com/
Charlotte Wilkinson, “The Wilkie Way” (NZ) in her last newsletter asks similar questions so I share her thoughts and questions.
Maths and The Arts
Traditional school maths with endless practicing of calculating. The standard written algorithms are procedures that have been taught for endless years since the introduction of the base ten algorithmic number system (About 2000 years).In making maths modern - mental strategies were the new way of solving - these quickly became more procedures for students to memorise (or not).
Why does school maths have such an unhealthy fixation with procedural knowledge?
The era of human computers has passed, so many of the arbitary skills promoted by school maths are also archaic - long multipication and long division, adding and subtracting fractions to name just a few.
We are presented with acronyms STEM and now STEAM which implies Maths is separate to Science, Technology and Engineering and now Art too.
While it is relatively easy to dismiss the stupidity of thinking mathematics is unrelated to science, technology and engineering let us now consider Mathematics and the Arts.
Bertrand Russell (Nobel Laureate, Philosopher, Mathematician) once said: “Mathematics, rightly viewed, possess not only truth, but supreme beauty - a beauty cold and austere...sublimely pure, and capable of stern perfection such as only the greatest art can show.”
GH Hardy Another famous mathematian in the earlier part of the 20th century known for being a harden purist advocating for rigour and abstraction, ultimately declared that: “I am interested in mathematics only as a creative art.”
If mathematics is an art form, what are mathematicians. Hardy called them “makers of patterns”. The late Maryam Mirzakhani, the only female recipient of the Fields Medal (the highest accolade in mathematics) was often mistaken by her daughter for an artist.
To mathematicians, school maths is something of a desecration of their subject. There is no doubt the rise of numeracy has crowded out more conventional arts subjects but it has also concealed the true nature of mathematics.
Paul Lockhart (American school maths teacher and research mathematician) wrote in his book A Mathematicians Lament - “No society would ever reduce such a beautiful and meaningful art form to something so mindless and trivial.”
Even where calculation has its place, the mathematican seeks rich representations that illuminate the procedures they call upon.
Do you see times tables as just a matter of memorising number facts (learn them by rote) or do you spend time exploring the myriad of patterns within a multiplication table and between the multiplication tables.
We spend alot of time talking about 21st century education - I see modern learning environments, I see school maths curriculums as completing workbooks. I see students working on laptops and maths apps but the mathematics I see them doing is still archaic, procedural and not the kind of mathematics our students need.
The kind of mathematics that our students need, that our world is increasingly dependent on, is much more aligned to its artistic tenent. I think this is why STEM has become STEAM. Skills like curiosity, persistence and resilience are not divorced from mathematics, they are the very traits that mathematicians through the ages have brought to their problems.
As with any art, there is a subjective element to deciding what should go into a mathematics curriculum, or how to assess these broader skills. However that is no excuse for persisting with an outdated brand of the subject that brings joy to so few and value to fewer still.
The history of mathematics is entwined with the history of technology. Humans have precedent for updating their ways of doing mathematics based on the tools available to them. (OK the complete change from using Roman numerals to the base 10 system took about 200 years). With the technologies now available at our fingertips, we can put calculation in its rightful place as the footnote to mathematical thinking power.
Calculation is simply the price we once paid to do mathematics.
When maths anxiety is a real issue for many people, and so many others show an indifference to a subject that promises such immense power and beauty, the price to continue with a fixation on procedural calculation as the backbone to school mathematics is too high.
Samantha, a year 5 student once said to me: “ I love doing sums (calculations) because you don’t have to think.”
How true - once a procedure is memorised no thinking is required.
While the content is the curriculum, how you choose to teach it to your students is dependent on your own creative flair and knowledge of the subject matter.
My own daughter’s advice to Primary school teachers given 5 years ago was
“Calculate less, estimate more”
Mathematics will never be replaced by the Arts.
Mathematics is an art, and it is time we embraced it as one.
©Copyright N C Wilkinsons Ltd 2019
Sunday, 7 July 2019
Why are we still ability grouping???
It is interesting to note that after much research into ability groups/class streaming(setting) and the danger they can cause to a child's learning, it is surprising that it is still happening and often encourage by the powers above us.
Recently a retired colleague(like myself retired) was sharing how her grandchild stopped reading because she was put in the "cant read/bottom" group. We believe her thinking was, "they have me in the bottom group with the children who cant read so I will show them by not reading" It took intervention by the grandmother and a retired (Reading Reading Recovery Teacher) to snap the child out of this thinking and get on with reading like she know how to.
30 years ago when working with my "bottom group" year 7/8 I was using materials to help them understand various number concepts. I looked up and the rest of the class had stopped what they were doing and wanted to join in. From there on it was open ended problems and investigations with groups of 2, groups of and a real cooperative learning approach.
Check out what Jo Boaler's experience is with open ended problems and students taking control of their learning.
30 years ago when working with my "bottom group" year 7/8 I was using materials to help them understand various number concepts. I looked up and the rest of the class had stopped what they were doing and wanted to join in. From there on it was open ended problems and investigations with groups of 2, groups of and a real cooperative learning approach.
Check out what Jo Boaler's experience is with open ended problems and students taking control of their learning.
The following is from this website: NCET "Not working in ability groups has been a revelation"NCETM "Not working with 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.
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.
…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’.
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.
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.
Saturday, 29 June 2019
Joining Squares
This
week's activity is a great one for manipulating 6 square pieces of card
to find out how many arrangements can be made.
It will test children's powers of observation as in mathematics a shape is unique (cant be rotated, flipped to make a new shape), it will also encourage perseverance to find them all.
Be prepared to find some have a break and
then come back to find more-there are quite a number.
It will test children's powers of observation as in mathematics a shape is unique (cant be rotated, flipped to make a new shape), it will also encourage perseverance to find them all.
Thursday, 20 June 2019
Figurate Numbers
Traditionally mathematics has been taught from numbers first and then into Geometry.
The Greeks would suggest that Mathematics started with Geometry and out of Geometry Numbers were created to help record and analyse.
Check out Donald in Mathemagicland(YouTube) Donald in Mathemagicland
Galileo suggested, ""Mathematics is the alphabet with which God has written the universe".
The Greeks would suggest that Mathematics started with Geometry and out of Geometry Numbers were created to help record and analyse.
Check out Donald in Mathemagicland(YouTube) Donald in Mathemagicland
Galileo suggested, ""Mathematics is the alphabet with which God has written the universe".
Wouldn't it be exciting if all maths' teaching was started from geometry, the real world, rather than from abstract Arithmetic! I am sure the majority of students would become more involved and interested.
From NCTM Student Explorations in Mathematics January 2012
Thursday, 13 June 2019
Common Factors
Common Factors: Once children have some understanding of
multiplication and division this activity is a great one to help
understand and practise factors(numbers that divide evenly to another,
OR, two numbers multiplied together to get a product)
This could be completed independently, but better still through discussion-parent and child, Never be afraid to try more difficult activities with younger children.
(With thanks to Leigh Childs and Nimble With Numbers)
This could be completed independently, but better still through discussion-parent and child, Never be afraid to try more difficult activities with younger children.
(With thanks to Leigh Childs and Nimble With Numbers)
Friday, 7 June 2019
Eight Queens on a Chessboard
This one is great for communication, perseverance, making mistakes and self correcting.
Most homes have a Chess Board tucked away so now is a time to bring it out and see if you can place the queens correctly.
I was at a school presentation yesterday and it was awesome to hear, a young girl about 7/8 say the following, "It is okay to make mistakes because we can learn from our mistakes" I would like to add, "We may not learn much by getting everything correct!"
Most homes have a Chess Board tucked away so now is a time to bring it out and see if you can place the queens correctly.
I was at a school presentation yesterday and it was awesome to hear, a young girl about 7/8 say the following, "It is okay to make mistakes because we can learn from our mistakes" I would like to add, "We may not learn much by getting everything correct!"
Friday, 17 May 2019
Squares and Rectangles on a ChessBoard.
A hardy annual but one that is good for finding patterns. When investigating rectangles you may wish to limit to one size to start with!!!
Thursday, 2 May 2019
Saturday, 13 April 2019
Monkey Business
An interesting problem, investigation using fractions. Would love to hear how you get on with the processes you use, children use to solve it.
Thursday, 4 April 2019
Sunday, 31 March 2019
Technology in classrooms?
I felt a need to share this article from the newspaper this morning:
https://www.stuff.co.nz/technology/digital-living/111691580/major-distraction-australian-primary-school-dumps-ipads-returns-to-paper-textbooks?cid=app-iPhone
After a few years of using tablets the children, when surveyed said that they were more comfortable using paper texts etc rather than the technology.
Good on the school for asking the students what they preferred rather than going along with what many people are saying is the "way forward"
A couple of years ago, I was sent a measurement activity by a colleague in Canada. By memory it required the students to do practical measurement tasks. The author asked for feedback about the effectiveness of the activity. Most were favourable as it was a great activity. One comment caught my eye, and it made me reply react negatively.
The comment, viz, "A great activity it would be better if it was an App for tablets as we are an iPad School"
You may want to know why I reacted as I did.
How does one understand measurement without physically measuring?
How does technology help you understand how long a metre is? how heavy is a gram or kilogram? Technology is working in the extreme abstract and students(many) do not think in the abstract but think in the "concrete"
It is similar to the debate about Analogue and Digital watches and clocks. For most students they can read time from a Digital output, but with an Analogue they can measure time as they see how far the hands move. To be able to measure time from a Digital Screen the students have to be able use 3 digit subtraction, understand that there are 60 seconds in a minute and 60 minutes in an hour (NOT 100)
To me, all measurement for children should start and be strongly practical.
We need to start with which COMPARISONS
Which one is longer/shorter/ heavier etc. Between two then increasing the numbers for the comparisons, when reasonable fluent in determining the correct comparisons we move to
Measurement by UNCONVENTIONAL UNITS how many Lego blocks long? How many Lego blocks does this weigh? How many bounces of a ball till Mary has run around the block? again as fluency and competence is shown we can move students to
Measuring with STANDARD UNITS
Please realise this is not and instant move from one to the other stage, but a gradual one that does in some cases take years.
When we converted to Metrics I had occasion to go and by some plasterboard. Into the buildre's yard I went and asked for a sheet of 1.2 x 2.4 Gibboard. Sorry sir but we do not sell that! What do you sell? 1200 x 2400 Gibboard. I would suggest this was an example of a person who did not have a great grasp of measurement or the decimal system
https://www.stuff.co.nz/technology/digital-living/111691580/major-distraction-australian-primary-school-dumps-ipads-returns-to-paper-textbooks?cid=app-iPhone
After a few years of using tablets the children, when surveyed said that they were more comfortable using paper texts etc rather than the technology.
Good on the school for asking the students what they preferred rather than going along with what many people are saying is the "way forward"
A couple of years ago, I was sent a measurement activity by a colleague in Canada. By memory it required the students to do practical measurement tasks. The author asked for feedback about the effectiveness of the activity. Most were favourable as it was a great activity. One comment caught my eye, and it made me reply react negatively.
The comment, viz, "A great activity it would be better if it was an App for tablets as we are an iPad School"
You may want to know why I reacted as I did.
How does one understand measurement without physically measuring?
How does technology help you understand how long a metre is? how heavy is a gram or kilogram? Technology is working in the extreme abstract and students(many) do not think in the abstract but think in the "concrete"
It is similar to the debate about Analogue and Digital watches and clocks. For most students they can read time from a Digital output, but with an Analogue they can measure time as they see how far the hands move. To be able to measure time from a Digital Screen the students have to be able use 3 digit subtraction, understand that there are 60 seconds in a minute and 60 minutes in an hour (NOT 100)
To me, all measurement for children should start and be strongly practical.
We need to start with which COMPARISONS
Which one is longer/shorter/ heavier etc. Between two then increasing the numbers for the comparisons, when reasonable fluent in determining the correct comparisons we move to
Measurement by UNCONVENTIONAL UNITS how many Lego blocks long? How many Lego blocks does this weigh? How many bounces of a ball till Mary has run around the block? again as fluency and competence is shown we can move students to
Measuring with STANDARD UNITS
Please realise this is not and instant move from one to the other stage, but a gradual one that does in some cases take years.
When we converted to Metrics I had occasion to go and by some plasterboard. Into the buildre's yard I went and asked for a sheet of 1.2 x 2.4 Gibboard. Sorry sir but we do not sell that! What do you sell? 1200 x 2400 Gibboard. I would suggest this was an example of a person who did not have a great grasp of measurement or the decimal system
Wednesday, 27 March 2019
Digit Puzzler
This activity is intriguing as it seems so simple but may take some time to find one solution, more importantly is there more than one solution? And can the learner create their own problem for sharing?
Please share your thoughts about this activity
Please share your thoughts about this activity
Saturday, 23 March 2019
Why is Arithmetic (Numbers) dominating our Teaching?
Galileo: "Mathematics is the alphabet with which God has written the universe".
If this is the case shouldn't we, with our students, be exploring the world around us so that they can look for and find the hidden mathematical gems that are everywhere.
The maths we are teaching/promulgating has not really changed since formal education was set up in the 1800's. Then there was a need for people to be very efficient with number so that they could become tally clerks, accountants etc during the Industrial Revolution. Since then I would suggest we have changed very little. There is still an emphasis on Arithmetic, especially Times Tables (as in our parents and grandparents days at school) What we are being told is that employers need Problem Solvers, Investigators, Creators as well as people who cooperate and communicate.
Our Curriculum, one of the best I have seen, it says viz "Through Problems Solving and Investigations students will learn and understand the Objectives below"
Why is it then we are still teaching arithmetic (with few different approaches) in similar ways to how we were taught as were our parents?
The bottom line is that numbers are people created, they are abstract and many people cannot work in the abstract they work in the concrete or representational. This not only at Junior school but also at secondary!! Look at the research done for the UK Cockcroft Report in the 80’s.
Maths is all around us, it is how “the creator “ created the world. Let’s start outside with Real Maths!
It has often been said- Bruner Piaget - that most students are at a concrete level of learning, they may then progress to representational (Drawing about what they did) and if lucky transfer to thinking in the abstract. This can be shown as follows in learning
Do- experiment create the concrete. (Blocks, lego, sand water...) when competent then
Say- they verbalise that they have been creating with materials etc ... when competent then
Write - they write what they found, created after they have verbalised. I would encourage the students to write in their first language BEFORE they write in mathematical language
I suggest this broadly is the way we teach reading!!!!!
To me the Problem, Open Question is like the “new book” we give kids, and then ask a series of open questions ensuring excitement and curiosity to tackle the book and learn new words, phrases through the context of the book
Check out some Fibonacci videos on YouTube might give you some ideas for including in your teaching. https://www.youtube.com/watch?v=SjSHVDfXHQ4
If this is the case shouldn't we, with our students, be exploring the world around us so that they can look for and find the hidden mathematical gems that are everywhere.
The maths we are teaching/promulgating has not really changed since formal education was set up in the 1800's. Then there was a need for people to be very efficient with number so that they could become tally clerks, accountants etc during the Industrial Revolution. Since then I would suggest we have changed very little. There is still an emphasis on Arithmetic, especially Times Tables (as in our parents and grandparents days at school) What we are being told is that employers need Problem Solvers, Investigators, Creators as well as people who cooperate and communicate.
Our Curriculum, one of the best I have seen, it says viz "Through Problems Solving and Investigations students will learn and understand the Objectives below"
Why is it then we are still teaching arithmetic (with few different approaches) in similar ways to how we were taught as were our parents?
The bottom line is that numbers are people created, they are abstract and many people cannot work in the abstract they work in the concrete or representational. This not only at Junior school but also at secondary!! Look at the research done for the UK Cockcroft Report in the 80’s.
Maths is all around us, it is how “the creator “ created the world. Let’s start outside with Real Maths!
It has often been said- Bruner Piaget - that most students are at a concrete level of learning, they may then progress to representational (Drawing about what they did) and if lucky transfer to thinking in the abstract. This can be shown as follows in learning
Do- experiment create the concrete. (Blocks, lego, sand water...) when competent then
Say- they verbalise that they have been creating with materials etc ... when competent then
Write - they write what they found, created after they have verbalised. I would encourage the students to write in their first language BEFORE they write in mathematical language
I suggest this broadly is the way we teach reading!!!!!
To me the Problem, Open Question is like the “new book” we give kids, and then ask a series of open questions ensuring excitement and curiosity to tackle the book and learn new words, phrases through the context of the book
Check out some Fibonacci videos on YouTube might give you some ideas for including in your teaching. https://www.youtube.com/watch?v=SjSHVDfXHQ4
Subscribe to:
Posts (Atom)