Tag Archives: problem solving

Easter holiday wishes – Readilearn

 

This week I have uploaded two new resources which are just as suitable for Easter holiday fun at home as they are for learning in the classroom.

Whose egg? A logic puzzle can be used with the whole class to introduce children to the steps involved in completing logic puzzles; or as an independent or buddy activity if children already know how to complete logic puzzles on their own.

Three friends, three eggs, and three baskets. But which friend has which egg and which basket?

Children read the story scenario and the clues, then use the information to deduce which friend bought which egg in which basket.

Great for reading comprehension and creative thinking; and for collaboration in a paired activity!

Continue reading: Easter holiday wishes – Readilearn

Delivery – just in time for Easter! – Readilearn

 

Many children around the world eagerly await the arrival of the Easter Bunny and his delivery of coloured, candy, or chocolate eggs or toys. The Easter Bunny has been delivering his gifts for more than three hundred years.

When Europeans arrived in Australia a little over two hundred years ago, they not only brought the Easter Bunny tradition, they brought real rabbits as a food source and for hunting. Cute little rabbits, you may say, but the rabbits were quick to breed. Without any natural predators, they soon became widespread, and created an enormous environmental problem. They contributed to the destruction of habitats and the loss of native animals and plants. They also became a serious problem for farmers.

One of the animals that suffered as a result of the introduced species is the bilby, a now vulnerable marsupial, native to the deserts of Central Australia. The cute bilby with its long rabbit-like ears and cute face is considered a possible native substitute for the Easter Bunny in Australia.  Chocolate makers and other organisations used the idea of an Easter Bilby to draw attention to its plight and to the Save the Bilby Fund, established to help its survival. (Check out the Save the Bilby Fund’s free education resources.)

This week I have uploaded some new Easter resources featuring bilbies. I hope you and your children enjoy them.

Continue reading: Delivery – just in time for Easter! – Readilearn

How do you know?

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Being able to verbalise the steps taken to arrive at an answer or a conclusion is a valuable skill. It is particularly important with mathematical thinking, even at beginning stages. Sometimes it feels as if the answer appears without the need for thought. Of course we aim for this with automaticity of number facts and times tables. However, I am referring to problems that may involve two or more different calculations.

maths problem

Unless one understands the processes involved in solving one problem, it can be difficult to apply the same strategy in other situations. Sometimes it may be difficult for a teacher who finds the answer effortlessly to understand a learner’s confusion leading to mis-steps and miscalculations.

I generally collect my six-year-old grandson (G1) from school once or twice a week.  Now that he’s a big year one boy he thinks he doesn’t need to hold my hand to cross the road. However, there is a bit of traffic around his school and I prefer him to do so, telling him it’s for my safety too.

holding hands to cross road

One day I, erroneously, told him he needed to hold an adult’s hand until he was ten. (Ten is closer to the age for riding a bike unsupervised.) While this post is about mathematical thinking rather than traffic safety, if you wish to do so, you may find some information about traffic safety with young children here.

Always on the lookout for teachable moments that encourage thinking, I then asked if he knew how many more years it would be until he was ten. It was a bit of a redundant question because, of course he did. He is an able mathematician, just like his dad who constantly extends his ability to compute and think mathematically.

When G1 didn’t answer immediately, I assumed that he was either ignoring my question as it was too easy for him and not worth answering; or that he was thinking of the implications of my initial statement about holding an adult’s hand until he was ten.  Then again, perhaps teacher-type questions from GM are sometimes better ignored, particularly after a day in school. I was happy to accept his silence as we continued across the road and didn’t press him for an answer.

Once safely on the footpath he said, “It’s four.”

“Know how I know?” he continued, pre-empting my question (he knows his grandmother well).

He held up both hands. “Because 5 and 5 are 10.” (He put down 4 fingers on one hand.) “And that’s 6. And 4 more makes 10.”

6 + 4 = 10

Although I hadn’t asked how he knew (on this occasion), I was pleased he was able to tell me, even though, in reality, he “knew” without having to work it out. On previous occasions when I had asked him how he worked it out, or how he knew, he hadn’t always provided an explanation. He may have shrugged, said “I don’t know” or simply ignored my question. Being able to explain his thinking demonstrates his growing mathematical knowledge and metacognition.

The ability to think through and verbalise steps is important to understanding. How many of you talk yourself through steps of a procedure you are following? I certainly do at times. While knowing that six plus four is ten is an automatic response for most of us. It wasn’t always so and we needed a strategy to help us understand the concept and recall the “fact”.

Opportunities for mathematical conversations occur frequently in everyday situations but are often overlooked. Recently I described some ways the children and I discussed different ways of combining five of us on an outing to show that 3 + 2 = 5.

maths in the car

Recently when two grandparents and two grandchildren were travelling together in the car four-year old G2, without any prompting from me, began describing how we could be combined to show that 2 + 2 = 4, for example

2 adults in the front, 2 children in the back, that makes 4. There were many different ways that we could be combined; and just as many that would group three together and leave one out, for example

1 driver and 3 passengers.

We had other mathematical discussions during that car trip. I had cut an apple for each child into a different number of pieces. Each was to guess how many pieces there were. G1 went first. I’d introduced him to prime number just once previously when I’d cut his apple into seventeen pieces so I didn’t expect him to be proficient with them. He certainly wouldn’t have been introduced to them at school at this stage.

These are the clues I gave him, the guesses he made and my responses supporting his growing understanding. I thought he did very well. He requests a guessing game each time I cut apple for him now. It’s sometimes a challenge for me to think of new clues.

pieces of apple

 

I had cut 15 pieces for G2. G1 helped her work it out when I told her that she needed to count all of her fingers and the toes on one foot.

For an additional challenge I asked G1 if he knew how many fingers and toes there were in the car all together. He thought for a moment before giving the answer. Then proceeded to tell me how he knew as I started to ask. He explained that he had counted in twos because each of us had twenty, and counting twenties was just like counting twos but they’re tens. A quicker and more effective way that adding on twenty each time which I may have suggested he do.

Asking how do you know or how did you work it out helps children think about their own thinking. Listening to their responses helps adults understand where they are in developing mathematical concepts. Asking questions about their thinking can challenge and extend them further, but it is important to not expect too much and to support their developing understanding.

What maths did you engage in today? Did you even realise or was it automatic?

Thank you

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I’ll just look that up: lazy or smart thinking?

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I often lament that I was born too soon. I love what can be done with information technology and am constantly learning more of its uses. I am in awe of what can be achieved with the aid of digital tools. Unfortunately, some things, because they can be done, are vastly overdone.

I remember being at an education conference in the early 80s, at the time when computers were becoming more common in classrooms and in homes. A presenter at the conference excited us about the wonders of digital technology and its ability to ease our work load. He predicted that computers would be used to do so many of our menial tasks that by the year 2000 we would have so much spare time we wouldn’t know what to do with ourselves.

His prediction, in my opinion, was way off the mark. While the use of computers has greatly enhanced our capabilities and our knowledge, it has also driven us to constantly do more. I notice this particularly with data collection in schools. If it can be quantified, then it must be quantified, analysed and compared. Whether what is being measured is of any value is of no consequence. If it can be done, it will be done.

1985 was the year I first used a computer at school and bought my first computer for home. They were Apple IIe (huge) desktop computers. I can remember how excited I was to be able to program little games using BASIC coding language. There were some good problem solving software programs on floppy disks I used with children at school; and my son played his way through the series of Ultima role playing games.

Back then, the thought of having a computer that could be carried in a pocket was as absurd, to the general population, as having a phone that wasn’t attached to a wall. Fortunately, there were others with imagination and vision who were able to make these things a reality.

I recently read a post on Daniel Willingham’s blog Science and education entitled The brain in your pocket. The brain that he is talking about I carry in my handbag. In fact, I often have two with me, though I’m not convinced that this supports the theory that two brains are better than one.

In the post Willingham shares some observations about our current use of technology to replace thinking. He suggests that, as thinking requires effort, people don’t like to engage it and find ways to avoid it. He referred to this as “miserly thinking”, a term coined by Robyn Dawes in the 1970s.

Two strategies for avoiding thinking include use of:

  • Memory – repeating earlier actions or doing things the way you’ve always done them; such as ordering the same item from a menu or always travelling the same route to work
  • Associations – using strategies that worked in other similar situations.

Willingham then shared this question as a test of miserly thinking:

bat and ball question

He suggested that if you, like many others, answered 10 cents you were using miserly thinking triggered by the word “more”, immediately thinking that subtraction was required and not checking to see if the answer was correct.

He used this to demonstrate a similar effect that use of the internet has had upon thinking in recent years, when answers to many questions are just a motion (click, tap or swipe) away. In more recent years of course nearly everyone is carrying a smartphone in a pocket or handbag, that is, if it’s not grasped firmly in hand. This easy access, he suggests, makes people less reliant on their own memories as they look to the internet for a quick answer.

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Research cited by Willingham suggests that a higher use of the internet for answers reduces the ability to solve problems like the bat and ball question shown above. He says thatpeople who are more cognitively miserly are more likely to search information out on their smartphone.” He adds that “The reason is not clear. It may be that low-cognitive-ability people seek information—look up a word meaning, calculate a tip—that high-ability people have in their heads.

He asks the questions:

daniel willingham questions

What do you think?

I love having the “external memory” that I can use to find out what I want to know when I want to know it. Previously I would have had to remember to look it up at some other time. If I didn’t know the right question to ask, or the appropriate term to look under, I may have been left in the dark forever.

I love being able to spell check my work or check a dictionary or thesaurus to confirm that I have used a word correctly. These things enhance my knowledge and improve my skills. I am a bit peeved at the idea that it is those with low cognitive ability who look things up. I thought it was a smart thing to do!

Do these actions make me a miserly thinker and decrease my cognitive skills? I really don’t want to think about that, but I sincerely hope not!

I first became familiar with Willingham’s work through his book Why Don’t Students Like School?: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom. I thought I had mentioned it in a previous post, but if I have, my search feature, upon which I am reliant, couldn’t find it. I’ll have to remember to do so in the future!

Thank you

Thank you for reading. I appreciate your feedback. Please share your thoughts.

 

@cesarharada, Encouraging innovation and problem solving through science

Cesar Harada

I found this TED talk by Cesar Harada totally engaging. Cesar, who describes himself as half Japanese half French, teaches science and invention to students from aged 6 to 15 at the Harbour School in Hong Kong.

Cesar opens his talk by explaining that, when a child, he was allowed to make a mess, but only if he cleaned up after himself. As he grew up he realised that he had been lied to: adults make messes too but they are not very good at cleaning up after themselves.

He closes his talk by suggesting that children should not be lied to. He says,

“We can no longer afford to shield the kids from the ugly truth because we need their imagination to invent the solutions.”

He then adds,

” we must prepare the next generation that cares about the environment and people, and that can actually do something about it.”

In between he describes some scientific thinking and inventions made by his students to solve local problems initially, then problems that affected other kids remotely, and finally problems that have a global impact.

I’m sure that you too can only be impressed by the learning and the positive actions that are being undertaken by these innovative students and their inspirational teacher. When I hear (true) stories like this, it certainly gives me hope for a better future.

I hope you enjoy Cesar’s talk as much as I did.

You can also find Cesar on Twitter.

Thank you

Thank you for reading. I appreciate your feedback. Please share your thoughts.

Are you game?

This week at the Carrot Ranch Charli Mills is talking about childhood games and has challenged writers to In 99 words (no more, no less) write a story that involves a children’s game or rhyme. I think she chose this topic just for me. Thank you, Charli.

I love games and am a strong believer in the use of games to enhance learning. I have memories of playing games that span my lifetime, from early childhood until the present, and have visions of playing games far into the future.

Johnny Automatic, cartoon of a girl and boy playing with a ball https://openclipart.org/detail/721/playing-ball

Johnny Automatic, cartoon of a girl and boy playing with a ball https://openclipart.org/detail/721/playing-ball

One of my earliest memories of an organised game was of “Drop the hanky” played at a birthday party. I was about five years old at the time. I think that perhaps, until this event, I had only ever played imaginative games with my brothers and sisters. I was obviously not familiar with the rules or the ethos of the game. I’ll let my flash (non-) fiction explain.

Plum pudding

We sat in the circle chanting,

“I wrote a letter to my love and on the way I dropped it.”

“It” skipped around the outside, waving a handkerchief.

“One of you has picked it up and put it in your pocket.

Not you. Not you. Not y-o-u!”

Suddenly “It” was running and children were scrabbling behind them.

“Run,” they called.

Then “It” was beside me.

“Plum pudding!” they all screamed hysterically.

The adult pointed to the centre of the circle. “We’ll have you for dessert,” he grinned.

I cried, wondering what it would be like to be eaten alive!

© Norah Colvin 2015

© Norah Colvin 2015

Obviously I was traumatised for the memory to be so vivid and almost nightmare-like since the memory ends abruptly with the fear. Obviously I wasn’t eaten for dessert, I survived the trauma and, to complete the fictional narrative, I guess you could say “I lived happily ever after.”

But games don’t need to be traumatic. Games are better when they are fun; and I have many more memories of having fun with games than I do of being traumatised by them. Some of my “best” memories are of the laughs shared playing games like “Balderdash” and “Billionaire” when we (hub, son, daughter and partners) set aside traditional holidays for playing games together as a family. My house may have shelves laden with books, but they also have cupboards bursting with games.

© Norah Colvin

© Norah Colvin

We didn’t always play purchased games. Sometimes we made up our own. It takes some skill in problem solving to think up a new game that will be fun to play with just the right amounts of challenge and competition, and an equal chance of “winning”, if there is a winner. Games without a winner, played for the fun of playing, are just as enjoyable.

I have always included games in my class program. As well as being fun, if carefully chosen they can also progress learning. Games can be played at the beginning and conclusion of sessions; at transition times to reenergise, refocus and refresh; and as part of the teaching/learning program with whole class, small group or individual participation for targeting practice of particular concepts.

One obvious benefit of playing games is the development of social skills such as:

  • Sharing
  • Taking turns
  • Cooperation
  • Dealing with competition
  • Accepting a loss
  • Accepting a win graciously

In their book “A New Culture of Learning: Cultivating the Imagination for a World of Constant Change”, Douglas Thomas and John Seely Brown talk about ““arc of life” learning, which comprises the activities in our daily lives that keep us learning, growing and exploring.” They say, “Play, questioning, and — perhaps most important — imagination lie at the very heart of arc-of-life learning.”

Throughout the book they talk about the importance of collaboration in engaging online in multi-player games and say that When understood properly . . . games may in fact be one of the best models for learning and knowing in the twenty-first century . . . Because if a game is good, you never play the same way twice.

monopoly

Robert Kiyosaki in his book “Why “A” Students Work for “C” Students and Why “B” Students Work for the Government” talks about the importance of learning through games and explains how he learned, and was inspired to learn more, about finance from playing “Monopoly”. He says that Games are better teachers than teachers.” While I prefer to not agree with that statement in its entirety (I don’t even like playing Monopoly), I could understand his reasons for making it.

Rarely a day would go by that at least one game wasn’t played in my classroom. We would play games in literacy groups that required children to read and think critically. We would play games in maths groups to practice skills in fun ways or to solve problems cooperatively. We would play games in science to try out ideas or research information. Some of the games involved physical as well as mental activity. Some were played with the entire class, and some on their own.

One game we used in maths groups as well as an activity in the last few minutes of the day was a problem solving game that I was involved with from its inception, The Land of Um or, as it is known in the UK, Scally’s World of Problems. (Also available as an app.)

http://www.greygum.com.au/nebula/index.php/the-land-of-um

Scally

 

 

 

 

 

 

 

When I was asked for an idea for a program, I suggested something that required children to explore to find out “what happens if” and “how things work”, much as they learn from their exploration of the “real world”. I also suggested that what they learn be consistent and apply at the next level. From that small seed and through the collaboration and synergy of a small group of creative people the “Land of Um” was born.

Because, in my recollections anyway, it was “my” idea, I am very proud of “Um” and enthusiastic about its potential to encourage children to develop the thinking skills involved in solving problems.

Um app

In my class the children worked enthusiastically and collaboratively in small groups on an interactive whiteboard, taking turns to control the “Um” while working together to find the solution to each puzzle. As the level of difficulty increased the children needed to plan ahead, to visualise steps and predict what would happen and the effects of different actions. At each new level and in each new world, while the basics remained consistent, there was always something different to learn and explore. The children never tired of the using the program and were always eager to be the one to suggest the solution to the next problem. It was/is a joy to know that I had a part to play in the design of this program that has so many benefits to learners, not least of which is the fun of working together to solve problems.

How significant are games in your life? What special memories do you have?

If you are interested, there are many more stories about games to read on Charli’s blog.

Thank you

Thank you for reading. I appreciate your feedback. Please share your thoughts on any aspect of this post or flash fiction.

 

 

 

Who wouldn’t be excited with high test scores?

Regular readers of my blog are aware of my attitude to didactic top-down, content and assessment driven methods of schooling students to become machines regurgitating meaningless facts on command. A bit of push and shove it in and belch it out.  For those of you who weren’t aware – now you are!

I probably should apologise for my indecorous description as I’m usually a little more temperate in the way I express my views, but I won’t as that is how I am feeling about it at the moment. The authorities who have the power to make the changes necessary are so caught up in their own murky visions that they fail to see either effects or solutions. Every time I read another report of test scores or hear of another child damaged by a faulty system my frustration grows.  It becomes one of those hysteria blossoming days.

bag

A few moments ago I read a post titled “Vietnam Wallops US on PISA. Vietnamese educators belittle value of PISA” on Diane Ravitch’s blog. Ravitch is an education historian.

As the title suggests, Vietnamese fifteen year old students did better than their US, UK and most other EU counterparts in the 2012 PISA tests, ranking 12th out of 76. What I found interesting about the article was not the results but the attitude of Vietnam’s Deputy Minister of Education and Training. His view that the tests don’t reflect students’ overall competence, reminded me of a letter, shared in my previous post, written by teachers to students sitting the national tests last week in Australia. (PISA are international tests).

In the article referred to by Ravitch, Dr Giap Van Duong was reported as making reference to UNESCO’s four pillars of learning: Learning to know, Learning to do, Learning to be and Learning to live together. His opined that PISA addresses only the first pillar, and in only a limited way. He said that while Vietnamese students did well on the tests, “many … students fail to land a job after graduation. (and that when) they study overseas, many have difficulties in meeting the requirements of advanced education systems like team-work, problem solving and creativity”. Perhaps they are not “out of basement ready” as described by Yong Zhao.

Duong said that the reason Vietnamese students do well on the tests is because the “The whole system operates to serve only one purpose: exams.”

Duong’s admission that Vietnamese students lack the ability to work in teams, to problem solve and to think creatively reiterates the fears of many teachers who are  ruled by expectations of high test results and provided little opportunity to inspire learning, which surely remains the real (if neglected) purpose of education. Counterbalancing one’s philosophy with an employer’s expectations sometimes seems like being caught between a rock and a hard place.

This week at the Carrot Ranch Charli Mills is talking about rocks and hard places. But Charli knows that good can often spring from those seemingly hard places through making connections. She has challenged writers to In 99 words (no more, no less) write a story that shows a hard place and a connection.

It is connections that are most important in my two main roles in life: parent and teacher. Neither is easy and neither will result in much good without making connections. I often worry about things I have said and the affect they may have had on others. To be truthful, occasionally it even keeps me awake at night. While I would rather think of my words and actions creating a positive ripple, there is no guarantee that, even when delivered with my best intentions, they won’t do harm.

Trevor Pilgrim shared a quote which puts it this way:

What-a-teacher-writes-on

In his article Pilgrim says,

“teachers have (the power) to develop their students and shape their future lives.  The power to turn them on or off academically, stimulate or dampen their minds and heighten or destroy their engagement and intellectual curiosity.”

Scary stuff!

At about the same time I read an article that said that the influence of teachers is not as great as one might think; that socio-economic status, amongst other things, is more important. While I am happy with the thought of having a positive effect, I definitely do not wish to ruin anyone’s life so am happy to know that my influence is not be the most important to the lives of my students.

For this challenge of Charli’s I am back thinking about Marnie’s art teacher and the hard place she found herself in when she saw the brown muddy mess that Marnie seemed to have made of her paints. That she must respond is a given; but how? Whatever she says will probably have a lasting impact so she must ensure that her response is appropriate. While her initial instinct is to express disappointment, she maintains her professional composure and delays commenting until she has thought it through.

Here is my response:

Brown.

She glanced at the child, usually so eager to please, and knew this was no ordinary day.

Downcast and avoiding eye contact, the child trembled. Her instinct was to reach out with comfort to soothe the hurt; but stopped. Any touch could end her career. What to say? Brown earth/brown rocks? would ignore and trivialise the pain. Any talk now would be insensitive with other ears listening. Any word could unravel the relationship built up over time. Nothing would harm more than doing nothing. Her steps moved her body away but her heart and mind stayed; feeling, thinking.

 Thank you

Thank you for reading. I appreciate your feedback. Please share your thoughts about any aspect of this post or flash fiction