Tag Archives: thinking

Dimity Powell, author, discusses the importance of libraries

readilearn: Libraries: A wondrous universe to explore — A guest post by Dimity Powell

This week I am delighted to introduce you to award-winning children’s author Dimity Powell.

Dimity likes to fill every spare moment with words. She writes and reviews stories exclusively for kids and is the Managing Editor for Kids’ Book Review. Her word webs appear in anthologies, school magazines, junior novels, as creative digital content, and picture books including The Fix-It Man (2017) and At The End of Holyrood Lane (2018).

She is a seasoned presenter both in Australia and overseas, an accredited Write Like An Author facilitator and a Books in Homes Role Model Volunteer in Australia.

Dimity believes picture books are soul food, to be consumed at least 10 times a week. If these aren’t available, she’ll settle for ice-cream. She lives just around the corner from Bat Man on the Gold Coast although she still prefers hanging out in libraries than with superheroes.

In this post, Dimity shares her love of libraries and explains why it is important to ensure every child has access to a library at school and every reader a local library.

Welcome to readilearn, Dimity. Over to you.

Continue reading: readilearn: Libraries: A wondrous universe to explore — A guest post by Dimity Powell

readilearn Lessons for the interactive whiteboard – Christmas – Readilearn

I loved the addition of the interactive whiteboard to my classroom about ten years ago. I embraced the use of computer technology from when I bought my first home computer in 1985 and first used computers in my classroom in 1986. The interactive whiteboard was a way of making use of the technology inclusive. Instead of one or two children taking a turn on the computer while the rest of the class were engaged in other things, we could all be involved at the same time, if desired.

I used the interactive whiteboard with the whole class for introducing topics, brainstorming ideas and explaining concepts. It was great for modelled writing lessons and collaborative reading. I found it particularly useful for demonstrating the processes to follow in the computer lab.

I used some purchased software, but also spent a lot of time creating activities to teach or practice particular concepts or skills. Versions of many of these lessons are now available here on readilearn.

Continue reading: readilearn Lessons for the interactive whiteboard – Christmas – Readilearn

Teaching critical thinking in early childhood classrooms with The Very Hungry Caterpillar – Readilearn

teaching critical thinking

Teaching critical thinking in early childhood classrooms is important. Discussions about The Very Hungry Caterpillar can help develop critical thinking

Continue reading: Teaching critical thinking in early childhood classrooms with The Very Hungry Caterpillar – 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

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

3 + 2 = 5 Let me count the ways!

Billboards

That we live in a print-rich environment is undisputed. Even in country areas one cannot travel far without being bombarded by print. In addition to road signs there is a plethora of billboards advertising the best places to sleep, eat, or play that can be found just ahead.

Environmental print is the genre with which many children first engage successfully with reading.  Ask any parent who’s detoured around fast food outlets, hidden shopping catalogues, or camouflaged cheaper brand names of identical products.

That we are immersed in mathematics in our daily lives is just as evident but doesn’t always receive the same recognition. I think this may in part be because people often think of mathematics as abstract algorithms and theorems that we (they try to get us to) learn in school; and that have no apparent application to our lives beyond the walls of the classroom.

algebra

However, even the examples mentioned above are just as rich in mathematics are they are in print. They include distances, and perhaps time, to the destination, cost of items, opening hours, and number of attractions. Anyone travelling a distance with young children will have answered questions such as “Are we there yet?”, “How much further?”, and “What time is it?

As I say in my statement about mathematics on my readilearn site,

“Mathematics is all around us. We use it every day for a huge range of purposes from deciding on the sequence in which we dress ourselves, to calculating how much time we have available for an activity.”

mathematics readilearn

One of the resources suggests 25 ways for parents to keep their children thinking mathematically over the school holidays. I have shared these ideas previously in Counting on the holidays.

25 ways to think mathematically

Recently I was at the gardens with my two grandchildren (G1 and G2, aged 6 and 4), their mother, and my Hub. The children consulted a map and signposted paths to follow the Children’s Trail which had various sculptures along the way. I am undecided about the value of distracting children from the trees and plants, as if the vegetation itself would not be interesting enough. However, the children enjoyed locating the sculptures in the sequence numbered on the map, and reading the accompanying information. They were engaged in purposeful reading and mathematical thinking in context: real life learning!

 © Norah Colvin 2016

Pandas on the Children’s Trail © Norah Colvin 2016

As we headed back, G2 made a comment that showed she was engaged in mathematical thinking of her own. She observed that there were two children and three adults, which made five of us all together.

“That’s right,” I confirmed. “There are five’. I thought for a little while, then added, “And do you know what? As well as two children and three adults, there are two boys and three girls.” The children looked at the group and confirmed that I was right. They laughed – a different interpretation.

This gave me an idea for a thinking game: how many other arrangements of three and two could there be?  I wondered if the children would like to play along. I had never attempted this before and had no idea if there’d be more, or if we had already exhausted all options.

I looked at the group. I noticed our shoes: three had closed shoes and two had open shoes. I thought about our names: three shared one surname, two another. Then we were on. Everyone was thinking of ways we could be arranged into groups of two and three.

Sometimes we sorted according to different characteristics, as in the previous examples. Others times we used a simple yes or no sorting, such as two have hats with brims and three don’t have hats with brims. This is the easiest sorting to do, and the first that children learn.

G2 made many suggestions of this type of sorting for one and four.  One has the characteristic, the others don’t. This was age appropriate for her, and it was great to see her joining in confidently and contributing to the discussion. G1 was able to engage in the more complex thinking required for the groupings of three and two.

 I was amazed at the number of different combinations we came up with, and that each of us was combined with others in many different ways.

These are some of the ways we arranged ourselves into groups of two and three (not physically, just in our discussion).

Arranging ourselves 3 + 2

This seemingly mundane activity has potential for developing thinking and learning by encouraging:

  • thinking about things in new and different ways
  • looking for similarities and differences
  • observing detail
  • sorting according to different characteristics – which is important to both maths and science (think animal and plant classification)
  • having fun with maths
  • having fun with family

But wait, there’s more: When we left for home, two went in one car and three in the other!

I think this would be a great activity to do with young children learning about number. It may be a challenge for teachers in Australia where children wear uniforms to school but I’m already thinking of how it could be done with toys or illustrations. It’s not quite the same as doing it with the children themselves, but it could be fun. What do you think?

teddy bear sorting

You won’t be surprised to discover that I have prepared a readilearn resource for sorting as well!

Thank you

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

 

Eroding thoughts

Uluru © Norah Colvin 2015

Uluru © Norah Colvin 2015

This week at the Carrot Ranch Charli Mills is talking about erosion, but not just the literal kind. She says “It can be natural, cultural or something different.” Of course I must answer my usual call to tackle the “something different”.

Generally, erosion refers to the wearing away of the earth. Sometimes it signifies the disintegration of our resolve, our self-image, or of our spirit. Just as various strategies can be employed to prevent erosion or to repair damage incurred by the land, there are strategies that can be used to shore up one’s resolve, build self-esteem, and mend a sagging spirit.

rejection slip

Perhaps nobody knows this better than writers with their stashes of rejection slips rated from encouraging to just plain rude, or non-existent. Few have achieved success without first receiving a downpour of those slips, who haven’t had to work at their skills and accept the edits without eroding their intended message. Sometimes it seems that, with every move, one lands on the “Go back to start” square; and that, while it feels like things are in motion, the end doesn’t appear any closer.

go back to start

Or maybe nobody understands the fragility of the spirit and self-esteem more than does a teacher; and of the importance of building on prior learning to take children from where they are to places they haven’t thought possible; to ensure their esteem stays strong and is not eroded by unrealistic expectations and the tedium of a repetitive diet of something meaningful only to others.

Welcome pack

Welcome pack

I have written many times previously about the importance of establishing a supportive classroom environment, and of using affirmations in growing children’s confidence and self-image.

This doesn’t mean a diet of empty praise, but it does mean that all individuals are recognised for what they can do, and are valued for the contribution they make to the classroom community. Included in these writings was a series, inspired by a Twitter discussion with Anne Goodwin, on praise culminating in Seeking praise – Stephen Grosz revisited and including a guest post by Anne.

The Clever Children Resource

I have also developed resources to support children’s growing confidence and self-image for inclusion on my in-progress website readilearn. One of these resources is a story called The Clever Children which teachers can personalise for use with their own class.

The Clever Children printable

Children write about and illustrate something they can do. The pages are then added to the story which is printed and collated into a book which can be placed in the reading corner or taken home to read to parents and siblings.  My children always loved being a part of this story. I am looking forward to other children being a part of it too. The story aims to build, rather than erode, self-esteem and a love of books and reading.

Which brings me back to Charli’s challenge to In 99 words (no more, no less) write a story, using the power of erosion.

The Nature Principle

For my flash I combine two ideas:

  • Richard Louv’s suggestion in The Nature Principle that, for physical and mental health, we need to be more attuned with nature
  • the need for resolve and inner strength when faced with issues that would erode it.

It’s not really a story, perhaps, but a moment in time. I hope you enjoy it.

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The rock

The rock, promising permanence, beckoned: perfect for contemplating expanses beyond while pondering life and one’s significance. She sighed, and succumbed. The waves, licking repetitively at the base, soothed somehow; as if each grain of sand stolen from beneath her feet loosened her tension. Becoming one with the rhythm, her heart sang the melody as her mind slowed, releasing all thought. Feeling whole again, as solid as the rock, and with renewed strength, she prepared to face those who sought to erode her. Though tides would rearrange and redecorate, and often do their best to annihilate, they could not obliterate.

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.