Monthly Archives: July 2016

The importance of feedback

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Feedback, whether inherent in the task itself or supplied by another, is essential to learning. This is true whether figuring out what happens when an item is dropped from a high chair (will it always land on the floor; will a carer always retrieve it?), how hard and at what angle to kick a ball to send it over the goalpost; how much a sibling can be antagonised before retaliation ensues; or whether your performance meets expectations.

In almost all of these cases, the tasks are self-selected and the feedback is integral and immediate, enabling the learner to adjust what happens next accordingly. While those conditions may also be true when considering the success of performance; such as our own assessment of our output, it is not always so.

F

Students and employees may be engaged in tasks that are not of their choosing, which provide little inherent feedback, and are reliant upon feedback from others that may be neither timely nor specific to the learners’ needs. Sometimes the feedback can be unhelpful and hinder, rather than encourage, learning, without any real explanation of how improvement could be made.

As a teacher, I found it necessary for an exchange of feedback between me and my students. This was sometimes supplemented with feedback from carers and other school personnel. How well the students engaged in the classroom, participated in class activities and performed tasks provided me with feedback on my performance as a teacher and provided important information about what to do next, which in turn involved feedback to students.

While feedback is an essential ingredient in any classroom task, one of the most enjoyable for me was the daily journal. Each morning the children would write to me and every afternoon after they had gone home I would read and respond to their messages. The children loved writing these diaries as much as I loved reading and responding to them. Responding was time consuming but I believe it was worth it:

  • The children had a purpose for writing
  • Their writing had an audience
  • They saw writing as a tool for communication

When responding to their writing, I would make neither corrections nor changes. However, I would model correct grammar, spelling and punctuation as I responded to the content of their messages. The children were then able to refer to my comment when writing their next message.

Sometimes the children would tell me about something different each day. Sometimes we would have conversations that could extend over weeks. I always felt it a privilege to have this window into the children’s lives. At the same time, it provided a record of their development as writers.

At the end of the year I would bundle up all of the journals that had been filled during the year and present them to the children to take home. Recently when I was talking to the mother of a child I taught in the eighties, she told me how they had been looking at those journals with his young children who are now at a similar age to his when he wrote them. How gratifying it is to know that they were treasured by at least one family.

thank you - rose

When I started blogging, unbelievably, almost three years ago, I had no idea of what to expect. I am a little more knowledgeable now, with thanks to those who provide feedback by reading and commenting. I am very grateful to all who have joined me along the way. The conversations here or on your own blogs are what have made the journey enjoyable and worthwhile.

yves_guillou_question

Now I have a decision to make and I would appreciate your feedback in helping reach it.

At the same time as I have been blogging, I have been preparing early childhood teaching resources for my website readilearn. I always expected readilearn to include a blog and a newsletter. I knew I couldn’t write that additional content alongside posting twice weekly here and preparing new readilearn resources as well. I thought to:

  • post once a week on this original blog by continuing to participate in the flash fiction challenges set by Charli Mills at the Carrot Ranch, as I have done for more than two years; and
  • post once a week on the readilearn blog with content written specifically for early childhood teachers rather than general readership.

However, it has recently come to my attention that it may not be possible for readers to leave comments on the readilearn blog, which leads to my quandary.

I enjoy the discussions in response to posts almost as much as writing them; and

I am disappointed when I am unable to “like”, leave a comment on, or share another’s blog post I have enjoyed.

megaphone

It seems some bloggers are more interested in broadcasting than engaging with a community, but that is not my way.

Newsletters differ from blogs, though, and the readilearn newsletter, which will provide information about new resources, teaching suggestions and other educational content, will “broadcast” and not invite feedback.

How important, then, is it to have a blog that doesn’t invite feedback. I’m thinking that, without feedback, I’ll quickly lose motivation.

What do you think?

When you read blogs, do you look for an opportunity to add your voice through a “like” button, leaving a comment, or sharing content on social media? Is the ability to engage with the writer important to you, or do you simply read?

As a blogger, do you welcome comments and discussion, or is it more important just to get your ideas out there?

Thank you

Thank you for reading. I am very interested to know what you think and appreciate your feedback. Please share your thoughts.

 

Desert surprise

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When you hear the word “desert”, what image does your mind conjure up?

Is it of endless sand dunes such as those of  Rub’ al Khali (“Empty quarter”) of Saudi Arabia?

Or is if of something a little less desolate?

This week at Carrot Ranch Communications, Charli Mills writes about a desert close to where she is staying in her temporary, though seemingly endless, state of imposed homelessness.

The desert Charli describes, in eastern Washington, is “flat and prickly” with “trees (that) are better described as shrubs and any ground cover growing out of the black sand has thorns.” She describes the “sagebrush with soft leaves of silvery blue and twisting trunks of brittle gray bark.” The images created by these descriptions is vastly different from those of endless sand dunes.

A desert is usually described as an arid area where there is little rainfall and conditions do not favour  plant and animal life. As much as one third of the earth’s land surface is arid or semi-arid. This is also true of mainland Australia with its ten named deserts which mostly lie in the centre.

Last year I was fortunate to visit Uluru and Kata Tjuta which are in semi-arid areas surrounded by desert in Central Australia. I have put together some images of the area to show the variation that occurs in the semi-arid landscape.

Thinking of the word “desert” (noun – arid area) also brings to mind its heteronym “desert” (verb – leave), which has its own homonym meaning deserved e.g.” just deserts” and homophone “dessert”. These words are often confused by both readers and writers with pronunciation and spelling indistinguishable out of context.

I have combined these different meanings to respond to Charli’s flash fiction challenge to in 99 words (no more, no less) write about a surprise from a desert. While not specifically about education, I also acknowledge the power of a teacher’s influence.

Deserts

They reminded her constantly what an inconvenience she was; that she’d never be anything; that she was simply trash like the one who birthed, and dumped her. Somehow she’d never believed them: their truth was not hers. She’d shielded her inner core with a shell over which their words flowed but could not penetrate. Not caring whether they ever knew, she’d prove them wrong. A favourite teacher inspired an interest in food science. As soon as possible she escaped to apprentice with master chef Jules. After years of determination and hard work, she opened her own patisserie “Just Desserts”.

Thank you

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

 

#Sugar and Snails BirthdayBlog Tour – The legacy of a Catholic childhood

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I have been friends with Anne Goodwin who blogs at Annecdotal for almost as long as I have been blogging. While there are many differences in our experiences, there is the right balance of agreement and divergence for friendly and robust discussion to occur. Anne regularly contributes to the conversations on my blog through her thoughtful comments.

Anne has also visited as a guest blogger twice before. The first was a discussion of The Examined Life by Stephen Grosz. In the second she wrote about the treatment of friendship in her debut novel Sugar and Snails. This post celebrates that novel’s first birthday! Congratulations, Anne. I wish you much success with this and future writing.

sugar-and-snails cover

In this post, Anne discusses the legacy of a Catholic childhood. I hope you will join me in welcoming Anne to my blog.

The legacy of a Catholic childhood

It was our last evening in Rome, and we’d grown weary of churches, even when they hosted a Caravaggio painting or a Bellini sculpture. But it seemed a shame to leave without a peek inside the church we’d passed almost every day that week on the way to some museum or other attraction. So while my husband walked back to our rented apartment for a pre-dinner cocktail, I pushed through the heavy door.

Just inside, I hesitated. I hadn’t expected there’d be a service in progress. I was mesmerised: the golden light; the scent of incense, the mournful melody of human voices accompanied by an organ. I registered this, not so much with my eyes and nose and ears, but in my gut. In another country, in a less magnificent church, this had been my childhood.

Ignoring the disapproving gaze of the usher, I passed through the rope barrier holding back the tourists, to take my place among the congregation. I no longer shared their faith, but I felt entitled to share the ritual.

My childhood, at Catholic schools, was passed within a bubble. It was something of a culture-shock to discover, at university, that the majority of people I encountered belonged to other religions, or none. Later still, more at ease in the secular world, it was always interesting when friends and colleagues outed themselves as former Catholics. Then there’d be that nod of recognition, a shared heritage marking our psyche more indelibly than the ashen cross the priest would thumb on our foreheads at the beginning of Lent.

I believe that we are strongly shaped by the past, so what is the legacy of a Catholic childhood? Some have found solace in the beauty of the liturgy and the sense of community while others have had their personalities destroyed through unimpeded clerical abuse. Many, like me, would place themselves somewhere in the middle, regarding Catholicism not as something to celebrate but to recover from.

The threat of eternal damnation incites fear, or disbelief, and neither is conducive to developing a person’s moral compass. Telling a child what she must believe, rather than letting her discover it, doesn’t facilitate an enquiring mind. While it might seem comforting to be able to believe there’s a God who will always take care of you, you’ve a more secure base if you’ve been brought up by parents who are responsive to your earthly needs. There seems to be a very fine line between putting your faith in magical solutions and the “delusions” of the psychotic mind. And the veneration of suffering and a tortuous death through crucifixion is decidedly odd. As for sex, the risky business of discovering a new kind of intimacy in adolescence is further distorted by the taint of shame.

sugar-and-snails cover

When it came to writing my debut novel, Sugar and Snails, it made sense to give my main character a Catholic childhood. Uncomfortable in her skin from childhood, Diana finds no salvation in the church. She recalls morbid childhood games and, aged about eleven, being taken on pilgrimage to Lourdes for a miracle cure for a problem no-one will name. As an adolescent in the 1970s, her knowledge of menstruation comes from the bizarre instruction manual, My Dear Daughter, an exercise in obfuscation of North-Korean proportions, which her mother surreptitiously places on her bed along with a packet of bulky sanitary towels. Although it would be unfair to blame it entirely on Catholicism, she doesn’t have sex until the age of twenty-five and then it’s so dreadful she is celibate for the next twenty years.

Yet I didn’t want to stuff my novel with my own issues. Firstly, because I don’t think that makes for a good read; secondly, I didn’t want to alienate potential readers, especially not the old school friends to whom my novel is partly dedicated, most of whom have stayed loyal to their childhood beliefs. Fortunately, my novel’s first year of feedback suggests I’ve managed on both counts.

In preparing this post, I realised that less than half the Catholic scenes from earlier drafts survived to the final version. While there are solid structural reasons for these deletions, it also strikes me that, in the almost seven years I’ve been writing this novel, I’ve become less angry about the past. Perhaps it’s because I’ve worked through it or maybe simply because, as in that church in Rome, I’ve been able to reclaim the good bits. No, I don’t go to church, but I do sing with a marvellous mixed-voice choir. While we have an eclectic repertoire, it’s the sacred works – Verdi’s Requiem, Handel’s Messiah and the like – that really make me tingle inside. For more on the music that shaped my novel, see my forthcoming post on the undercover soundtrack.

birthday blog tour final

Please check out some other stops and posts on the Birthday Blog Tour.

Anne Goodwin’s debut novel, Sugar and Snails, about a woman who has kept her past identity a secret for thirty years, was published in July 2015 by Inspired Quill and longlisted for the 2016 Polari First Book Prize. Her second novel, Underneath, about a man who keeps a woman captive in his cellar, is scheduled for publication in May 2017. Anne is also a book blogger and author of over 60 published short stories. Catch up with Anne on her website: annethology or on Twitter @Annecdotist.

In honour of its first birthday, Sugar and Snails is available in Kindle format at only £0.99 / $0.99 until 31 July 2016.

Amazon UK 

Amazon.com

Thank you

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

Life is for living

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I first published this post two years ago. I am sharing it again as I continue to hear of similar things happening. I apologise to those who may have read it the first time around. 🙂

Many would agree that to enjoy life to the full we must live in the present moment, appreciating what we have and being mindful of our surroundings and others.

Most would also agree that a certain amount of preparation for the future is necessary to both enjoy and deal with what lies ahead.

marshmallow 5

In previous posts I have referred to related ideas including The importance of emotional intelligence and the ability to delay gratification, for example when studying towards a degree or saving to purchase a car. Recently I wrote about future-proofing kids by preparing them to embrace the future. Schooling is often considered a preparation for the future, for ‘what you want to be when you grow up’.

firefighter and nurse

Are the concepts of living in the present moment and preparing for the future contradictory?

Generally I would say that a balance is needed. We need to live in the present while making some preparation for the future. Hopefully the choices made can still be appreciated now and enjoyment is not all delayed until the future “When I . . .”

Recently I read an article that caused me some concern because, it seemed to me, there was little balance between appreciating the present and preparation for the future. Of greater concern was that the one for whom balance was lacking was not the one making the choice.

 

The article described a situation in which a 3½ year old was being taught to use scissors by an occupational therapist. The teaching, which had been occurring in regular sessions for over seven months, began before the child was three years of age.

Like I did, you might assume the child had a developmental delay which required regular sessions with the occupational therapist (OT). However no mention of that was made in the article.

The parent, writing the article, described feeling sad while watching the child experience difficulty in using the scissors.  Additionally, it was mentioned that the child had not been requested by the parent to use scissors at home as it just made the child miserable.

After seven months the parent finally broached the subject with the OT, asking why the use of scissors was being pushed at this time.

It was the reported response of the OT that caused me greatest concern.

The OT explained that when the child entered kindergarten at age five, the ability to use scissors appropriately would be expected. The lessons in learning to use scissors were being given to avoid the child being behind when beginning kindergarten. The OT went on to further explain that the use of scissors was not developmentally appropriate until age five!

The OT, presumably a trained professional, who believed it was not developmentally appropriate for a child to be using scissors until age five, began teaching a child to use scissors before that child was even three years of age!

The child was miserable when using scissors and the parent was saddened when viewing the attempts!

If using scissors is developmentally appropriate at age five, then when the child is entering kindergarten, unless there is a development delay, coordination or muscular problem, that child will easily learn to use scissors appropriately, without the need for lessons from an OT. Forcing a child to practice a skill before developmentally ready is definitely not in the child’s best interests.

Think of the wonderful things about a child of two or three years of age; the things they are learning and doing. I am always amazed at how quickly children learn and progress. They grow up so quickly and are only little for such a short time. Why try to pressure them through to stages beyond their current development? These years of enormous growth and potential are precious. We are adults for most of our lives. What is wrong with appreciating the special two-ness or three-ness of a child? It will not matter in the future if scissors can be used at age three, age five or age seven.

If the child is constantly pressured to perform in ways that are not developmentally appropriate then feelings of inadequacy, loss of confidence and self-esteem may ensue, resulting in an ‘I can’t do it attitude’, a fear of failure and unwillingness to have a go. I believe many perceived behaviour problems are problems only because the expectations are not relevant to a child’s stage of development.

When adults strive for a child to achieve beyond the age expected norms they are not appreciating, but rather showing a lack of respect for, who the child is and for the stage of development. This is not living in the present. It is attempting to live in the future, which can become very scary if one does not feel it can approached with confidence.

One may hope this scissors example is an extreme and isolated incident, but sadly pressure placed upon children by expectations that are not developmentally appropriate is far too common.

Teaching colleagues here in Australia often express their dismay that children in the first three years of school are crying every day because they find the expectations upon their learning and behaviour too great.

I hear similar stories about trying to rush the children through from the UK, Canada and the USA. Maybe it is happening in other places too. Sadly the pressure of unrealistic expectations doesn’t achieve anything positive for the students, the teachers or the parents.

How different would schools be if, instead of being considered a preparation for life, they were focused on living life now? If three year olds were appreciated and respected as three year olds, five year olds as five year olds, and eight year olds as 8 year olds, rather than as apprentices for the adult they will one day be, how different would their school situation be?

An affirmation song I used to sing with my classes is one by Anne Infante called Just the way I am.

The song is made up of a series of verses about appreciating oneself just as one is – now, not in the future – including characteristics such as responsible,  lovable, confident and friendly; for example:

I am beautiful and I like me,

I am beautiful and I like me,

I am beautiful and I like me,

Just the way I am.

I have written about using Anne’s songs of affirmation in previous posts, here and here.

What do you think? How have you seen developmentally appropriate programs in action? How have you seen them disregarded? What have been the effects?

Further reading: The Cost of Ignoring Developmentally Appropriate Practice

Thank you

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

 

 

How should reading be taught in schools?

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The ability to read is empowering and a fundamental right. Sadly, many children leave school either unable to read or disinterested in reading. There are many reasons for this. Unfortunately, for many children, it is a learned disability. There are almost as many opinions about how how reading should be taught as there are people willing to give them. I don’t always agree with those opinions, but I do with this one by Misty Adoniou, which first appeared in The Conversation on June 21, 2016.
Thank you
As always, thank your for reading. I appreciate your feedback. Please share your thoughts.

How should reading be taught in schools?

Misty Adoniou, University of Canberra

When my son was nine years old, he put aside the large Harry Potter novel he had been slowly, but enthusiastically, reading each evening and instead began ploughing through lots of fairly uninspiring books that he brought home from school each day.

It turned out the Year 4 teachers had devised a competition at his school – whichever class read the most books would be rewarded with an end of term pizza party.

The aim, I presume, was to motivate the children to read. It is ironic then that the effect was that my son stopped reading for pleasure and instead began reading for the numbers.

Reading is now increasingly being reduced to a numbers game in schools.

What level is your child at?

At pick up time, parents quiz each other about what reading level their child is on. Inside the school staff room, teachers are directed to have children on level 15, 20 or 30 by the end of the school year.

Six year olds are deciding whether they are good readers or not based on how many books they have ticked off on their take home reader sheet.

These levels are based on algorithms that calculate the ratio of syllables to sentences, or measure word frequency and sentence length.

The rationale is that these formulae can be applied to rank books on a scale of readability and thus guide teachers to match books with children’s reading ability.

There are two key problems with this numbers approach to reading. First, the algorithms are faulty. Second, publishers misuse them.

What makes a book hard or easy to read?

The missing variables in readability algorithms are the authors’ intentions, the readers’ motivations and the teachers’ instruction.

These are key omissions, and they seriously reduce the usability of the algorithms and the credibility of the reading levels they produce.

Fictional stories often use familiar and high frequency vocabulary, and many authors use relatively simple sentence structures.

However the use of literary tools like allegory and metaphor, along with challenging text themes, increases the difficulty of works of fiction in ways that are not captured in readability algorithms.

For example, readability formulae give Hemmingway’s “The Old Man and the Sea” a reading level suitable for primary school students. They may be able to decode the words on the page but comprehension of the book is less likely.

The same formulae may rank a non-fiction book on dinosaurs, for example, as only suitable for high school students because of its uncommon vocabulary, lengthy sentences and multi-syllabic words.

Yet a child’s interest and familiarity with the topic, or a teacher or parent’s support and instruction, can make that non-fiction book very readable for younger children.

Reading schemes

As readability formulae are not always a good fit for books, the solution has been, instead, to write books which fit the formulae. And publishers have been very keen to supply those books.

These are the books that our children take home each evening. They are written according to the numbers – numbers of high frequency words, numbers of syllables, numbers of words in a sentence.

What is missing in those books is author intention and craft, reader engagement and interest, and teacher support and instruction.

Essentially, then, what is missing in these books is the very essence of reading.

What books should children read?

We have been using the reading scheme system for decades and we still have children struggling to read.

When we use these quasi books to teach reading, we are not adequately preparing them for real reading.

These books, written to fit algorithms, don’t build broad vocabularies in our children. They don’t teach our children how to read complex sentence structures or deal with literary language or read between the lines. In many cases, they turn children off reading altogether.

Children learn to read by reading a book that is a little beyond what they can already read. The gap between what they can read and what they could read is reduced when the child:

  • is highly motivated by the content of the book;
  • has existing background knowledge about that content;
  • is receiving good instruction from a teacher.

We don’t need books arranged in coloured boxes labelled with level numbers to teach a child to read.

Beautifully written pieces of children’s literature will do the job.

Books full of carefully crafted writing by authors whose intentions are to engage, entertain and inform.

Books that teachers can work with in the classroom showing how sounds work in words, and how words work in sentences to make us feel, see or think new things.

Beautiful books that parents can also buy and delight in reading with their children.

Why it matters

The way we teach children to read will fundamentally influence what they understand the purpose of reading to be.

When we teach children to read through schemes that tally their books, we teach them that reading is simply about quantity. If reading is about getting a reward of a pizza, then children are less likely to read for intrinsic rewards.

The claims made for well-written children’s literature are many and varied.

Reading books to your children brings you closer to them, can teach them philosophy and about world issues.

But they can do something else. They can teach our children to read.

The Conversation

Misty Adoniou, Associate Professor in Language, Literacy and TESL, University of Canberra

This article was originally published on The Conversation. Read the original article.

What the world needs now

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This week at the Carrot Ranch Charli Mills is talking about needs. She questions why necessities sometimes feel like luxuries and why basic necessities, such as drinking water and access to a bathroom, incur a fee. While she is temporarily homeless, she is seeing first hand some of the ongoing difficulties of others faced with long-term homelessness. Surely to be treated with some compassion and afforded the dignity of respect is equally a basic human need and a right.

what do living things need

Young children begin to learn about needs when they start caring for plants and animals. In science they learn about the needs of living things and how those needs are met. It is not long before they start to learn about the differences between a need and a want. This understanding, and acceptance, can take a long time to develop. Some never develop it.

need want

Perhaps if there was a greater understanding of the difference between a need and a want, the gap between those who have much and those who have little would decrease. But perhaps not. While there is little increase to basic needs over time, the wants increase exponentially; and the more one has, the more one wants.

If it is difficult for adults to distinguish between needs, wants and must haves, imagine how much more difficult it is for young children. It is possibly even more difficult for young children in an age with frequent replacement of one model for another, one gadget and one gimmick for another; the latest is always the best.

This difficulty is the focus of my flash fiction response to Charli’s challenge to in 99 words (no more, no less) write a story that explores human needs.

The latest thingamajig

“But Mum, I need it. Everyone’s got one.”

“Who?”

“Marco; and Christopher; and … everybody!”

Mum pictured their big houses and flashy cars.

“Has Yin got one?”

“No.”

“Amir?”

“No.”

“Why do you want it?”

“They won’t play with me if I don’t have one.”

“Who?”

“Marco and Christopher.

“I thought Yin and Amir were your friends.”

“But Marco and Christopher are cool.”

“And you want to be cool like Marco and Christopher?”

His eyes flickered.

“Will you still be cool when they get the next best thing? What about Yin and Amir? Will they still be your friends?”

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In a recent post Home is where the start is, I wrote about the importance of the early years to a child’s development. I suggested that it is difficult to regain what is missed in those early years. However, as Sarah Brentyn who blogs at Lemon Shark said: it may be difficult, but not impossible to make improvements. Sarah was concerned that parents may not make an effort if they thought it was too late. I agree with Sarah that it is never too late to make improvements. However, it is much more difficult to change established patterns and to make up for lost learning time. Not impossible. Difficult. It is even more difficult for those who have not had their basic needs met.

An article in the Huffington Post on June 30 compares two boys who were born on the same day in the same town, but will have dramatically different lives. The boys are now five years old. One boy who received a diet of nutrient-rich foods is now at school, making good progress, and has many friends.

The parents of the other boy were too poor to do the same for their child. He now suffers from chronic malnutrition, or “stunting”, which affects growth, strength of the immune system, and brain function. According to the article, 1 in 4 children worldwide suffer from chronic malnutrition. The statistics reported in the article are quite confronting, and challenge a privileged view of needs and wants.

After reading the article, it is with some embarrassment that I now admit to a need to be away from the blogosphere for the next few weeks. I will be back intermittently to read and respond to your comments. I apologise in advance for any delay in doing so. Please know that I do enjoy our conversations and appreciate your comments. I will be back to respond to you as soon as I can.

Thank you

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

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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