Today, Miya completed the Khan Academy K-2nd Grade maths course.
This is the result of just doing a little bit every day -- no more than maybe half an hour or so, and often less -- seven days a week.
Well done to her.
She is now starting 3rd Grade.
Wednesday, 2 November 2016
Tuesday, 1 November 2016
Book review: The Narnia series
For the past several months, I have been reading C. S. Lewis' Narnia books aloud to Mulan and Miya. We have just finished the seventh and final book in the series.
Why did I choose to read this series to the girls?
Mostly it's because I enjoy fantasy and science fiction stories. I like the direct, exciting adventures in them, and I like that the well-written ones are usually also morality stories examining the human condition. They are a great way to get us thinking about who we are and our place in the world.
The Narnia series is a fantasy adventure written for younger children, in simpler language. The books are also famous classics, and recommended reading for children. I'd read them as a young teen, and my recollection was that they are fun and exciting.
So, I'd been looking forward to the girls being old enough to listen to me read aloud these books, and I started out very positive about them. But sadly, on re-reading them, I discovered a few imperfections. Such is life.
With the books being so well known, I don't need to give too much explanation of them here. Mostly, my aim in this post is to briefly put in writing my thoughts on re-reading the books, and the girls' reactions to the books (as usual with my blogging book reviews, I haven't done any research on what others have thought of the books -- this is just our opinions). Nonetheless, a few initial words of explanation may help.
Published in the early to mid 1950s, the books are, in order of story chronology (Lewis wrote the books in a different order):
(The only book in the series that does not centre on any of the English children is The Horse and His Boy. This book also does not centre on Narnia, which we learn is a small kingdom in a much wider world, but instead on another neighbouring land.)
The first book, The Magician's Nephew, is set a couple of generations (England time) before all the other books, in late Victorian times. In it, we learn that there are uncountably many worlds in existence, of which our seemingly-recognisable world of England is one such world. Magic is used to travel between worlds, and in this first book the nephew (Digory) and his friend (Polly) use magic rings that the magician had developed to travel to Narnia just at its creation.
All the other books are set (England time) around the time that Lewis was writing the books -- that is, they are set over a period of a few years during and immediately after the Second World War.
Each time the English children (there are eight English children who visit Narnia, though not all at the same time) enter Narnia, they are faced with some current event or crisis that they must participate in and help with. Mostly, but not always, this involves bad leaders who must be overthown. As with many sword and sorcery books, there is plenty of travelling and exploring. The majority of the series is direct storytelling, detailing the adventurers moving from place to place and their encounters in each new location.
Any explanation of the Narnia books must also include the fact that Lewis was a Christian who wrote theological works (both literary and argumentative essays), and the series includes many Christian and spiritual elements. But it is also a children's book series (in The Silver Chair he explicitly writes under the title that it is for children), and as such any interpretation needs to balance the theological references with the child-directed storytelling.
Firstly, then, the immediate good stuff about the books. Simply put, they are a great read. The girls were always happy to hear me read more, and the stories are exciting adventures. In this sense alone, they are well worth reading and I highly recommend them. Sometimes, the books were a little too exciting for the girls' ages (especially for Miya), and they preferred me to read them earlier in the day rather than in the evening before bed.
Now to the more negative stuff.
1. Mysteriousness
Some fantasy writers choose to develop their stories in ways that show that their worlds are systematically believable, understandable and law-like (even if the laws are very different from those of our world). Lewis is not this type of writer. In the Narnian universe, while things are on the surface similar to our own world, they are clearly quite different underneath. But we never really get to know, in a systematic way, how, where and why they are different. For example, we know that time runs differently between different worlds in the Narnian universe, such that minutes may pass in one world but many years in another, but time passes inconsistently and no one seems to try to work out any underlying rules. We also learn in Dawn Treader that the Narnian world is flat, not spherical, and the stars are people, not suns, but there is no explanation of how it could all possibly work; it is just left as a blunt fact.
As I see it, this lack of systematic explanation is part of Lewis' storytelling style. I think he is wanting to create a theological mysteriousness -- that in the Narnian universe the powers and gods are beyond understanding and are inherently mysterious. There is either an arbitrariness about the universe, or things happen at a level of explanation that is impossible for people to properly understand. Thus, in the Narnian world it is absurd to try to understand things beyond a fairly simple (Medieval, animal, child-like) level, and those who try to do so (eg Eustace initially in Dawn Treader) miss the point and miss out.
I have two thoughts about this:
Firstly, I think that, as a storytelling technique, sometimes this works for Lewis and sometimes it doesn't. I think that sometimes Lewis' writing comes across as too artificially mystery-mongering and a little bit clumsy. That is, even if one is wanting to show that one's story-world is inherently mysterious, as a writer one still needs to keep the storytelling clear, and not resort to convenient plot devices or just-so explanations that struggle for coherence.
Secondly, I have a touch of concern about too much mystery-mongering, and how it might influence our perception of our own world. Our actual world that we live in (not the Narnian story-universe) can be a complicated place, but whether it is complicated because it is inherently mysterious, or because it just takes a bit of effort to understand, is an open question. I think it is a mistake for us, in our real world, to give up too soon and assume it is mysterious, without first having a go at trying to figure it out.
So, I think there is a danger that the Narnian books can induce in people more of an inclination to just accept as mysterious things that are puzzling, without having a go at struggling to understand as well. The Narnian books can trick people into assuming that our world is just like the Narnian world, when we really don't know that it is. It can make people think that it is uncool and silly to be a bit like Eustace was initially, in trying to make rational sense of the world.
To put this directly, I think the Narnian series has the potential to influence people in a bad way, regarding how much effort we should put into questioning and seeking explanations of things. It is a little bit anti-intellectual, and may promote anti-intellectualism.
2. Casual violence
We all know the saying, that when all you have is a hammer everything looks like a nail. I think the characters in the Narnian world often make this mistake.
The Narnian world is basically Medieval in its level of society and technology. There are castles and kings, swords and shields. The male nobility go about in their everyday life wearing mail armour and carrying swords (at the end of The Last Battle, when they find themselves dressed in their ideal, most comfortable clothes, they are all still wearing mail and carrying swords).
And this attitude of carrying around a deadly weapon while dressed in heavy, defensive clothing dominates their interactions with other people. If they disagree with someone, they are just as likely to draw their swords and go charging in to strike at them (eg, in Prince Caspian, where Caspian, Peter, Edmund and Trumpkin kill Nikabrik, etc, when they had a disagreement during council over how to proceed). And if they meet a stranger, they have a habit of thinking the worst and preparing for battle.
The Narnian world does not promote discussion, compromise and understanding of other perspectives. It promotes battles, fights and killing when faced with disagreements and differences.
Moreover, after they have killed someone there is almost no sadness at the pain and suffering they have caused, nor any deep soul-searching over the tragedy that led to it. None of the characters seem to feel, in any deep way, any of the pain that a healthy human being should feel in such a moment. They are far too casual and cold-hearted.
Mulan and Miya picked up on this, both disliking this aspect of the main characters throughout the series. As we read about the last battle, in The Last Battle, we asked each other which side of the battle we would have been on, as it started. We identified four sides:
Again, to summarise, the Narnian series has the potential to influence people in a bad way. It trivialises and normalises the carrying of a weapon in everyday life, as well as using it far too readily when one has a disagreement. And it normalises a cold-hearted, casual attitude to violent death, where one just carries on afterwards, largely unaffected by it all.
3. Casual sexism
There are very strong gender roles in the Narnian series, with the males as the leaders and fighters and the females as the nurturers and healers.
Time and again, when they suited up for battle, the boys were given swords and hurried to the front to fight, while the girls were at best given bows and told to get in behind and be safe.
Mulan and Miya quickly picked up on this, pointing out how silly it all was every time we read about a battle.
Even the portrayals of the baddies was sexist. The main female baddies (eg the White Witch, The green Witch in Silver Chair, the hag in Prince Caspian) all seemed to get their power through magic and deviousness, while the male baddies were more directly physical and up front. This buys into all sorts of gender stereotypes, which most of us are now familiar with.
Could this sort of casual sexism be influential in this day and age? I don't know and I hope not. My children just found it laughably ridiculous. But even if it isn't influential, it is clearly completely inappropriate.
4. Casual horror
Similar to the casual violence, the girls and I felt that the occasional casualness of human tragedy was quite off-putting.
The most graphic example of this was in Dawn Treader, when the main characters came across the gold statue in the pool on the island. It turned out, in some unexplained way, that the water in the pool turned everything to gold (I'm not sure how this might be possible, as surely the water would also seep into the ground, turning the surrounding land to gold). Someone, at some time in the past, had dived into the pool and they had turned into gold, sinking to the bottom. One minute a living, breathing human being, feeling hot after walking up the hill to the lake, the next minute they are dead and gone, a gold statue.
Mulan was quite horrified at the thought of that, and for the first time that I'm aware of she had a bad dream about something that we/she had read (and that is saying something; I've read Greek myths to Mulan).
I really don't think there was any need for Lewis to include those sorts of graphic ideas in a children's book. It was highly inappropriate and insensitive to children's feelings.
And once again, this shows a cold-hearted callousness towards living beings that is plain wrong. I admire Mulan for being disturbed by the imagery, and I hope she never loses her automatic reaction to first feel for others.
5. Casual racism and English cultural superiority
Broadly speaking, throughout the Narnian books, on the one hand there is a lot of positive associations for English cultural traditions, while on the other hand there is a lot of negative associations for non-Western cultural traditions. Some of this is innocuous, while other bits are disturbingly racist and show up as an arrogant sense of English cultural and racial superiority.
Firstly, it is clear that Narnia is very traditionally English in almost every conceivable way -- the landscape, weather, clothing, food/drink, recreational activities, buildings and social class structures. Narnia is a re-creation of an old, imagined and idealised English aristocracy. The main characters, as part of the nobility, have a grand time with parties, court life, hunts and sailing. They drink wine (even the children) and go hunting on horseback. The decent, normal, non-noble folk are happy to live in cleanly simple conditions, going about their everyday lives and being ruled by the nobility.
But scratch the surface, and already some disturbing class-based assumptions are there. The nobility are humans -- elegant, smooth, tall, light-skinned and refined. As the true rulers, they have the right to rule through their heritage, as descendants of the English folk who were appointed rulers by Aslan (God). Those who they rule are variously simple, clumsy, innocent, slow, lumpy, bumpy, cute and generally well-meaning in their more limited way. Each is apparently born into their place, and the light-skinned humans rule the hairier, smaller, darker others in a paternal, if sometimes somewhat bemused, way.
Just like England was, Narnia is an empire, with its dependencies and colonies. But Narnia's empire is sanitised, and its subjects are grateful for Narnia's rule. Narnia is an idealised England, without the inconvenient atrocities. The Lone Islanders are grateful to the Narnians for driving away the baddie who was terrorising them, so they let Narnia rule them forever. The island of the Monopods, in Dawn Treader, has a smart, sophisticated English-like ruler, benevolently ruling over the simple-minded, ungainly, amusing little natives who are incapable of looking after themselves properly and so need to be told what to do. The main characters recognise the necessity of this rule, as they watch the natives in amusement from the grand residence above.
Clearly, anyone who reads this, and has a passing familiarity with England's history, is going to read into it an attempted, rose-coloured-glasses, defence of England's dodgy colonial past.
Turning to the other cultures in the Narnian world, the most obvious is the Calormenes. Their southern lands are hotter and drier than Narnia/England, and with deserts. The people wear turbans and robes, and carry curved scimitars instead of straight swords. They are called "darkies", and are described as dirty. They are mostly rough, ruthless and conniving, making treacherous plans to increase their own power. Their god is ugly, spiky and revengeful. I don't know how else we can see this but as a thinly-veiled attempted parallel of Islam and the Middle East.
The dwarfs, who live in the Narnian lands, also raise red flags. They are lumpy, bumpy, and small, with big noses. Mostly, the Narnians see the dwarfs as troublemakers, and frequently the dwarfs side with the Narnian enemies. A few dwarfs are friends with the Narnians, though often in a slightly amusing way. They may be advisors, but there is never any suggestion that they could be rulers -- it is only the tall, straight humans who could really rule. In The Last Battle, the dwarfs sat in the stable, not seeing Aslan's world around them. Does this sound like the dwarfs are the Jewish people of the Narnian world? And does their depiction sound a bit like anti-Semitism? I think so.
Read altogether, in my opinion the Narnian books promote a form of racism that sees the English as racially superior, and that this justifies English rule, in a paternalistic way, over the intellectually-inferior and funny-looking lower races.
6. Aslan as a moral role model
No discussion of Narnia would be complete without mentioning Aslan.
Aslan is the lion, of The Lion, the Witch and the Wardrobe. He is the creator of Narnia in the first book, and shows up in each book to help the main characters and sometimes kill the baddies. He is clearly extremely powerful, but just how powerful he is remains unclear throughout. Nonetheless, frequently he is able to magically make things happen in ways that go far beyond everyone else. The Narnian characters worship Aslan, treating him as their god. Aslan dies and comes back to life in The Lion, the Witch and the Wardrobe, and occasionally he refers to his father, the Emperor-over-Sea, suggesting that he is intended as the Jesus character of the series.
Aslan's help in each book is unclear and mysterious. Sometimes he intervenes directly and solves the key problems. Sometimes his intervention is indirect and is more like a nudge to direct the main characters to do things for themselves. And sometimes he does not intervene at all, even when the main characters seem in big trouble and are suffering badly.
Given that Aslan is trusted by the main characters, and they tend to follow him unquestioningly, we may see him as the moral role model -- the being who does what is good and right, and who we should follow if we also want to do what is good and right. Certainly, at the very least, he seems to do a lot of good, helping to get rid of the baddie leaders who want to oppress and hurt the people.
But does he always do the right thing? Is he really perfectly good, to be followed unquestioningly? Is he really worthy of worship? Or is he just mostly good, and it's possible to show that he sometimes gets things wrong? And if he sometimes gets things wrong, or even if it is a live question that he might sometimes get things wrong, is it wrong for the main characters to follow him so unquestioningly?
Part of the difficulty of answering these questions is that Lewis has intentionally made Aslan's reasons and motives unclear. We see some of his actions, but we often don't get to see the details of how the world really is, to be able to clearly evaluate whether Aslan's actions were truly appropriate to the situation. That is, we are often not given enough information to understand why Aslan intervened in this situation but not in that situation, or why he directly killed the baddie here, but not there.
Nonetheless, over the course of seven books we have got some information to work with.
Mulan, Miya and I first started to really question Aslan's goodness in The Horse and His Boy. This was especially when Shasta, Aravis and the horses were being chased by the lion, and the lion badly scratched Aravis' back. Later in the book, we learnt that the lion was Aslan, and we were told that his motive had been to force the group to move faster, so that they would get to King Lune in time to warn them of the Calormene invasion.
The girls and I all thought this explanation was completely implausible. There could have been any number of other ways to encourage them to go faster, without the need to hurt someone so badly. Or Aslan could have intervened in some more direct way to stop the invasion. Why all the trickery? Why did he create all that extra unnecessary suffering? We all concluded that surely Aslan hurt Aravis for no good reason.
From that point on, other events also seemed questionable. We all started to doubt that Aslan really had to do things in the way that he had. Too often, there seemed extra, unnecessary trouble that could have been resolved more simply and with less suffering.
All this meant that none of us are especially pro-Aslan. Yep, he is powerful, and yep, he is pretty good. But nope, none of us think he deserves all that worship and unquestioned devotion. He is probably not ideally good, and he is not a clear moral role model who we should follow.
7. Spirituality
It has been suggested to me that I am reading all of this too directly, and that the books should be read more spiritually. That is, I think, it should be read a bit more like Pilgrim's Progress, in that the characters are not supposed to be seen as real people, but more as representations of abstract ideas or character traits. Battling a character in the books is not really to be seen as battling a person, but instead as battling a bad idea or bad character trait.
If this is the case, then my treating this as representative of real interactions between real people is missing the point.
While I can see this as a possible interpretation, and one that adults may get a lot of value out of, I remain unconvinced of this for the purposes of a children's book. Children are going to read the books more directly, and they are going to take notice of the interactions at a more personal level. The issues that I have raised above are still going to influence children in these bad ways, regardless of whether Lewis or other adults are getting more abstract spiritual values out of it.
More pointedly, if Lewis was really trying to write merely at a spiritual level, why were the characters depicted so similar to real, earthly people? Was he really so blinded by his own social and racial prejudices that he didn't notice that he was describing earthly politics and society?
Conclusions
As I said at the beginning, I initially started out very positive about the Narnia book series, and I still think they are fun and exciting stories. They are a pleasure to read.
But sadly, the more I read the more I became opposed to the political, moral and social values expressed by Lewis. Hopefully, these days Lewis' views are merely a historic relic, and not too many people would take them seriously. Nonetheless, books like these may work subtly to somewhat normalise these wrong attitudes in children.
This means that I think it is important for these points to be explicitly raised with children as they are reading the books. Pointing out and discussing how and why they are wrong can help to nullify any influence they might have.
Used as teaching resources, and pausing to discuss ideas as they are raised, can still make these books extremely worthwhile. It is in this sense, and with these qualifications, that I recommend the Narnia series of books.
Postscript
Mulan read this post, and fact-corrected a minor point about the story. She often has a better memory for the details of stories than I do. She said that she agreed with what I had written.
Why did I choose to read this series to the girls?
Mostly it's because I enjoy fantasy and science fiction stories. I like the direct, exciting adventures in them, and I like that the well-written ones are usually also morality stories examining the human condition. They are a great way to get us thinking about who we are and our place in the world.
The Narnia series is a fantasy adventure written for younger children, in simpler language. The books are also famous classics, and recommended reading for children. I'd read them as a young teen, and my recollection was that they are fun and exciting.
So, I'd been looking forward to the girls being old enough to listen to me read aloud these books, and I started out very positive about them. But sadly, on re-reading them, I discovered a few imperfections. Such is life.
With the books being so well known, I don't need to give too much explanation of them here. Mostly, my aim in this post is to briefly put in writing my thoughts on re-reading the books, and the girls' reactions to the books (as usual with my blogging book reviews, I haven't done any research on what others have thought of the books -- this is just our opinions). Nonetheless, a few initial words of explanation may help.
Published in the early to mid 1950s, the books are, in order of story chronology (Lewis wrote the books in a different order):
- The Magician's Nephew
- The Lion, The Witch and the Wardrobe
- The Horse and His Boy
- Prince Caspian
- The Voyage of the Dawn Treader
- The Silver Chair
- The Last Battle
(The only book in the series that does not centre on any of the English children is The Horse and His Boy. This book also does not centre on Narnia, which we learn is a small kingdom in a much wider world, but instead on another neighbouring land.)
The first book, The Magician's Nephew, is set a couple of generations (England time) before all the other books, in late Victorian times. In it, we learn that there are uncountably many worlds in existence, of which our seemingly-recognisable world of England is one such world. Magic is used to travel between worlds, and in this first book the nephew (Digory) and his friend (Polly) use magic rings that the magician had developed to travel to Narnia just at its creation.
All the other books are set (England time) around the time that Lewis was writing the books -- that is, they are set over a period of a few years during and immediately after the Second World War.
Each time the English children (there are eight English children who visit Narnia, though not all at the same time) enter Narnia, they are faced with some current event or crisis that they must participate in and help with. Mostly, but not always, this involves bad leaders who must be overthown. As with many sword and sorcery books, there is plenty of travelling and exploring. The majority of the series is direct storytelling, detailing the adventurers moving from place to place and their encounters in each new location.
Any explanation of the Narnia books must also include the fact that Lewis was a Christian who wrote theological works (both literary and argumentative essays), and the series includes many Christian and spiritual elements. But it is also a children's book series (in The Silver Chair he explicitly writes under the title that it is for children), and as such any interpretation needs to balance the theological references with the child-directed storytelling.
Firstly, then, the immediate good stuff about the books. Simply put, they are a great read. The girls were always happy to hear me read more, and the stories are exciting adventures. In this sense alone, they are well worth reading and I highly recommend them. Sometimes, the books were a little too exciting for the girls' ages (especially for Miya), and they preferred me to read them earlier in the day rather than in the evening before bed.
Now to the more negative stuff.
1. Mysteriousness
Some fantasy writers choose to develop their stories in ways that show that their worlds are systematically believable, understandable and law-like (even if the laws are very different from those of our world). Lewis is not this type of writer. In the Narnian universe, while things are on the surface similar to our own world, they are clearly quite different underneath. But we never really get to know, in a systematic way, how, where and why they are different. For example, we know that time runs differently between different worlds in the Narnian universe, such that minutes may pass in one world but many years in another, but time passes inconsistently and no one seems to try to work out any underlying rules. We also learn in Dawn Treader that the Narnian world is flat, not spherical, and the stars are people, not suns, but there is no explanation of how it could all possibly work; it is just left as a blunt fact.
As I see it, this lack of systematic explanation is part of Lewis' storytelling style. I think he is wanting to create a theological mysteriousness -- that in the Narnian universe the powers and gods are beyond understanding and are inherently mysterious. There is either an arbitrariness about the universe, or things happen at a level of explanation that is impossible for people to properly understand. Thus, in the Narnian world it is absurd to try to understand things beyond a fairly simple (Medieval, animal, child-like) level, and those who try to do so (eg Eustace initially in Dawn Treader) miss the point and miss out.
I have two thoughts about this:
Firstly, I think that, as a storytelling technique, sometimes this works for Lewis and sometimes it doesn't. I think that sometimes Lewis' writing comes across as too artificially mystery-mongering and a little bit clumsy. That is, even if one is wanting to show that one's story-world is inherently mysterious, as a writer one still needs to keep the storytelling clear, and not resort to convenient plot devices or just-so explanations that struggle for coherence.
Secondly, I have a touch of concern about too much mystery-mongering, and how it might influence our perception of our own world. Our actual world that we live in (not the Narnian story-universe) can be a complicated place, but whether it is complicated because it is inherently mysterious, or because it just takes a bit of effort to understand, is an open question. I think it is a mistake for us, in our real world, to give up too soon and assume it is mysterious, without first having a go at trying to figure it out.
So, I think there is a danger that the Narnian books can induce in people more of an inclination to just accept as mysterious things that are puzzling, without having a go at struggling to understand as well. The Narnian books can trick people into assuming that our world is just like the Narnian world, when we really don't know that it is. It can make people think that it is uncool and silly to be a bit like Eustace was initially, in trying to make rational sense of the world.
To put this directly, I think the Narnian series has the potential to influence people in a bad way, regarding how much effort we should put into questioning and seeking explanations of things. It is a little bit anti-intellectual, and may promote anti-intellectualism.
2. Casual violence
We all know the saying, that when all you have is a hammer everything looks like a nail. I think the characters in the Narnian world often make this mistake.
The Narnian world is basically Medieval in its level of society and technology. There are castles and kings, swords and shields. The male nobility go about in their everyday life wearing mail armour and carrying swords (at the end of The Last Battle, when they find themselves dressed in their ideal, most comfortable clothes, they are all still wearing mail and carrying swords).
And this attitude of carrying around a deadly weapon while dressed in heavy, defensive clothing dominates their interactions with other people. If they disagree with someone, they are just as likely to draw their swords and go charging in to strike at them (eg, in Prince Caspian, where Caspian, Peter, Edmund and Trumpkin kill Nikabrik, etc, when they had a disagreement during council over how to proceed). And if they meet a stranger, they have a habit of thinking the worst and preparing for battle.
The Narnian world does not promote discussion, compromise and understanding of other perspectives. It promotes battles, fights and killing when faced with disagreements and differences.
Moreover, after they have killed someone there is almost no sadness at the pain and suffering they have caused, nor any deep soul-searching over the tragedy that led to it. None of the characters seem to feel, in any deep way, any of the pain that a healthy human being should feel in such a moment. They are far too casual and cold-hearted.
Mulan and Miya picked up on this, both disliking this aspect of the main characters throughout the series. As we read about the last battle, in The Last Battle, we asked each other which side of the battle we would have been on, as it started. We identified four sides:
- The Narnian king Tirian, with the English Eustace and Jill
- The Calormenes
- The dwarfs
- The animals who left the battle and didn't fight
Again, to summarise, the Narnian series has the potential to influence people in a bad way. It trivialises and normalises the carrying of a weapon in everyday life, as well as using it far too readily when one has a disagreement. And it normalises a cold-hearted, casual attitude to violent death, where one just carries on afterwards, largely unaffected by it all.
3. Casual sexism
There are very strong gender roles in the Narnian series, with the males as the leaders and fighters and the females as the nurturers and healers.
Time and again, when they suited up for battle, the boys were given swords and hurried to the front to fight, while the girls were at best given bows and told to get in behind and be safe.
Mulan and Miya quickly picked up on this, pointing out how silly it all was every time we read about a battle.
Even the portrayals of the baddies was sexist. The main female baddies (eg the White Witch, The green Witch in Silver Chair, the hag in Prince Caspian) all seemed to get their power through magic and deviousness, while the male baddies were more directly physical and up front. This buys into all sorts of gender stereotypes, which most of us are now familiar with.
Could this sort of casual sexism be influential in this day and age? I don't know and I hope not. My children just found it laughably ridiculous. But even if it isn't influential, it is clearly completely inappropriate.
4. Casual horror
Similar to the casual violence, the girls and I felt that the occasional casualness of human tragedy was quite off-putting.
The most graphic example of this was in Dawn Treader, when the main characters came across the gold statue in the pool on the island. It turned out, in some unexplained way, that the water in the pool turned everything to gold (I'm not sure how this might be possible, as surely the water would also seep into the ground, turning the surrounding land to gold). Someone, at some time in the past, had dived into the pool and they had turned into gold, sinking to the bottom. One minute a living, breathing human being, feeling hot after walking up the hill to the lake, the next minute they are dead and gone, a gold statue.
Mulan was quite horrified at the thought of that, and for the first time that I'm aware of she had a bad dream about something that we/she had read (and that is saying something; I've read Greek myths to Mulan).
I really don't think there was any need for Lewis to include those sorts of graphic ideas in a children's book. It was highly inappropriate and insensitive to children's feelings.
And once again, this shows a cold-hearted callousness towards living beings that is plain wrong. I admire Mulan for being disturbed by the imagery, and I hope she never loses her automatic reaction to first feel for others.
5. Casual racism and English cultural superiority
Broadly speaking, throughout the Narnian books, on the one hand there is a lot of positive associations for English cultural traditions, while on the other hand there is a lot of negative associations for non-Western cultural traditions. Some of this is innocuous, while other bits are disturbingly racist and show up as an arrogant sense of English cultural and racial superiority.
Firstly, it is clear that Narnia is very traditionally English in almost every conceivable way -- the landscape, weather, clothing, food/drink, recreational activities, buildings and social class structures. Narnia is a re-creation of an old, imagined and idealised English aristocracy. The main characters, as part of the nobility, have a grand time with parties, court life, hunts and sailing. They drink wine (even the children) and go hunting on horseback. The decent, normal, non-noble folk are happy to live in cleanly simple conditions, going about their everyday lives and being ruled by the nobility.
But scratch the surface, and already some disturbing class-based assumptions are there. The nobility are humans -- elegant, smooth, tall, light-skinned and refined. As the true rulers, they have the right to rule through their heritage, as descendants of the English folk who were appointed rulers by Aslan (God). Those who they rule are variously simple, clumsy, innocent, slow, lumpy, bumpy, cute and generally well-meaning in their more limited way. Each is apparently born into their place, and the light-skinned humans rule the hairier, smaller, darker others in a paternal, if sometimes somewhat bemused, way.
Just like England was, Narnia is an empire, with its dependencies and colonies. But Narnia's empire is sanitised, and its subjects are grateful for Narnia's rule. Narnia is an idealised England, without the inconvenient atrocities. The Lone Islanders are grateful to the Narnians for driving away the baddie who was terrorising them, so they let Narnia rule them forever. The island of the Monopods, in Dawn Treader, has a smart, sophisticated English-like ruler, benevolently ruling over the simple-minded, ungainly, amusing little natives who are incapable of looking after themselves properly and so need to be told what to do. The main characters recognise the necessity of this rule, as they watch the natives in amusement from the grand residence above.
Clearly, anyone who reads this, and has a passing familiarity with England's history, is going to read into it an attempted, rose-coloured-glasses, defence of England's dodgy colonial past.
Turning to the other cultures in the Narnian world, the most obvious is the Calormenes. Their southern lands are hotter and drier than Narnia/England, and with deserts. The people wear turbans and robes, and carry curved scimitars instead of straight swords. They are called "darkies", and are described as dirty. They are mostly rough, ruthless and conniving, making treacherous plans to increase their own power. Their god is ugly, spiky and revengeful. I don't know how else we can see this but as a thinly-veiled attempted parallel of Islam and the Middle East.
The dwarfs, who live in the Narnian lands, also raise red flags. They are lumpy, bumpy, and small, with big noses. Mostly, the Narnians see the dwarfs as troublemakers, and frequently the dwarfs side with the Narnian enemies. A few dwarfs are friends with the Narnians, though often in a slightly amusing way. They may be advisors, but there is never any suggestion that they could be rulers -- it is only the tall, straight humans who could really rule. In The Last Battle, the dwarfs sat in the stable, not seeing Aslan's world around them. Does this sound like the dwarfs are the Jewish people of the Narnian world? And does their depiction sound a bit like anti-Semitism? I think so.
Read altogether, in my opinion the Narnian books promote a form of racism that sees the English as racially superior, and that this justifies English rule, in a paternalistic way, over the intellectually-inferior and funny-looking lower races.
6. Aslan as a moral role model
No discussion of Narnia would be complete without mentioning Aslan.
Aslan is the lion, of The Lion, the Witch and the Wardrobe. He is the creator of Narnia in the first book, and shows up in each book to help the main characters and sometimes kill the baddies. He is clearly extremely powerful, but just how powerful he is remains unclear throughout. Nonetheless, frequently he is able to magically make things happen in ways that go far beyond everyone else. The Narnian characters worship Aslan, treating him as their god. Aslan dies and comes back to life in The Lion, the Witch and the Wardrobe, and occasionally he refers to his father, the Emperor-over-Sea, suggesting that he is intended as the Jesus character of the series.
Aslan's help in each book is unclear and mysterious. Sometimes he intervenes directly and solves the key problems. Sometimes his intervention is indirect and is more like a nudge to direct the main characters to do things for themselves. And sometimes he does not intervene at all, even when the main characters seem in big trouble and are suffering badly.
Given that Aslan is trusted by the main characters, and they tend to follow him unquestioningly, we may see him as the moral role model -- the being who does what is good and right, and who we should follow if we also want to do what is good and right. Certainly, at the very least, he seems to do a lot of good, helping to get rid of the baddie leaders who want to oppress and hurt the people.
But does he always do the right thing? Is he really perfectly good, to be followed unquestioningly? Is he really worthy of worship? Or is he just mostly good, and it's possible to show that he sometimes gets things wrong? And if he sometimes gets things wrong, or even if it is a live question that he might sometimes get things wrong, is it wrong for the main characters to follow him so unquestioningly?
Part of the difficulty of answering these questions is that Lewis has intentionally made Aslan's reasons and motives unclear. We see some of his actions, but we often don't get to see the details of how the world really is, to be able to clearly evaluate whether Aslan's actions were truly appropriate to the situation. That is, we are often not given enough information to understand why Aslan intervened in this situation but not in that situation, or why he directly killed the baddie here, but not there.
Nonetheless, over the course of seven books we have got some information to work with.
Mulan, Miya and I first started to really question Aslan's goodness in The Horse and His Boy. This was especially when Shasta, Aravis and the horses were being chased by the lion, and the lion badly scratched Aravis' back. Later in the book, we learnt that the lion was Aslan, and we were told that his motive had been to force the group to move faster, so that they would get to King Lune in time to warn them of the Calormene invasion.
The girls and I all thought this explanation was completely implausible. There could have been any number of other ways to encourage them to go faster, without the need to hurt someone so badly. Or Aslan could have intervened in some more direct way to stop the invasion. Why all the trickery? Why did he create all that extra unnecessary suffering? We all concluded that surely Aslan hurt Aravis for no good reason.
From that point on, other events also seemed questionable. We all started to doubt that Aslan really had to do things in the way that he had. Too often, there seemed extra, unnecessary trouble that could have been resolved more simply and with less suffering.
All this meant that none of us are especially pro-Aslan. Yep, he is powerful, and yep, he is pretty good. But nope, none of us think he deserves all that worship and unquestioned devotion. He is probably not ideally good, and he is not a clear moral role model who we should follow.
7. Spirituality
It has been suggested to me that I am reading all of this too directly, and that the books should be read more spiritually. That is, I think, it should be read a bit more like Pilgrim's Progress, in that the characters are not supposed to be seen as real people, but more as representations of abstract ideas or character traits. Battling a character in the books is not really to be seen as battling a person, but instead as battling a bad idea or bad character trait.
If this is the case, then my treating this as representative of real interactions between real people is missing the point.
While I can see this as a possible interpretation, and one that adults may get a lot of value out of, I remain unconvinced of this for the purposes of a children's book. Children are going to read the books more directly, and they are going to take notice of the interactions at a more personal level. The issues that I have raised above are still going to influence children in these bad ways, regardless of whether Lewis or other adults are getting more abstract spiritual values out of it.
More pointedly, if Lewis was really trying to write merely at a spiritual level, why were the characters depicted so similar to real, earthly people? Was he really so blinded by his own social and racial prejudices that he didn't notice that he was describing earthly politics and society?
Conclusions
As I said at the beginning, I initially started out very positive about the Narnia book series, and I still think they are fun and exciting stories. They are a pleasure to read.
But sadly, the more I read the more I became opposed to the political, moral and social values expressed by Lewis. Hopefully, these days Lewis' views are merely a historic relic, and not too many people would take them seriously. Nonetheless, books like these may work subtly to somewhat normalise these wrong attitudes in children.
This means that I think it is important for these points to be explicitly raised with children as they are reading the books. Pointing out and discussing how and why they are wrong can help to nullify any influence they might have.
Used as teaching resources, and pausing to discuss ideas as they are raised, can still make these books extremely worthwhile. It is in this sense, and with these qualifications, that I recommend the Narnia series of books.
Postscript
Mulan read this post, and fact-corrected a minor point about the story. She often has a better memory for the details of stories than I do. She said that she agreed with what I had written.
Saturday, 22 October 2016
Sal Khan and teaching for mastery
Sal Khan's TED Talk makes a lot of sense to me.
His point is, don't set a fixed time to cover some learning material. And don't be satisfied with a passable level of understanding of that material, before moving on to the next topic/level.
Instead, set the content of what you want learnt, and make sure that is mastered before moving on to the next topic. The length of time taken to master it is not important. He says:
For those of us who homeschool, and with only a few students to teach, it is easy to have this sort of mentality.
For teachers who have more students, it can understandably be trickier to accomplish. Khan addresses this issue from 5 min 45 sec onwards, and is optimistic that new technologies in on-demand learning make it possible to do this in the classroom.
And while this all sounds very exciting and hopeful, I still do wonder how easy it is to find the right teaching point, with just the right nuance of explanation, with on-demand video teaching. At this stage, I still don't feel confident to leave Mulan and Miya unsupervised on Khan Academy to watch the instructional videos and answer the questions on their own. They still seem to do much better with my in-person interactive explanations than with the video explanations.
Nonetheless, good on Sal Khan for doing what he does, and I have no doubt that as these on-demand teaching materials get better and better, it will get easier and easier to find the right teaching point at the right time, and at least sometimes they will take over from teacher-dad's explanations.
His point is, don't set a fixed time to cover some learning material. And don't be satisfied with a passable level of understanding of that material, before moving on to the next topic/level.
Instead, set the content of what you want learnt, and make sure that is mastered before moving on to the next topic. The length of time taken to master it is not important. He says:
Instead of artificially constraining when and how long -- fixing when and how long -- you work on something, pretty much ensuring that variable outcome, the A, B, C, D, F, do it the other way around. What's variable is when and how long a student actually has to work on something, and what's fixed is that they actually master the material. ...
It will reinforce the right mindset muscles. It makes them realise that if you got 20% wrong on something, it doesn't mean that you have a C branded in your DNA somehow. It means that you should just keep working on it. You should have grit. You should have perseverance.Very well said. I agree completely.
For those of us who homeschool, and with only a few students to teach, it is easy to have this sort of mentality.
For teachers who have more students, it can understandably be trickier to accomplish. Khan addresses this issue from 5 min 45 sec onwards, and is optimistic that new technologies in on-demand learning make it possible to do this in the classroom.
And while this all sounds very exciting and hopeful, I still do wonder how easy it is to find the right teaching point, with just the right nuance of explanation, with on-demand video teaching. At this stage, I still don't feel confident to leave Mulan and Miya unsupervised on Khan Academy to watch the instructional videos and answer the questions on their own. They still seem to do much better with my in-person interactive explanations than with the video explanations.
Nonetheless, good on Sal Khan for doing what he does, and I have no doubt that as these on-demand teaching materials get better and better, it will get easier and easier to find the right teaching point at the right time, and at least sometimes they will take over from teacher-dad's explanations.
Wednesday, 19 October 2016
Home educated students trialling school
As I am sure you all know, Mulan and Miya are homeschooled -- we have Certificates of Exemption (from enrolment at a registered school) for them.
The quick reason that we homeschool the girls is that it works for us. Our teaching them has been ongoing from their births; it is the default option. Why change to a different system when the current system is working successfully?
What helps make it work for us is:
So, I am all in favour of more interaction between homeschoolers and registered schools.
So, while preparing the exemption application for Miya a few months ago, I was very interested to see on the New Zealand Ministry of Education website a section about trialling school. This is what it says:
Trialling a school
I thought, what a great idea, homeschool children can trial attending school. They can learn what attending school is like, and so have a better understanding of what most children experience. Since school life is so ingrained into our culture, giving homeschoolers a time at school can allow them to enter into local mainstream culture in a more direct and personal way.
This can also be an awesome bridge between the homeschooling community and the registered school community -- shared experiences, better communication, closer relationships and improved community interactions. As I see it, anything that improves community relations is surely a good thing.
So, I made contact with our local primary school, Takapuna Primary, introduced ourselves, explained what I had found on the Ministry of Education website, and briefly explained my thinking as above.
I got a very positive email back from the Principal of Takapuna Primary, who was very welcoming of us. We both agreed that it would make sense for this to happen at the beginning of the new school year in 2017, and we would make contact again in November when they had sorted out which teachers would be teaching which classes.
Since the Ministry of Education website said to contact the local Ministry office for more information, I sent them an email today, also explaining my thinking.
Within a couple of hours I got a phone call from the person at the local Auckland Ministry office who is in charge of working with homeschoolers (no need to give names).
If I had to describe her manner on the phone, I would say that she was adversarial rather than cooperative. As I see it, a cooperative conversation is one in which the other person's ideas are always treated charitably -- seen in the best possible light and in their strongest way -- to work together to jointly find the best solution. An adversarial conversation is one in which one tries to beat the other, using rhetorical strategies such as misdirections and uncharitable interpretations. Words and meanings get twisted to one-up the other, and the truth can get lost in the struggle.
But despite the adversarial nature of the conversation, I learnt a few things from it.
Firstly, and most tellingly, she said that the nature of the homeschooling exemption is that it is a complete opting out of the state education system. Consequently, the state has no responsibility to assist in any way with the educational needs of homeschoolers. Moreover, she seemed to go so far as to imply that this meant that it was inappropriate for the state to help in this way, perhaps even to the point of it being offensive to suggest it.
I think she was treating schooling as an all-or-nothing concept. Either the children enrol at a registered school, and in which case they are required to attend for the long term. Or they get an exemption, and then the family unit is entirely on its own, using its own resources. No middle ground, and no cooperation or interaction.
My armchair sense of this is that it is surely not in the best interests of either the children or society. But I would be interested in her reasoning for seeing education in this absolutist way. (I wonder if her political orientation is more lone horseman than Amish?)
Secondly, she emphasised that the policy of trialling a school was intended only for students who were intending to continue on at that school. It was not intended for students trialling it for the purposes I was suggesting.
I can accept that, though I am puzzled why that was not made clear on the website.
But more importantly, just because something is originally intended for one purpose, there is no reason to think that it cannot be used for other purposes also, and especially if those other purposes are good.
To put it more directly, just because a policy was intended for children planning to return to a registered school, it doesn't necessarily mean that it can't be also used by those who want to trial school for other reasons. Pointing out the original intent doesn't necessarily exclude my idea.
In the course of the 12-minute conversation, she raised an objection that if the policy is opened up to other purposes, then homeschoolers will take advantage of it and there will be too many homeschoolers overburdening schools, and with many doing it for the wrong reasons. She gave two possible wrong reasons homeschoolers might use: (a) lazy parents wanting a break, and (b) lazy parents wanting to use it for "socialisation", when they should be providing opportunities for their child's socialisation themselves.
Her argument is very weak:
Thirdly, she directly contradicted the Ministry website regarding the effect trialling at school will have on the exemption. Note above that the website says that trialling school for under ten weeks will have "no effect on your Certificate of Exemption". She said that it will have an effect.
She said (and I hope I am using the proper terminologies): When the student trials a school they will enrol there, and that enrolment information will be sent to the Ministry, which will then record that the student is registered at that school. It is not possible for a student to be both registered at a school and also have an exemption certificate, so the exemption will immediately be deactivated. If, within the ten weeks, the student decides not to continue at that school the school will notify the Ministry and the student's school registration will be deleted. But the exemption will not be automatically reactivated. The student must then contact the Ministry within the ten weeks to ask for the exemption to be reactivated (if it is after the ten weeks then the exemption cannot be reactivated and the student must apply for a new exemption).
Given all of this, I am inclined to think it best to not pursue the idea of the girls trialling school. While I think it would have been good for the girls to get a better understanding of school culture, as well as for the school and local community to develop deeper community interactions, I'd only want to do it with the support of the Ministry and schools.
Naturally I am disappointed for the children, but not sending them to school does mean that I'll have less work to do now!
The quick reason that we homeschool the girls is that it works for us. Our teaching them has been ongoing from their births; it is the default option. Why change to a different system when the current system is working successfully?
What helps make it work for us is:
- We have enough financial security that I can treat it as an (unpaid) job,
- I have a solid educational background to know what and how to teach,
- My personality suits working with children, and I enjoy it,
- We also have expertise in subjects that we think are important, but are generally not taught in schools (such as Chinese, critical thinking and moral education).
So, I am all in favour of more interaction between homeschoolers and registered schools.
So, while preparing the exemption application for Miya a few months ago, I was very interested to see on the New Zealand Ministry of Education website a section about trialling school. This is what it says:
Trialling a school
Home educated students may trial attending a school. For more information about this process, contact your local Ministry office.
Your Certificate of Exemption and home education supervision allowance may be impacted, depending on how long your child attends school:
- 0-28 days – no effect on your Certificate of Exemption or allowance
- 29 days – 10 weeks – no effect on your Certificate of Exemption, but your allowance will be reduced, based on the length of time that your child was attending school
- More than 10 weeks – your Certificate of Exemption will cease. If you want to go back to home educating your child you will need to apply for a new Certificate of Exemption.
I thought, what a great idea, homeschool children can trial attending school. They can learn what attending school is like, and so have a better understanding of what most children experience. Since school life is so ingrained into our culture, giving homeschoolers a time at school can allow them to enter into local mainstream culture in a more direct and personal way.
This can also be an awesome bridge between the homeschooling community and the registered school community -- shared experiences, better communication, closer relationships and improved community interactions. As I see it, anything that improves community relations is surely a good thing.
So, I made contact with our local primary school, Takapuna Primary, introduced ourselves, explained what I had found on the Ministry of Education website, and briefly explained my thinking as above.
I got a very positive email back from the Principal of Takapuna Primary, who was very welcoming of us. We both agreed that it would make sense for this to happen at the beginning of the new school year in 2017, and we would make contact again in November when they had sorted out which teachers would be teaching which classes.
Since the Ministry of Education website said to contact the local Ministry office for more information, I sent them an email today, also explaining my thinking.
Within a couple of hours I got a phone call from the person at the local Auckland Ministry office who is in charge of working with homeschoolers (no need to give names).
If I had to describe her manner on the phone, I would say that she was adversarial rather than cooperative. As I see it, a cooperative conversation is one in which the other person's ideas are always treated charitably -- seen in the best possible light and in their strongest way -- to work together to jointly find the best solution. An adversarial conversation is one in which one tries to beat the other, using rhetorical strategies such as misdirections and uncharitable interpretations. Words and meanings get twisted to one-up the other, and the truth can get lost in the struggle.
But despite the adversarial nature of the conversation, I learnt a few things from it.
Firstly, and most tellingly, she said that the nature of the homeschooling exemption is that it is a complete opting out of the state education system. Consequently, the state has no responsibility to assist in any way with the educational needs of homeschoolers. Moreover, she seemed to go so far as to imply that this meant that it was inappropriate for the state to help in this way, perhaps even to the point of it being offensive to suggest it.
I think she was treating schooling as an all-or-nothing concept. Either the children enrol at a registered school, and in which case they are required to attend for the long term. Or they get an exemption, and then the family unit is entirely on its own, using its own resources. No middle ground, and no cooperation or interaction.
My armchair sense of this is that it is surely not in the best interests of either the children or society. But I would be interested in her reasoning for seeing education in this absolutist way. (I wonder if her political orientation is more lone horseman than Amish?)
Secondly, she emphasised that the policy of trialling a school was intended only for students who were intending to continue on at that school. It was not intended for students trialling it for the purposes I was suggesting.
I can accept that, though I am puzzled why that was not made clear on the website.
But more importantly, just because something is originally intended for one purpose, there is no reason to think that it cannot be used for other purposes also, and especially if those other purposes are good.
To put it more directly, just because a policy was intended for children planning to return to a registered school, it doesn't necessarily mean that it can't be also used by those who want to trial school for other reasons. Pointing out the original intent doesn't necessarily exclude my idea.
In the course of the 12-minute conversation, she raised an objection that if the policy is opened up to other purposes, then homeschoolers will take advantage of it and there will be too many homeschoolers overburdening schools, and with many doing it for the wrong reasons. She gave two possible wrong reasons homeschoolers might use: (a) lazy parents wanting a break, and (b) lazy parents wanting to use it for "socialisation", when they should be providing opportunities for their child's socialisation themselves.
Her argument is very weak:
- I doubt that many homeschoolers would be that interested in sending their children to school for a short time -- many, if not most, homeschool parents who I have talked with have withdrawn their children precisely because their children were having problems in school.
- It is unlikely to be the case that sending children to school for a term would give caring homeschool parents a break. If anything, there would be more parental work involved in preparing them beforehand, as well as helping them throughout to adjust to a different environment and system.
- The "socialisation" thing is really not a thing for homeschoolers. When she implied that my real, more selfish, underlying, reason for wanting to send my children to school was to provide them with "socialisation", I listed out some of the regular social activities we do -- ballet, swimming, music, art, athletics, tennis, critical thinking, Chinese, basketball, netball ...
Thirdly, she directly contradicted the Ministry website regarding the effect trialling at school will have on the exemption. Note above that the website says that trialling school for under ten weeks will have "no effect on your Certificate of Exemption". She said that it will have an effect.
She said (and I hope I am using the proper terminologies): When the student trials a school they will enrol there, and that enrolment information will be sent to the Ministry, which will then record that the student is registered at that school. It is not possible for a student to be both registered at a school and also have an exemption certificate, so the exemption will immediately be deactivated. If, within the ten weeks, the student decides not to continue at that school the school will notify the Ministry and the student's school registration will be deleted. But the exemption will not be automatically reactivated. The student must then contact the Ministry within the ten weeks to ask for the exemption to be reactivated (if it is after the ten weeks then the exemption cannot be reactivated and the student must apply for a new exemption).
Given all of this, I am inclined to think it best to not pursue the idea of the girls trialling school. While I think it would have been good for the girls to get a better understanding of school culture, as well as for the school and local community to develop deeper community interactions, I'd only want to do it with the support of the Ministry and schools.
Naturally I am disappointed for the children, but not sending them to school does mean that I'll have less work to do now!
Wednesday, 28 September 2016
Using a nonsense maths question
On Monday, the children and I had an excellent maths / critical thinking lesson, based around a couple of YouTube videos that had popped up on my YouTube homepage. (You know how it is -- you watch a few videos on a topic, and then YouTube suggests more videos on the same theme.)
The first video showed up because I had been watching Sal of Khan Academy introduce Common Core (the US maths standards) in a series of videos. YouTube then suggested lots more videos about Common Core, including this one.
In the 3-minute video, the authors introduce a maths question, which they claim is a US 4th Grade Common Core question, asking a few "random people on the street" to have a go at answering it.
Of course, it is all fun and funny, because the random people fail completely. These stereotypically-standard middle-class USers flounder around with half-starts and guesses to a question supposedly for 9-year-olds. Most finally give up and conclude that the question doesn't have enough information to be meaningful -- that it is a nonsense question.
While nothing is said directly by the video authors, I assume they are trying to imply that Common Core is Bad and Wrong, as it includes crazy nonsense questions like this one that no normal adult could answer.
I am not going to get into a discussion here about whether this question is a genuine one, or a genuine Common Core one, or whether Common Core is Bad and Wrong.
What I want to do here is show that the question asked in the video is actually an excellent question to ask children, and it can form the basis of an excellent lesson. In my opinion, it is definitely not a worthless question.
If you haven't clicked on the YouTube link above, here is the question:
A lot of 4th Grade maths work is about getting familiar with using the basic multiplication and division facts, and learning to divide by one-digit numbers with and without remainder. Word problems verbally similar to this one are introduced to check that the students understand the meanings behind the equations (one of the big aims of Common Core is to ensure understanding, not just rote memorisation).
But there are a few weird things about this particular question:
So, knowing that this was a weirdly-worded question, albeit structurally similar to questions that Mulan is familiar with, I introduced the question to her and Miya, then sat back and waited to see what they would do.
Just like the adults in the video, Mulan wanted to know how many friends Juanita has. She puzzled for a while over the ambiguity of bags/stickers, as well as the 4 or 6 bag thing.
But then Mulan came up with her own solution, and one that I hadn't thought of.
Mulan said that Juanita could rip the stickers to divide them evenly among her friends. Then they could draw in the other parts themselves. So, it really didn't matter how many stickers she bought or how many friends she has.
This solution is typical Mulan, seeing sharing, compromises and communal DIY pen-and-paper activities as the way to go. She would not see it as important to buy more of something to make it even between everyone, but just jointly use whatever they have got to keep things fair.
I immediately agreed. Solution number 1.
But then I challenged Mulan further by adding a new requirement that they want to keep the stickers whole and so won't rip them.
At this point the three of us discussed it together for a few minutes. I can't remember exactly what any of us said, but one thing I did want to emphasise to both Mulan and Miya was the importance of not being fooled by distracting information.
We observed together that the 4 or 6 bag point was not phrased as a definite requirement, but simply that Juanita was unsure of what to do. I hoped the girls would see that people can easily get into the habit of scanning a maths question for numbers and then thinking that any number mentioned must be part of the calculations. But it need not be; extra, unnecessary numbers may be sneakily put in to test our understanding of the question. And we all agreed that the 4 or 6 bags thing was surely there as a distraction.
Mulan then returned to the problem of the missing information about how many friends there were. She said that, since she couldn't rip the stickers, she would buy as many stickers as there were friends.
I then suggested that we could let x stand for the number of friends that Juanita has. Mulan quickly caught on, and said that then she could buy multiples of x stickers.
Solution number 2.
I then said that there was one more possible solution that I could see. When they stalled, the girls asked for a hint. So, I directed them to the idea that there is one number of stickers in which there will always be no remainder, no matter how many friends there are.
Still no bites. So I wondered out loud if it is always necessary to buy things.
At that, Mulan's grin grew wider with understanding, and she said that Juanita could buy 0 stickers. 0 stickers divided by any number of friends will always have 0 remainder.
Solution number 3.
Mulan liked the question so much that she wrote it out by hand to show the cousins.
Yesterday, with great delight, Mulan and Miya presented the question to two of their cousins (ages 11 and 9). Without any adult initiation or involvement at all, the four of them discussed it together in a very systematic way. I didn't catch all of the conversation, but I overheard Mulan clearly and accurately articulating the points that we had made the day before.
At the same time, I asked the question to Mama. Mama immediately said that Juanita could buy all the stickers in the shop. After all, there would then be no stickers left over in the shop.
Brilliant. Solution number 4.
When our two discussion groups came back together, I pointed out Mama's new solution. 11-year-old cuzzie immediately said that she had said the same thing.
So, there you have it. Excellent discussions and four possible solutions from a maths question that at first glance looked like silly nonsense.
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The second YouTube video we watched on Monday was this one from Derren Brown.
For those who don't know, Derren Brown is a UK TV personality who has been doing TV shows for several years centred around hypnotism, mind reading, etc, but from a psychological / scientific perspective. After the impressive trickery, he points out some of the main psychological techniques.
This particular video that I showed to the girls showed up the unconscious aspects of advertising. (I thought it fitted in with the theme of appearances and question misdirections.) It is pretty impressive. I highly recommend it.
After watching the video, Mulan made the connection between this and the political advertising that we are seeing around our home these days (local body elections). This then turned into a discussion about how the politicians use advertising to try to influence us unconsciously to vote for them.
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UPDATE 29/10/2016: I see over at Math Mammoth they mention this question (Example 2 in the section titled Bad examples of "common core" or "new math").
They focus on the 4 or 6 bags of stickers sentence, linking to a conversation on The Math Forum and agreeing with Bart Goddard, who writes:
While I can see that this is one possible interpretation of the situation -- that the reason she is not sure how many bags she needs is because she is friends with unreliable twins -- I think it is important to remember that this was not what was actually written there.
What they have done is give a possible interpretation, which includes additional made-up information that has consequently constrained their answer. But this possible interpretation is not a necessary one (Juanita's uncertainty may have been for other reasons than what they have presumed), and so the constraints they put on the answer are also not necessary.
To put it another way, I think it is important to always read exactly what is written in a question, and not invent extra requirements through our own presumptions and interpretations. The Math Mammoth answer is wrong because it adds requirements and constraints which were not part of the question, as written.
The first video showed up because I had been watching Sal of Khan Academy introduce Common Core (the US maths standards) in a series of videos. YouTube then suggested lots more videos about Common Core, including this one.
In the 3-minute video, the authors introduce a maths question, which they claim is a US 4th Grade Common Core question, asking a few "random people on the street" to have a go at answering it.
Of course, it is all fun and funny, because the random people fail completely. These stereotypically-standard middle-class USers flounder around with half-starts and guesses to a question supposedly for 9-year-olds. Most finally give up and conclude that the question doesn't have enough information to be meaningful -- that it is a nonsense question.
While nothing is said directly by the video authors, I assume they are trying to imply that Common Core is Bad and Wrong, as it includes crazy nonsense questions like this one that no normal adult could answer.
I am not going to get into a discussion here about whether this question is a genuine one, or a genuine Common Core one, or whether Common Core is Bad and Wrong.
What I want to do here is show that the question asked in the video is actually an excellent question to ask children, and it can form the basis of an excellent lesson. In my opinion, it is definitely not a worthless question.
If you haven't clicked on the YouTube link above, here is the question:
Juanita wants to give bags of stickers to her friends. She wants to give the same number of stickers to each friend. She is not sure if she needs 4 bags or 6 bags of stickers. How many stickers could she buy so there are no stickers left over?For those of us who have recently been doing maths at around the 4th Grade level, the question seems structurally pretty familiar. There are stickers and there are friends, and we want to share the stickers evenly between the friends and have no stickers left over.
A lot of 4th Grade maths work is about getting familiar with using the basic multiplication and division facts, and learning to divide by one-digit numbers with and without remainder. Word problems verbally similar to this one are introduced to check that the students understand the meanings behind the equations (one of the big aims of Common Core is to ensure understanding, not just rote memorisation).
But there are a few weird things about this particular question:
- We don't know how many friends she has.
- We don't know the relationship of bags to stickers -- is Juanita buying stickers and then putting them into her own bags, or is she buying bags of stickers directly?
- How does the 4 or 6 bags fit in?
So, knowing that this was a weirdly-worded question, albeit structurally similar to questions that Mulan is familiar with, I introduced the question to her and Miya, then sat back and waited to see what they would do.
Just like the adults in the video, Mulan wanted to know how many friends Juanita has. She puzzled for a while over the ambiguity of bags/stickers, as well as the 4 or 6 bag thing.
But then Mulan came up with her own solution, and one that I hadn't thought of.
Mulan said that Juanita could rip the stickers to divide them evenly among her friends. Then they could draw in the other parts themselves. So, it really didn't matter how many stickers she bought or how many friends she has.
This solution is typical Mulan, seeing sharing, compromises and communal DIY pen-and-paper activities as the way to go. She would not see it as important to buy more of something to make it even between everyone, but just jointly use whatever they have got to keep things fair.
I immediately agreed. Solution number 1.
But then I challenged Mulan further by adding a new requirement that they want to keep the stickers whole and so won't rip them.
At this point the three of us discussed it together for a few minutes. I can't remember exactly what any of us said, but one thing I did want to emphasise to both Mulan and Miya was the importance of not being fooled by distracting information.
We observed together that the 4 or 6 bag point was not phrased as a definite requirement, but simply that Juanita was unsure of what to do. I hoped the girls would see that people can easily get into the habit of scanning a maths question for numbers and then thinking that any number mentioned must be part of the calculations. But it need not be; extra, unnecessary numbers may be sneakily put in to test our understanding of the question. And we all agreed that the 4 or 6 bags thing was surely there as a distraction.
Mulan then returned to the problem of the missing information about how many friends there were. She said that, since she couldn't rip the stickers, she would buy as many stickers as there were friends.
I then suggested that we could let x stand for the number of friends that Juanita has. Mulan quickly caught on, and said that then she could buy multiples of x stickers.
Solution number 2.
I then said that there was one more possible solution that I could see. When they stalled, the girls asked for a hint. So, I directed them to the idea that there is one number of stickers in which there will always be no remainder, no matter how many friends there are.
Still no bites. So I wondered out loud if it is always necessary to buy things.
At that, Mulan's grin grew wider with understanding, and she said that Juanita could buy 0 stickers. 0 stickers divided by any number of friends will always have 0 remainder.
Solution number 3.
Mulan liked the question so much that she wrote it out by hand to show the cousins.
Yesterday, with great delight, Mulan and Miya presented the question to two of their cousins (ages 11 and 9). Without any adult initiation or involvement at all, the four of them discussed it together in a very systematic way. I didn't catch all of the conversation, but I overheard Mulan clearly and accurately articulating the points that we had made the day before.
At the same time, I asked the question to Mama. Mama immediately said that Juanita could buy all the stickers in the shop. After all, there would then be no stickers left over in the shop.
Brilliant. Solution number 4.
When our two discussion groups came back together, I pointed out Mama's new solution. 11-year-old cuzzie immediately said that she had said the same thing.
So, there you have it. Excellent discussions and four possible solutions from a maths question that at first glance looked like silly nonsense.
---
The second YouTube video we watched on Monday was this one from Derren Brown.
For those who don't know, Derren Brown is a UK TV personality who has been doing TV shows for several years centred around hypnotism, mind reading, etc, but from a psychological / scientific perspective. After the impressive trickery, he points out some of the main psychological techniques.
This particular video that I showed to the girls showed up the unconscious aspects of advertising. (I thought it fitted in with the theme of appearances and question misdirections.) It is pretty impressive. I highly recommend it.
After watching the video, Mulan made the connection between this and the political advertising that we are seeing around our home these days (local body elections). This then turned into a discussion about how the politicians use advertising to try to influence us unconsciously to vote for them.
---
UPDATE 29/10/2016: I see over at Math Mammoth they mention this question (Example 2 in the section titled Bad examples of "common core" or "new math").
They focus on the 4 or 6 bags of stickers sentence, linking to a conversation on The Math Forum and agreeing with Bart Goddard, who writes:
Presumably she's giving one bag to each friend (although this is a bit ambiguous, too) so she is expecting either 4 or 6 friends to show at the meeting. (I suppose that there's a set of twins who have a habit of not RSVP-ing, but crashing the party anyway.)This means that they treat the question as a common multiple one. Since common multiples of 4 and 6 are 12, 24, 36, ..., they think that any multiple of 12 is the correct answer.
While I can see that this is one possible interpretation of the situation -- that the reason she is not sure how many bags she needs is because she is friends with unreliable twins -- I think it is important to remember that this was not what was actually written there.
What they have done is give a possible interpretation, which includes additional made-up information that has consequently constrained their answer. But this possible interpretation is not a necessary one (Juanita's uncertainty may have been for other reasons than what they have presumed), and so the constraints they put on the answer are also not necessary.
To put it another way, I think it is important to always read exactly what is written in a question, and not invent extra requirements through our own presumptions and interpretations. The Math Mammoth answer is wrong because it adds requirements and constraints which were not part of the question, as written.
Friday, 23 September 2016
Maths update: Khan Academy
Every once in a while I like to write a post on what we are doing with our maths. It is useful to keep a record of where we are at, at specific moments in time. And who knows, it may be helpful for the one or two readers who happen upon this blog.
Both Mulan and Miya signed up at the online Khan Academy just over a year ago. We played with it at the time, and for several months afterwards they did the odd day dotted here and there. But just over three months ago, in mid-June, we started working on it more seriously, using it daily as our primary maths resource.
What follows is our experience of Khan Academy, used as a main maths resource for two primary-aged children.
For those who are unfamiliar with Khan Academy, it is a free online educational resource with several different subjects, but primarily focused on maths.
The maths at Khan can either be approached by subject (ie topic) or by US grade. Each subject or grade level contains dozens of different skills (grouped together by type), with questions for each skill. Skills are Practiced (by answering correctly a few questions specific to that skill) and then eventually Mastered (by answering correctly questions for that skill when presented together with questions from several other skills). Progress is made by completing a combination of Practices and Masteries. Once all skills for a particular subject or grade have been Mastered, then that subject or grade is completed.
Most skills are also linked to a short video lesson, of a few to several minutes, which teaches that skill.
Incentives are given in at least five different ways: (a) daily login acknowledgement and a count of the daily "streak", (b) points awarded for questions answered, (c) leveled mastery progress for each skill, (d) percentage progress for each section, and (e) "badges" awarded for achievements.
Mulan (9 1/2 years old):
When we first started on Khan, we headed for the subject section rather than the US grade section because, well, we are not in the US and have no special attachment to their schooling system. The "Arithmetic" subject section looked interesting, so we tackled that first.
We got into a routine of logging in every day and working on it for maybe about 45 minutes or so. Almost always, I sit beside Mulan as she works on the questions. If she has any problems, I step through them with her, discussing and explaining as needed.
Occasionally (maybe once every week or two), we watch a video lesson. Typically, we will watch a video if either (a) we are not completely sure of the question meaning or terminologies, or (b) we want a second opinion on how to solve a problem. As we watch the video we typically stop and start as needed to discuss together what is being presented.
In our opinion, the videos are clear and teach the points well. They are definitely a useful, though minor, supplement to our in-person teaching, and they give us confidence that we are on the right track with what we are doing. Occasionally, however, we feel that the way they have taught things in certain videos is not the easiest way of solving some problem. So, while we watch and understand their approach, we sometimes choose to solve problems differently.
At about two thirds of the way through the "Arithmetic" section, Mulan got to the point where the going was getting too tough. It had reached her limit. So, since we were still enjoying Khan, we looked around the website and decided to give the US grade sections a go.
We figured at the time that if Mulan was in the US, she would probably be coming to the end of 3rd Grade, so we turned to that section. After having been struggling with the Arithmetic section, Mulan found the 3rd Grade extremely easy, and completed it all within a couple of weeks.
Next, we moved on to 4th Grade, and Mulan finished all of that within another couple of weeks. With both the 3rd and 4th Grades, Mulan almost never needed my (or the videos') help on anything. Nonetheless, I have no doubt that she was learning a lot, and it gave her a good solid skills base as well as a lot of confidence.
At the beginning of August, Mulan started Khan's 5th Grade. Getting into this section, we felt that this was more properly her level. It was challenging, but often doable by herself. Anything that I explained to her was almost always immediately understood and internalised.
Mulan finished 5th Grade within about five weeks, and a couple of weeks ago she returned to the Arithmetic section. With a few more months of maths tuition under her belt, Arithmetic was no longer beyond her abilities. And today, Mulan completed the Arithmetic section and started on the 6th Grade section.
We are not sure how much longer Mulan will be able to continue with 6th Grade before she reaches her limit, but we will keep going with it every day and just see what happens.
Miya (6 years old):
There is not nearly as much work available on Khan for Miya's level as there is available for Mulan's level, and Miya has very quickly reached her limit.
In the US grade section, there is one section called K-2nd. This is exactly equivalent to the "Early Math" subject section. Miya completed 80% of this, before reaching her limit.
At the moment, and since Miya still likes to do a bit every day to keep her daily streak going, Miya logs in and re-Practices, for several minutes, a few skills that she has already Mastered. As I see it, it is all good, as it keeps her numeracy skills up. But it would be much better if Khan Academy extended and developed the questions for younger learners.
---
Some final thoughts:
Both Mulan and Miya signed up at the online Khan Academy just over a year ago. We played with it at the time, and for several months afterwards they did the odd day dotted here and there. But just over three months ago, in mid-June, we started working on it more seriously, using it daily as our primary maths resource.
What follows is our experience of Khan Academy, used as a main maths resource for two primary-aged children.
For those who are unfamiliar with Khan Academy, it is a free online educational resource with several different subjects, but primarily focused on maths.
The maths at Khan can either be approached by subject (ie topic) or by US grade. Each subject or grade level contains dozens of different skills (grouped together by type), with questions for each skill. Skills are Practiced (by answering correctly a few questions specific to that skill) and then eventually Mastered (by answering correctly questions for that skill when presented together with questions from several other skills). Progress is made by completing a combination of Practices and Masteries. Once all skills for a particular subject or grade have been Mastered, then that subject or grade is completed.
Most skills are also linked to a short video lesson, of a few to several minutes, which teaches that skill.
Incentives are given in at least five different ways: (a) daily login acknowledgement and a count of the daily "streak", (b) points awarded for questions answered, (c) leveled mastery progress for each skill, (d) percentage progress for each section, and (e) "badges" awarded for achievements.
Mulan (9 1/2 years old):
When we first started on Khan, we headed for the subject section rather than the US grade section because, well, we are not in the US and have no special attachment to their schooling system. The "Arithmetic" subject section looked interesting, so we tackled that first.
We got into a routine of logging in every day and working on it for maybe about 45 minutes or so. Almost always, I sit beside Mulan as she works on the questions. If she has any problems, I step through them with her, discussing and explaining as needed.
Occasionally (maybe once every week or two), we watch a video lesson. Typically, we will watch a video if either (a) we are not completely sure of the question meaning or terminologies, or (b) we want a second opinion on how to solve a problem. As we watch the video we typically stop and start as needed to discuss together what is being presented.
In our opinion, the videos are clear and teach the points well. They are definitely a useful, though minor, supplement to our in-person teaching, and they give us confidence that we are on the right track with what we are doing. Occasionally, however, we feel that the way they have taught things in certain videos is not the easiest way of solving some problem. So, while we watch and understand their approach, we sometimes choose to solve problems differently.
At about two thirds of the way through the "Arithmetic" section, Mulan got to the point where the going was getting too tough. It had reached her limit. So, since we were still enjoying Khan, we looked around the website and decided to give the US grade sections a go.
We figured at the time that if Mulan was in the US, she would probably be coming to the end of 3rd Grade, so we turned to that section. After having been struggling with the Arithmetic section, Mulan found the 3rd Grade extremely easy, and completed it all within a couple of weeks.
Next, we moved on to 4th Grade, and Mulan finished all of that within another couple of weeks. With both the 3rd and 4th Grades, Mulan almost never needed my (or the videos') help on anything. Nonetheless, I have no doubt that she was learning a lot, and it gave her a good solid skills base as well as a lot of confidence.
At the beginning of August, Mulan started Khan's 5th Grade. Getting into this section, we felt that this was more properly her level. It was challenging, but often doable by herself. Anything that I explained to her was almost always immediately understood and internalised.
Mulan finished 5th Grade within about five weeks, and a couple of weeks ago she returned to the Arithmetic section. With a few more months of maths tuition under her belt, Arithmetic was no longer beyond her abilities. And today, Mulan completed the Arithmetic section and started on the 6th Grade section.
We are not sure how much longer Mulan will be able to continue with 6th Grade before she reaches her limit, but we will keep going with it every day and just see what happens.
Miya (6 years old):
There is not nearly as much work available on Khan for Miya's level as there is available for Mulan's level, and Miya has very quickly reached her limit.
In the US grade section, there is one section called K-2nd. This is exactly equivalent to the "Early Math" subject section. Miya completed 80% of this, before reaching her limit.
At the moment, and since Miya still likes to do a bit every day to keep her daily streak going, Miya logs in and re-Practices, for several minutes, a few skills that she has already Mastered. As I see it, it is all good, as it keeps her numeracy skills up. But it would be much better if Khan Academy extended and developed the questions for younger learners.
---
Some final thoughts:
- Since Khan is an online teaching resource, the questions asked have got to have clearly answerable questions that can be marked unambiguously by a computer. And it is pretty hard to mark open-ended discussions. This means that I sometimes feel that, for a maths resource, too many of the questions are equation-style and too few are problem-solving style. This is not only the case from a balanced teaching perspective, but it is also the case from a student-interest perspective -- Mulan is becoming a little bored with too many straight equations, and is not so keen to be bothered answering them.
- Khan Academy is clearly from the US. It uses US spelling, US school grade levels, US non-metric measurements, US maths terminologies (such as reversing trapezoid and trapezium), US money, US education standards (Common Core), and US cultural references in questions. While it is understandable who their market is, it is still disappointing that there is little attempt to provide a more international feel.
- Given that Mulan completed entire grades at her age level in a couple of weeks, and both girls are reaching their limit within a few months of daily use, it is clearly the case that Khan Academy has too few questions to last as a daily long-term maths resource.
Sunday, 11 September 2016
Solo dad
I've been trialling being a solo parent (again) these last few days.
Don't fear, Mama and I haven't split. But Mama is on the opposite side of the world at the moment.
Laolao's (Mama's mama) cancer has returned, so it is back to the hospital for another operation. On Tuesday, Mama went up to Beijing to be with Laolao, while the children and I stayed back home. Mama will probably be there for a couple of weeks until Laolao has recovered from the surgery.
So far, the children and I are surviving okay without Mama. The main daily-life things I have noticed are:
Other than that, our life is continuing much as before, with lessons, outings to classes, meals and play.
More importantly, I hear that Laolao's operation went smoothly, and she is recovering well.
Don't fear, Mama and I haven't split. But Mama is on the opposite side of the world at the moment.
Laolao's (Mama's mama) cancer has returned, so it is back to the hospital for another operation. On Tuesday, Mama went up to Beijing to be with Laolao, while the children and I stayed back home. Mama will probably be there for a couple of weeks until Laolao has recovered from the surgery.
So far, the children and I are surviving okay without Mama. The main daily-life things I have noticed are:
- Mama usually organises dinner, and it is at that time of the day that I am most tired and like to rest on my own. Without Mama, I have to keep going and force myself through my tiredness to do dinners. Consequently dinners are fairly quick, easy and unimaginative -- steamed greens, boiled potatoes/kumara/carrot/pumpkin, eggs/canned fish, canned soup, etc.
- Miya still likes to come into the big bed during the night, sleeping with Mama. Without Mama in the bed, Miya is with me, and she does like to wriggle around. Too often I get kicked awake, and these days I am waking in the morning not nearly as refreshed as I'd like to be.
- Mama teaches most days here at home, so without students coming and going things are a lot quieter and more relaxed. But on the downside, we are also getting less money coming in.
Other than that, our life is continuing much as before, with lessons, outings to classes, meals and play.
More importantly, I hear that Laolao's operation went smoothly, and she is recovering well.
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