The Little Mermaid

A small part of Mulan and Miya's recent ballet performance, The Little Mermaid, is now up on YouTube here.

Mulan's solo starts at 10 min 27 sec.  Some of both girls' group dances are also there.

Sewing and ukulele/guitar

After music, art, basketball, ballet, swimming and athletics, our next two outside activities to finish for the year were sewing and ukulele/guitar.

But in case you were wondering how we can afford to pay for so many classes, these ones were free, taught by the grandparents, Nainai and Yeye.  On Saturday, at our family Christmas party, they showed us all what they have been doing.

This term, Nainai has been teaching the girls hand sewing for an hour each week.  They have been making table mats, cutting and edging the material and then sewing designs.  It is still a work in progress, and they will continue with it next year.  I hear terms thrown around like blanket stitch, cross stitch, chain stitch, and so on, and it is all coming together very nicely.  Mulan is putting her name in each corner (English and Chinese), and will do some more designs in the middle.  Miya is working on a picture of our cat, Kitty, and will also add a picture of our other cat, Maggie.

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In addition to their weekly music lessons at Belmont Music Centre, the girls are also learning ukulele and guitar from Yeye.

Both Mulan and Miya did some introductory ukulele at Belmont, but once they got beyond what was being taught there Yeye took over.  This term, Yeye has been giving them each a 30-minute individual lesson once a week.

At our Christmas party, the three of them played some songs together.  Very nice!

Swimming and athletics

And the next activity to finish for the year was swimming.  (After music, art, basketball and ballet.)

Mulan and Miya have both, for the past two years, been having weekly 30-minute lessons at Swim Lovers' Swim School in Belmont.  The owner and main teacher, Jean, is awesome with the kids.  She is the main reason that we go there.

When we first started two years ago, Mulan was able to float and bob around and put her head under the water, but that was about it.  Now, she has a beautiful freestyle stroke, can confidently do backstroke and breaststroke, and is improving well with butterfly.

As for Miya, two years ago she was a complete beginner who wasn't even putting her face under the water.  Now, she can do a few breaths with her freestyle, and has almost clicked with being able to keep going.  Her backstroke is very good, and she is working on dolphin kick.

I think swimming is one of those essentials that all children should learn when they are young.  It is such an important skill to have in life.

I also think it is important to learn swimming in a steady, long-term way.  I noticed in China that many Chinese parents send their children to swimming lessons in a short intensive burst, such as daily over a single school holiday.  Then they treat it as if they don't need to keep going after that, as the child seemingly then knows how to swim.  I think that is a mistake, as I think only with the steady, long-term learning can a child truly pick up how to swim properly.

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Mulan, Miya and I are all members of Takapuna Athletics Club.  This is the girls' second season there, while I have been there on and off since I was ten.

Clubnights are on Wednesday evenings.  Occasionally we also do athletics training sessions (Mondays with the club or Tuesdays as a family), though this season we have done very little extra training as we have been too busy with other things.

I had thought that we had one more clubnight next Wednesday 21st (with fun, non-points events), but it seems that sadly they have stopped doing the fun end-of-year special evening this season.  The final clubnight was this week, though we didn't attend it as it was the evening of the girls' ballet performance.

As I say, I started athletics when I was ten.  It was my main sport as a child, and I used to train for it for a couple of hours every day as a teenager.  I got to the point where I was competing at a national level, and I got three New Zealand national championship medals in the triple jump.  But then injuries, which I still have today, forced me to stop competing when I was 22.

These days, I still hobble around the track as best I can, trying to be a good role model for the kids (and reliving my youth!).  Last year I broke the club long jump record for veteran (over 40s) men, jumping 5.57 metres.  Not bad considering it was done with almost no training and having not seriously competed in almost 20 years!  This year I have had even more aches and pains, and haven't been able to do as much as I would like.

Athletics is the sort of sport where it is easy to compare people with each other, with exact times, distances and rankings.  So, it is easy to see how Mulan and Miya compare with others their ages.  It is also the sort of sport where natural talent plays a big part, and for many children, no amount of training, with either fitness or technique work, will jump them up to the top ranks.

But I emphasise to the girls that athletics is just as much about personal achievement as it is about comparing ourselves to others.  While it is nice to think about placings, if the children are doing the best they can at each moment, and making regular improvements in their times/distances, then that is the most important thing (and that they are enjoying it!).  So, each week we write down our times and distances after our events, putting them on the computer to see how they improve over time.  (It also works as a good computing and maths lesson!)

Having said that, outside of club athletics, Mulan and Miya aren't bad runners, seeming to be faster than most their age.  At our local club, they both come about in the middle of their grades for all the running events.

Field events are more about technique, and both girls have been working on getting the right movements.  Mulan's discus is starting to look very smooth, and she is generally in about the top three at the club.  She is also doing pretty well in the long jump, with the occasional win and in the top three or so.  Miya, at Grade 6, isn't officially doing any field events, but with our family practices she is beginning to get the hang of the field event movements.

While it is clear that athletics is unlikely to be the girls' main sport, I think it is a good sport to keep doing.  I think the sorts of body movement skills taught, for both track and field events, are extremely useful for many areas of life.  Equally importantly, we are all enjoying it.

Ballet

I wrote before about how our music, art and basketball activities finished for the year.  Next to finish was ballet, which had its final event last night.

Mulan is an old hand at ballet.  When she was three she decided that ballet was her thing, and she had her first lesson at 3 1/4.  She started having regular classes just before her fourth birthday, and has been doing it ever since.

Here in New Zealand, since Term 2 of last year, Mulan has been having lessons twice a week at Ballet Theatre of Auckland.  The teacher, Estelle, is brilliant -- both really wonderful with the children and also very experienced at ballet.  Knowing how pushy ballet can be, I have been delighted to read Estelle's posts on BTOA's Facebook page about being sensible with stretching and training, and not overdoing things.  Having also watched some lessons, I feel I can trust Estelle to get the right balance in training.

In the third term this year, Mulan sat the Grade 3 Cecchetti exam, gaining honours.  Last year she sat the Grade 2 exam, also gaining honours.

After watching Mulan for many years, Miya decided at the beginning of this term that she also wanted to do ballet.  And she is loving it.

This term, the focus for BTOA has been their production of The Little Mermaid, and for the past couple of months we have been going to practices three times a week.

Finally, last night, at The Rose Centre in Belmont, they performed the show.  In my admittedly very biased opinion, it was excellent -- very professionally done and very enjoyable to watch.  All the girls did an awesome job.

The main parts of the show were performed by a few of Estelle's teenage students, who all look like they have several years of experience.  They dance en pointe, and are very elegant.

Mulan is one of half a dozen pre-teen grade-level students.  During the show they performed a few dances together in a group.  Mulan was the only grade-level student who also had a solo dance in the performance, where she danced during the wedding scene.

Miya was one of four pre-grade students.  They also danced a couple of dances together in a group, all looking very cute.

What else can I say, but I had a very proud daddy moment, watching both my girls performing so beautifully up on stage.  Well done to both of them!

Art and basketball

As I wrote here, Mulan and Miya's music was our first activity to finish this year.

Our next two activities to finish were art and basketball, which had their last sessions yesterday.  Both of these were held at the Northcote YMCA through HASCA.

Art:
Back in China two years ago, the girls attended an art class, where they learnt about famous art works as well as created their own masterpieces.  It was well worth it, and I could see that Mulan especially picked up some good techniques during the year she attended.  (Miya was a little young, and only attended a few lessons.)

But since moving to New Zealand, the only art the girls had done had been at home.  That is, until they started an art class this term.

The girls have enjoyed the lessons, and it has been a good experience for them.  The overall theme of the course was animals, and each weekly lesson was about a different animal.

At the beginning of each lesson, the class gathered together while the teacher showed some computer printouts of artworks depicting the animal of the week.  This might range from cave drawings, to sculptures, to paintings, to tapestries, to ceramics.

While this was a nice intro, I sometimes felt that the discussions were a little on the light side.  The girls' art teacher in China had also done a similar thing, though I think they analysed the techniques more to understand better the methods used to produce the artworks shown.  In China, they also showed the artworks on a big screen computer rather than an A4 printout, meaning that they could see more detail.

After the art history intro, the class then turned to producing their own artwork.  All works were paper based.  Here is about half of the girls' work produced this term; the other half is fairly similar:

(In case you are wondering, Miya's is on the left door and Mulan's is on the right.)

While the classes were good and enjoyable, we have decided not to return in 2017.  The main reason is that we feel that we overdid things a bit this term, and we need to cut back on our outside activities.  Of the classes that we do, we feel that this has probably been the least important and the least value for money.  (For the size of the class, we feel that it is a little overpriced, when compared with other classes we do and also the classes we teach.  This art teacher is probably getting twice the hourly rate that Mama is getting.)

Basketball:
This is an activity that Mulan is doing without Miya.  She started basketball in term 3 this year, after getting dragged along there by her netball teammates.

Prior to this, Mulan had done pretty much zero basketball in her life, although she had done two seasons of netball.  So, it was a bit of an adjustment for her, learning how to bounce the ball and getting used to the faster in-your-face approach.  She has done really well, and is steadily getting the hang of the game.

Each week, Mulan does one hour of skills training followed by a 30-minute team practice and followed by a 30-minute game.  After all this, on our bike ride home Mulan often comments that her legs are pretty wobbly from all the running around.

Mulan's basketball team did very well, winning their grade competition.  Their prize-giving was last Thursday.

Mulan is loving basketball and we plan on doing it again in 2017.

Music at Belmont Music Centre

The end of the year is fast approaching, and already one of our activities has finished up for the year.  Amazingly, music lessons at Belmont Music Centre finished at the end of November.  The end-of-year concert and prize-giving was two days ago.

Mulan completed her second year at the music centre, learning first-year flute and second-year recorder.  Miya completed her first year there, learning recorder.  Both girls would like to continue learning these instruments next year, with Miya also wanting to pick up the violin.

(As well as having lessons at the Music Centre, both girls are also learning ukulele and guitar from Yeye -- these lessons haven't stopped yet.)

Four bands played on Saturday at the concert.  Mulan was in the Junior Wind Band, and played three pieces, while two of her cousins also played in bands.  It all went very well, and we were all very impressed.

At the small prize-giving after the concert, about a dozen or so children received special recognition (and a medal) for their achievements during the year.  I think I am right to say that each teacher picks out one or two students from their classes who are doing exceptionally well.  Mulan got an award for her flute and recorder, and two cuzzies got awards, too.  (It seems that Miya's first-year introductory classes don't get awards.)

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Practicing:
I think the key to the girls doing well with their music is firstly that they are enjoying it, but secondly that they practice out of class a few times each week.  When the children are enjoying it, they are happy to get their instruments out to practice.  Mostly, all I need to do with the girls is occasionally say, "how about you have a music practice after you finish this," and they will happily play their instruments for 20 or 30 minutes.  They know what they need to do, and I simply listen to them playing from another room.  (As much as they enjoy playing the music, I notice that if I don't gently remind them, they just won't get around to practicing, as they will get caught up in other activities.)

When it comes to the lessons at the music centre, it really is this sort of practice that makes the difference.  I almost always sit in on the children's classes, quietly observing what is going on, and it is very obvious to see who practices and who does not.  By the end of the year, many of the classes are very split, with the non-practicing students half a year or more behind those who practice.

Unfortunately, I don't see that the teachers are strongly encouraging out-of-class practicing.  And most parents clearly aren't helping either.  I really do think that children this age need adults to create the supporting environment for enjoyable practice to happen.  Children will rarely do it themselves, without adults first taking the initiative.

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Which music centre:
There are three other similar music centres in our local area (Glenfield, Birkdale and Mid-Bays).  We initially chose to go to Belmont Music Centre because the cuzzies go there (it is within walking distance of their home), and it is also fairly convenient for our other activities.  (It is also the music centre I went to as a child, when I learnt the recorder.)

Lately, though, we have been wondering about going to one of the other local music centres.  To put it bluntly, recently there have been some issues at Belmont which, as we see it, have not been good for learning.  And we have been wondering if other places would be better.

For us, the key practical priorities are that the children enjoy music and their learning goes well.  I understand that running a school is a complicated business (Mama was HOD of a language school in China for several years), and there can be all sorts of other management concerns, in addition to these primary purposes.  So, I can be fairly sympathetic to management that they have to balance many things, and these primary purposes can't always be completely satisfied.

But having said that, we have been a little worried about Belmont.  The main practical things for us are:

Firstly, it is essential in a school that the junior teachers are getting adequate professional development and mentoring to improve as teachers.  Teaching is not something that can simply be done if you know your subject.  Teaching is a separate skill in itself, that needs separate training.  We are concerned that the junior teachers at Belmont Music Centre are not developing as teachers, and are still unguided in classroom management, lesson planning, etc.  At the beginning of last year, I saw the previous manager getting involved with mentoring the junior teachers, by sitting in on classes and giving practical advice; clearly the previous manager was an experienced teacher and knew what to do in the classroom.  But since then, and since the current manager took over at the end of last year, I have seen no further assistance to these junior teachers.  Consequently, these teachers are stagnating as teachers, continuing to make the same mistakes, week after week, month after month.

To be clear, most of these teachers seem very nice people, and I have no reason to doubt their musical competence.  But I do think that with some of them their classroom teaching is not up to standard.  And this needs to be addressed by management.

Secondly, some of the instruments taught at the music centre are very expensive to buy.  Typically, music centres hire out decent quality instruments to students to make learning more affordable.  Unfortunately, the new management is making hiring instruments more difficult.  (a) They are suggesting that they will stop hiring out their instruments.  (b)  They are significantly putting the hiring fees up.  (c) They are stopping hiring over summer, meaning that for a couple of months each year students cannot practice.  (d) They are encouraging students to hire from private businesses that are not government subsidised (as the music centres are), meaning higher costs to learn.

Thirdly, there seems to be far too many weeks during the year in which there are no lessons.  (a) Finishing classes in November is surely too early.  (b) They have three weeks break between terms instead of the standard two.  (c) The entire third term is disrupted because of recitals, resulting in many lessons missed.  I have found that it is best not to choose classes at the 10:30 time, as these are the ones that get cancelled in favour of recitals.

Fourthly, even though theoretically the lessons are 45 minutes long, often in reality they are much shorter, with teachers starting late and/or finishing early.

Fifthly, there doesn't seem to be an adequate relief-teaching system.  On some occasions when teachers were sick, and they could not find any relief teachers, classes were lumped in together or taught by teachers who did not know the instrument being learnt.  On their website they even say that if they cannot find relievers then they reserve the right to simply cancel the class -- I find this unacceptably unprofessional, when students are paying for these classes.

But there are also several things favouring Belmont, including:

• Two of the other music centres appear to have stricter age restrictions, meaning that Miya would be too young to join their classes.
• It appears that none of the other music centres teach the recorder beyond an introduction; both Mulan and Miya want to continue with this instrument.
• We are beginning to know the good teachers at Belmont.  Three of the four classes that Mulan and Miya would be in next year are taught by teachers we trust (we have not yet met the teacher of the fourth class).  We think that the recorder teacher, Kevin, is brilliant at teaching music creativity.  He teaches an ability to play with music, creating something out of seemingly nothing.  His classes are always fun and exciting.  We also like the way the flute teacher, Susannah, teaches an awareness of the feel of a composition, understanding how the background history and composers' motivations influence the feel of the pieces as they are played.  Her classes are calmer, and, for more mature students who are prepared to sit more still, provide a good contrast to Kevin's dynamic playfulness.

Given all this, on balance we think that we will return to Belmont in 2017.  When we are in China over Christmas/New Year, we will see about buying a flute for Mulan and a violin for Miya, to avoid the whole hiring instrument unpleasantnesses.

Bullying in NZ schools

A couple of days ago, this article appeared in the local newspaper.

Apparently, about a quarter of Mulan-aged students (in maths and science) are bullied in New Zealand schools on a weekly basis.  And New Zealand is one of the worst countries in the world for bullying.

Bullying in schools has always been one (among several) of my reasons for choosing to homeschool.  So, obviously, if we are to work in with our local state school, we need to be reassured that bullying is not out of control there.  Is our local school any better (or worse!) than these averages cited in the report?

I simply don't know.

In our brief visits around schools in our area, I have always felt that the children are very nice, and I have seen no sign of bullying.  But of course that is going to be the case.  Bullying is going to happen much more subtly, in the non-observed interactions between children.

In my discussions with local homeschoolers who started with school but stopped, I have heard quite a few anecdotes from both parents and children about bullying (I hear stories from the students in the critical thinking classes I teach; I aim to create safe spaces for these children to discuss anything they want, and many are happy to talk about their school experiences).

This all leads me to wonder if it is worth the risk to send Mulan and Miya to school part time.  Will the possible advantages of getting to know what schools are like outweigh the possible disadvantages of experiencing the negative aspects of school such as bullying?

A field trip to the local state school

On Tuesday, the four of us spent two hours at our local state primary school, Takapuna Primary School (TPS), getting a guided tour of the classes and facilities by the Principal.

There are far too many interesting things that we saw in our visit to detail them all here, so I'll just pick out a few things that especially jumped out at me as noteworthy.

First off, a big thanks to Cindy Walsh, the Principal of TPS, for taking an hour out of her busy schedule to be our tour guide.  We really appreciate it.  She has been marvelous with her friendliness to us and openness to include us.

This "field trip" to the school came about as a result of my looking into how home educated children might trial school.  As it turned out, it is not possible to trial school in the sense I initially thought, but Cindy has been open to the possibility of Mulan and Miya joining in with classes at the school in some (as yet undecided) part-time sense.  So, this visit was an initial get-to-know-each-other meeting, to see if, and in what way, it might work.

I already knew the school area quite well, as I attended TPS between 1981 and 1986 (Nainai also attended there back in her day), but things have obviously changed a bit since then.

In recent years, our family has also had a few experiences inside younger children's schools, including:

• In 2009, we had a similar visit to a Montessori kindergarten in China.
• In 2010, as part of Mama's professional academic research she visited and observed several schools around Auckland, with a focus on documenting and assessing their Chinese language teaching materials to determine their needs for future textbook design.
• Last year, Mulan joined Bayswater Primary School's netball team.  Weekly practices were at the school with two of the teachers.
• For the past two years, the girls have had weekly music lessons in the classrooms at Belmont Intermediate School (through Belmont Music Centre).
• For the past two years, we have lived next door to Takapuna Normal Intermediate School.

So, while we mostly knew what to expect, it was very useful to see classes in action at our local state primary school.

On to my thoughts about the visit.

1.  The classrooms
The biggest thing about TPS that stood out for me was how the physical architecture of the place paralleled and complimented the learning structures TPS appeared to be emphasising.  That is, both the physical architecture and the learning environment emphasised a plurality of smaller parts rather than a singular, regular, clearly-defined hierarchical structure.  I'll try to explain.

As we all know, for the most part, schools have rectangular classrooms.  They are usually longer than they are wide, and have a board at one end where the teaching is mostly based at.  The schools listed above that I have seen lately all still follow this rule.

Again, as we all know, back a few generations ago, and sometimes still in my day as a pupil, in these rectangular rooms the desks, one for each student, would all face the front blackboard in rows.  The teacher would then mini-lecture from the front.  This created a regular, structural authority to the room, as the teacher was based at the front and there were no hidden corners.

When I was at TPS in the 1980s, teachers were often experimenting with different desk arrangements in these rectangular rooms, with the desks not always directly facing the front blackboard.  Desks might be in small groups facing together, or in a U-shape, or other various creative combinations.  At the time TPS was also trying out having large doors between classrooms, which could be opened to provided larger spaces for more than one class to work together.

When I did my ESOL teaching training (CertTESOL) in the early 2000s, it was suggested to us that we could "break the rules" even more, turning the class around when teaching so as not to be facing the board at all.  Teach from the back or the side of the room if we want, and get away from the authority-based structure of board teaching.  (Although interestingly, my TESOL trainers instructed us to always stand while teaching, in direct contrast to my university tutoring trainers who instructed us to always sit while teaching.)

But all of this was still within the confines of a basically rectangular classroom.

We saw on Tuesday that TPS is intentionally breaking this rectangular-classroom rule.  In recent years, they have redesigned classrooms to be extremely irregular in shape, with various-sized alcoves and partitions zigging and zagging in and out to create separate, more private learning zones, while the classrooms themselves are often overall big enough for a few classes/teachers.  Their latest room was redone last year (we saw the renovations at the time when we frequently drove/rode past the school).  In this sort of irregular-shaped classroom, there is no "front" that I could identify for a single authority to occupy (nor did I notice any panopticon-style central viewing area that could authoritatively overlook every part of the classroom.)

With this sort of classroom structure, learning can potentially happen (a little) more privately.  There can be zones of relative privacy where individuals or small groups can work (a little more) away from others.

Furthermore, within these irregular-shaped classrooms, TPS has done away with the one-desk-per-student approach.  Instead, the various learning zones have a wide variety of desk/chair styles and combinations, where the students are free to choose whatever suits their needs at the time.  There are high desks to stand at or to sit at with bar-stool style seats, as well as standard height desks/chairs, low desks/chairs, comfy seats, and floor spaces to work on the ground at.

All these zones are strewn around the classroom in a fairly natural, slightly irregular looking way.  In fact, if I had to describe it, I would say that TPS's latest modern classroom looks quite similar to a homeschooler's indoor learning environment (that is, if homeschoolers were able to get $10,000 a year per child from the government instead of $600 per year).

Learning in these sorts of classrooms is thus much more small-group based, and apparently rarely entire-class based.  A few to several different activities may be happening simultaneously, in different areas of the classroom.  What we observed is that the teacher then calls various individuals or small groups to the "workshop" (at the teacher's chair), where the students show and discuss what they have been doing and suggestions/corrections are made by the teacher.  We were informed that the senior students are even able to choose their individual classroom learning timetable, so that those who are morning-people can get their brainwork done early and those who are night owls can wait until later.

It is very interesting to see that to make this pluralistic learning environment work TPS has implemented some of what Sal Khan was talking about here, at least in the sense of on-demand learning (I have no idea if TPS is mastery-based).  Cindy mentioned that they work with Reading Eggs and Mathletics.

I only ever saw teachers addressing their entire class twice in our visit there.  Once was at the end of a lesson before morning tea, when the entire class was called to the "workshop" for a couple of minutes to get a couple of children to present their ideas to the rest of the class.  The other time was to quiet the class down when they were getting too noisy.

2.  The lessons
After our hour-long tour with Cindy through the classrooms and around the facilities, there was about 20 minutes of class time left before the 30-minute morning tea break.  Cindy suggested that we spend the time in any of the classrooms that we choose, then join the other kids out in the playground for the break.

Since no one else was making a decision, I suggested that maybe the Mulan-aged classrooms would be less suitable, as they all appeared to be midway through longer projects (and often using tablets/notebooks for their written work).  Miya quietly said that she would like to join a maths lesson we had seen at her age level that looked easy and nonthreatening, so we headed to that.

Unfortunately, when we got there they had finished maths and were instead completing a writing lesson that the teacher said they had started the day before.  But the teacher was very nice, and welcomed us in to join them.

As we were heading in, the teacher asked if Miya had done compound sentences.  I wasn't quite sure how to respond, as I didn't think that 5- or 6-year-olds would need to know that sort of jargon just yet, so I stammered out a surprised, "not explicitly."

But it turned out that it was more that they were writing a few to several sentences about something that they had done recently, while trying to include words like "so" or "because" in them as much as possible.  A couple of children (I think the best ones in the class) read aloud their stories to us.  Both children had amazingly beautiful handwriting (maybe even better than mine!), and their stories were extremely well composed.  We were very impressed.  (Since I am not sure how long it took them to do it, or how much adult help they had, it is hard to make any real comparisons.)

We set Miya up with paper and pencil, and she made a small start with her story, agreeing with me that it would be good to write about our visit to the Botanic Gardens on Sunday.  (I was a little bit more leading than I normally would be, given our time constraints.)

When she got stuck on the spelling of "Sunday", I asked one of our deskmates if they had classroom dictionaries (I've just recently given Miya her own junior dictionary, and taught her the basics of finding words; she now uses it sometimes with her own independent writings at home).  Our deskmate didn't know what a dictionary was, but the teacher gave us a word list on a card, which she said the children are expected to know by the end of the year, and showed us a class dictionary.  I asked Miya if she knew all the words on the card (there might have been about 30-50 of them, with words like "went" and "then") and she said she did.

From what I could see, the teacher's approach to teaching spelling was to get the children to try to write the words out on their own, by sounding them out.  They clearly didn't use dictionaries.  After they had finished, the teacher would then write the correct spelling in pen above any incorrect words.

I am not sure which method is better, but I will probably continue to spell out words to Miya when she asks me, rather than let her to write out wrong words.  I wonder if seeing wrong words on paper might reinforce wrong spelling habits.  Also, as I wrote here, Miya's word learning style tends to be not as phonics-based as Mulan's was, and I am happy to follow Miya's own learning style.

During the remaining few minutes before morning tea, Miya had time to write her first sentence, "On Sunday we went to the Botanic Gardens.", asking me also how to spell "Botanic" and "Gardens", which I told her, and correctly spelling the rest.  We have brought Miya's story home with us, and we will probably finish it soon.  Clearly, written compositions is something that we could work on a little more with both children.  This visit has inspired us to do a bit more.

At the end of our time at TPS, we exited via the school office, where on the wall they had several sets of maths exercises, at varying levels of difficulties, presumably for children to take away to do.  Mama grabbed about half a dozen of the most challenging ones, which looked appropriate for Miya (they were all much too easy for Mulan).  Miya did two of them yesterday (with a little bit of advice from me):

3.  Our interactions with Cindy
As I say, Cindy was extremely friendly and personable.  She was very likable, and I felt we got on well with her.  She seemed to have good relations with everyone at the school, and clearly knew quite a few of the students by name, talking with them in a very interested and encouraging way about what they were doing.  It all came across as very genuine and natural, and I liked her teaching/interaction style with the children.  Interestingly, these students all called Cindy by her given name.

Clearly, though, Cindy gave us the appearance of her seeing our visit as mostly for advertising the school, rather than as a genuine discussion between educators about educational approaches.  Two incidents especially spring to mind:

Firstly, while walking around the grounds, Cindy told us about how they have a Mandarin teacher who has been sent from China (through the Confucius Institute).  I mentioned that one of Mama's professional academic duties in China was to train these teachers on how to teach Mandarin in schools, and that some of her ex-students had similarly come to New Zealand to teach in schools like TPS.  Mama then added that it was a worldwide thing, and they went all over the world.

I had hoped that mentioning this might turn the conversation to comparisons between New Zealand and China with regards to teaching and teacher training.  I had hoped to be a quiet listener to an interesting conversation between two senior, experienced, professional educators.

Unfortunately, Cindy ignored this, closing off that topic with a decisive remark that their Mandarin teacher was excellent, and then moving on to the next point on the tour.  (There was not even any small-talk acknowledgement or interest in Mama's years of experience as a trainer of these teachers who Cindy finds excellent.)

Secondly, after observing that in the classrooms there were always several small groups working independently on different activities, Mama mentioned how it must be challenging for the teachers to have many different small-group activities going simultaneously.  Cindy's response was that that is what they are trained to do and it is part of their expertise, before once again moving on to the next point on the tour.

Well, of course Mama has 20 years of classroom experience, teaching a subject that typically has students at unequal levels and with unequal needs.  I'm sure Mama knows very well about this sort of thing, and I guess she was aiming to turn the conversation to the specifics of the various ways this might be accomplished.

All this left me thinking that, as nice and as decent a person as Cindy undoubtedly is, there nonetheless seemed to be (consciously or unconsciously) something of a professional arrogance in her manner.

To be clear, of course I am not questioning Cindy's or the TPS teachers' expertise in teaching.  I was extremely impressed by what I saw of the teachers and in the classrooms, and I like the way I saw them doing things at TPS.

But what was slightly disconcerting was that there seemed to be an assumption by Cindy that the content of this teaching expertise need not be communicated or explained to us.  That it was sufficient merely to assert excellence or expertise as explanation enough in conversation.

From our perspective, clearly it wasn't sufficient, and so it left us a little dissatisfied with the overall feel of the visit.

Obviously, though, this slightly odd feel of professional arrogance would not stop us from being interested in Mulan and Miya working in with TPS to some extent and in a part-time way.  We feel that there is definitely a lot of potential, if managed well.  We ended the visit with Cindy suggesting that we recontact in the new year to see about starting at that time.

Books

We acquired some more books in the past few weeks, and since there was no room left in the bookshelves, we had to do a bit of sorting.

This is Miya's English-language picture book collection.

This is my main bookshelf.  The bottom two shelves on the right are for the children's chapter books.  The bottom shelf on the left is for children's non-fiction books and our photo albums.

And these are the books that Mulan has read in the past two years (since we arrived in New Zealand).  They don't fit on the shelves so we will box them away until Miya is ready for them.

Countdown

Yesterday evening, during my relaxing time, I watched an episode of 8 out of 10 cats does countdown.

If you are not familiar with the series, it is a bunch of comedians (sometimes) doing smart things with numbers and words.  Funny and intellectually stimulating -- the perfect match.  (Occasionally there are some more mature jokes, so I wouldn't show it to the younger children without previewing it first.)

One of the regular number games they do is that they are given several random numbers and, using basic mathematical operations, have to make another given random number.  Just to make it even tougher, they only have 30 seconds to do it in.

I try to play along at home, but mostly I never get it.  With some of the panelists, their numeracy skills are both impressive and inspiring.

But yesterday, I actually got one (!!!), and happily Miya happened to be sitting with me at the time and I was able to (hopefully) impress her.

These are the numbers they (we) were given (at 26:19 into the video):

100, 8, 6, 6, 4, 2

And they had to make 162.

Can you do it?  There are several possible answers.

Within the 30 seconds, I got:

8(6+6-4)-2+100=162

I paused the video, and stepped Miya through it, getting her to do all the addition and subtraction.

Miya then wrote down the numbers and took them to Mama and Mulan to do.

Mulan sat for a few minutes and got:

2*100-4*8-6=162

Within a couple of minutes Mama got:

100*2-6*8+6+4=162

and then:

8*6+4*2+6+100=162

UPDATE 18/11/2016: A few times now, Mulan has asked to do more of these; she says they are fun.

Which voting system to use

It seems that in the recent US elections overall more people voted for Clinton than Trump, though Trump got the presidency.  Sometimes, who wins or loses depends on the voting system used.

This is a very good short video introducing some of the challenges of deciding which voting system is best.

Well done Miya

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.

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 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 books are a sword and sorcery fantasy series, primarily set in the imaginary land of Narnia.  They are mostly centred around pre-teen children from England discovering a way into Narnia, and the adventures they have while there.

(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:

1. The Narnian king Tirian, with the English Eustace and Jill
2. The Calormenes
3. The dwarfs
4. The animals who left the battle and didn't fight

Miya picked in order of preference: animals, dwarfs, Narnians, Calormenes.  Mulan picked: animals, dwarfs, Narnians/Calormenes.  Both had a hard time choosing between the Narnians and Calormenes, thinking both were pretty much as bad as each other.  They were both fairly sympathetic towards the dwarfs, agreeing that they had often been bossed about and treated unfairly by the Narnian humans.

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.

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:

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.

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:

1. We have enough financial security that I can treat it as an (unpaid) job,
2. I have a solid educational background to know what and how to teach,
3. My personality suits working with children, and I enjoy it,
4. 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).

But even though we have chosen to homeschool Mulan and Miya, I believe that schools can be, and for the most part are, good places for children to be and to be educated.  I am not anti-school.

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:

1. 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.
2. 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.
3. 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 ...

She also expressed an objection to my reason for wanting my children to trial school (which I briefly explained above).  She pointed out that there are about 6000 homeschoolers in New Zealand.  If I understand her correctly, the aim of her point was to weaken my claim that attending school is mainstream culture.  But her objection is weak, as my point relies on proportions, not direct numbers.  The latest statistic is that 0.7% of children in New Zealand are homeschooled.

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!

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:

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:

1. We don't know how many friends she has.
2. 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?
3. How does the 4 or 6 bags fit in?

It is obvious that if this was a standard 4th Grade maths question we would say, as the adults did in the video, that there is important information missing.

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:

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.