Exponential learning

Austin and Skye have been working through the Khan exercises on exponents this week. He's been doing pretty well but Skye thought an exercise to make things more visible might help him get a better idea of what exponents "look like." 


This was the result (photo). 

They hand-calculated about 1/2 of the numbers seen on this wall. This was great practice in multiple-digit addition and multiplication. Once they got to the higher numbers Skye showed him how to calculate exponents using a scientific calculator.

It didn't take him long to first notice how quickly numbers grow when you move from one base to another (somewhere around 3^6) and then the interesting relationships between base 2, base 4, base 8 and base 16.

They took a short detour into computer science to discuss how computers are based on a base 2 number system.

Fun!



For base-9 digits, Skye showed Austin that he can reduce every solution to 9, by adding up the digits and reducing them until only a single digit remains. For example, the solution to 9^9 is 387,420,489. 3+8+7+4+2+0+4+8+9 = 45; 4+5 = 9! This way, Austin can double-check to see if he has calculated the correct result.


Carla showed Austin that he can do the same for base-3 digits, and the final result will be 3, 6 or 9 (all multiples of 3).


Austin is enjoying exponents so much, that he has been teaching the concept to Aidan. Aidan is a good sport about it and is enjoying finding patterns on the grid.


I overheard Austin encouraging Aidan at one point. I hadn't heard what Aidan said, but I heard Austin say, "You ARE smart! You found patterns that even I hadn't noticed!" This teaching experience has been good for their relationship. In fact, I've noticed that they are getting along better, overall, these days. Hope it's not only because Santa's watching ;)

Exponents

Austin's been working on exponents ... X squared, x cubed, x to the y, x to the negative y, x to the 1/2 (square-root), multiplying exponents that have the same base, fractional exponents and scientific notation.

This was all done on Khan Academy lessons:
- exponents 1
- exponents 2
- exponents 3
- exponents rules 1
- scientific notation

UC Davis Protest

Skye shared this link with me today. I watched the first video (Aidan saw part of the footage with the pepper-spraying) and Austin, Aidan and I watched the second video together.

The first video was quite disturbing to watch. A police officer seemed to be casually spraying seated, peaceful protesters with pepper spray. According to the report, 50 protesters were sprayed in this fashion. Apparently, the police communication stated that the protesters had been given until 3pm to leave their tents, that some of the protesters were wearing protective gear and others were carrying batons. In the video footage I saw, I couldn't identify any students in protective gear, or any students armed with batons.

I was puzzled by the chancellor's request for police to remove "trespassers" from the campus. These so-called "trespassers" were students at the university. How can they be labelled trespassers on their own university campus?

Both Austin and Aidan thought the peaceful "shaming" of the chancellor was pretty cool, given that 1 student of 1,000 had suggested this demonstration. Austin said it's pretty amazing how one person could have so much power over angry people (assuming the students would be angry that their friends had been pepper-sprayed). I then talked to Austin about the difference between power and influence, and he agrees that it was more likely "influence" than "power" used by the single student who orchestrated the peaceful demonstration to shame the chancellor as she left her office.

Primaeus Serpentus

Austin designed a primate snake with Hero Factory parts.

This primate snake has a horn on its head which has metallic components to strengthen the bone. The spikes that go down along the tail are also composed partly of metal.

The armour on the tail restricts upward movement, so that's why they still (ie. evolution hasn't gotten rid of them) have legs to be able to push themselves upward. They have very stiff necks. Their teeth can move individually, as well as having a jaw movement.

Their brain capacity is very low, so they weren't the smartest of creatures. They lived from about 100 million years ago to 55 million years ago. They died out from exposure. They survived the KT, but they died when the rainforests started to disappear and give way to desert.

They spent most of their time in water, because that's where their huge bodies could fit.

Reading Day

Our Scholastic book order arrived today. Those who know me, know my weakness is books. Aidan's book order was so big that the mother who coordinates the Scholastic orders for the class, took pity on Aidan and decided to save him from having to carry his big order all the way home after school. So, she dropped it off at our house this morning! Thanks, Susan!!

Several Big Nate books and the latest Rick Riordan arrived in this order. Austin has already finished reading the three Big Nate books he hadn't already read, and is now digging into "The Son of Neptune," the second book in the Lost Hero series. It may take some convincing to get Austin to put the book down so he can get some sleep tonight. He's been known to read for hours, uninterrupted, when he gets hooked on a good piece of fiction.

Closing the Feedback Loops

Austin has expressed some concern, this week, about his future. He said that he's afraid he may have wasted too much time, just sitting around playing Lego, when he should have been "in school." He's worried that he is now too far behind his age-peers in what they have been learning all these years. He described one of his fears as himself, "slobbering" around high schools in his 20s and 30s. 


He said that he's happy to be doing some advanced math, but worries that he doesn't understand fractions unless he has something he can touch, and he can't subtract decimals. He knows those are math topics that were taught in grades 4 & 5. He says that he isn't "really" studying chemistry - he's not actually "doing" chemistry - he's just been watching videos on the Khan Academy website.

He's worried about his health, as well. He's self-conscious of his teeth, which are not very white. He's worried about his weight (particularly around his middle) and fat on his legs.

Austin is highly competitive. He likes to do things early, and he likes to do things well - he's most comfortable being "the best." However, he's become acutely aware, recently, of the aspect of his personality that steers him away from things that are difficult. He's worried that he has steered away, now, from too many things. He seems to have hit a bit of a plateau on the Khan website, with the math exercises. Perhaps, if Skye and/or I sit with him through some of those exercises to reinforce the learning, it will become easier? He needs to be ready for that, though, because I tried to sit with him on a couple questions using radians and degrees, and since I had to work through the answers, myself (I didn't just "know" the answer), he was impatient and decided just to skip it.

Austin expressed concern, even, about the possibility of going to university. While he would be interested in becoming a paleontologist, he wants to hang out with people who would rather discuss the subjects they are studying, than party. He's nervous about interacting socially. He doesn't have the same interests as many people his own age, and he doesn't want to just go out and party. I think he may feel differently if he met more people who shared his interests. I was wondering if he would qualify for joining the gifted program in the North Van school district, or if he would have to be registered in a public school in the district? Self Design operates by BC Ministry of Education guidelines, so maybe he could be considered, even though he is in a DL program of studies? He does have a G/LD (Gifted/Learning Disability) designation, with the disability being diagnosed as "dysgraphia."

I think Austin wants to know where he stands, as compared with his age-peers. While he's hoping that he might be ahead in some areas, he is well aware that he is "behind" in many. I told him that the BC Grade 7 curriculum is available on the internet, so I could show him that whenever he wants to see it. He seemed interested. Also, I guess he can choose to write the FSA for grade 7 this year. For his sake, if he does want to write it, I'd like to be able to help him prepare, somehow, if there's any preparation suitable.

He told me that he's worried that he won't be able to get a good enough job, that pays well enough for him to be able to live in an area he loves, and buy the things he wants to buy.

Teaching Aaron to Swim

Aaron is registered in Tiny Tot 2 on Monday mornings at 11:00. Last week, I took Aaron to the pool by myself and I noticed that his teacher (Ty) was surprised that Aaron couldn't keep his face in the water while propelling forward. I told Ty that I would try to come for family swim sometime, so Austin and Aidan (Ty has taught each of them in the past) could play with Aaron a bit in the water during his class. Ty agreed that would be an excellent strategy to make Aaron more comfortable.

This week, I brought Austin with me to Aaron's class. Aaron had a substitute teacher (Hessam, who recently taught Austin 1:1 in I Can Swim Stage 4) today. For everything Hessam asked the class (only 2 students - the other 4yo boy is a good swimmer) to do, Austin would show Aaron. He did a starfish backfloat, kicked off from the edge of the pool, swam forward with his face in the water, lifted up his belly and kicked his legs while floating on his back. Aaron tried to copy Austin and Hessam helped Aaron a bit, then took every opportunity to let Aaron go on his own. Whenever Aaron was swimming successfully on his own, Hessam would congratulate him and make him aware that he had done it himself.

One time, Aaron swallowed some water and started to cough. As everyone does, Aaron hates to swallow water or get it up his nose. Hessam playfully plucked the air by Aaron's face and said, "Did you swallow a fish? I'm going to catch that fish!" then casually gestured a tossing aside of the fish, saying, "There, it's gone."

At the end of the class, Austin and Aaron stayed in the water for a few minutes. Austin asked Aaron if he would say, "Hi!" to him underwater. Then, Austin ducked under and Aaron copied him, staying down for a few seconds to pause and wave to his big brother. Until this point, Aaron had always done split-second dunks to avoid being underwater for long.

Austin knew that Aaron's next hurdle is to keep his face underwater while moving/swimming. Austin first asked Aaron to take a walk underwater while saying, "Hi," but Aaron kept saying he couldn't. Then, Austin invited Aaron to climb onto his tummy and they swam along, tummy to tummy until Austin dropped down. The first few attempts, Aaron resisted putting his face in the water, but by about the fourth try, Aaron's face went underwater as Austin swam them both along, looking into each other's eyes.

At one point, Aaron swallowed water while he was with Austin and Austin tried the "fish distraction" that Hessam had used. I noticed that Austin employed several good teaching techniques that he's seen all the instructors use with small children, over the years.

I was really impressed with Austin's teaching methods. When they left the pool, another instructor (Andrea) asked me if Austin wants to be a swimming instructor someday. I told her he really does, and is taking the lifesaving courses now, even though he's only 12. She said that's when she started too. Then, she went on to tell me that having a job like this has been the only way she can earn enough to put herself through university. Her sisters both work in restaurants, earn less than her and work very hard, often having to put up with some mistreatment. Andrea spent a month working as a waitress and she said that experience renewed her appreciation of her job as a lifeguard and swimming instructor. Andrea told me to let Austin know that if he ever wants some tips or just wants to ask questions about the job, he should feel free to ask any of the guards at the pool, anytime.

Junior Masters and Bronze Medallion

Austin is registered in three swim classes every week. On Mondays, he is in Junior Masters 2, which is a fast lane-swimming course in which swimmers try to keep beating their personal best times and improve their strokes.

Last week, Austin described the class as "humiliating," because he was constantly being passed by other swimmers and getting in their way. I think this was frustrating and a bit upsetting for him. He's worried about this class - he feels pressured and knows he's the slowest swimmer. He far prefers competing only against himself, but we can't create that without private lessons.

I suggested that he ask his teacher to let him know if he is getting faster with his personal times, instead of worrying about what the other swimmers are doing. I also told him that it's the passing swimmer's responsibility to get out of his way, not his responsibility to avoid kicking swimmers who are coming up behind him.

He's also registered in Bronze Medallion, which is the course that follows Bronze Star. He likes the other students in the class, and has been partnered with a boy named Charlie. Austin thinks Charlie is in grade 8.

The beauty of chores

Austin has a renewed motivation to earn money. His good friend showed him a new Hero Factory (Lego) toy online, and ever since, he's been driven to buy it.

This week was definitely focussed on money-making activities. As a side benefit, our house is cleaner than it would have been, and Austin has improved some living skills.

Austin knew that he would need to save enough to cover taxes. I've been chuckling to myself as he applies the 12-times-tables to each potential purchase. He's worked out that he can multiply the price by 12 then convert from cents to dollars (ie. divide by 100). So, since he wanted to buy the Hero Factory Witch Doctor, which costs $39.99 before tax, he worked out that 40 x 12 = 480 and 480 cents = $4.80. Rounding up, he determined that he would need to earn $45 to cover his purchase. And here is how he did it:

Money left in his wallet: $9
Vacuum house (hallway, living room, Mom & Dad's bedroom) $3
Sweep floors (entry hall, kitchen, dining room, bathrooms) $3
Mop floors (entry hall, dining room, kitchen, bathrooms) $3
Wash car with Aidan $5
Mow front and back lawns: $15
Babysitting: $9

Total earned and saved: $47

He was thrilled to tie in the purchase event with a sleepover with very special friends.

And it all culminated in Austin disassembling Witch Doctor, sorting all 331 pieces by colour, and coaching Mom to build this evil dude, following the step-by-step instructions.

Quote of the day

This morning, around 7:50, I entered Austin's room and turned on the light so he could gradually wake up. He awoke with a cheery "Good morning!"

I responded with, "It's the big day." (sleepover at his friends' place)

Then, he said, "The sun is shining, the tank is clean and we are getting out of here!" (the image of "Gill" from Finding Nemo emerges)

It was so appropriate, as we both admired his clean, vacuumed floor. Even Austin, who absolutely hates to clean up, loves a clean space.

Inspired to Write

During a recent visit with a friend, Austin was inspired to write a prologue to accompany her brilliant fantasy story. She offered him her iPad, and he busily typed away for about 30-45 minutes.

Today, Austin and I worked together on a first revision of his writing. Halfway through this exercise, Austin wanted to stop - revision seems to be quite the opposite of inspiring!

Here are the first two drafts of Austin's prologue:

Austin's Story prologue.

1. First draft

It was night in terraplenta but in this part it was always dark

This part of terraplenta was called the black mountains

The reason it is called the blackmountins is the inhabitants here are dragons

.These are no ordinary dragons that breath fire and horde treasure no

These dragons brethe darkness a darkness that can even consume the soul

 one day in the nere by village of

Ignea little did the dragon know that the village was preparing to driVe them

from the black mountains . The dragons awoke with a start at first they

Thought it was visitors coming early after all the black mountains are the only

Safe haven for dragons. When they saw what had cosed the commotion

They were startled to see a army from ignea the closest fairy village they

Were cot off garde the dragons fled with the chief taiking up the rear

The chief stoped suddenly as he herd the ditresed call of his offspring

He rushes back to the den only to find them dead and his mate had suffered

the same fate they fled the black mountains as they got further away the

Black mountains That he called there kingdom vanish from sight.that night the

chief made a Vow to destroy the ones who killed his family.

2. Second draft (focus on spelling and punctuation)

It was night in Terraplenta, but in this part it was always dark. This part of Terraplenta was called the Black Mountains.

The reason it is called the Black Mountains is the inhabitants here are dragons. 

These are no ordinary dragons that breathe fire and horde treasure. 

These dragons breathe darkness, a darkness that can even consume the soul.

One day, in the nearby village of Ignea, little did the dragons know that the village 

was preparing to drive them from the Black Mountains. The dragons awoke with a start. At first, they thought it was visitors coming early. After all, the Black Mountains are the only safe haven for dragons. When they saw what had caused the commotion, they were startled to see an army from Ignea, the closest fairy village. They were caught off guard. The dragons fled with the chief taking up the rear. The chief stopped suddenly as he heard the distressed call of his offspring.

He rushed back to the den only to find them dead and his mate had suffered

the same fate. They fled the Black Mountains. As they got further away, the

Black Mountains that he called their kingdom, vanish from sight. That night, the chief made a Vow to destroy the ones who killed his family.

Swimming and Life-saving

Austin completed and received a certificate for Bronze Star, last month. This course is a pre-requisite for the life-saving course, Bronze Medallion, which Austin is eager to take next month. He enjoyed the group os students who completed Bronze Star with him. They ranged in age from 13-15, with most of the group over 13. Austin is looking forward to learning with that group, again. He is very motivated to become a lifeguard at his earliest opportunity. He has to be at least 16 years old.

In that course, he learned basic CPR and practiced saving a drowning person, even while wearing clothes.

September 12-22, Austin has been taking I Can Swim 4 on M/T/W/Th for 30 minutes per day, 5:00-5:30. He is getting private lessons, because noone else signed up for the course.

Austin's instructor, Hessam, told me that Austin takes instruction very well and he was impressed by Austin's mature response to the question, "What is your favourite stroke?" Austin responded, "The breaststroke, but that's most likely because it's the one I'm best at. I should probably practice other strokes to get better at them, too."

Austin told me that Hessam is getting Austin to work on improving his endurance. Austin has been getting good daily exercise, hiking in the hills around our home, as we walk little brothers to their respective schools.

Khan Academy mathematics

I like the learning tree on the Khan website. Austin is very motivated to earn points and badges. The site colours subjects in orange, if it's time for Austin to refresh what he has learned. Then, he can return to that subject and answer questions to demonstrate that he has remembered what he learned.

Austin spends most of his time with the Khan Academy, working independently. However, I worked with him on angles last week. We watched the video, "The Angle Game," together, and he intuitively was able to solve for the missing angles. Before Salman told us that two lines were parallel, Austin assumed that they were, so was able to identify corresponding angles and solve for supplementary ones. He was very quick with these exercises, clearly enjoying the work.

The blue colour indicates that Austin is proficient in the subject, green indicates the subject is suggested, and orange is selected for review.

Cosmology and Astronomy

Austin has been learning about cosmology and astronomy on the Khan Academy website.

The green-coloured font of the video title indicates that Austin has watched that movie. Since Austin has an enduring interest in this subject, he has already been exposed to many of these topics.

His own library card

Austin got his own library card last Friday. For the first three months, he can have up to ten items out at a time. After three months, he can sign out as many as 100 items!

This library card has given Austin a little more personal freedom and he likes to walk/skateboard up to the library on his own.

A few days ago, he took out books 7 and 9 of the Ranger's Apprentice series. He has already read books 1-6 and book 8.

Lego Explosion

Now that's more like it ...

Austin has been busy setting up his "projects." Now, I think he feels more at home in his room.

We have an agreement for him to keep the floor clear.

Cooking Tacos

One of Austin's favourite meals is tacos. He likes to be the cook who seasons the beef. It's neat to watch him at work, testing and tasting, sprinkling in a little more of this and that. He uses garlic, chili powder, paprika, cayenne, oregano, cumin, seasoning salt and pepper. He says that he prefers to use as little water as possible, because he doesn't want to water down the flavour, but Skye explained that the water helps the flavours to blend and be enriched, so I think he's had a change of heart.

Building his loft bed

We've been slowly moving back into the upstairs of our home these past two weeks.

Austin undertook to build his own loft bed. He worked from instructions on the Ikea website, located all the necessary hardware, and assembled the bed primarily on his own. Skye or I had to hold some pieces in place while he screwed in the bolts.

I think he was pleased with the result.

Austin's Learning Plan - September 2011

Austin and I spent a bit of time this afternoon sketching out some ideas for his learning plan to get this "year" started. Click the image to see the full size version.

A1's Learning Plan - Captured using a Bamboo tablet and stylus

One of the big shifts from previous years is that he has a strong interest in pursuing an academic topic. He has decided to "go deep" in learning as much as he can about Chemistry. To support this he is also brushing up on his math skills and our friend Iain MacKenzie who is a research chemist now working at UBC TRIUMF has offered to show him around and provide some mentoring.

Emotions

A2: "I wish anger didn't exist as an emotion."

A1 and I have been arguing quite a lot over the past few days. I guess he's been pushing my buttons and I have been explosively reactive. When I ask him to help with something and he responds with, "I'm not in the mood to be helpful right now," the fireworks fly. And A2 ends up in tears.

A2: "I wish we only had two emotions: sadness and happiness."

A1: "Sadness? Why wouldn't you only want happiness?"

A2: "We need sadness because, if a baby were hungry but happy all the time, they wouldn't be able to tell us they need to eat. So they could starve to death."

A1: "I think anger's important too, because it helps us through our fears. Anger always leads to fear. And anger comes from fear."

A2: "And if we didn't have fear, we might just walk up to a cougar and say, 'Here kitty, kitty ...' and then, Gulp! We'd be eaten by the cougar."

Lifeguard in Training

Yesterday, we spent most of the day at the marina pool. There were three families, totalling 7 kids. Aidan hung out with his friend, Brendan (8), Austin was mostly practicing diving to the bottom of the deep end, and trying to swim underwater for as long as possible, and Aaron was in and out of the pool, playing with balls. As you can imagine, it was a busy pool.

The other children were aged 6 and 2. The 2-year-old boy (Miles) spent most of his time playing at the edge of the pool with a Playmobil boat on a string. He's not keen to swim without his mum for now. He wears water wings to keep him safe, poolside.

Miles doesn't like to wear the water wings all the time, and at some point, he wasn't wearing them anymore.

There were three mothers by the pool, all of them trying to get a better internet connection than we've been able to get with the marina.

None of us saw him go in.

I remember hearing Austin's voice, "Whoa! Miles." I was standing at the shallow end, looked up and saw Miles floating on his back and appearing to be gasping for air. It was an awful sight, but Austin was going to Miles and speaking to him calmly. When I got to the deep end, I couldn't reach Miles (he was about 1.5 meters from the edge), Austin was supporting his head and swimming him to me. I picked Miles up under his arms as I was saying, "What a good boy!" (it was all I could think of at the time) and passed him directly to his mum.

Due to Austin's quick and calm response, there was no panic and I didn't see fear in Miles' eyes.

I think we all learned something from this event.

For me, being the mother of a boy who is only 4 months older than Miles, I was really struck by the seriousness of what happened, and how bad it could have been. I'm even more vigilant about watching Aaron near water, and we keep him in his lifejacket most of the time.

Since Aaron wears his lifejacket so much, I've once seen him boldly follow Austin into the sea from the shore, he was submerged, his blonde hair floated up, then he surfaced, sputtering and crying. Fortunately for us, we all saw what happened and Austin was right there. Aaron is so accustomed to being buoyant in the water, that he is less fearful now, and he's not always aware that he's not in his lifejacket. I think Miles may have thought he still was wearing his water wings when he went into the pool to fetch his boat (he told his mum he was trying to get his boat when he went into the pool).

I noticed that Miles was found floating on his back. All my kids were afraid to swim on their backs when they first learned to swim, and Aaron is still terrified of this position. Miles was practicing leaning back into the water earlier in the day, with his mum. His big sister is a very strong swimmer and he's seen her swim on her back a lot. We don't know how long Miles was in the water, but I think he was better off on his back and able to get some air. I want to start helping Aaron to get more comfortable lying back in the water.

Austin's calm response and the absence of fear and panic in his rescuers has left Miles with a positive memory of the event. He told his mummy that he went "swimming under the water." He doesn't think he had an accident and he isn't more fearful of water. I remember a swimming instructor telling me that it can be difficult for parents to teach their children to swim, because the parents are too nervous about letting their little ones put their heads under water. Sometimes the parents, themselves, are nervous about being submerged. I remember that teacher being able to get Austin, at the age of 1, to hold his breath as she glided him underwater for a couple seconds. The technique was to blow air into his nostrils, then immediately bring his whole body, head first, under water. I have to admit that I was always hesitant to do this move. I'd blow into his nostrils, see the look of bewilderment in his face, then take him underwater too late, or I couldn't bring myself to take his face into the water at all. Anyway, I was reminded how much it helps people to learn to swim with teachers who are confident swimmers.

My final observation is that, when there are several adults supervising together, it's easy for us to have a false sense of security and to let down our guard. After this experience, I hope to be even more careful about keeping our kids safe around water.

First fish

Austin caught his first fish. It was a small (15cm) Horse Eye Jack caught while trolling in True Blue Bay Grenada.

We were shopping in St. Georges Grenada at a marine store earlier in the day and decided to buy some fishing gear for use while sailing. Austin was pretty excited about this. He found a book section that contained a few references to salt water fishing. He picked up one of these, a small 35 pager, and read it through. He then picked out some large flashy lures in the hopes that we'll be able to catch a large-ish fish. He really wanted to go after the big marlins but we just don't have the need or skills or equipment for that kind of fish. We also decided to pick up a small rod, reel and lure kit for the boys to share. It was on this rod that he caught his fish.

When we got home that evening I showed him how to tie a lure onto the line and how to cast. He caught on pretty quickly then also did some jigging. After we had dinner the two of us took the dingy out into the bay and trolled for an hour or so.