They have begun with infinite series. Starting with an 8x8 square Ian is progressively colouring in half and then half again and then half again while at the same time adding together what he has coloured. At this point he has broken down the square into 1/2048ths and has coloured in 2047/2048 of the entire square. His predictions are both that the parts to be coloured are never ending and that he will keep colouring in parts until the entire square is colored.... hmmm.... he will keep working on it to see what occurs.
Amber sat with us during the class and perused the book shelves while Ian worked. Afterwards she commented that she had forgotten how much she liked working with Lori and that she might want to again in preparation for college algebra. I commented that I could likely help her get through the prep work so we are going to give it a shot, but I think she also misses the mystery of the problems that she was working on there - different than the type of things one does when one is just "doing algebra" or "doing geometry" or what have you. We are going to explore it some more.
Wednesday, July 15, 2009
Sunday, July 12, 2009
Sometimes it's just nice to be...
There is a lot of critique these days regarding the over scheduling of childhood. While as a family as a whole we do participate in a lot of activities, we also make every attempt to prioritize downtime with friends (lots of sleep overs!), downtime with family, and simply time alone (sometimes this is easier said than done). Truth be told though, we are on the go a lot!
This is why I am truly enjoying the summer break from most of our organized activities. Sure we still meet with friends to go swimming once a week and another day is spent at the park. There are camps and vacations and a rather surprising number of birthday parties... But as I work on putting together our fall schedule I realize how much we are *not* doing. This is leaving long days to think and talk and read. The oldest three are truly enjoying the world of literature these days with the oldest two swapping novel suggestions on a regular basis. We've had some great discussions about all sorts of topics, often kicked off by the ever present NPR or a little periodical we've been reading called The Week. But as the back-to-school sales begin to pop up (our favorite time of year! Cheap supplies and it means the museums will not longer be packed full) we are looking toward our fall schedule.
I am making every effort to combine the days that we are out so that we can have full days at home. We find it easier to get into in-depth projects at home when we have entire days to devote to them instead of having to stop half-way through to rush off to something or try to begin after coming home from an already full day.
So this is what I have so far....
Monday
Wednesday
Friday
Of course many of these activities have outside preparation, otherwise known as "homework". We'll need to figure out when we'll get up to see the math coach (unfortunately she's a bit of a drive). The older two are interested in doing more foreign language work, both preferring to work independently at home rather than with a group or tutor. And the oldest boy is interested in learning middle English in order to better understand Shakespeare (this is a new request, so we are just beginning to figure out how one would go about doing this -- seems to be this would be more a study of linguistics, but I'm open to suggestions!). Middle daughter has decided she wants to give spelling bees a shot and being the ultimate spelling-phobe this is also a new area for me.
And then we simply want to leave time for those experiences that may just fall in our laps. The random field trip or interest that is as yet unpredicted. The friendship or hobby that needs to be nurtured. But at least we know nothing is set in stone and it is up to us to be constantly aware if these are truly the choices we want to be making.
This is why I am truly enjoying the summer break from most of our organized activities. Sure we still meet with friends to go swimming once a week and another day is spent at the park. There are camps and vacations and a rather surprising number of birthday parties... But as I work on putting together our fall schedule I realize how much we are *not* doing. This is leaving long days to think and talk and read. The oldest three are truly enjoying the world of literature these days with the oldest two swapping novel suggestions on a regular basis. We've had some great discussions about all sorts of topics, often kicked off by the ever present NPR or a little periodical we've been reading called The Week. But as the back-to-school sales begin to pop up (our favorite time of year! Cheap supplies and it means the museums will not longer be packed full) we are looking toward our fall schedule.
I am making every effort to combine the days that we are out so that we can have full days at home. We find it easier to get into in-depth projects at home when we have entire days to devote to them instead of having to stop half-way through to rush off to something or try to begin after coming home from an already full day.
So this is what I have so far....
Monday
- The first and third Monday morning with be 4-H
- Hopefully the second Monday morning will be our Non-violent Communication Study group
- Monday afternoon/ evening will be the performing arts coop for the middle three (this is a new addition to the schedule, after leaving separate gymnastics/ ballet classes last year.)
- Monday evening the oldest will attend class at the local community college.
Wednesday
- Wednesdays are reserved for our coop class days which have generally been running from 10-4. I'm not sure what the offerings are this year, but in the past have included
- Spanish
- Mythology
- Art
- Drama
- Odyssey of the Mind
- Photography
- Stop Motion Animation
- Various types of science
- Math Games
- Banned Book Club
Friday
- Trying to decide if we will continue our First Lego League participation. Great group, but not sure if it is the right fit for us at this point. However, the second half of the year which is more of an open ended math/science club was absolutely wonderful so we may work through the kinks to get to that point. This runs from 9-3, but we cut out early for...
- Cool Kids Care. This is a group of pre-teens and teens that get together weekly for volunteer activities, team building, field trips, etc. The oldest three have been actively participating, so older "tags" sometime come along as well.
- If we are able, the older two want to get back into their Parkour class for the fall.
Of course many of these activities have outside preparation, otherwise known as "homework". We'll need to figure out when we'll get up to see the math coach (unfortunately she's a bit of a drive). The older two are interested in doing more foreign language work, both preferring to work independently at home rather than with a group or tutor. And the oldest boy is interested in learning middle English in order to better understand Shakespeare (this is a new request, so we are just beginning to figure out how one would go about doing this -- seems to be this would be more a study of linguistics, but I'm open to suggestions!). Middle daughter has decided she wants to give spelling bees a shot and being the ultimate spelling-phobe this is also a new area for me.
And then we simply want to leave time for those experiences that may just fall in our laps. The random field trip or interest that is as yet unpredicted. The friendship or hobby that needs to be nurtured. But at least we know nothing is set in stone and it is up to us to be constantly aware if these are truly the choices we want to be making.
Friday, July 10, 2009
Math?
An essay regarding the teaching and learning of mathematics recently came through one of my email lists. I probably run across 2-3 interesting looking articles every day and have an email folder which contains hundreds that I intend to get to, but for some reason Lockhart's Lament caught my attention.
As a child I had always believed that I was good at math. And that I liked it. Because there was one right way to do things and one right answer and boy did I have a talent for following those rules. Until I got to calculus, where I realized that I actually sucked a math and it didn't make any sense at all and I didn't have anything else to do with it until I had to take quantatitive research statistic in graduate school.
However, as I began to read this 25 page polemic, which I confess I am only part way through, within the first several pages I began to realize just how badly I had misunderstood what exactly "it" is, when it comes to math. Dr. Lockhart argues that math is art, that it is about creativity and discovery -- two things that often left me uncertain in school, because I couldn't figure out how to tell if you got them right or wrong. What happened when I got to upper levels of math is that I simply wasn't prepared to function outside of the formulas and proofs which I didn't quite understand, but had previously been able to use well enough to get an answer.
As I processed this epiphany about my own math education I began to think about my oldest son. He has always enjoyed analytical games and has a knack for calculation (he was able to figure out how much 1/4 of 1 3/4 was prior to having any formal training in fractions - oh and in his head). He had worked with a math coach in the past, but had recently been doing "more creative" pursuits working on stop motion animation, drawing, photography, etc. I had wondered if perhaps I had been premature in seeing him as a "math mind" and that perhaps he was more suited to the arts....
I would imagine that you can see where this is going :).
So yes, after checking in with him we contacted his old math coach and he will be returning to her tutelage beginning next week. I shared with her that it was Lockhart's Lament that brought us back and she said that she had read and enjoyed the paper and offered Brain Rot as a similar perspective from another mathematician.
I am excited that we had this coach as a resource in our lives. I have no question about my ability to lead my children through what passes for math in our school system. But to quote Dr. Lockhart
As a child I had always believed that I was good at math. And that I liked it. Because there was one right way to do things and one right answer and boy did I have a talent for following those rules. Until I got to calculus, where I realized that I actually sucked a math and it didn't make any sense at all and I didn't have anything else to do with it until I had to take quantatitive research statistic in graduate school.
However, as I began to read this 25 page polemic, which I confess I am only part way through, within the first several pages I began to realize just how badly I had misunderstood what exactly "it" is, when it comes to math. Dr. Lockhart argues that math is art, that it is about creativity and discovery -- two things that often left me uncertain in school, because I couldn't figure out how to tell if you got them right or wrong. What happened when I got to upper levels of math is that I simply wasn't prepared to function outside of the formulas and proofs which I didn't quite understand, but had previously been able to use well enough to get an answer.
As I processed this epiphany about my own math education I began to think about my oldest son. He has always enjoyed analytical games and has a knack for calculation (he was able to figure out how much 1/4 of 1 3/4 was prior to having any formal training in fractions - oh and in his head). He had worked with a math coach in the past, but had recently been doing "more creative" pursuits working on stop motion animation, drawing, photography, etc. I had wondered if perhaps I had been premature in seeing him as a "math mind" and that perhaps he was more suited to the arts....
I would imagine that you can see where this is going :).
So yes, after checking in with him we contacted his old math coach and he will be returning to her tutelage beginning next week. I shared with her that it was Lockhart's Lament that brought us back and she said that she had read and enjoyed the paper and offered Brain Rot as a similar perspective from another mathematician.
I am excited that we had this coach as a resource in our lives. I have no question about my ability to lead my children through what passes for math in our school system. But to quote Dr. Lockhart
The truly painful thing about the way mathematics is taught in school is not what is missing— the fact that there is no actual mathematics being done in our mathematics classes— but what is there in its place: the confused heap of destructive disinformation known as “the mathematics curriculum.” (p.14)Because we have decided to homeschool and therefor have autonomy over the learning choices we make we are not tied to any such "mathematics curriculum". Our coach nurtures this creativity and discovery and shares this view of math.
Mathematics is about problems, and problems must be made the focus of a students mathematical life. Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process— having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other’s work. Specific techniques and methods will arise naturally out of this process, as they did historically: not isolated from, but organically connected to, and as an outgrowth of, their problem-background. (p. 16)I am excited to see where this journey takes us.
Monday, July 6, 2009
Sunday Evening
A number of the teens have developed a game based on the Harry Potter books and dubbed Quidditch. The games take about three hrs and are held in a park in the city, about 30 min from home. It wasn't worth making the round trip drive so I packed dinner and took Marley, Hayden and Rachael with me. A friend met us for the first two hours and then went home to dinner. We decided at that point to walk over to the pond and feed the ducks.
And one from the walk back to the car...
Sunday, July 5, 2009
Fourth of July
It was a relaxing, fun day. Went to a friend's with a pool, watched several area fireworks displays from the back deck. Nice and cool too (well not as nice for the swimmers....)
Here are a couple of pictures from the afternoon.
Here are a couple of pictures from the afternoon.
Amber swimming with friends
Ian seeking revenge
Marley and Daddy
Marley coloring with the older girls
Sunday, June 21, 2009
The Mountains
What good is a trip to Colorado without getting to spend some times in the mountains? You can't tell from the pictures, but this location was crowded! In fact, we were the last two cars that they let into the park until people started to leave.
Monday, June 1, 2009
Old Shawnee Town
One of our homeschool groups organized a field trip to Old Shawnee Town. The time period was intended to be during the 1920s and 30s so we enjoyed imagining how life was during the childhood of their Great Grandfather who was born in 1917.
Several of the buildings had docents who gave us a tour and background information. In the sheriff's office was a flag with 48 stars and he quizzed the kids as to the two "missing" states. After getting Hawaii they were struggling to come up with the other. Ian started snapping his fingers... he almost had it... he said "that state with the almost vice-president..." Alaska!
The larger group broke into smaller parts for exploration and we did our tour with friends. The eight children between the ages of 1.5 and 10 enjoyed the entire facility, taking their time to try their hand at various activities.
After being shown how to do the washing without a machine the kids gave it a shot
Several of the buildings had docents who gave us a tour and background information. In the sheriff's office was a flag with 48 stars and he quizzed the kids as to the two "missing" states. After getting Hawaii they were struggling to come up with the other. Ian started snapping his fingers... he almost had it... he said "that state with the almost vice-president..." Alaska!
The larger group broke into smaller parts for exploration and we did our tour with friends. The eight children between the ages of 1.5 and 10 enjoyed the entire facility, taking their time to try their hand at various activities.
After being shown how to do the washing without a machine the kids gave it a shot
They also weighed out some merchandise at the dry goods store.
Monday, May 25, 2009
Homeschoolers vs. the State
Two weeks ago, during the last week of the Missouri legislative session, an omnibus education bill was put forth. Unfortunately, the bill had the unintended consequence of affecting the upper end of the mandatory attendance age of homeschoolers. Instead of simply reaching the age of 16, teenagers (and adults?!) would not be released from compulsory attendance until they had achieved "successful completion of sixteen credits toward high school graduation."
"Why would this be a problem?" you ask... well Missouri homeschool law does not ask families to record "credits", but "hours". So who would decide when a homeschooled child had completed 16 credits? The fear of homeschoolers was that the state, through the judicial process, would be at liberty to define a homeschool credit any way they wished.
So what is a good homeschooler to do? Rally of course! Which is exactly what we did. The day after the homeschooling community became aware of the problem several thousand descended on the grounds of the capital to lodge their opposition.
Here a couple of pictures from my phone. The first is from behind the speakers looking down on to the lawn and the second is facing the steps of the Capitol.
"Why would this be a problem?" you ask... well Missouri homeschool law does not ask families to record "credits", but "hours". So who would decide when a homeschooled child had completed 16 credits? The fear of homeschoolers was that the state, through the judicial process, would be at liberty to define a homeschool credit any way they wished.
So what is a good homeschooler to do? Rally of course! Which is exactly what we did. The day after the homeschooling community became aware of the problem several thousand descended on the grounds of the capital to lodge their opposition.
Here a couple of pictures from my phone. The first is from behind the speakers looking down on to the lawn and the second is facing the steps of the Capitol.
Pretty impressive if I do say so myself ;-).
Thanks to the work of our homeschool lobbyist compromise language was reached which defines a homeschool high school credit as 100 instructional hours. The law currently requires a minimum of 1000 instructional hours each yr, so even following the minimum requirements, homeschoolers will have completed their required high school credit within two yrs of beginning their high school studies.
While easy enough to follow through with, I am still left feeling a bit uncomfortable with homeschool regulations being included as part of an omnibus education bill. The more divergent our regulations become the easier it is for them to get out of hand.
However the take home message for legislators was "Don't mess with homeschoolers!" so I don't think we have to worry about additional changes any time soon.
Saturday, April 4, 2009
Saturday, February 28, 2009
Subscribe to:
Posts (Atom)