Sunday, March 5, 2017
Long Distance Running Day
For Family Night last week we did our long distance running day. We talked to the kids about how running helps their heart and will help them live longer, then we told them about the world records in the mile, the four minute mile barrier, ultramarathons, and the fact that their uncles and aunt had run 26 miles straight. That got them in the mood to time their one mile time. They did it in about 16/19 minutes. Simeon got angry that Christian was so far ahead of him, but I explained to him that the real test will be when he can run faster than Christian's 16 minutes when he's as old as Christian. At one point it was getting dark and I couldn't see Christian so I wanted to cut it short, but exhausted Simeon insisted on going until he was where Christian was.
Future
When they get older it would be fun to go on family runs. Also, Chariots of Fire is on the must-watch list, but that might be more appropriate for sprinting day. Completing a marathon in a decent time is on my bucket list, but for now I'm going to focus on weight lifting while I have such easy access to weight equipment.
Sunday Edition: Noah's Flood
Sunday Disclaimer
Our Sunday home learning is religion/morality oriented. As we are Mormon, the lessons will reflect a Mormon approach. Within Mormonism there is also room for theological variation, and what is taught here represents what we feel is true.
Lesson
The Bible tells the story of Noah's flood, where God decides to destroy the world by flooding it because of the wickedness of its inhabitants. There is a version of this story in many cultures across the world, leading some to speculate that the idea of a flood story might be in our brains naturally, while some people think that it might be based on some real flood that happened to our ancestors long ago. However, there's strong scientific evidence against some of the details of the story: there was no flood that covered everything in the world and destroyed all life just a few thousand years ago. Furthermore, the animal species we see today were not dramatically reduced to just two per species. We would have detected such a reduction genetically, they would probably have not been able to start a whole new group with just two because of problems that come with siblings marrying siblings and cousins marrying cousins, and all the species we have today would not have come close to fitting on the boat. God could have made all these things happen and intentionally changed the evidence in our genes and the geological layers, but then that would be a God that intentionally tries to trick us. He expects us to use our minds.
Like the creation story, the flood story has several different versions in the one story in the Bible, leading some researchers to believe that it was a combination of several stories combined together. However, some of the stories are different in regards to how long the flood lasted and how many animals were taken on board. This shows that the people putting it together didn't care about the differences since they allowed both versions to stand side by side.
Throughout the Bible there are things that happen that people see as symbols for something else. Many Christians have seen Noah's flood as being symbolic of a baptism of the entire earth. Later, when God introduces the gift of the Holy Ghost (which we receive after baptism) he refers to it as a "baptism by fire," many Christians believe that the second destruction of the earth will come by fire, in a way baptizing it by fire like it was previously baptized by water. Also, Christ's baptism was represented by a dove, as was the baptism of the earth.
In one of the Noah's flood stories, he sent out a dove to look for dry land, and it returned with an olive branch. The dove is symbolic of a lot of things like peace and holy Ghost, and its use here may be symbolic as well.
After Noah landed he had three sons, Ham, Shem, and Japheth; some early people thought that these three sons went on to populate the entire earth, and that different races came from these different sons; however, we know that race is much more complicated. For example, a lot of black people are more closely related to white people than they are to other black people.
Similarly, some people think that the Tower of Babel story, where God changes everyone's languages, is the reason why people speak different languages, but now we know that linguistic change happens across thousands and thousands of years, and didn't happen all at once.
Future
When the children are older I want to show them the Noah, the excellent Darren Aronofsky film.
Reading for Parents
Origins of the World's Mythologies by Witzel. Unlike some comparative mythology works, this one is solidly academic and tries to limit the speculation. It makes a compelling case that the similarities seen in the world's mythologies (most prominently exemplified by the ubiquitous flood story) are derived from a common proto-culture and religion we had as a species coming out of Africa.
Saturday, February 25, 2017
Gibbons Zoo Day and Russia Day
We were a little behind on our planned home learning activities, so today we had Russia day and went to the zoo. Every time we go to the zoo I try to learn a lot about one of the animals, and we talk about it on the way. Today it was the gibbons. Fun facts: gibbons can reach nearly 30 miles per hour swinging from trees. They also have the longest arm span compared to their legs of any primate, with arms so large that they have to walk with them up when they are bipedal in order to keep their balance.
Afterwards we had our Russia night, making homemade beef stroganoff from scratch (more difficult than I thought it would be), and we watched Hunt for Red October.
Afterwards we had our Russia night, making homemade beef stroganoff from scratch (more difficult than I thought it would be), and we watched Hunt for Red October.
Sunday, February 19, 2017
Adam, Eve, and the Fall
Sunday Disclaimer
Our Sunday home learning is religion/morality oriented. As we are Mormon, the lessons will reflect a Mormon approach. Within Mormonism there is also room for theological variation, and what is taught here represents what we feel is true.
Adam fell that men might be, and men are, that they might have joy. -2 Nephi 2:25
Lesson
We don't know how much of this story happened and how much of it is literal. We do know that God used this story to tell us about how things are.
The Book of Genesis is the first book of the Bible, it tells us the creation story as understood by the ancient Hebrews. If you read it closely, there are multiple versions of the story in Genesis, so scholars think that there were various related stories that were combined together at some point long ago. This was their best effort at figuring out how the world was made. They didn't know about supernova or hydrogen atoms.
In one account in Gensis, the world before the creation was an ancient, dark, chaotic sea, without any organization. A lot of early ancient groups like the Mesopatamians and Norse thought that the early universe was a lot of chaotic material. While most Christians believe that the Creation began with the creation of matter, Joseph Smith revealed that the Christian of the world consisted of the organization of pre-existing matter that was floating around.
The ancient Hebrews, along with a lot of other people back then, thought that the world was a plate surrounded by a big world ocean, and that the disc was floating on a lot of other underground oceans. They also thought that the sky was a dome over that disc, that's why Genesis talks about the "firmament," when it mentions the sky, which means in place. If you read Genesis closely, you can see hints about what they thought the earth was like.
One of the first things God does in the creation in Genesis is creating light: he says "let there be light." Some people think that there was a double meaning here. God creates light, he also shines spiritual light and truth in the darkness.
After God created the world, he created the stars in the night sky in order to let the Hebrews know about dates and holidays. Back then you only knew dates from the stars, you knew that it was Christmas, for example (except they didn't have Christmas back then), when a certain star was in a certain place in the sky.
God also created the plants bearing seed after their own kind, and created animals who multiplied after their own kind. This is important, before then the world was lifeless, inert matter. God animates things and give them life. The ancient Hebrews (and others) attributed life to the "breath of life" that God gave things. God tells them to fill the earth; God wants there to be lots of fish in the sea and birds in the sky.
God created Adam. Adam means "all humans," but it's also a name. Sometimes in the Bible we don't know whether it is talking about a specific person or whether it is talking about all humans when it says "Adam," this is maybe one way that God is showing us that Adam represents all of us.
God placed Adam in the Garden of Eden. This was like our life with God before we came to this earth. Nobody was sick, and nobody was ever hurt. Nobody was ever unhappy because there was nothing there that made people unhappy. However, we can't really experience good things without bad things. If things were always good we wouldn't recognize that they were good. Also, we can't grow without difficult things happening.
Adam was in this place without any hurt or suffering, but God said that it was not good for a human to be alone, we need other people. Specifically, Adam, like us, needed a companion, not just a friend to spend time with, but his other half. God then created Eve, who was named Eve because Eve means "mother of all living," it was an important title because motherhood, the carrying, giving birth to, and raising of children is a holy position.
There were lots of different trees in the Garden of Eden, but two were very important: the tree of life and the tree of knowledge of good and evil. God told Adam and Even that they could eat of any of the trees except for the tree of knowledge of good and evil. God told them that if they ate of the tree of knowledge of good and evil that they would be cast out of that perfect world, and would eventually die. Satan later came to Eve and told her that if she ate of the tree that she would be like God, knowing good and evil. This is something that makes us different from the animals and more like God, is that we do know about good and evil. She decided to take the step forward in her progression and ate of the fruit. She went to Adam and, since she ate of the fruit and was going to be cast out, and since he was commanded to have children with her, he ate of the fruit as well, they both agreed that it was better that they know the good from the evil and be able to grow.
They were thrown out of the Garden of Eden, and God put guards in front of the tree of life so that they couldn't eat of the fruit and become immortal while they were still sinful. A lot of other societies back then had stories about trees owned by Gods that would give people immortality. In this story, immortality is exchanged for wisdom and experience.
God told them that now they had to work the dirt as farmers, and could only eat if they worked for their food. This is a true today, as God expects us to work for our food and survival throughout our life.
In the book of Genesis there is a motif with dirt, a motif is a theme throughout the story. God tells Adam that he was formed from the dirt, and will return to the dirt after he dies, and has to work with the dirt to keep himself alive. Some scholars think that this is suggesting that Adam's mortal life is bound to the fallen world.
However, because they partook of the fruit, we are as the Gods, and know good and evil, and eventually we can repent and return into the presence of God, like Adam being able to return to the Garden of Eden. However, after we return we will become more like God because we were able to grow because we had to deal with bad things and suffering, and because we know the difference between good and evil. Eventually, through progression if we deal well with these things, we will become a God.
When Adam and Eve were thrown out, they were also able to have a little bit of divinity with them in their ability to create life. They (and us) are commanded to multiply and replenish the earth. The ability to create after himself and create forever is one of the reasons why God is God, and we have a part of that in our ability to create life here on earth.
Suggested Readings
For Mormons, the Two Trees by Mormon Scholar Valerie Hudson is a good LDS account of the Fall. Most scholarly Genesis commentaries point out the themes above.
Future
I want to read more early Christian/philosophical/artistic commentary on the creation and fall. It's a very primal account so its themes show up throughout Western writings, even though not-insignificant differences between Mormon interpretations of the Fall and traditional Christian interpretation necessarily limits the amount I'll be able to get from it. For sure I want to read C.S. Lewis's space trilogy that addresses some of these themes.
Monday, February 13, 2017
Papua New Guinea Day
The Papua New Guinean national dish, mumu, is simple and economical to make. Most recipes call for slow cooking over a pit of coals, or at the very least the use of a Dutch oven in an electric oven. We used a slow cooker and it seemed to do the job. Very simple, I threw in a layer of spinach, a layer of sweet potatoes, a layer of chicken, a layer of pineapple, another layer of chicken, and a layer of spinach, onion, and garlic, all drowned in coconut milk (that last step is very important). The meat cooks in the fruit juice, coconut, and garlic/onions, giving it a sweet but subtle tang.
As the meat was cooking we watched the first part of Guns, Germs, and Steel, where Jared Diamond talks about the Papua New Guineans and the unparalleled human and natural diversity of the island. His books go much more in-depth and are required reading for adults (example, some languages in Papua New Guinea are as different from each other as Chinese is from English). On the way to the store to get ingredients I taught Simeon facts about Papua New Guinea so that he could give the lecture at the map. He loved being the expert.
As the meat was cooking we watched the first part of Guns, Germs, and Steel, where Jared Diamond talks about the Papua New Guineans and the unparalleled human and natural diversity of the island. His books go much more in-depth and are required reading for adults (example, some languages in Papua New Guinea are as different from each other as Chinese is from English). On the way to the store to get ingredients I taught Simeon facts about Papua New Guinea so that he could give the lecture at the map. He loved being the expert.
The Mountains Call, and I Must Go: Bouldering
The university I work at has a rock climbing wall and bouldering area in the middle of campus that faculty, staff, and students can use, with free climbing gear rentals. They’re cool like that. Consequently, I’ve been intermittently taking advantage of the free rock climbing, and have progressed from a 5.8 to a 5.10. I wanted to introduce my kids to this world, but they still aren’t keen on heights, but they love clambering on trees and boulders in the local parks, so I thought bouldering would be perfect. We played around in their bouldering area before, but it’s hard to do that kind of thing with a crowd of rowdy kids (especially with anxious college students not wanting kids scrambling around underneath them while they’re climbing) so I took my wife with my this time to help out.
To prep the kids I told them about the bouldering ratings (V0 to V15), and how only a few people in the world can climbing V15s. Kids love the “only a few people in the world can do this” line, and it naturally piques their curiosity about what they’re capable of.
After about half an hour of bouldering we called it to make way for the patient college students. Later that night, we went to my office and watched on Youtube some of those “best climbers in the world” that I alluded to earlier in the day (both the world bouldering championships and Adam Ondra’s first ascent of La Dura Dura [5.15]), as of now the hardest wall in the world.
Future
Since ropes wear out over time, if you’re going to invest in one there’s an obligation to use it frequently, and I just don’t think I’ll be able to get that kind of time for the next decade or two, so for now I think bouldering might be a good step to take with my kids, since all it takes is a crashpad, chalk bag, and pair of shoes. (And the crash pad can double as a very comfortable sleeping pad--free soloing legend Alex Honnold uses his this way in the van he lives out of).
In the future I’d love to do the vagabonding, camping/bouldering/mountain biking all day thing at Moab, Utah; Joshua Tree National Park, California; and Squamish, British Columbia.
Saturday, February 4, 2017
Dressing for future success: Fashion and apparel
“Pure, intense emotions. It’s not about design. It’s about feelings.” — Alber Elb
Lesson
Lesson
How you dress, what clothes you wear, how you wear them, and how clean they are, affect how you look, and people treat you better if you look better. Looking good can also be like an artist making a pretty picture, and it can make life more pretty for yourself.
What exactly looks good depends changes from year to year. What looks good now is different than what looked good when mommy and daddy were your age. You should pay attention to what people around you are wearing because that helps you know what looks good right now. What looks good is influenced by what famous people wear, it’s also influenced by clothing artists who live in big cities, design clothes, and show off their clothes in shows.
However, no matter what looks good, you can always make sure that you have clean clothes when you’re going to be around people. Also, some colors go better with each other no matter what specific clothing you’re wearing. For example, there are warm colors like yellow, red, and orange, and cool colors like blue and purple; often a cool color and a warm color mixed together look good.
White, black, and grey can go with either warm or cool colors, they are neutral colors. It’s often good to wear at least one neutral color so that people will focus on the other color better.
Also try not to wear colors together that are on opposite sides of the color wheel. They will clash. If you do put them together, make one lighter than the other.
Colors right next to each other on the color wheel also work well together, since they are easy on the eyes.
Black doesn’t go with either blue or brown. Grey doesn’t go with brown. Brown often goes with the warmer colors to create an earth-toned look.
Try to pair light with dark things, don’t have an all-dark outfit or an all-light outfit.
Some sunday clothes have patterns like checkers or lines. If you are wearing two things with patterns, make sure the patterns aren’t the same size.
With Sunday clothes, always make sure they fit, if they’re too loose your clothes can look like you’re wearing a sheet. If they’re too tight they crunch up and tense up. They should be snug but comfortable.
When you’re older, how big your face is and other things about your body will help determine how big your lapels and other parts of your clothes should be.
Also, what looks good for Sunday clothes doesn’t change a lot. Many men wear suits and ties, a which is a coat with a matching pair of pants. Some men wear a tan pant call a khaki along with a shirt and tie. Sometimes they wear a pant and a coat that isn’t the same color, but they still match. More and more men are wearing coats without ties. Generally the important aspects of Sunday clothes for men are: the belt, shoes, socks, pants, shirt, tie, handkerchief (optional), vest (optional), sweater (optional), overcoat (optional).
Activities
Iron a shirt, polish shoes, go to a menswear place in the mall, watch a fashion show on Youtube. Critique their clothes (in a non-judgey, purely aesthetic way). Critique and discuss the outfits of other people. Let them pick out your clothes for the day. Emphasize their favorite colors.
Future
When they are older go to a fashion show. Go shopping with them and help them pick out clothes.
Sunday, January 29, 2017
New Zealand Day!
Our son Christian chose New Zealand for his country day. We made the national dessert, Pavlova, a cooked meringue dish. Daddy learned that egg whites don't whip into a meringue in two minutes like strongly implied in the YouTube video (more like 30 minutes of hard elbow grease), and that next time they would be better off using an egg-beater. We used the homemade whipped cream leftover from the Pavlova for the fresh strawberries and kiwis, and to give it a slightly more NZ taste supplemented it with fish.
For the movie, we wanted to watch Whale Rider, one of Rachel's favorites and considered one of the best New Zealand films. However, neither the local library, the Baylor library, Netflix, nor Amazon carried it. Ditto Hunt for the Wilderpeople, and Once Were Warriors seems a bit dark for our kids, but all three of those films are on my get-to list. We thought about watching Fellowship of the Rings, but our library didn't have a copy of that either, so we ended up watching some New Zealand All-Blacks rugby instead.
For the movie, we wanted to watch Whale Rider, one of Rachel's favorites and considered one of the best New Zealand films. However, neither the local library, the Baylor library, Netflix, nor Amazon carried it. Ditto Hunt for the Wilderpeople, and Once Were Warriors seems a bit dark for our kids, but all three of those films are on my get-to list. We thought about watching Fellowship of the Rings, but our library didn't have a copy of that either, so we ended up watching some New Zealand All-Blacks rugby instead.
In the Beginning: The Big Bang and the Early Universe
"I could be bounded in a nutshell, and count myself a king of infinite space" - Hamlet, Act 2, Scene 2
Lesson
Where was the stuff that makes up your body before you were born? Where was it before the earth was made? Where was it before then? Eventually, if we go back far enough, before the first stars, before planets or anything else that we see in the universe, the universe was a big cloud of invisible gas and was completely dark, before then, it was filled with a glowing white hot cloud that you couldn't see through. Before then it was a tiny dot, but even if you were in that tiny dot, the universe would look infinitely large, even though outside of it only looked like a tiny dot.
Alternative approach:
About 14 billion years ago everything you see in the sky and on the earth, everything in the universe existed in a tiny point smaller than the smallest speck of dust you have ever seen. For some reason (we don't know why), it started expanding. It's not that everything was in a point in space, space itself was in that point. Also, time started at that point. Some people think that if you started now and asked somebody and kept asking "what's before that," that eventually you'd get to the Big Bang, and you could say not only that there's nothing before that, that there isn't even a before.
Because everything in the universe was crammed into such a small space, it was so hot that a special state of matter above gas happened called plasma. For about 400,000 years the entire universe was a filled with a big glowing, white-hot fog as it expanded. After 400,000 years the fog dissipated, and the earliest air was formed. These gases were invisible though, so the entire universe was completely black, there were no stars, galaxies, or planets, just a lot of invisible air floating through space. Eventually some of that gas started to pull together because of gravity, and enough gas came together that they lit on fire and became the very first stars.
The universe is expanding faster than the speed of light. Because of this, when we look at very far away galaxies, we are looking at galaxies that are very young, we are basically looking back into time. [Show them a picture of the Hubble Deep Field image with the really dull red ones in back and explain that these are some of the earliest galaxies ever]. The more powerful our telescopes, the farther back we can see, except we can see some light from the Big Bang itself called the Cosmic Microwave Background radiation [show them a map of the COBE]. This light is a color that we can't see called microwave, this is the same light we use to cook our food in microwave ovens.
However, because both time and space are expanding, space can be infinite (we have infinite galaxies, planets, and suns) within a ball, because time is different in different places in that ball. So even when the universe was the size of a room from the outside, if we were in that room-sized universe it would still look infinite to us.
Some scientists think that there are other universes besides ours, some of the math predicts that there are.
Additional activity: Blow up balloon, draw points on it representing stars and galaxies and show how they all move away from each other when the balloon is expanding, explain that that's how we found out about the Big Bang.
Recommended reading for adults
Our Mathematical Universe, Mag Tegmark (first, Big Bang-relevant parts).
Future
I don't quite get the inflation-era stuff and need to brush up on that when my kids get older. Also, I don't quite understand how the volume of the interior of an inflating sphere can be infinite while the sphere is finite from the outside. It was explained in the Tegmark book above but it's one of those things I'll need to set aside some time to really focus on.
Sunday, January 22, 2017
Canada Day!
We've decided that once a week we're going to have a day dedicated to a certain country, where we eat meals from that country and watch a movie from that country (or a good movie we want them to see anyway that takes place in that country). Before we got married Rachel was heavy into international cinema, while I was a bit of an experimentalist foodie, and now our kids are old enough that we can enjoy these interests of ours with them. Hopefully this won't be something that sounds fun but dithers out after a few weeks. The rules are 1) you can't repeat the same country twice, and 2) we go in order from youngest to oldest on deciding which country we'll do. In our experience, whenever we give the kids an option it exponentially increases the fun that they derive from the activity.
So this week our youngest (3) wanted to do the "leaf flag country." We had a lunch of pancakes with real maple syrup and a few slices of Canadian Bacon from the Butcher's shop.
For dinner we found one food truck in Waco that served Poutine, the national dish of Canada: fries, cheese curds, and gravy (with mushrooms and beef in ours). It tastes a lot better than it sounds. All washed down with Canada Dry Ginger Ale (Rachel's favorite, which according to our brief Wikipedia research was in fact started in Canada).
At night we finished it off with another of Rachel's favorites--the first episode of the Anne of Green Gables 1985 Canadian miniseries. With all boys Rachel wants them to get at least some exposure to girlish things.
So this week our youngest (3) wanted to do the "leaf flag country." We had a lunch of pancakes with real maple syrup and a few slices of Canadian Bacon from the Butcher's shop.
For dinner we found one food truck in Waco that served Poutine, the national dish of Canada: fries, cheese curds, and gravy (with mushrooms and beef in ours). It tastes a lot better than it sounds. All washed down with Canada Dry Ginger Ale (Rachel's favorite, which according to our brief Wikipedia research was in fact started in Canada).
Saturday, January 14, 2017
Organizing the Univese: Base Ten and Zero
"God created the integers. All the rest is the work of man." -Leopold Kronecker
Introduction
The base ten concept is necessary for knowing how to add, subtract, multiply, and divide large numbers. When I was younger I was only taught the steps necessary to do these operations without really appreciating the concepts behind them, and it's easy to take for granted the power of places to compress so much information into few numerals. It's rather simple, but the development of places and zero is the doorway to being able to access everything interesting about mathematics above the basic business-oriented functions it was used for anciently like measuring out land and pyramid dimensions (with a few, limited exceptions such as Pythagoras above). This lesson is part utilitarian--they do need to have this down solid to do more than basic arithmetic, but I also hope to convey the power that human constructs have in organizing and making sense of the universe. The concept of "carrying the one" may be a bit difficult to grasp for younger children. My 7-year old almost has it down. Mileage may vary.
Lesson Plan
One way of counting is to make one mark for each item you have. In this way, if we wanted to show one hundred, we would have one hundred tally marks (show them how this might look). As you can see, this would take a long time to both make and count every time you saw it. Some early cavemen did numbers this way, often by putting notches in bones or counting out pebbles, but they usually didn't have to count very high, so it was okay. Some ancient societies would only have numbers up to four, and then every number after that was " a lot." Ancient Romans would only name the first four children, then all of the ones after that became "the fifth," "the sixth," etc. Some people think that this group of four rule is because that's as many as you can count to before you get to all the fingers on the hand. V for five is almost as universal as I for one.
Another way might be to have a different symbol for every numbers. But here you would have to memorize every single symbol, so to memorize all the numbers up to 100 you would need 100 different symbols. Also, it would be very hard to add these symbols together. Some ancient languages would use letters as symbols for numbers, so in Hebrew the first letter equals 1, the second equals 2, and so on. People could then use groups of letters to show numbers. Some religions would believe in sacred numbers because they would add up to the name of God, or something like that. In the Bible it says that the mark of the devil is 666, so some people think that a bad person's name near the end of the world will have letters that add up to 666. This shows you how powerful numbers could be for religions.
The way most ancient societies counted things is groups of symbols. They would have a few symbols that would represent certain numbers. This way, they would only have to memorize a few symbols, it was easy to add, and it didn't take long to count up the number of symbols.
[Show examples from Roman numerals, Ancient Egyptian]
However, for really big numbers it was still hard to add a lot of numbers together, and still took a long time to write. The ancient Babylonians started to use places, so instead of having lots of symbols showing groups of different amounts, the Babylonians made each place equal sixty of the earlier place. They needed to do this because they were one of the first empires in the world, and had to figure out how much money they could get from the people they ruled, so they needed to use big numbers. Some Indian groups used places as well, but they would use it on a knot of cords, and wouldn't write it down, so people would have to bring the knot with them wherever they went to show people a certain number. Being able to just write down the number made things a lot easier.
Nowadays each place is ten of the place to the right of it, this is how most number systems today work. However, they had to somehow show if there was one place that was missing, so for example 406 is different from 46, so they came up with a symbol that meant that showed that four is four groups of one hundred, even though there are no groups of ten.
[Those color-coded blocks of 1, 10, 100, and 1000 are very helpful here to show them the idea of groups of ten]
The Babylonians came up with a placeholding symbol, but it wasn't the same as zero. Zero had not been invented yet. At first they used a space to show the gap, but it was sometimes confusing because the spaces often weren't big enough, so a sign that represented a space, or nothing became very useful.
[At this point an abacus is useful to show them the idea of groups represented by different symbols/colors, with a space equaling a space in the groupings].
The Greeks and Hebrews didn't like the idea of nothing, so they never used zero. Eventually the Indians used zero, and it caught on fast because with zero they were able to do very large calculations. The Mayans on the other side of the world invented zero independently.
With zero you have a lot of tricks for adding and subtracting large numbers [show them carrying the one, subtraction, etc.]. It would be very hard to do this without zero or places (try it with Roman numerals).
With the base ten system that we have today, you can do large calculations with very big numbers, like 10 billion, 543 million... + [another big number--for kids used to adding 3 +5 this blows them away]. Because it's 10 groups of a billion, 500 groups of a million, 40 groups of a million, 3 groups of a million.... So if you add the same groups together you get the two numbers added together.
We still do use a base one system though for computers, because one means a switch is on and zero means a switch is off. So for a computer 100 is four.
Future Lesson Development
The real significance of zero kicks in when we get to calculus. I'll use Xeno's paradox and the Greek's inability to solve it without zero as a launching point for the discussion of calculus, and how mathematics stalled for almost two thousand years because people didn't see the full implications of zero.
Reading for Parents
There are a lot of "history of numbers" books that are worthwhile reads. For zero, Zero: A Biography of a Dangerous Idea does an excellent job of describing the implications of place notation and zero in a non-mathematician, reader-friendly way.
Video Resources
The Story of One is a BBC documentary on the history of numbers that looks promising, but I haven't watched it yet so I don't know if it's age appropriate.
Introduction
The base ten concept is necessary for knowing how to add, subtract, multiply, and divide large numbers. When I was younger I was only taught the steps necessary to do these operations without really appreciating the concepts behind them, and it's easy to take for granted the power of places to compress so much information into few numerals. It's rather simple, but the development of places and zero is the doorway to being able to access everything interesting about mathematics above the basic business-oriented functions it was used for anciently like measuring out land and pyramid dimensions (with a few, limited exceptions such as Pythagoras above). This lesson is part utilitarian--they do need to have this down solid to do more than basic arithmetic, but I also hope to convey the power that human constructs have in organizing and making sense of the universe. The concept of "carrying the one" may be a bit difficult to grasp for younger children. My 7-year old almost has it down. Mileage may vary.
Lesson Plan
One way of counting is to make one mark for each item you have. In this way, if we wanted to show one hundred, we would have one hundred tally marks (show them how this might look). As you can see, this would take a long time to both make and count every time you saw it. Some early cavemen did numbers this way, often by putting notches in bones or counting out pebbles, but they usually didn't have to count very high, so it was okay. Some ancient societies would only have numbers up to four, and then every number after that was " a lot." Ancient Romans would only name the first four children, then all of the ones after that became "the fifth," "the sixth," etc. Some people think that this group of four rule is because that's as many as you can count to before you get to all the fingers on the hand. V for five is almost as universal as I for one.
Another way might be to have a different symbol for every numbers. But here you would have to memorize every single symbol, so to memorize all the numbers up to 100 you would need 100 different symbols. Also, it would be very hard to add these symbols together. Some ancient languages would use letters as symbols for numbers, so in Hebrew the first letter equals 1, the second equals 2, and so on. People could then use groups of letters to show numbers. Some religions would believe in sacred numbers because they would add up to the name of God, or something like that. In the Bible it says that the mark of the devil is 666, so some people think that a bad person's name near the end of the world will have letters that add up to 666. This shows you how powerful numbers could be for religions.
The way most ancient societies counted things is groups of symbols. They would have a few symbols that would represent certain numbers. This way, they would only have to memorize a few symbols, it was easy to add, and it didn't take long to count up the number of symbols.
[Show examples from Roman numerals, Ancient Egyptian]
However, for really big numbers it was still hard to add a lot of numbers together, and still took a long time to write. The ancient Babylonians started to use places, so instead of having lots of symbols showing groups of different amounts, the Babylonians made each place equal sixty of the earlier place. They needed to do this because they were one of the first empires in the world, and had to figure out how much money they could get from the people they ruled, so they needed to use big numbers. Some Indian groups used places as well, but they would use it on a knot of cords, and wouldn't write it down, so people would have to bring the knot with them wherever they went to show people a certain number. Being able to just write down the number made things a lot easier.
Nowadays each place is ten of the place to the right of it, this is how most number systems today work. However, they had to somehow show if there was one place that was missing, so for example 406 is different from 46, so they came up with a symbol that meant that showed that four is four groups of one hundred, even though there are no groups of ten.
[Those color-coded blocks of 1, 10, 100, and 1000 are very helpful here to show them the idea of groups of ten]
The Babylonians came up with a placeholding symbol, but it wasn't the same as zero. Zero had not been invented yet. At first they used a space to show the gap, but it was sometimes confusing because the spaces often weren't big enough, so a sign that represented a space, or nothing became very useful.
[At this point an abacus is useful to show them the idea of groups represented by different symbols/colors, with a space equaling a space in the groupings].
The Greeks and Hebrews didn't like the idea of nothing, so they never used zero. Eventually the Indians used zero, and it caught on fast because with zero they were able to do very large calculations. The Mayans on the other side of the world invented zero independently.
With zero you have a lot of tricks for adding and subtracting large numbers [show them carrying the one, subtraction, etc.]. It would be very hard to do this without zero or places (try it with Roman numerals).
With the base ten system that we have today, you can do large calculations with very big numbers, like 10 billion, 543 million... + [another big number--for kids used to adding 3 +5 this blows them away]. Because it's 10 groups of a billion, 500 groups of a million, 40 groups of a million, 3 groups of a million.... So if you add the same groups together you get the two numbers added together.
We still do use a base one system though for computers, because one means a switch is on and zero means a switch is off. So for a computer 100 is four.
Future Lesson Development
The real significance of zero kicks in when we get to calculus. I'll use Xeno's paradox and the Greek's inability to solve it without zero as a launching point for the discussion of calculus, and how mathematics stalled for almost two thousand years because people didn't see the full implications of zero.
Reading for Parents
There are a lot of "history of numbers" books that are worthwhile reads. For zero, Zero: A Biography of a Dangerous Idea does an excellent job of describing the implications of place notation and zero in a non-mathematician, reader-friendly way.
Video Resources
The Story of One is a BBC documentary on the history of numbers that looks promising, but I haven't watched it yet so I don't know if it's age appropriate.
Friday, January 6, 2017
Where We Came From: Human Evolution
“In the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil.”- Genesis 3:5 King James Version
Introduction
This is a subject where the forest can easily get lost in all the trees of the technical debates about the different possible evolutionary lines and species. Consequently, I try to focus on the big picture climate and evolutionary changes, and only mention the most major species (e.g. Homo Erectus). Presumably later iterations of this lesson will get into more detail about the other species.
Throughout the lesson I refer to other hominids as “our ancestors” or “your great, great, great… grandparent or grand uncle” I’ve found that the idea the idea that our ancestors were different animals naturally peaks children’s interest.
Also, I refer to the other hominids as “other kinds of humans.” This is technically correct, and once again the connection to “other humans” peaks children’s interest more than just “other animals” does.I'll sometimes use dogs as a touchstone("just like there are different types of gods, there used to be different types of humans").
Lesson Plan
A long time ago our great great… grandparents and monkey’s great great… grandparents lived in trees in Africa. At some point, however, some of the trees started to die off and there were a lot of fields and bushes instead. Our ancestors moved into those forests with lots of fields and bushes, while another group stayed in the trees. The group that stayed in the trees became chimpanzees, and the group that left the trees eventually became us.
The group of monkeys that left the trees eventually started to walk on two legs, some scientists think that this is because the ones that walked on two legs were better able to survive in the fields because they were able to look over the tall grass, and maybe protect their bodies from sunburns.
These monkeys looked like monkeys, only they walked on two legs (show them a picture).
Eventually, because they walked on two legs, they could use their hands for gathering things and creating sharp rocks and other things to hunt. They could not have done this without walking on two legs because their hands would not have been free.
Once their hands were free, the smartest ones survived and had more children because they were able to figure out how to use their hands to make stone weapons and tools, so their brains started to get bigger.
At this point there were some humans that were able to make tools, but they still weren’t as smart as us, they couldn’t talk a lot to each other, and they still looked like monkeys walking on two feet.
Because the brains started to get bigger, women had to deliver babies earlier because their heads were getting too big to fit through their legs. Because babies were getting delivered earlier they had to spend more time with them. They couldn’t just have them and then leave them after a short time like some animals. They also had to he social and like families and groups, so that their groups and families could help raise their children. Because they had to protect their babies for a long time they formed groups. Usually women die after they’re too old to give birth, but in humans women keep living, and we think that it’s so that they can help with their grandchildren.
Eventually, some of these humans started to take care of their older people and weaker people. They also started to use fire to cook food so that they could hunt bigger animals and not get sick from their meat. Up to this point all of the humans were in Africa, but some started to leave and search for living areas elsewhere. One type of human that came out of this was Homo Erectus. Homo Erectus is the longest living type of human, they were on the earth 9 times as long as we’ve been. Homo Erectus went to South Asia (show them migration routes on a map). Some of them must have crossed oceans, so maybe they had early boats. Another human was Homo Heidelbergensis that was the first to live in really cold areas (Northern Europe). We think that they were the ancestors to Homo Neanderthals, which were a species of human that lived next to us in Europe. Also, some scientists think that Neanderthals and us had babies together, and that some of our ancestors were both Homo Sapiens and Homo Neanderthals. Homo Neanderthals may have had white skin and red and blond hair.
Eventually, since we were getting smarter and formed groups, some of our ancestors invented language and started talking. We don’t know if it was our own species or one of the earlier ones that first started talking. Eventually all of the different humans but us died off. The last two to die off were the Neanderthals in Europe, and a dwarf species of humans that lived in Indonesia that only died out about 10,000 years ago. Some scientists think that we killed them off.
Future Lesson Development
The Smithsonian National Museum of Natural History has some lesson plans for Jr. High-level students. I’ll look into those when my children are older. Also, I’ve taken them to the exhibit before, but the Smithsonian’s Human Origins exhibit in Washington D.C. is incredible.
Reading for Parents
The Third Chimpanzee: By far the most readable, enjoyable work on human evolution out there.
Also, from a more spiritual perspective, Hugh Nibley’s “Before Adam” is a good discussion from a Mormon perspective (although sometimes he’s a little too skeptical about the science).
Web Resources
Human Evolution Interactive Timeline
http://humanorigins.si.edu/evidence/human-evolution-timeline-interactive
Video Resources
BBC’s excellent Walking With series has some good episodes that involve early hominids. Specifically, they have the four-part Walking with Cavemen series, as well as the latter half of the Walking with Beasts series.
Material Resources
The classic charts that show a linear progression from earlier forms to Homo Sapiens can be misleading as they imply a higher level of certainty about relationships than we have--and possibly will ever have. The particulars about who descended from who is fiercely debated in human anthropology, and most of the details about the “family tree” type charts are highly arguable. Posters that take the overlapping timeline approach may be useful.
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