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World on the Weekend: Ecuador and the Inca Empire

The Inca empire only lasted approximately 80 years, but they left their mark on the Andes in the form of the terraces and monuments at the famous Macchu Picchu site.  There are also intriguing stories involving the Inca leader, Atahualpa, hiding gold from Spanish conquistador Pizarro, which, according to legend, still exists though none have found it.  Tragically, the Inca people who did not succumb to influenza and other foreign diseases brought by the Spanish, were either slaughtered or enslaved by the European invaders.  As a result, we have been left with tantalizing relics of a truly remarkable civilisation that we can only guess at.  Quipus are an excellent example: they consist of ropes of intricately knotted cords that we know were some form of communication, but whether the knots represented only numbers or words as well is still a subject of heated debate.  There is no-one alive today who can read a quipu.  As for the terraces, they were an agricultural marvel in that they used the steep slopes of the Andean mountains as a way to grow different crops at different altitudes and irrigate them all with a minimum of waste.  The government would have been centralized around a single monarch, this much we know from the historical battles that took place between successive generations of brothers. The empire itself at its height extended from the south of present day Colombia down as far as Chile though Macchu Picchu was its capital.  There would have been extensive trade between the different regions though food distribution was centralized so that the peasants would have received food through a system of hierarchical government and taxation. 

Note: This lesson came about after our lessons about the ancient civilisations in Greece, Egypt and Rome, when Child requested something closer to our home in Ecuador. 

Activities

Geography

Make a giant map of Ecuador or South America on butcher block paper.  You can make a simple glue out of flour, cornstarch and water which can be applied with a paintbrush.  This allows you to glue broccoli florets on the map to show the Amazon rainforest.  The Andean mountain range can a series of vertical paper triangles, the highest of which can painted white at the tip to represent snow.  The coast can be covered with green and gold glitter to show the mangroves and beaches.  Feel free to glue on pictures of local animals in the different regions such as

  • Giant tortoises and blue footed boobies in the Galapagos Islands. 
  • Monkeys, parrots, toucans, piranha and anaconda in the rainforest
  • Spectacled bears in the Andes

Music

Listen to traditional Andean music:  the Ecuadorian highland group Jayac, and the Bolivian band Los Kharkas are very good.

Math

You can make quipus by attaching several strings to a stick at the top.  Then you can use them to count (European-style) in several ways:

  • You can have the first string represent thousands, the next hundreds, the next tens and the last ones, so if you make 4 knots on the first string, three on the second, 6 on the third and 1 on the last, the number will read 4361.
  • You can tie the same number of knots on each string (ex: 5), and multiply the knots by the number of strings (ex: 4) and have the whole quipu represent the total (in this case 20).
  • You can have the last two strings on the right represent the amount in cents and the rest of the strings to the left represent dollars and write out prices.
  • You can also invent a secret code where the number of knots on a string corresponds to a letter of the English alphabet and “write” out words.  Even better, look up basic words in Quechua to write.

STEM, food

One of the nicest things the Incas cultivated was cacao used in, you guessed it, the making of chocolate. You can build a terrace in the style of the Incas in the nicest way possible: make layers of cookie or sweet bread dough and place them on top of each other in the style of a terrace.  Before you bake the dough, be sure to make little “irrigation channels” running from the top of the terrace to the bottom.  After taking it out of the over, let it cool and run chocolate sauce over it.  Use the chocolate pool at the bottom as a dip for Andean fruit such as bananas, strawberries and pineapples  

Discussion

In researching the Incas, I was fortunate to have access to a brilliant pool of history professors at Universidad de Los Hemisferios, to whom I owe my gratitude and probably another round of coffee. In many schools in Ecuador, saberes ancestrales or ancestral knowledge, is a required school subject, as well it should be.  Because of her father’s work as a tour guide, Child has been fortunate enough to meet Indigenous people in Ecuador and visit their communities, mainly those of the Kichwa, and the Siona – Secoya Amazon tribes in Tena and Succumbios provinces respectively.  She has seen how they still have huts with plaited grass roofs for ceremonies and how, though they usually wear jeans and t-shirts, they still wear ceremonial clothes with woven bird feathers and paint their faces with the red seeds from the achiote fruit.  She learned how they make chocolate by toasting and grinding the seeds of the cacao plant and how they make bread and a type of fermented drink from yucca roots.  Not all children have this opportunity, of course, but similar benefits can be had from both watching videos and documentaries, such as Global Grover, and simply by talking to the elderly in your own family or community.  My mother worked in a senior citizen’s day centre in the heart of the Jewish community, and I spent many hours after school visiting with the people there.  Many of them told me of their experiences surviving the Holocaust, and I certainly listened to them more attentively than I did to my teachers at school and probably learned a lot more.

Learning ancestral knowledge from our grandparents is a valuable education though the elderly are seldom used as a resource in today’s school curricula.  This is a situation best remedied within the family, if not with one’s  own relatives, then by visiting knowledgeable elders wherever they are found, whether in universities, parks or hospices.

Love&Logic: Edible games

You’ll need 10 different foods on a plate, ideally 8 healthy and one treat. I suggest

  • 0=carrot sticks
  • 1=celery sticks
  • 2= red pepper slices
  • 3=cheese cubes
  • 4=apple slices
  • 5=raisins
  • 6=almonds
  • 7=peanuts
  • 8=tangerine wedges
  • 9=marshmallows

Use an ordinary deck of cards. Face cards=10, A=1 and every other card is face value.

Game: The first player draws two cards, identifies the higher and lower numbers and subtracts the lower from the higher. They eat the food corresponding to the difference. For example, if I draw a 5 and a 2 then 5 – 2 = 3, so I eat a cheese cube. Then it’s the second player’s turn.

The game ends when all the marshmallows are eaten.

Imagining a new curriculum

We assume that the curriculum we have at school is the most obviuous and natural way to break down learning: you have reading, math, science (later divided into biology, physics, chemistry), history, geography, language arts. The details may change from school to school or between districts, but essentially kids are taught the same thing at schools all over the world.

J.K. Rowling did something pretty incredible in the Harry Potter books: she re-invented the school curriculum. She added subjects like «care of magical creatures» and «defense against the dark arts» that we muggles could learn from. Imagine a school subject where you learn to care for animals, or you learn to defend yourself against bigotry, chauvenism and intolrance.

That got me thinking. If I could invent a whole different curriculum, what would it look like? Here’s what I came up with:

Global citizenship
More than simply a superficial study of the history and geography of different nations, this subject would open students’ eyes to different ways of thinking, doing and being.  They would learn both tolerance and critical thinking as they consider how each society has come to develop and rank its values. (Fernando Reimers and his team have created an actual curriculum to teach this called «Empowering Global Citizens: A World Course»)
Media literacy
Students would read and watch all kinds of things, fiction and non-fiction, comics, social media, news, textbooks, documentaries and all kinds of other materials.  The discussions that follow would help them consider the differences between such concepts as fact, truth and opinion, as well as between bias, willful distortions and outright lies. (Various curricula already exist for this)
Social-emotional intelligence
Respect and empathy for oneself and for others is the cornerstone of any society. Great literature and profound discussion are the essential ingredients in any well-founded study of the humanities (This exists too: https://empoweringeducation.org/what-is-sel/).
Art creation and appreciation
Dance, poetry, film, literature, music painting, sculpting, theatre: the performance arts and the fine arts represent not only the pinnacles of human achievement, but, some might even argue, the very purpose of human existence.
Environmental awareness
We are all connected and interdependent on this small blue marble.  This is a value that must be instilled in the young before it is too late.
Logical-mathematical thinking
Patterns, sequences, causality, these and other ways of thinking are the foundation of any rational argument
Scientific inquiry and innovation
The question «what would happen if…?» is hard wired into every human baby.  As they grow, this line of inquiry must be tempered with a coherent code of ethics if our society is to progress.

Love&Logic: Elemental gifts

This link http://elements.wlonk.com/ has a gorgeous periodic table with bright, colorful pictures of what the elements are found in.

October happens to be a big month for birthdays in our family, but our family lives too far to buy them actual gifts. So we printed out the periodic table from the site, and chose pictures we thought each person would like. Then with Monopoly money, we «bought» the element. Gold (Au), for example, has an atomic weight of 79 (I haven’t actually explained atomic weights to Child yet), so we would have to «pay» $79 to buy it. Unfortunately, Monopoly money doesn’t include a $79 bill, so she had to work out that she would need $50+$20+$5+$1+$1+$1+$1. That’s alot of math! Then we took a picture of Child with the picture and the money and a handwritten birthday card and sent it to the family.

A gift appreciated by all!

World on the Weekend: England

ENGLAND

England has a fascinating history, from the Angle and Saxon tribes (among others) which gave the Anglo-Saxons their name, to the Norman invasion in 1066 which revolutionized our language, to the various kings and queens who each had their own fascinating and  often gruesome stories, to the expansion of the British empire and its subsequent collapse, all the way to the first Royal baby of African ancestry born not recently to the Duchess of Sussex (Princess Meghan Markle to you and me).  Since England has played such a dominant role in world history, it’s essential knowledge for any child growing up in our globalised society.

However, for younger children, I would say the most fascinating histories of England are those which didn’t actually happen.  The tales of King Arthur and the Knights of the round table and Robin Hood and his merry men are wonderful stories in their own right and form an integral part of our shared culture.  They represent ideals which, though based in fiction, are nonetheless beautiful.  Our visions of gallantry and gentlemanly chivalry come from the tales of sir Lancelot and his beloved, yet ever unattainable Queen Guinevere.  Our idea of military honor shows up in the tale of Sir Gawain and the green knight, while our belief in equality and justice for all is embodied in the tale of Robin Hood who stole from the rich and gave to the poor.

Activities

Language arts

We read lots of stories about King Arthur and the knights of the round table.  We acted out the story of how Arthur pulled Excalibur from the stone after all of the others had tried and failed.

Disney made an excellent animated version of Robin Hood in 1973 which we enjoyed.  We made  a «wanted» poster of Robin Hood by drawing his picture on a paper, and then «aging» the paper by rubbing a tea bag on it and gently burning the edges.

On a walk down to the local ice cream shop, I told Child the story of Romeo and Juliet.

Math

We read Sir Cumference and the First Round Table and other Sir Cumference books by Cindy Neuschwander .  Those are always a great favorite and highly recommended.

History

We watched footage of the royal weddings of Diana and Charles, William and Kate, and Harry and Meghan on YouTube, because naturally Child was enamoured of the idea that princesses really do exist.

We looked at pictures of the current Queen Elizabeth from when she was young until today: I printed some out and it was fun to sequence them. We did the same with Child’s own photos.

Food

Lunch was sandwiches which were said to have been named, if not exactly invented by, the Earl of Sandwich.  Dinner was fish and chips. 

Discussion

In a future lesson, I will probably delve further into the real history of England, since this time I focused primarily on the legends and folktales.  However, most of the late afternoon was rainy and lent itself well to storybooks and movies. 

«Sir Cumference» is an excellent series of story-based math books each with a different focus.  Sir Cumference and the First Round table is about how Sir Cumference tried all different shapes for the table before finally Lady Di of Ameter and their son Radius finally convinced him to try a circle.  It plays upon the tradition of the nobility of knights in the context of King Arthur’s Camelot. 

Child was thrilled to discover that England has a real royal family, which she had thought confined only to the realm of Disney fiction.  She was particularly impressed since her best friend happens to be named Megan. 

Love&Logic: «The solar system» Snake Board Game

Make a simple game board, like the one above, though it doesn’t need to be as fancy. Don’t write numbers on the squares, because the challenge is to work out ways to count to the square you need. However, for younger children, you can use post-it notes or small slips of paper to mark the multiples of 5 or ten.

Find simple pictures of the planets of our solar system and place them on the different squares in order. You can decide whether to inclue Pluto, the Kuiper Belt and other elements in our solar system. You don’t need to place a planet on each square, every two or three squares will do.

The aim of the game is to be the first to collect all of the planets in the solar system as well as the sun.

To play: Take turns drawing two numbers from a bag. Decide which way to read them, so if, for example, you draw a 2 and an 8, you can choose whether to go to square number 28 or 82. If there is a planet on the square you land on, keep it and continue playing until someone collects the whole set.

Math skills: This snake activity (and I will post many more related ones in future posts) helps children learn effective skip counting and addition. For example, if you draw 82, it’s much easier to count by fives (every blue) or even tens (every other blue) until you get to eighty and then add two more.

World on the Weekend: Ancient Rome

The contrast between the ancient Romans and the majority of their neighbours is impressive to say the least.  The people the Romans called «barbarians» included the Celts, Germanic tribes, the Viking tribes, the Gauls and others, and most lived in more or less the same way: mainly in small settlements of absolute filth and squalor.  They did have agriculture and they raised animals, and they did have religions and trade and a form of government after a fashion; but the Romans had armies and paved roads and baths and books and nice clothes and written laws.  The Romans had, in a word, a civilization.  That’s not to say they were any more charming than their heathen counterparts: they still had slavery, gruesome executions, used women as chattel, child labor and engaged in human rights violations of every kind.  What the Romans and barbarians really had in common was war: every man believed in fighting for honor and glory to the death.  The difference was in the techniques and strategies used to wage it: the Romans had legions of standing armies marching in thrilling formation and executing maneuvers with terrifying precision.  The barbarians did not, and tribe by tribe they were either slaughtered, pushed away or assimilated into the great Roman Empire as far north as the British Isles. 

Why is it worth teaching kids about the Roman Empire?  For older kids, it’s worth having them note that if the Greeks gave us democracy, at least as an ideal if not a model, the Romans gave us the idea of laws and justice, though again, not justice by our current standards (depending on what country you live in).  For younger children, it is interesting to continue the story of Ancient Greece, for they believed in the same pantheon of gods albeit with different names, and the story of Ancient Egypt, linked in many ways but most notably through Cleopatra’s relationships with Julius Caesar and Mark Antony.

Activities

Math:

Roman numerals are a useful math lesson in addition for younger children.  One fun way to practice is to turn the living room into a Roman marketplace by draping «togas» (sheets or scarves) around.  You can add fruit stands or jars of honey as well.  Place a price tag on each item in Roman numerals, give each person some play money and go shopping.  Notice that if you include the idea of bargaining, older children can practice the idea of dividing down the middle: for example, if the «seller» demands XXXX ($40) for a scarf and the «buyer» only wants to pay XXX (30) then a fair price is XXXV (35).  Younger children might need to be helped to count down and count up until they reach the agreement mark.

STEM:

We used rocks to build a road from Rome to England (from the tree to the fence).  Another challenge was to attempt to build an aqueduct to get water from the sink to the bathtub in the bathroom.  We used cut open plastic bottles, funnels, and everything else we could think of.  We had to prop the aqueduct up on blocks and stools. 

Science:

Most of the planets are named for the different Roman gods, so this was a good occasion to review the solar system.  We tried to guess why the planets have the names they do: for example, Mars is red because the God of war would have drawn blood; from a distance, Venus is the brightest and most beautiful as befits the goddess of love, though looking up close we realized we certainly wouldn’t want to live there.  We had to look up whatever we didn’t know about the planets, their moons and their names.

The Romans also worked on correcting the calendar: the Julian calendar was an improvement on the Alexandrian calendar and was later refined by the Gregorian calendar which we now use. Younger children can practice remembering the months by filling in a blank calendar and drawing pictures of important days in each month.  If they are able, they can also apply the «thirty days hath September» rhyme and try to fill in each month with the correct number of days.  This can lead to discussions of how to define a day, a month, and a day according to the motions of the sun, the earth and the moon, and why a precise calendar is so important.  Child was interested to know that the traditional Hebrew calendar starts in approximately September or October rather than January. She also wanted to know why we consider that a day starts at midnight rather than when the sun rises.

Interestingly for children, days and years on other planets are of different lengths.

Food:

Tomatoes, bread, cheese, herbs and olive oil, in essence true Italian-style pizzas were enjoyed by all.  Incidentally, pizzas provide excellent practice in early division in two ways: first the toppings must be evenly spread and then the pizza must be cut in equal pieces.  Watching the time as it cooks is also good for understanding how long 10 minutes really is.

Discussion

I don’t really remember studying much about the Roman Empire at school, and so, as an adult, I didn’t really consider its importance.  Child, however, really enjoyed the day.  That day, a friend of mine came, a fellow educator as it happens, which allowed Child to have fun with both of us.  She very much enjoyed the «shopping» game and draping scarves about herself, toga-style.  She even traced her feet on paper to make sandals and we used flowers and branches to make the type of laurels the emperor would have worn on his head. 

The aqueduct was a colossal failure, though a hugely entertaining one, because everything kept falling and we got wet. 

We built the «road» out of stones, but we only put them down in single file and they were hard to balance on.  We did enjoy «conquering the barbarians» (we informed our dogs they were henceforth under the command of Centurion Child and Centurion Mummy; they seemed happy enough, but otherwise unimpressed).

Learning the calendar was frustrating and so I reminded Child that «Rome wasn’t built in a day»; she eventually remembered the months after a few weeks of practice.

Naturally, Child enjoyed both the preparation and the eating of the pizzas, as did the rest of the family.

World on the Weekend: Ancient Greece

Ancient Greece didn’t actually exist in the way that we would define a country today.  It was a collection of city states including Sparta, Athens, Corinth, Crete, Macedonia and Thebes though the boundaries and number of city states was subject to much change over the time period.  Ancient Greece is important to know about because of the enormous contributions it continues to make even to the present day.  Greek mythology, which later gave rise to the Roman pantheon is a constant source of cultural reference, from the planets in our solar system which are named for the Roman gods, to Nike, the popular sportswear brand named for the Greek Goddess of Victory.  In fact, in Ecuador there used to be a domestic airline with what I thought was a rather unfortunate name: Icaro, possibly named by a not-quite-literate-enough owner (Icarus was the overly-ambitious demi-god with wings of wax who flew too close to the sun.) I refused to fly it.

The Greeks were also famous for their prodigious forays into science (Aristotle), math (Pythagoras, Euclid), philosophy (Plato, Socrates), medicine (Hippocrates), and literature (homer).  Each of these obviously constitutes  a massive field of study in itself, but the basic concepts as well as the biographies of these great men  can certainly be discussed with a child.

Activities:

Language arts and art

Reading stories about Ancient Greek mythology is always fun.  You can easily find coloring pages illustrating them if you’re into coloring on a rainy afternoon by the fireplace.  You can also act them out or even cut out pictures for a puppet show.  You can also look at famous paintings depicting scenes from the great stories.

Math and language arts

Game: Decide on a problem you might have, such as hosting a dinner party, or planting a garden or hunting a monster.  Take a hundred board and place the names of some of the gods and other mythical figures on different numbers.  Draw two numbers from a hat, ex 8 and 2.  See if there is a name on 28 or one on 82.  Decide if this god  can help you solve your problem.  If you think he or she can, you will have to perform a service for the god first such as

Drawing hearts for Aphrodite, goddess of love

Scoring a soccer goal for Nike, goddess of victory

Lifting something heavy for Hercules

Singing a song for Apollo, God of music

Throwing something at a target for Diana, goddess of the hunt

Drawing flowers for Gaia, goddess of nature

Telling the time for chronos, God of time

…or another character-related challenge.  Then you can write the god a letter telling him or her what you want them to do and burn them up in the fireplace as an offering.  How you continue the game is up to your imagination.

Math

Euclidean geometry is the study of planes and lines in two and three dimensional space.  There are many websites with explanations, games and practice tasks, and most children will eventually learn all of the key ideas at school. However, for Sunday afternoon play with younger children, games with blocks or flat puzzles such as tangrams are a good way to discuss geometry. 

One game we played was quite simple but fun.  I made a number of solid geometrical shapes from templates, along with cards with the name of the shape and the 2D picture.  The shapes go on the table with different coins inside.  The cards are shuffled and each player draws one, finds the matching 3D shape and takes the coin inside.  The winner is the one with the most money at the end.  Or, you could just pool the money for a treat.

Food

Greek cuisine often pairs something warm and flavourful such as lamb with something light and refreshing such as the yogurt and cucumber dip known as tzatziki. Greek sweets are often honey and nut based: Try baklava.

Discussion

We had a lot of interesting discussions about  values and morality in discussing the Greek myths. Though she enjoyed the stories, it often seemed to Child that the punishments were hugely disproportionate to the crimes or insults.  The story of King Midas, for example was almost shocking in its petty cruelty: he wishes for wealth and is granted the power to turn all he touches to gold. Then, horrifyingly, his young daughter comes running to him and she turns to gold the minute her picks her up.

Child loved the game where she had to perform services for the different gods because the tasks were physically active and challenging. 

The geometry game was harder than it looked because we had to work out from a flat drawing what the three dimensional shape would be. The names of the shapes were also hard to pronounce.  However, spending the winnings on the Greek sweets was a delicious way to end the game. 

Love&Logic: Harriet Tubman

Harriet Tubman was an amazing woman who risked her life not once but many times to help slaves escape North along the «Underground Railroad». She escaped first herself and discovered to her surprise how many people were willing to help with food and a place to hide during the day. As soon as she crossed the border to Pensylvannia, she resolved to go back down to Maryland and bring more slaves to freedom, and in the end managed to safely make the journey thirteen times. You and your child might enjoy the following version of the story on Animated Hero Classics: https://www.youtube.com/watch?v=YWVr57o_ElU

The game is a fairly abstract representation of the journey. You’ll need a simple map like the one you can find here: https://www.pinterest.com/pin/544513411178944902/?lp=true

I drew ten points on the line. Child and I both placed our tokens on the starting point in Maryland. Hers was Harriet Tubman, while mine was the slave catcher. The objective is simple: to rescue as many slaves as possible before the slave catcher catches her (land on the same point).

Child rolled the dice first and moved that many points. Once she reached the last one, she continued back. So if she rolled a 6 on the first turn, she moved 6 points, and if she rolled 6 on her second turn, she would move north 4 points and back south 2. When she got back to the starting point in Maryland, she would pick up an additional token representing another slave and continue playing, leaving the second slave token when she got to Pensylvannia and returning alone to get another. On my turns, I aim to roll whatever number will allow me to land on the same space as Child. When I finally succeed, I catch Harriet Tubman plus the slaves she is travelling with, at which point the game ends. In the games we played, Child managed to «save» as many as four slaves before I caught up with her.

Love&Logic: Evens and Odds

Child is very story oriented so I try to make math games around that idea.

I noticed she was having trouble skip counting by twos, though she can skip count other numbers like 3, 5 and 10 easily. I also wanted her to make the connection with evens and odds, which, surprisingly, she does seem to understand quite well.

She started by drawing a picture of a girl named Flower. We wanted to know what Flower likes/dislikes. But Flower can’t talk, she can only give us a yes or no through a special sign: we have to flip cards (ordinary playing cards without faces will do) and add them up. If the number is even, the answer is «yes», if odd, «no».

As it turned out Flower liked broccoli but not ice cream, and dogs but not cats.

Tomorrow, we plan to see if Flower and her friend like and dislike the same things. This is a rather sneaky way to repeat the whole exercise and give her more practice!