Thought Overflow…Golda’s BlogIf memes are like genes, then having a conversation in which you share ideas and come up with new ones is like…?


Archive for the ‘Education’ Category

So I was riding my bike back from Trader Joe’s on my lunch break, and a thought occurred to me (all my best work is on a bike, or in the shower…). If the universe is close to 14 billion years old, and the furthest galaxies we can detect are close to 14 billion light years away, have they been traveling away at the speed of light to get that far? Because I didn’t think stars moved that fast.

But yep – its the fabric of space that expands, and even faster at large enough distances. I hadn’t thought about that before.

This Is How Distant Galaxies Recede Away From Us At Faster-Than-Light Speeds

Need to write this up as another thought-provoking thing for kids just learning physics. There is so much we could do by letting kids think about the questions for at least a little bit before providing the answers!

0 Binary Kids

Golda to Education,Kidstuff  

This variation on Twenty Questions teaches kids a bit of information theory and lets them take a different approach to powers of 2.

First, the kids should be familiar with the regular game of Twenty Questions.

Then, ask as an open-ended question: “Suppose instead of the whole world. you were only allowed to think of certain objects. How many questions would it take to find the right one? What if the questions had to have only yes/no answers?”

0 1/3

Golda to Education,Kidstuff  

Here is another opportunity for discovery: one-third. For kids who have learned how to divide and get decimals (or show a child briefly who has learned long division and knows what decimals are). Ask simply, what is one-third in decimal?

The discovery that 1/3 = .33333333… the repeating decimal, is surprising enough on its own for a child who has never seen an infinite series before. What usually will tweak their curiousity, though, is to continue – ok, what is 2/3? Then wait a moment, and see if they think of 3/3 by themselves. The idea that 3/3 = .999999999… may get the child saying, wait a minute – 3/3 = 1!

They have just proved that an infinite series can equal a whole number; if your child doesn’t want to accept it, that is ok. Just assure them that if the series stops anywhere, it is less than one, it only equals one if it is really infinite.

The fun thing is, this can be done by a 4th grader.

0 Zeroth Power

Golda to Education,Kidstuff  

For kids who have been introduced to exponents but haven’t been taught specifically about what it means to take ‘N to the zero power’, this is an opportunity for a small ‘Aha!’ moment.

If a child already knows what is ten to the 2 (10^2 = 10 * 10 = 100) and 10^1 = 10, ask them what is 10^0.

Let them think a bit. Many kids will answer ‘zero’. Ask, well, then what is zero times 10? If its not 10^1, then that can’t be right.

Explain that 10^0 must be the thing that you multiply by 10 to get 10^1. This should be enough of a clue that they realize that 10 to the zero is 1.

Then, without any other explanation, ask something that sounds hard – “what is eighty-seven to the zeroth power?” With a bit of thought, your child may be able to come to the sudden realization that everything to the zeroth power is 1!

(This only works if they haven’t already been taught this fact in school – it is fun to discover things that no one has told you. So don’t be afraid to try this somewhat early, before most schools cover it.)

Here is a fun way to introduce kids to the concept of modulus (without ever saying the word): ask, why does a week have 7 days? Suppose you could change it – how many days would you put in the week? Then ask some questions about ‘in X days, what day would it be?’

It helps to ask the child to consider the days as being named by number at first, to look at the patterns, starting with Zero-day and continuing as One-day, Two-day (which conveniently becomes Tuesday if Sunday is Zero-day), etc.

Start with simple questions like “So if your week has 5 days, and today is Three-day, what day will it be in 6 days?”

Make sure to ask several with the modulus “If your week has 4 days, and today is Zero-day, what day will it be in 4 days? 8 days? 16 days?”

Once they realize that it always goes back to the same day every time the number is a multiple of the days in the week, kids can have fun answering what sound like ‘hard’ questions: “So your week has 9 days, today is Seven-day, what day will it be in 80 days?” (answer – Six-day, one before the same day since 80 is one before an even multiple of 9)

Other interesting questions might be ‘can we have a half-week?’ Or for more advanced students, suppose you have weeks and grods, weeks are 8 days and grods are 4 days. Is it always the same weekday on the same grod-day? What if weeks are 7 days?

Back when my kids were smaller, I collected clever (ok, I thought they were clever) teaching techniques and published them to a website…a drupal6 website. Since I don’t want to maintain drupal, I’ve moved the bits I’m really attached to here…

Just found P2PU – Peer to Peer University – on a list at reddit of online learning resources

This looks really cool. The ones I’m most excited about so far are

BOINC for citizen scientists

tools for content curation

Books, language, reading are so foundational to everything that it doesn’t seem to need saying. I’ve been thinking for some time of a site that would be ‘’ or something similar, for people to donate books to other individuals.

This site is not exactly what I was thinking of, but close. Found it from a Rafe Esquith video on Youtube. Seems worth checking out. If its good, will post the details on
update: looked at the site, while the causes they support seem positive, I’m really looking for something much less scripted and controlled. For instance they have a program specifically giving African-themed stories (“Tinga Tinga tails”) to schools in East Africa. This is all right, but it feels to me a bit patronizing; and ‘Conspiracy for Good’ which is a sort of live drama but it is unclear to me from reading it what part, if any, of the story is true? I am not saying not to support, it is certainly doing good and is getting the job done of delivering thousands of books where they are needed! I am only thinking that at some point I would like to see a person-to-person solution that helps people give specific books that they feel are valuable, and helps others get books they specifically want (whether or not the solution involves supporting libraries or clearinghouses).

When I talked several years ago to the owner of a company involved with maquiladoras in Mexico, he was not interested in discussing living standards or wages of his employees, but expressed willingness to donate to a local library. It may be that US companies operating overseas could be tapped to donate to libraries in the areas where they operate. This particular company was a client of mine, thus I had at least one time access to speak to the owner, but I find that following the five-F policy (Fair, Fast, Friendly, Factual, Frank) it is often possible to get a short conversation even with very busy and important people.

* I read of the five-F’s many years ago in a public relations book, but I think they apply in many other contexts as well.

I’ve been wanting to start this site for years, finally doing it. Its not themed yet, but a bit of content is there: – everyday ideas for learning and teaching. The idea is to capture teaching ideas, large and small, and relate them to subjects, age groups, philosophies, etc. Its not as formal as lessonplanet, the ideas can be informal descriptions of games you can play in the car as well as more detailed teacher-style plans. Its intended as a resource for parents, teachers and older kids, but not as a fully fledged curriculum source.

Check it out, and feel free to add ideas!