Sep 222014

I love gummy bears (jelly babies). So do my kids and the neighbors’ kids. And probably the whole universe. To limit sugar consumption and its effect on teeth my wife and I introduced a candy day: Sunday every week.

That way the “damage” is limited to one day of the week. Also begging for sweets has almost disappeared. The kids have secured one whole day for eating candy that makes it much easier to focus on begging for other things on other days 🙂

Both the neighbor kids and mine (this time only three at aged four, six and eight years) look forward to their candy adventure march. Paying something on their own is still somewhat exciting for some of them – also being free and responsible puts them in the perfect state to learn things and have fun.

Last time I ended up going with them. When I discovered they would simply get the bag of gummy bears (€ 1.99) – which matches their budget of €2.00 almost perfectly, I asked why they did not consider a different bag which gets them more (slightly different) bears for the same or less money. It turned out they did not think about that. I pointed out that there were always two prices. One for the whole bag and one for 100 gummy bears. I am not sure how much the 8 year old neighbor kid understands me since I don’t speak Finnish. So I simplified things for the younger ones…

They started pondering and comparing numbers. The four year old was a little lost here, but was copying what she thought the others were doing. Eventually we approached the area where various types of gummy bears could be purchased per piece/weight. The price was given per weight and a scale needed to be used to determine the total. Initially they were reluctant to use the system on their own.

They did select candies like this before, but they did not have to fit a given budget (and did not feel responsible for anything since they only came along with the grown ups) – also a grown up usually did they weighing. This time they are responsible and only had €2.00.

When I said it looked like these were cheaper by weight, they became very interested and started shoveling bears and other candies into bags. Then the weighing began. The six year old’s bag cost €1.35. He would have been happy with that. I mentioned he could go back and add more candy until the scale shows €2.00. Off he went to do just that.

The eight year old understood very quickly and managed to fill her bag with candy worth €2.00 in the second attempt.

The six year old needed to add more candy a few times and when the scale showed 2.15 I only mentioned that he may need to remove about four bears or two of the heavy big chocolate things. It turned out this was not correct and the scale was still showing €2.08. He figured he would need to remove 4 more bears and finally reached €2.00. This produced a great smile and we high-fived each other.

The four year old was weighing and optimizing her bag too. The eight year old was helping her and they managed to reach €2.01. The eight year old asked me if that is ok and I said yes.

At the checkout when they handed over their 2€ each to the smiling lady behind the counter, I pointed out how the 1 cent (€2.01 of the four year old) did not show up on the screen. I think the six year old registered that, but we did not discuss this any further. He showed no interest.

Apart from feeling more independent and grown up now, I think, especially the six year old has begun to develop a feel for associating weight with numbers, decimals and perhaps how to get more candy for the same amount of money. He also became more confident to weigh things and not to be afraid to take candy back using the scoop. He also found another important use for numbers in his life which could boost his motivation to understand them further.

Perhaps I should mention that (on a good day) the six year old can easily count to 100 (actually the four year old is almost there too). He also reads simple books (perhaps two sentences per page) to his 4 year old sister (in English or Finnish) and he finds it fun to add together very long numbers which he gets mostly right. We had never talked about decimals before though. I still did not mention the word “decimal”. In Finland school only starts at age seven – so children have more time than in most countries to learn at their own pace and what they are interested in.

I am not sure what the 4 year old got out of the candy weighing game. I think she too may have realized that numbers can be very useful when it comes to candies.
She may have also learned that €2 can get her different amounts of candy depending on her choice. She is probably a little annoyed that her older brother can do another thing she is struggling with but she may know from experience that she can do that soon too. She too of course is not afraid to put candies back and she knows now a little better what that scale is for.


Keywords: understanding decimal numbers, weighing game, candy shopping game, learning decimals


Sep 162014

Someone posted in an instructional design forum the following question: If learning is not trackable is it still learning?
Below is my somewhat modified answer. I thought I would post it here too, as I have never seen this topic discussed in an ID context and people seem to find it useful.

If it is (in principle, for nobody, ever!) not possible to detect any traces that some sort of learning have occurred, then – of course – no learning in any practical sense – has occurred.

The question “If learning is not trackable is it still learning?” is a great example of what some call an ill-defined question/problem. Ill-defined questions are surprisingly common. They usually occur as a result of a good idea and intentions, but sloppy or rushed phrasing (it happens to all of us!). Often this can lead to wasted time and resources when people get lost in the hopeless search for correct – but impossible or meaningless – answers.

However, sometimes it is fairly obvious what the asker wanted to know and the inaccuracies in the phrasing don’t matter or even go unnoticed.
Chess players know this phenomenon as a “double blunder”. Both sides messup (one made a mistake, but the other one did not see it) but in practice it doesn’t matter since no-one noticed.

I think this may be the case with the above question too. However, it is not quite that clear to me.I think the OP probably meant something like “If learning occurs but could not be detected by the usual methods (often only automated summative assessment), can it still be called learning?” Perhaps she also meant “… can it still be a successful learning program?”

“Successful”, would also need clarification in this context. The learner may have learned something for “herself” only. Or perhaps the learner could have learned something that is useful for “the company” that sponsored the implementation of the learning program. Or both.

The great thing with these types of questions is that it can be easy to find the answers simply by realizing it is an ill-defined question and trying to formulate the question more precisely. It is not always so easy to spot these nasties though – or find the right phrasing. This is where good critical thinking skills are helpful.

Identifying and avoiding ill-defined questions is something I found extremely effective when designing and improving learning programs.

I have been chasing these tricky guys for years and still create or overlook them more often than I should. Nobody is safe from them and they seem to like hanging around me a lot.

The term “ill-defined” is also not my choice but a common term in areas like critical thinking and problem solving. We could also call them – perhaps more respectfully – “inaccurately formulated questions” or perhaps “misleading questions”.

Occasionally these questions do have useful (side) effects or can be used purposefully. For example, in order to trigger higher level learning experiences by trying to mislead the learner first, then let him discover his own mistakes and flaws in his original method.

The ill-defined question in this example could have such side effect. I certainly learned and refreshed a few things already while reading, writing and reflecting during this post. Thank you, ill-defined question.

Happy learning,


Keywords: exposing ill-defined questions, instructional design tips

Sep 162014

Ask George, an average person, what questions he has about quantum mechanics. I would guess he could only formulate one question – probably something like:

  1. What is quantum mechanics?

He may soon learn that quantum mechanics is the science of the very small: the body of scientific principles that explains the behavior of matter and its interactions with energy on the scale of atoms and subatomic particles.

After learning the answer to his single question, George will look for answers to questions such as:

  1. What are the scientific principles?
  2. What are examples of subatomic particles?
  3. When do things get small enough?
  4. How small are atoms?

While some answers may be answered to his full satisfaction without generating more immediate questions, answers to the more complex questions will most likely create new questions – often more than one. In other words, just a a few answers tend  to create a lot of questions.

I had many questions when I began to study physics. At the end of my studies I realized I had even more questions than at the beginning.  I did not expect that. First, I was disappointed. I even feared I had failed to learn things well enough. It was the moment when I became aware of my interest in “questions”.

I was fortunate to be surrounded by many knowledgeable people for many years. Both Cambridge, UK but also Silicon valley, USA were hotspots in that respect. One thing I noticed was that people I liked to learn from where those who also had questions. They often said that they do not know something – or they would love to know more about x.

Those who did not express their questions typically also did not share much of their knowledge. Perhaps it is harder for reluctant communicators to accumulate and create reliable knowledge? I could not help but suspect they did not know as much as their question loving peers. Occasionally I could confirm these when they could not answer the questions I had.

Later I found that question-lovers tend to be more knowledgeable in practically any area (where they ask questions..) – not just in academia.

Recently I asked my kids who they think knows more: a person who is not afraid of asking questions or one who does? It got them to think. I am pretty sure there are exceptions. However, as a rule, I rather ask if I feel I can learn something.


Keywords: asking questions, good questions, fear of asking a question