Accuracy, Precision, Sig Fig – Intro Activities

In order to introduce the concepts or accuracy and precision, I ask my class to take out a watch (stopwatch from their phones are fine, but I also like having someone use a wrist watch) and time Usain Bolt’s 100m run for themselves.

Although I don’t cover up his actual time, one could edit the video to remove it for more “authenticity”.  After the video, I take a list of times students have measured.  It may look something like this:

• 9.90s
• 10s**
• 8.90s
• 10.10s
• 9.30s
• 9.48s
• 9.61s
• 9s**

Bolt’s actual time is 9.58s.

**these times would be ones that come from a wrist watch; most/all smartphones time up to 2 decimal places.

Having a list of numbers for comparison, I ask the students to discuss what accuracy and precision might mean.  Although the concept of accuracy is relatively simple for students, I find this intro gets students thinking about precision and significant figures more closely.  To discuss all these concepts, I may use leading questions like:

• What do you think precision is? How might it relate to the times we’ve measured?
• Why do you think I got everyone in this class to take measurements?   Would it have been better if I asked a single student to measure the time?
• What’s the difference between a stopwatch vs a wrist watch for measuring time?
  • If we re-measured the time with both measuring devices again, what do you think would happen?
• How come our time measurements are different from the value from the video?
  • What kind of things do you think the timekeepers did to ensure accuracy?

The depth of the discussion would of course depend on the class makeup and experience of the teacher in facilitating discussions.

A follow up activity would involve length measurements. Each group of students would receive two rulers measuring rulers (printed on paper, shown below) and are asked to measure the width of an object, such as their textbook:

This could potentially lead into a discussion of significant figures and precision.  Once again, the quality of the discussion would depend on the questioning skills of the teacher and class make-up!

 

Chicken and Egg

Innovation.  It’s a word that has been constantly poking and prodding in my mind like a hangnail especially over the past few days.  Innovation as in what are the steps we can take to meaningfully change things in education?

Reading and pondering about this led me to revisit a couple of chicken and eggs problems I’ve always wondered about:

Do our assessment methods change how we teach or does teaching change the way we assess?

I’ve been following the old I’m-going-to-try-whatever-I-think-seems-interesting-and-deal-with-the-consequences-later approach.  In my earlier attempts, I’d always change the way I taught something and then think about how to assess later.  I could espouse some intellectual rationale behind it but it’d be a lie.

Over the years, I’ve developed quite an allergy to marking labs, tests and pushing papers in general.  I usually needed to steel myself (with the aid of beverages for example) prior to spending the next couple of hours of my life doing it.  If I ever thought about assessing or marking this and that, I naturally got kind of turned off doing whatever it is I planned to do. So I didn’t.

I now take into account assessment strategies in the learning design process, but it took a while to stomach the idea.  I suppose it’s kind of like eating broccoli. (I enjoy broccoli for the record)

There are frameworks out there such as assessment for learning that preaches formative assessment strategies as a way to improve teaching.  It makes no mention of how to design learning processes and frankly it doesn’t seem to matter since it can fit into any system.

Does the educational climate affect teaching in the classroom or does inspired teaching lead to changes in the educational climate?

Pasi Sahlberg did a talk asking a very similar question – would it make a difference in the United States if they simply swapped teachers with Finland and kept the educational climate (policies, culture, etc.) the same?  (Hint: his answer is not much.)

It’s not all about teachers. I think we need to have good teachers, but I also think we need to have something else. – Pasi Sahlberg

Another way to put this is whether the most impactful innovation in education comes from the classroom or whether it comes from above (i.e. ministry of education).  If a teacher is doing something really innovative, it may not actually change much because of the poor culture he/she is surrounded in.

I thought about a lot of the well known people in education (including bloggers I follow) I heard of and I realized that a lot of them live or work in the United States. Pasi Sahlberg (Finnish, works for Harvard), Linda Darling-Hammond (Stanford), Dan Meyer (CEO Desmos, US born), Sal Kahn (Kahn Academy, based in USA), etc…

So if USA has a lot of these innovators in education, why is it that by many standards of measure (PISA being one) it is considered to be below average?  I honestly can’t think of any educational leaders from top ranked countries such as Korea, China and Singapore.  Either this suggests educational climate is more important than teachers or it might just simply be an embarrassing highlight of my ignorance and my Western bias.

On the other hand, do educational reforms lead to better teaching? No Child Left Behind, Race to The Top and other initiatives are heavily criticized for making the state of education even worse.  The charter school system is often thought of as being promising – people like Bill Gates seem to be enthusiastic about this idea.  I don’t know if there is any data out there on the performance of US charter schools vs other countries, but I’d imagine the PISA rankings include them and it doesn’t seem to significantly improve the system as a whole in the States.  Maybe it’s just a case of it being too soon to tell.  Or maybe charter schools don’t really improve education.  Either way it doesn’t quite answer the chicken and the egg problem.

Artificial Intelligence and Learning

Recently, I’ve been following the Go matches between Lee Sedol and Google Deepmind’s Alphago.  Even when IBM’s Deep Blue beat Gary Kasparov in chess, I wasn’t really interested (partly because I was only a kid then) and didn’t think it was such a big deal – after all, a computer could just simply calculate out all possible positions within a much faster time period compared to a human.  Therefore, it wasn’t a shock – I had almost dismissed it with an air of inevitability.

Go (or Baduk in Korean) is supposed to be different.  There are simply too many moves for a computer to “brute force” their way through a game.

“If you ask a great Go player why they played a particular move, sometimes they’ll just tell you it felt right… Go is a much more intuitive game, whereas chess is a more logic based game.” – Google’s DeepMind CEO, Demis Hassabis (link to video here)

Does this mean they have figured out a way to program machines to be intuitive? This got me hooked and I started looking into it more.

It turns out since computers can’t simply calculate every single possible move in Go, Alphago has been programmed to gather data and learn each time on how to play the game better – a learning machine.  I thought then that if Alphago has essentially been modeled after how humans think and learn (and arguably do it better), it might just have some profound implications on education as a whole.

So how does Alphago learn and think exactly? Although I only have a partial understanding, from what I gather it comes down to a combination of four main techniques: Monte-Carlo Tree Search, Policy Network, Value Network and Reinforcement Learning.

Monte-Carlo Tree Search (MCTS) is a mathematical model or algorithm that creates a branching list of possible moves, but takes a random sampling of the possible moves.  So in Go, MCTS would create a branching list of the possible moves the computer can play and follows through the next few moves to be able to analyze it.  Each move that’s analyzed is then given a rating of how good it is.

Monte Carlo Tree Search, taken from Wikipedia

The Policy Network seems to provide the program with a way to choose which move to play/analyze, so the chosen move isn’t random.  The policy network is able to choose the best move(s) based on it’s match history (i.e. a large data bank of past professional Go matches and past games Alphago itself has played).

The Value Network analyzes the overall impact a move might have towards the win conditions.  I’d imagine Alphago not only takes into account the total number of immediate “points” a move earns, but also looks at future impact of a move.  I take this akin to a person secretly going out for a smoke when their spouse isn’t aware – it might have horrible consequences later, so is it worth it?

The three above together work really well, but the quality of its play is really dependent on the size of its match history.  If Alphago’s memory or data bank is too shallow, it won’t be able to “judge” the best moves from its Policy Network properly.

This is where Reinforcement Learning comes in.  Every time Alphago plays a match, its data bank grows.  Slowly over time, with enough matches in its data bank it’ll be able to play more and more effective moves.  Prior to playing the Go master Lee Sedol, Alphago supposedly played millions of simulated Go games by itself.  Alphago’s programmers never coded instructions on exactly which move it should play.  It simply programmed the game objectives and gave it tools to best “figure out” how to play the best moves.

So essentially Alphago:

1. Looks at a board position
2. Estimates all reasonable moves based on it’s memory
3. Picks the one that is likely to provide the best chances for fulfilling the game objectives

This is very much like how humans learn, isn’t it?

Humans would:

1. Take note of empirical data or observation
2. Estimate or build a rationale on what’s happening and/or what to do based on our past experiences
3. Pick the best course of action based on our objectives

So what kind of insights on learning and education can we gain from Alphago (and AI in general)?  Here are a few:

• Alphago in a sense supports constructivism as a mechanism for acquiring knowledge and as a consequence supports the validity of inquiry based learning such as PBL.
• It would also place a lot of importance in learning and gaining expertise through practice, something that in my opinion is getting lost in the shuffle with the new curriculum.
• Artificial intelligence is going to change the world.  Our education system needs to place greater importance in STEM subjects including computer science to provide society with a way to better understand the world around us.
• Studying/building AI is in a sense constructing a working model of how humans learn.  Just as we use models to describe the atom and its interaction with each other, we can do the same using AI.  Not only that, just as we use various models depending on how the circumstances suit us (i.e. Bohr model, VESPR theory, MO theory, etc.) perhaps there is more than one way to create AI models to mimic different aspects of human learning.  If a particular AI doesn’t work, then it could potentially put doubt into the educational psychology model on which it is based on.

There are also potential insights or avenues to explore from what artificial intelligence currently can not do:

• Where does motivation come from?  Alphago had to be programmed with the objectives of the game and its whole design is to become better at it.  A human being can know the objectives but may not care too much about playing the game.
• Where does purpose come from? How are we able to perform tasks in which there are no clear given goals, unlike in a game? Humans can figure out what the overall goal is in an environment without ever being explicitly told.

Equilibrium PBL – Student Misunderstandings

The equilibrium PBL started about a week ago.  I put students in groups of three and each group was given a challenge.  One of the things I found out quite quickly is that some challenges are easier than others.  Below is a characterization of each challenge from what I’ve seen in my class thus far:

Water Challenge

Students had a tough time trying to figure out what equilibrium would work with water.  There was actually a lot of variety in the potential equilibrium students “came up” with.  This showed me a couple of things:

• Students don’t know how to use Google or search engines – they are not very good at identifying idea words and incorporating into good search terms.  There’s a tendency for students to type in entire questions in Google. (“water equilibrium” on Google would probably turn up the ionization of water, which wouldn’t be helpful)
• Students tend to only look at either the first couple of search hits and when they see something promising, they don’t look for additional sources to gain greater understanding and corroborate the findings (i.e. make sure it’s valid).

An interesting equilibrium (that I didn’t expect) students came up with were:

• Using anhydrous copper II sulfate/copper II sulfate hydrate equilibria to detect water.

Both groups “found” the Cobalt II chloride equilibrium I originally had in mind and were able to figure out the how to shift the equilibrium and determine if its endo or exothermic.

Iron Challenge

This was probably the easiest challenge, in terms of figuring out what the equilibrium reaction could be (Thanks, Google).  There could have been multiple acceptable solution, but searching for the terms iron and equilibrium normally pops up the iron-thiocynate equilibrium pretty quickly.

The other potential solution could potentially involve the production of a precipitate (i.e. creating a saturated solution).

Even though they had looked up the equilibrium, they didn’t know how to start in terms of creating the equilibrium and how it might be able to detect the presence of iron ions in a solution.  This issue was prevalent through all the challenges.  I think this exposed a flaw in their understanding in how equilibrium systems work:

• They didn’t understand that an equilibrium will be established even if we start only with reactants or products.
• The “detector” could just simply consist of one of the reactants and the other reactant could simply be the chemical being detected.  This would push the equilibrium (a la Le Chatelier’s Principle) to the product side, which would need to have a distinct colour.

The groups designed and performed a series of experiments to demonstrate that they can shift the equilibrium left or right.

The second part of the challenge is by far the toughest task involved in all three challenges – to demonstrate whether the Keq is <1 or >1 or ~1 at room temperature.  Students struggled on exactly how to do this and they may not be able to design a credible experiment.  Instead of looking for the result, I’ll be looking for their thought process.

Drug Challenge

Students had a lot of trouble on figuring out what to do.  Some students thought it was the drugs that undergo the equilibrium (which aspirin or ASA does since it’s a weak acid).  Interestingly enough, the caffeine pills when placed in water produced a neutral solution when sources state that it’d be basic (which I expected as well).

This was a tougher challenge since students were lost on how to start and they needed to develop an understanding of what indicators are.  Once they figured out how indicators work (i.e. they are weak acids/bases) and that the equilibrium shifts in the presence of an acidic solution, it became much easier for them.  They didn’t get to explore/research what kind of other drugs their detector can differentiate (I’m looking for a basic drug, since caffeine is apparently neutral), but I anticipate they may have some problems with this.

Concluding Remarks

I would have loved to include some pictures of the students exploring, collaborating and experimenting with the chemicals.  There seemed to be much better teamwork, and they worked with a greater sense of purpose.  It was also very enjoyable from my point of view guiding each group, asking probing questions, and seeing the cogs in student’s brains working to build connections with the course material.  I’m excited to see what the groups end up doing by the end of this PBL!

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