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Christopher Anand mixes programming, user interface design, and a step-by-step process to create problem-solving software.

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This video video outlines an outreach program focused on teaching coding and design thinking to children, predominantly in Canada. The program aims to enhance the training of mentors and develop educational materials, specifically a book. It identifies a gap in existing software's ability to teach creative problem solving effectively, an area of research interest for the program.

The program incorporates a programming language called Elm, which was developed to modernize web development for self-taught programmers. Elm's success led the team to create a graphics library to further simplify teaching coding, making it accessible to young children.

The curriculum emphasizes "algebraic thinking" to prepare students for challenges in secondary education, particularly in algebra, and focuses on debugging and functional programming. The instructors aim to develop students' critical thinking skills through practical problem-solving approaches, including the classic Tower of Hanoi problem as a teaching tool.

This video video discusses the importance of human-centered design, stemming from the works of Herbert Simon and George Dantzig during World War II. It highlights the need for empathy in design and education, emphasizing the importance of preparing students for a rapidly changing job market with an emphasis on creative problem solving over rote learning.

Furthermore, the program incorporates projects where older students create games to teach younger students math concepts, illustrating an engaging method of learning. This video video concludes with reflections on the future of education in the context of AI and automation, stressing the need for a balance between rote learning and developing concrete skills necessary for problem-solving.

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X-TIMESTAMP-MAP:LOCAL=00:00:00.000,MPEGTS=900000

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We have an outreach program where we teach coding

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and design thinking to children across the world,

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mostly in Canada.

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And, we wanted to have a better way

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of training our mentors.

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And we have created some videos,

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but I, we thought we could do a better job with the book.

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Um, I also teach two undergraduate courses

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that would benefit from having the book.

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So there were multiple reasons to write the book.

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Um, now coding, I mean,

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software is obviously helps people in all kinds of jobs.

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I mean, including making this high quality video

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that I've seen you guys put on your website, you know,

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you've got all these tools.

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Um, but we think that there's a, there's a gap.

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Software is not helping, helping

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teach children about creative problem solving

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as well as it could.

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Um, I think people haven't thought about it that enough.

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And that's kind, that's our research focus

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and to enable that, we're teaching coding

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and we're teaching design thinking,

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and we just keep experimenting

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with different combinations of those.

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And the book will support that.

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ELM was actually invented by a Harvard undergraduate

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student, Evan Polsky,

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and he invented it

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to bring some modern programming

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techniques to web developers.

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A lot of web developers are, are self-taught, so

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they just don't have awareness

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or access to the latest tools.

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Um, and I think he did a great job of doing that.

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So we adopted in a, in our outreach program,

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and I mean, it, it worked

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so much better than everything we had tried

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before,

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that we thought, well, we've gotta build on this.

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So we built a graphics library

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to even further simplify.

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I mean, we really were just, extending the ideas that,

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that we attribute to Evan,

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and making it even simpler

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and focusing it on, things

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that even young children can understand so

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that anybody could get an entry to programming.

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Um, and then the other thing is that we, you know,

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we've seen research that says the number one barrier

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to success in, in secondary school is that

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introductory algebra course,

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which in different countries can be in different years,

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but if students don't do well in that,

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they have a high likelihood of dropping out of school.

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They have a very low likelihood of getting into,

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STEM programs or other, you know, good career paths.

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So we wanted to use programming as a tool

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for preparing students for that jump from

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basically from arithmetic to algebra, which

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Is a big jump.

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And they, you know, they all have to make it

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to be successful in secondary school,

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in functional programming, a lot of the debug techniques.

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So debugging is when we identify

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that our program isn't doing what we want it to do,

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and we try to figure out why that is.

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Um, a lot of the techniques people use in other programming

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languages don't work very well with functional programming.

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Um, it's a lot easier to write the program

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right the first time.

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And of course everybody would love to do that.

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Um, there are techniques that work.

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I mean, it's a little bit more effort to,

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master those techniques,

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but that's part of our goal in the way that we're teaching.

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We want people to be thinking about what they're doing

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and have in their mind,

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even if they don't write it down on paper, an argument

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for why their program will do what it's supposed to do.

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And so the, the functions that a lot of people would use

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for debug, they're really not as useful for debug,

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but they are useful for developing, for,

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if you are looking at a small piece of code

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and you want understand how it works,

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they are useful for that.

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And, the elm debug library,

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it can't be included in a optimized application.

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So if you want your code optimized,

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so it would run more quickly if the compiler won't allow

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that, if you have that debug library included.

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So it really does play more the role of development

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and for non-programmers is a very long answer.

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Um, but it does capture, you know, the spirit of, of

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what we're doing, I guess.

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So we actually call our curriculum algebraic thinking.

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There's a big movement

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to develop computational thinking in children.

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We think that the name, isn't quite right.

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It ends up being just teaching programming.

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But we think that there is something that's easier

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to define called algebra thinking,

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and it's about structuring things.

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So breaking problems down into smaller pieces

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and, understanding how to take solutions

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to smaller problems

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and putting them together into

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solutions for bigger problems.

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Um, and there are very technical ways in which this works.

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And then there are, sort of problem

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strategy ways in which this works.

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So you can look at it from multiple levels of abstraction,

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and we think that this is something, you know,

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that should be explicitly a goal of teaching algebra.

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And that the way

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that we teach coding helps children with that.

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So we don't have a lot of hard evidence,

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but, you know, I mean, we have a lot

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of teachers excited about how, you know, certain students

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who were balking at certain topics, like

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they couldn't understand why we needed negative numbers

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or, you know, why do we need these coordinates?

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Or, because we can show them

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how these things can be very concrete.

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They accept those, they accept those

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as being useful concepts.

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And then a lot of our concepts,

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they can be used in more sophisticated ways.

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So they, there's a very concrete way to use them,

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but then they can use them in a less concrete way.

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And the concrete is a building block

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for developing the abstract understanding.

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The Tower of Hanoi has been used

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teach about computation even before we had computers.

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So it's just a, it's a very simple problem

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that uncovers a lot of issues that we have

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with designing algorithms.

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Um, so the idea,

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people will recognize the problem probably in terms

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of a children's toy.

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Um, a lot of children have this toy with rings

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of different colors, and so you can stack them up.

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Sometimes there's one place to stack them or multiple.

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So in the tarno, there are three places to stack them.

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And we have a rule, which is

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that you can't put a larger level on top of a smaller level.

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So they have to be stacked in order of size,

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and you can only move one level at a time.

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And there are three places that you can stack them.

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So the question is, if you've got a tower in one place,

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can you moving one level at a time

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move it to any other place?

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Um, and obviously the answer is yes,

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otherwise it wouldn't be a very interesting problem.

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But, what is the shortest,

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what's the least number of steps

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that would be required to do this?

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So if students can understand that,

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if they can write a proof that their answer is correct,

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they've actually mastered quite a few

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of the ideas we want 'em to know in computer science.

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So, we thought it's really important.

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So why don't we, make a really nice picture

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of the Tower Hanoi so

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that people can just have a little bit more fun,

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because they will get a bit frustrated.

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Some people are gonna see the insights right away,

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and others are just not gonna see the insights.

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You know, they can do it step by step,

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but how do I put this into an algorithm

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that I can express in a, in a compact form?

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And so the way to do that, so the most concrete expression

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of that is as a recursive function.

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And a recursive function is a concrete representation of

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what we call a divide and conquer strategy.

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So the divide and conquer strategy is look at a problem

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and identify one

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or more sub problems that are smaller than the big problem,

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but that have the same type.

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And then you say, okay, if I were going according to size

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of problems, assuming that, you know,

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I've been working on this for a while,

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I've already figured out how to solve the smaller problems,

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so now all I have to do is figure out how

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to put those together and solve the bigger problem.

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And often the putting together step is very simple.

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So the hard part is just to recognize

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that the bigger problem contains a smaller problem.

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And so for the tower, of course, we've got, you know,

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the whole tower and then sub towers.

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So there is kind of an obvious sub problem,

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but it's still for beginners.

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It takes a while to figure out how to express that

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and how to turn that into an expression

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for the number of steps that you need.

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Um, and all that's, it's definitely doable by,

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with a little bit of mathematics knowledge.

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And then once, you know, they master that divide

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and conquer strategy, there's more

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and more sophisticated versions of it.

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I mean, some of the biggest problems

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that we solve in computer science, they're solved

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with divide and conquer.

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Um, it's just

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that the individual steps now are a lot more complicated.

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And we have, I mean, we have a lot of work in making

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the, the glue of putting the smaller problems together into

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the bigger problems so that it can run on thousands

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of computers in parallel.

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You know, people have done a lot of work to make

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that possible so

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that we can focus on the most interesting part, which is

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what is that sub problem In our collaboration with,

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with IBM, we do a lot of work on optimizing code.

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Um, these days it's for machine learning,

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we wanna make machine learning faster.

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So we do a lot of analysis of expressions

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and, everybody I'm sure has memories of

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or learning the order of operations.

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And you know, that when we see parentheses, we have

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to operate on what's inside the parentheses before that.

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And in North America, we usually call it bed mass,

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and there are different, names for it around the world.

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Um, but it's a key thing that people learn.

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Well, I mean, what's fundamental in this is that

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we have a very small number of simple ways

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of building our expressions.

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So we can take two expressions and add them together,

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or multiply them or divide them.

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We have some simple operations.

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And when, you know, no matter

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how complicated this expression is, when we go about trying

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to optimize it, we are doing it by

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trying to optimize the smallest parts

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and then use those solutions to try to optimize more

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and more complicated expression.

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So overall, it looks very complicated,

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and we do look at the overall structure,

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but fundamentally we're saying, you know, well,

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if we can do the optimization for the smallest parts

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and then we figure out how to combine solutions,

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we can solve the most complicated problem, right?

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Given a powerful enough computer to express something

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as a recursive function, the

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sub problems have to have the same structure,

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or sometimes we have say, three different types

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of sub problems, and we look at the bigger problem when we

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recognize a combination of those.

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And in the expression case, you know, we do,

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we treat addition differently than multiplication.

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Okay? So there are different sub problems, but,

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and technically people call it co recur, co recursion,

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once you have a different set of sub problems,

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but really, you know, it's, it's the same.

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Um, so to solve that's,

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that's why it is sometimes difficult.

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It's, and it's especially the first step or the last step.

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So those, to get those to look the same as the other steps

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might be a bit tricky because the first way

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that the problem is presented, it's not obvious that

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you can present them in the same way.

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And that's why people get computer science degrees,

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I would say, you know, is to figure out how to do that.

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Um, because, you know, there's, there's a lot of research

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that says the more lines of code people write,

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the more bugs there will be.

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And I mean, there are differences with different languages,

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but overall, so if you can find this compact representation

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of your solution in terms of just,

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it's a recursive function,

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and this is what we do at each step

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to combine our solutions.

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And then usually we do have

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to do something different at the very bottom.

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So when we get to the smallest problems, then

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those are handled a little bit differently,

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but sometimes not very much differently.

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So now the thing is the divide

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and conquer, we can, we can apply it, you know,

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to human problems as well.

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Um, and then yes, we usually make,

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there are variations in, in

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how things work at different levels

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because, you know, if people are carrying it out,

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we can expect them to just, you know,

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do make obvious adjustments when the problem is changing.

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But computers aren't gonna do that, right?

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First of all, if we want to talk about the origins

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of design thinking,

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and we wanna talk about Herbert Simon.

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Um, and I draw a parallel to numerical optimization

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and the work of George Dansik.

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Um, there's a fascinating period, that started

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during the second World War when people faced, you know,

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really immense problems in order to win that war.

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There were immense scientific and technical challenges,

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and it caused people to break down a lot

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of disciplinary barriers to look for solutions

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and to look at things that people didn't really recognize

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as problems before as being problems

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that could be solved scientifically.

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So, George Danzig, he

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developed a standardized way

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of writing problems mathematically algebraically

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for solving logistics problems

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and design problems, sort of technical design problems.

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Um, and Herbert Simon, he asked, how,

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how do people make decisions

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and how can they make good decisions?

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And then I think it wasn't really till

15:31.925 --> 15:35.545
after the war, he asked why,

15:35.965 --> 15:38.305
why do people graduate from engineering colleges

15:38.305 --> 15:39.705
and they can't really build things?

15:40.405 --> 15:44.605
Um, so, and really it's

15:44.605 --> 15:49.285
because people didn't, people didn't wanna recognize design

15:49.865 --> 15:54.005
as being, something that you could study, something

15:54.005 --> 15:55.005
that you could understand.

15:55.665 --> 15:59.685
Um, they didn't, you know, in my own career

16:00.645 --> 16:01.965
applying mathematical optimization,

16:02.115 --> 16:04.445
I've definitely seen people say

16:05.885 --> 16:07.325
Computers can never do that, right?

16:07.555 --> 16:10.285
It's, it's all, it requires human intuition.

16:10.425 --> 16:12.285
And we have a whole career

16:12.775 --> 16:14.405
where we've built up this intuition.

16:14.875 --> 16:16.045
Well, it may be hard,

16:16.825 --> 16:18.885
but so far we haven't found those problems

16:19.595 --> 16:21.525
that computers cannot solve.

16:22.145 --> 16:25.565
So, I don't know if, you know,

16:26.355 --> 16:27.605
they really knew each other

16:27.705 --> 16:29.045
or thought that they were working on

16:29.045 --> 16:30.165
the same kind of problems.

16:30.465 --> 16:35.045
Um, but they, they were looking at different ways for us

16:35.065 --> 16:37.485
to systematize how we make decisions,

16:37.485 --> 16:40.485
including decisions about designing new products.

16:40.905 --> 16:43.445
So, that

16:45.275 --> 16:47.395
I think people now recognize it is science,

16:47.655 --> 16:50.155
or it's least part of it is economics.

16:50.415 --> 16:52.635
People don't always recognize economics

16:52.635 --> 16:55.635
as being in the same, you know, basket as,

16:55.635 --> 16:56.795
physical sciences.

16:57.135 --> 17:00.115
But, you know, I think the results are speaking

17:00.115 --> 17:04.155
for themselves and these, this,

17:04.615 --> 17:08.835
design thinking has been adopted now so widely,

17:09.505 --> 17:12.235
that I don't think you can really argue it,

17:12.235 --> 17:13.995
that it isn't a success.

17:14.255 --> 17:17.235
Now, human-centered design,

17:19.595 --> 17:22.465
human centered design is really common sense.

17:22.575 --> 17:24.745
It's saying that if you're designing something for people,

17:25.965 --> 17:27.985
you have to take those people into account.

17:28.885 --> 17:32.025
And, so I think it's Don Norman

17:32.045 --> 17:34.185
who really popularized this term.

17:34.445 --> 17:37.265
And he has this book Design of Everyday Things, which

17:37.845 --> 17:40.665
he actually wanted to call it philosophy of Everyday Things,

17:41.405 --> 17:44.385
or was originally called that in the first edition.

17:44.885 --> 17:46.465
So,

17:48.525 --> 17:50.245
he introduced these simple rules

17:51.275 --> 17:55.485
that you could explain in terms of psychology, in terms

17:55.505 --> 17:58.005
of human cognition,

17:58.915 --> 18:01.485
that you should follow in order to make

18:02.405 --> 18:03.725
whatever device you're designing

18:03.745 --> 18:07.365
or whatever system, something that people could understand.

18:08.425 --> 18:12.405
Um, because, you know, when we design for machines,

18:12.625 --> 18:16.205
we recognize that machines have all kinds of limits.

18:16.585 --> 18:17.805
So we have an amplifier

18:17.905 --> 18:21.325
and it can, it's got a maximum level of amplification,

18:21.345 --> 18:22.765
it can produce a maximum voltage.

18:23.225 --> 18:25.485
Um, people have all kinds of limits as well.

18:25.985 --> 18:29.645
And if we design systems that require people

18:29.665 --> 18:33.285
to go past those limits, then when they fail,

18:33.395 --> 18:36.725
it's not really the fault of the people, it's the fault

18:37.025 --> 18:39.085
of the designer of that system, right?

18:40.105 --> 18:42.725
So obviously people are very concerned about this when it

18:42.725 --> 18:46.725
comes to controlling nuclear reactors or flying airplanes,

18:47.305 --> 18:51.695
but, it's, it's really important

18:51.795 --> 18:55.375
for every, every product that people are designing,

18:55.785 --> 18:57.855
every process that people are designing.

18:58.275 --> 19:00.815
The reason why I think it's so important

19:00.955 --> 19:04.895
for software professionals is that we can build things

19:04.995 --> 19:08.255
so quickly, so we can build great things quickly

19:08.355 --> 19:11.735
and we can build terrible apps just as quickly.

19:12.555 --> 19:17.415
And, human des center design is helping people

19:18.035 --> 19:21.215
to slow down and think about things from

19:21.215 --> 19:22.295
the point of view of the user.

19:22.915 --> 19:25.615
And, one of the things we have

19:25.615 --> 19:28.975
to do is develop empathy in our students.

19:29.775 --> 19:31.135
I think it's easier for us

19:31.135 --> 19:34.095
to do it when their students then wait till they graduate

19:34.275 --> 19:36.295
and have to figure it out on their own.

19:36.635 --> 19:38.455
But you have to be able

19:38.455 --> 19:41.455
to understand something from another point of view,

19:42.635 --> 19:44.735
and that's, that's empathy.

19:45.155 --> 19:46.415
So,

19:47.355 --> 19:51.125
and we found that, you know, it's, this is something that

19:51.825 --> 19:53.205
can be taught,

19:54.585 --> 19:57.685
and it's some, this is one of the things

19:57.685 --> 20:01.445
that teachers are really able to absorb quickly

20:01.545 --> 20:03.645
and put into practice in their classrooms.

20:04.305 --> 20:07.965
So, whether they're using it in terms

20:07.985 --> 20:12.085
of designing an app or they're designing something else.

20:12.425 --> 20:15.845
So one of the funnest things that we did is had children,

20:16.705 --> 20:19.725
had had children from grade seven, so

20:21.205 --> 20:22.565
13-year-old children go

20:22.565 --> 20:26.765
and interview, younger children, just beginning school

20:26.865 --> 20:28.325
and talk to 'em about math.

20:28.455 --> 20:31.325
First of all, talk to 'em about what things, you know,

20:31.325 --> 20:32.325
are they interested in,

20:32.425 --> 20:34.805
and, what do they do in their spare

20:34.805 --> 20:35.845
time and things like that.

20:36.305 --> 20:39.045
And then talk to 'em about math, what's their experience

20:39.045 --> 20:40.765
of learning math in school?

20:41.265 --> 20:43.245
And, you can imagine some

20:43.245 --> 20:44.525
of the kind of answers that they got.

20:45.065 --> 20:49.965
And it was, really exciting for us to see those,

20:50.745 --> 20:54.205
grade seven students, you know, walk down the hallway

20:54.265 --> 20:58.565
and they turn from like, turn from little kids to

20:59.125 --> 21:00.725
suddenly little adults.

21:01.125 --> 21:04.565
I mean, they, you know,

21:05.635 --> 21:08.085
they put on, they, they were on their best behavior.

21:08.085 --> 21:09.805
They were intently listening,

21:09.805 --> 21:12.165
they were role modeling all the behavior

21:12.165 --> 21:14.565
that you would like children to role model.

21:14.745 --> 21:17.045
So I think it was a great experience in that way.

21:17.345 --> 21:21.565
But then they went back and they built physical games

21:22.275 --> 21:25.725
that would help the kids with the math concepts

21:25.725 --> 21:27.445
that they found difficult.

21:28.225 --> 21:31.885
And, so we've got a video on, on

21:32.425 --> 21:37.205
our outreach website that includes, a garbage volcano.

21:37.425 --> 21:41.845
So, the, this group

21:41.905 --> 21:45.565
of younger children, they, I, they were talking about

21:45.625 --> 21:47.005
how they love volcanoes

21:47.705 --> 21:49.725
and then somebody said, math is garbage.

21:49.985 --> 21:52.845
So, the older children, they turn this whole thing

21:52.845 --> 21:56.645
around and they so said, okay, we're going to, you know,

21:57.415 --> 21:59.685
every time they get a math problem, right,

21:59.685 --> 22:01.125
they're gonna get a piece of garbage

22:01.155 --> 22:02.845
that they can put in their volcano,

22:03.465 --> 22:05.365
and they physically built this volcano.

22:06.265 --> 22:09.365
And when they get to a certain place on the game board,

22:09.825 --> 22:13.245
the volcano will explode and garbage will go everywhere.

22:13.245 --> 22:15.645
And the more mouth problems they solve, the more garbage,

22:16.385 --> 22:18.445
will fly around the classroom.

22:18.625 --> 22:22.725
So, I'm, it's one of the most creative,

22:22.885 --> 22:25.845
applications of, of this that we've seen.

22:26.065 --> 22:27.725
And the teachers loved it.

22:28.085 --> 22:31.365
I mean, we should have told them, you know,

22:31.985 --> 22:33.125
you've gotta figure out

22:33.185 --> 22:35.165
how your game is gonna get taken apart

22:35.165 --> 22:37.125
and put into a box of a certain size

22:37.625 --> 22:39.885
so teachers can store it in their classroom.

22:40.465 --> 22:42.725
But, the teachers loved it and they all,

22:42.745 --> 22:44.565
and they wanted to keep all of those games.

22:45.545 --> 22:47.045
Um, the volcano was a bit

22:47.045 --> 22:48.525
of a problem 'cause it was pretty big.

22:48.585 --> 22:52.285
So I think every educator is a little bit worried about AI

22:52.785 --> 22:56.965
and I mean, we've got all kinds of new things coming out

22:57.425 --> 23:02.405
and, what's the world gonna look like when our,

23:02.715 --> 23:04.245
when our students graduate,

23:04.305 --> 23:06.165
and are we giving them the skills that they need?

23:07.045 --> 23:11.045
A lot of education is built around rote learning,

23:12.305 --> 23:14.395
and doing clerical work.

23:15.095 --> 23:17.595
And a lot of those things we know are gonna be automated.

23:18.215 --> 23:20.915
So economists have, have thought about this

23:21.655 --> 23:23.475
and they've identified the skills that,

23:24.445 --> 23:26.815
that they think we're gonna need in the future.

23:27.555 --> 23:30.575
Um, and that is number one, creative problem solving.

23:31.715 --> 23:36.415
And so, you know, that's why our focus is there

23:37.035 --> 23:39.295
on trying to figure out how

23:39.295 --> 23:41.175
to best teach creative problem solving.

23:41.915 --> 23:44.775
And since it isn't really part,

23:45.115 --> 23:48.165
it's not established in any curriculum anywhere

23:48.185 --> 23:49.485
to the level it needs to be.

23:49.945 --> 23:52.525
So we're really thinking about it across the

23:52.525 --> 23:53.685
whole range of ages.

23:54.145 --> 23:56.325
So how do you teach creative problem solving?

23:57.345 --> 24:00.775
Um, in grade four, that's really where we start

24:01.115 --> 24:03.215
and how do you teach it to PhD students?

24:03.435 --> 24:07.335
So, and we've done experiments, you know, trying

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to introduce this across all those levels and,

24:11.075 --> 24:12.215
and it's, it's fun.

24:12.755 --> 24:14.175
So people have fun with it,

24:14.585 --> 24:16.495
can't build problem solving on nothing.

24:17.195 --> 24:22.095
So they do need concrete skills that they can use

24:22.155 --> 24:23.455
to solve problems.

24:23.955 --> 24:27.765
Um, I don't think people have the right

24:27.765 --> 24:28.965
answer to this.

24:29.185 --> 24:31.045
How much, what's the right proportion?

24:31.445 --> 24:33.285
I don't think you can get rid of all rote learning.

24:33.745 --> 24:37.805
Um, but you can't, if you're only teaching rote learning,

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it's gonna be a problem because, another thing

24:41.285 --> 24:46.205
that people are looking at is using AI to automate teaching.

24:47.145 --> 24:49.985
But, you know, I'd,

24:50.205 --> 24:54.065
I'd certainly bet anybody on this that, anything

24:54.065 --> 24:57.825
that we can use AI to teach, we can automate with ai.

24:57.885 --> 25:00.345
So we didn't need to teach it in the first place, right?

25:00.685 --> 25:03.985
So it's, it's a very difficult thing to figure out how

25:03.985 --> 25:07.025
to use AI effectively in education.

00:00 - We have an outreach program where we teach coding and design thinking to children across the world, mostly in Canada. And, we wanted to have a better way of training our mentors. And we have created some videos,

00:18 - but I, we thought we could do a better job with the book. I also teach two undergraduate courses that would benefit from having the book. So there were multiple reasons to write the book. now coding, I mean, software is obviously helps people in all kinds of jobs. I mean, including making this high quality video that I've seen you guys put on your website, you know, you've got all these tools. but we think that there's a, there's a gap.

00:50 - Software is not helping, helping teach children about creative problem solving as well as it could. I think people haven't thought about it that enough. And that's kind, that's our research focus and to enable that, we're teaching coding and we're teaching design thinking, and we just keep experimenting with different combinations of those. And the book will support that.

01:16 - ELM was actually invented by a Harvard undergraduate student, Evan Polsky, and he invented it to bring some modern programming techniques to web developers. A lot of web developers are, are self-taught, so they just don't have awareness or access to the latest tools. and I think he did a great job of doing that. So we adopted in a, in our outreach program,

01:42 - and I mean, it, it worked so much better than everything we had tried before, that we thought, well, we've gotta build on this. So we built a graphics library to even further simplify. I mean, we really were just, extending the ideas that, that we attribute to Evan, and making it even simpler and focusing it on, things

02:09 - that even young children can understand so that anybody could get an entry to programming. and then the other thing is that we, you know, we've seen research that says the number one barrier to success in, in secondary school is that introductory algebra course, which in different countries can be in different years, but if students don't do well in that, they have a high likelihood of dropping out of school. They have a very low likelihood of getting into,

02:42 - STEM programs or other, you know, good career paths. So we wanted to use programming as a tool for preparing students for that jump from basically from arithmetic to algebra, which Is a big jump. And they, you know, they all have to make it to be successful in secondary school, in functional programming, a lot of the debug techniques. So debugging is when we identify that our program isn't doing what we want it to do,

03:13 - and we try to figure out why that is. a lot of the techniques people use in other programming languages don't work very well with functional programming. it's a lot easier to write the program right the first time. And of course everybody would love to do that. there are techniques that work. I mean, it's a little bit more effort to, master those techniques, but that's part of our goal in the way that we're teaching.

03:41 - We want people to be thinking about what they're doing and have in their mind, even if they don't write it down on paper, an argument for why their program will do what it's supposed to do. And so the, the functions that a lot of people would use for debug, they're really not as useful for debug, but they are useful for developing, for, if you are looking at a small piece of code and you want understand how it works, they are useful for that.

04:10 - And, the elm debug library, it can't be included in a optimized application. So if you want your code optimized, so it would run more quickly if the compiler won't allow that, if you have that debug library included. So it really does play more the role of development and for non-programmers is a very long answer. but it does capture, you know, the spirit of, of what we're doing, I guess. So we actually call our curriculum algebraic thinking.

04:46 - There's a big movement to develop computational thinking in children. We think that the name, isn't quite right. It ends up being just teaching programming. But we think that there is something that's easier to define called algebra thinking, and it's about structuring things. So breaking problems down into smaller pieces and, understanding how to take solutions to smaller problems

05:13 - and putting them together into solutions for bigger problems. and there are very technical ways in which this works. And then there are, sort of problem strategy ways in which this works. So you can look at it from multiple levels of abstraction, and we think that this is something, you know, that should be explicitly a goal of teaching algebra. And that the way that we teach coding helps children with that.

05:45 - So we don't have a lot of hard evidence, but, you know, I mean, we have a lot of teachers excited about how, you know, certain students who were balking at certain topics, like they couldn't understand why we needed negative numbers or, you know, why do we need these coordinates? Or, because we can show them how these things can be very concrete. They accept those, they accept those as being useful concepts.

06:14 - And then a lot of our concepts, they can be used in more sophisticated ways. So they, there's a very concrete way to use them, but then they can use them in a less concrete way. And the concrete is a building block for developing the abstract understanding. The Tower of Hanoi has been used teach about computation even before we had computers. So it's just a, it's a very simple problem that uncovers a lot of issues that we have

06:41 - with designing algorithms. so the idea, people will recognize the problem probably in terms of a children's toy. a lot of children have this toy with rings of different colors, and so you can stack them up. Sometimes there's one place to stack them or multiple. So in the tarno, there are three places to stack them. And we have a rule, which is that you can't put a larger level on top of a smaller level.

07:10 - So they have to be stacked in order of size, and you can only move one level at a time. And there are three places that you can stack them. So the question is, if you've got a tower in one place, can you moving one level at a time move it to any other place? and obviously the answer is yes, otherwise it wouldn't be a very interesting problem. But, what is the shortest, what's the least number of steps

07:39 - that would be required to do this? So if students can understand that, if they can write a proof that their answer is correct, they've actually mastered quite a few of the ideas we want 'em to know in computer science. So, we thought it's really important. So why don't we, make a really nice picture of the Tower Hanoi so that people can just have a little bit more fun, because they will get a bit frustrated.

08:06 - Some people are gonna see the insights right away, and others are just not gonna see the insights. You know, they can do it step by step, but how do I put this into an algorithm that I can express in a, in a compact form? And so the way to do that, so the most concrete expression of that is as a recursive function. And a recursive function is a concrete representation of what we call a divide and conquer strategy. So the divide and conquer strategy is look at a problem

08:41 - and identify one or more sub problems that are smaller than the big problem, but that have the same type. And then you say, okay, if I were going according to size of problems, assuming that, you know, I've been working on this for a while, I've already figured out how to solve the smaller problems, so now all I have to do is figure out how to put those together and solve the bigger problem. And often the putting together step is very simple.

09:08 - So the hard part is just to recognize that the bigger problem contains a smaller problem. And so for the tower, of course, we've got, you know, the whole tower and then sub towers. So there is kind of an obvious sub problem, but it's still for beginners. It takes a while to figure out how to express that and how to turn that into an expression for the number of steps that you need. and all that's, it's definitely doable by,

09:34 - with a little bit of mathematics knowledge. And then once, you know, they master that divide and conquer strategy, there's more and more sophisticated versions of it. I mean, some of the biggest problems that we solve in computer science, they're solved with divide and conquer. it's just that the individual steps now are a lot more complicated. And we have, I mean, we have a lot of work in making

10:02 - the, the glue of putting the smaller problems together into the bigger problems so that it can run on thousands of computers in parallel. You know, people have done a lot of work to make that possible so that we can focus on the most interesting part, which is what is that sub problem In our collaboration with, with IBM, we do a lot of work on optimizing code. these days it's for machine learning, we wanna make machine learning faster.

10:32 - So we do a lot of analysis of expressions and, everybody I'm sure has memories of or learning the order of operations. And you know, that when we see parentheses, we have to operate on what's inside the parentheses before that. And in North America, we usually call it bed mass, and there are different, names for it around the world. but it's a key thing that people learn. Well, I mean, what's fundamental in this is that we have a very small number of simple ways

11:07 - of building our expressions. So we can take two expressions and add them together, or multiply them or divide them. We have some simple operations. And when, you know, no matter how complicated this expression is, when we go about trying to optimize it, we are doing it by trying to optimize the smallest parts and then use those solutions to try to optimize more and more complicated expression.

11:37 - So overall, it looks very complicated, and we do look at the overall structure, but fundamentally we're saying, you know, well, if we can do the optimization for the smallest parts and then we figure out how to combine solutions, we can solve the most complicated problem, right? Given a powerful enough computer to express something as a recursive function, the sub problems have to have the same structure, or sometimes we have say, three different types

12:10 - of sub problems, and we look at the bigger problem when we recognize a combination of those. And in the expression case, you know, we do, we treat addition differently than multiplication. Okay? So there are different sub problems, but, and technically people call it co recur, co recursion, once you have a different set of sub problems, but really, you know, it's, it's the same. so to solve that's, that's why it is sometimes difficult.

12:43 - It's, and it's especially the first step or the last step. So those, to get those to look the same as the other steps might be a bit tricky because the first way that the problem is presented, it's not obvious that you can present them in the same way. And that's why people get computer science degrees, I would say, you know, is to figure out how to do that. because, you know, there's, there's a lot of research that says the more lines of code people write, the more bugs there will be.

13:18 - And I mean, there are differences with different languages, but overall, so if you can find this compact representation of your solution in terms of just, it's a recursive function, and this is what we do at each step to combine our solutions. And then usually we do have to do something different at the very bottom. So when we get to the smallest problems, then those are handled a little bit differently,

13:47 - but sometimes not very much differently. So now the thing is the divide and conquer, we can, we can apply it, you know, to human problems as well. and then yes, we usually make, there are variations in, in how things work at different levels because, you know, if people are carrying it out, we can expect them to just, you know, do make obvious adjustments when the problem is changing.

14:18 - But computers aren't gonna do that, right? First of all, if we want to talk about the origins of design thinking, and we wanna talk about Herbert Simon. and I draw a parallel to numerical optimization and the work of George Dansik. there's a fascinating period, that started during the second World War when people faced, you know, really immense problems in order to win that war. There were immense scientific and technical challenges,

14:49 - and it caused people to break down a lot of disciplinary barriers to look for solutions and to look at things that people didn't really recognize as problems before as being problems that could be solved scientifically. So, George Danzig, he developed a standardized way of writing problems mathematically algebraically for solving logistics problems and design problems, sort of technical design problems.

15:22 - and Herbert Simon, he asked, how, how do people make decisions and how can they make good decisions? And then I think it wasn't really till after the war, he asked why, why do people graduate from engineering colleges and they can't really build things? so, and really it's because people didn't, people didn't wanna recognize design as being, something that you could study, something

15:54 - that you could understand. they didn't, you know, in my own career applying mathematical optimization, I've definitely seen people say Computers can never do that, right? It's, it's all, it requires human intuition. And we have a whole career where we've built up this intuition. Well, it may be hard, but so far we haven't found those problems

16:19 - that computers cannot solve. So, I don't know if, you know, they really knew each other or thought that they were working on the same kind of problems. but they, they were looking at different ways for us to systematize how we make decisions, including decisions about designing new products. So, that I think people now recognize it is science,

16:47 - or it's least part of it is economics. People don't always recognize economics as being in the same, you know, basket as, physical sciences. But, you know, I think the results are speaking for themselves and these, this, design thinking has been adopted now so widely, that I don't think you can really argue it, that it isn't a success. Now, human-centered design,

17:19 - human centered design is really common sense. It's saying that if you're designing something for people, you have to take those people into account. And, so I think it's Don Norman who really popularized this term. And he has this book Design of Everyday Things, which he actually wanted to call it philosophy of Everyday Things, or was originally called that in the first edition. So, he introduced these simple rules

17:51 - that you could explain in terms of psychology, in terms of human cognition, that you should follow in order to make whatever device you're designing or whatever system, something that people could understand. because, you know, when we design for machines, we recognize that machines have all kinds of limits. So we have an amplifier and it can, it's got a maximum level of amplification, it can produce a maximum voltage.

18:23 - people have all kinds of limits as well. And if we design systems that require people to go past those limits, then when they fail, it's not really the fault of the people, it's the fault of the designer of that system, right? So obviously people are very concerned about this when it comes to controlling nuclear reactors or flying airplanes, but, it's, it's really important for every, every product that people are designing, every process that people are designing.

18:58 - The reason why I think it's so important for software professionals is that we can build things so quickly, so we can build great things quickly and we can build terrible apps just as quickly. And, human des center design is helping people to slow down and think about things from the point of view of the user. And, one of the things we have to do is develop empathy in our students. I think it's easier for us

19:31 - to do it when their students then wait till they graduate and have to figure it out on their own. But you have to be able to understand something from another point of view, and that's, that's empathy. So, and we found that, you know, it's, this is something that can be taught, and it's some, this is one of the things that teachers are really able to absorb quickly

20:01 - and put into practice in their classrooms. So, whether they're using it in terms of designing an app or they're designing something else. So one of the funnest things that we did is had children, had had children from grade seven, so 13-year-old children go and interview, younger children, just beginning school and talk to 'em about math. First of all, talk to 'em about what things, you know, are they interested in,

20:32 - and, what do they do in their spare time and things like that. And then talk to 'em about math, what's their experience of learning math in school? And, you can imagine some of the kind of answers that they got. And it was, really exciting for us to see those, grade seven students, you know, walk down the hallway and they turn from like, turn from little kids to suddenly little adults.

21:01 - I mean, they, you know, they put on, they, they were on their best behavior. They were intently listening, they were role modeling all the behavior that you would like children to role model. So I think it was a great experience in that way. But then they went back and they built physical games that would help the kids with the math concepts that they found difficult. And, so we've got a video on, on

21:32 - our outreach website that includes, a garbage volcano. So, the, this group of younger children, they, I, they were talking about how they love volcanoes and then somebody said, math is garbage. So, the older children, they turn this whole thing around and they so said, okay, we're going to, you know, every time they get a math problem, right, they're gonna get a piece of garbage that they can put in their volcano,

22:03 - and they physically built this volcano. And when they get to a certain place on the game board, the volcano will explode and garbage will go everywhere. And the more mouth problems they solve, the more garbage, will fly around the classroom. So, I'm, it's one of the most creative, applications of, of this that we've seen. And the teachers loved it. I mean, we should have told them, you know, you've gotta figure out

22:33 - how your game is gonna get taken apart and put into a box of a certain size so teachers can store it in their classroom. But, the teachers loved it and they all, and they wanted to keep all of those games. the volcano was a bit of a problem 'cause it was pretty big. So I think every educator is a little bit worried about AI and I mean, we've got all kinds of new things coming out and, what's the world gonna look like when our,

23:02 - when our students graduate, and are we giving them the skills that they need? A lot of education is built around rote learning, and doing clerical work. And a lot of those things we know are gonna be automated. So economists have, have thought about this and they've identified the skills that, that they think we're gonna need in the future. and that is number one, creative problem solving. And so, you know, that's why our focus is there

23:37 - on trying to figure out how to best teach creative problem solving. And since it isn't really part, it's not established in any curriculum anywhere to the level it needs to be. So we're really thinking about it across the whole range of ages. So how do you teach creative problem solving? in grade four, that's really where we start and how do you teach it to PhD students?

24:03 - So, and we've done experiments, you know, trying to introduce this across all those levels and, and it's, it's fun. So people have fun with it, can't build problem solving on nothing. So they do need concrete skills that they can use to solve problems. I don't think people have the right answer to this. How much, what's the right proportion?

24:31 - I don't think you can get rid of all rote learning. but you can't, if you're only teaching rote learning, it's gonna be a problem because, another thing that people are looking at is using AI to automate teaching. But, you know, I'd, I'd certainly bet anybody on this that, anything that we can use AI to teach, we can automate with ai. So we didn't need to teach it in the first place, right? So it's, it's a very difficult thing to figure out how to use AI effectively in education.

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