An algorithm for introducing algorithms

This was originally posted on Grok Learning’s blog – a site worth visiting!

Some years back I blogged about teaching coding, including how I introduced programming. Some months back I wrote about computational thinking (CT) and coding and the need to distinguish the two.

This time, I’d like to dive deeper into introducing algorithms as a product of computational thinking which may not necessarily lead into coding. In particular, I want to go into concepts involved with algorithms, and not just the mechanics of CT. Click back on links above to see some of my previous algorithms for introducing algorithms. These CT models via Conrad Wolfram and Grok Learning (printable PDF) are valuable resources as well.

Algorithms Essentials

When I was planning how to introduce algorithms to my 10 Information and Software Technology class, I listed concepts relevant to algorithms as essential learning. I wanted students to engage in active learning and, by deduction, realise that these are indeed essential aspects of algorithms.

  1. Representation/notation — how to encode the algorithm
  2. Granularity — level of detail of instructions
  3. Accuracy — correctness of the algorithm, does it solve the problem correctly?
  4. Efficiency — does the algorithm save /waste time and effort
  5. Interpretation — is it ambiguous or open to interpretation?

I could add more, such as scalability, variability and bias, but decided not to, at this stage.

Intro Lesson

I started by asking the students if they knew what algorithm meant knowing most if not all would have heard the term, quite likely in maths. True enough, we came down to ‘a set of instructions designed to achieve a task or solve a problem’.

I got everyone to count off 1 to 4 and based on their number would do one of the following:

  1. Draw the steps for making toast
  2. Draw movements for a favourite dance step/sequence
  3. Write how to get from the classroom to the train station
  4. Write how to perform ‘Happy birthday’ in instrument of choice

This was a no-talking activity. If they were drawing, they couldn’t use words and if they were writing, they couldn’t use symbols or drawing.

Those doing #3 took the longest but after about 15 minutes, I got everyone to move and look at another student’s work. I also asked those who were viewing #2 to attempt to do the dance sequence.

Ensuing class discussion raised some interesting points:

  • One student quoted “using your legs, walk to the door…” which raised the issue of granularity
  • When asked whether his dance sequence was interpreted correctly, the response of “open to interpretation” raised the issue of ambiguity and ‘limitations’ of interpreters
  • “Is that even a slice of bread?” raised the representation aspect
  • Representation and accuracy were problematic for the song and the student resorted to musical notation although admittedly unsure that the notes are in fact accurate
  • Another students toast’s drawing with power setting set to maximum raised the question of efficiency — possibly saves time but risks waste

The activity allowed students to see the challenges involved when designing algorithms; and, we had the language to talk about it.

Student work samples from the intro lesson.

Follow-up Lessons

I started the next lesson by getting 2 volunteers. The first one had to add 25 and 12 (2-digit addition with no carry). The next student had to add 275 and 38 (with carry). The plan was to focus on the process of abstraction for a fairly well-known algorithm and introduce various control structures.

We talked about the term ‘abstraction’ (pick out essence, general patterns) as we discussed the algorithm for solving each of the problems above. Much merriment ensued as the students struggled to articulate the steps, especially as they could not remember the term ‘place value’ (ha!). Once we got the first sequence right, the second one presented the opportunity to introduce selection control structure, i.e. if the sum exceeded 10 and there is a carry.

From here, it was not too much of a stretch to introduce the concept of repetition control structure. So, students were then challenged to abstract further and re-write our selection-sequence algorithm to handle addition of multiple digits and numbers. Those who’ve done IST previously and familiar with pseudocode, got straight into representation without worrying about ‘How do I say this?’ that the others struggled with. And thus, I no longer had to justify why they needed to learn the key words.

“Your algorithm is different from mine.” How wonderful to hear that!

On the third lesson, the focus was on ensuring the algorithm is correct. I taught them how to desk-check, a manual process of checking algorithm logic . I premised it on this was just like their table of values when doing Algebra — and that in fact, designing algorithms is like finding the equations given a table of values. A majority of my class like maths so this was a safe bet.

We are currently on deliberate practice, necessary to develop most new skills. A quick web search generated plenty of sites giving me a range of problems varying in terms of difficulty, complexity, context/interest. Grok Learning also has heaps.

Maybe I should ask them to dance the algorithms…

The bubble-sort algorithm expressed as a folk dance.

So then…

I’m really happy with how this turned out for me. I think the students have a deeper understanding of algorithm design plus they have the vocabulary to articulate this understanding. There’s more to learn but I believe the foundation is sound.

Please share your algorithm or perhaps thoughts on how mine could improve.

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Measuring Hope

Earlier in the year, I blogged about my action research on hope. Since then, I’ve refined my research question (and Lit Review) to ‘Does systematic integration of self-regulating processes into a year 12 Software Design & Dev class impact on student wellbeing?”

After many iterations of defining my construct, I settled on what I started off with…HOPE. It is one of ACARA’s dimensions for wellbeing and aligns strongly with my school’s aspiration to inspire global hope.

I also kept the notion of ‘active hope’ where hope is found in actions and belief that such actions would lead to improvements. It’s true that a huge element of this aligns with Bandura’s self-efficacy which helped with finding literature for the review and fleshing out my project. However, I also wanted to maintain the social aspect of hope that extended beyond self-efficacy.

This ‘extension’ was partially driven by the need to find something more easily observable and measure. It was also because the classroom is ultimately a social context and each student is a contributor, not merely a recipient of social influences. I think James Arvanitakis said it well in  From Despair to Hope – The Curiosity Lecture Series (available here),

…if openly shared and freely distributed, hope can spread throughout the community.

I did not set out to measure inspiring societal (or global) hope as such but one of my action research ‘interventions’ (if you will) was to have students act as peer models. That was a bit of a stretch for ‘freely’ but there was definite sharing and distribution of active hope.

I haven’t fully analysed my research data but it is likely that it will empirically support my observation that YES, integrating self-regulation processes does impact student wellbeing (hope) positively and negatively (the 2-tailed question was intentional). I imagine many teachers suspect as much but now I’ve got data to (hopefully) prove it, notwithstanding the risk of observer-expectancy effect and other risks to the validity of my meager social research attempt.

It would be premature to state a conclusion prior to data analysis but were I to generalise my learning so far, I daresay my teaching practice even when targeting academic achievement does impact student wellbeing. While it often seemed futile to measure hope, I am glad I’ve made this attempt.


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Musings on Memory work

Recent fascination with brain science and its relevance to learning has led me to think about the importance of good memorisation skills. A bit of context to provide premise:

This video (TED talk) by Lara Boyd describe how the brain changes due to stimuli and learning. It ranges from chemical, structural to functional.

It ties in nicely with Information Processing theory  which posits that learning happens when stimulus processed in working-memory (Boyd’s chemical change) moves to long-term memory (Boyd’s structural change). This learning theory makes sense to me, perhaps because of its strong parallelism with how computers work (full disclosure: I’m a computing teacher so this may be rather biased).

It also ties in nicely with Retrieval Practice which the Learning Scientists explain as a useful study method for what we want to remember later, i.e. really learn.  This corresponds to Boyd’s structural change in the brain.

Good memory is important for long-term learning. Yet, as a “lower-order thinking” skill,  it is not given enough focus and sometimes ridiculed as a process of regurgitating useless facts. On an old post on multiplication, I said that one of the problems kids have is that they don’t know their times table. The lack of automacity creates extra cognitive load and can create/exacerbate maths anxiety.

I’m an ESL-speaker. I work hard at growing my vocabulary and that means memorising new words. When I’m tired, words don’t come as easily and I’m more prone to make grammatical mistakes. It can be like this with students learning subject-specific jargon. We’ve got to give them opportunities to learn and memorise the words.

Anyway, I thought that perhaps the reason memory work has low value currently is due to wide espousal of Blooms Taxonomy, a hierarchy learning objectives with Remembering right at the bottom of the hierarchy.  My musings on this include:

  • ‘Taxonomy’  is a way to classify, not necessarily a hierarchy.
  • ‘Levels’ don’t necessarily equate to value; lower levels provide the foundation on which higher levels build upon.
  • Why is it sequential instead of spiral?
  • It’s more a system. A spiral system that cycles from recall up to synthesis and on through next lot of learning material

I was actually surprised to see that my criticism based on experience have already been noted in Wikipedia’s entry.

Memorisation is not evil. I admit it shouldn’t be the only focus and we should develop higher order thinking skills. Sometimes, when we focus on one thing, we do forget the bigger picture. This post is to re-calibrate the import of  memorisation as a crucial thinking and learning skill.

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Inspiring hope…I hope to do so

My school “hopes to inspire hope in others and be a source of hope in the future”. In other words, it seeks to inspire global hope.

I’ve been ruminating this since starting there last year. What is hope? How can we inspire global hope? What does it mean to inspire? Am I hopeful? Do I inspire? Do I inspire hope? Can I help my students inspire and be a source of hope?

I have a chance to answer some of these questions as part of an action research towards experienced teacher accreditation.

Action research is  a good way for me to be more systematic about how I gather and use data as I refine my teaching practice. I think John Spencer explains what it is very well in this video:


The focus of my action research is wellbeing, and in particular, fostering hope. Just as John said in the video, the research project started with a lit review. Defining terms was difficult; ditto for finding what data to collect and how. My lit review (PDF) pretty much documents my journey into defining what it means for me to promote hope, as a classroom teacher conducting an action research. Here’s an excerpt:

Hope is one of the wellbeing dimensions (ACARA, 2010). Hope is also a contextual word that implies optimism or positive mutability. Hope is also associated with grit, defined as passion and perseverance to pursue long-term goals (Duckworth, 2016) or higher-order goals students deem personally worthy of on-going effort (Shechtman et al., 2013). Thus, hope can be viewed as a ‘skill’ that can be learned and exercised with effort in the context or pursuit of valued goals.

Hope is not blind faith. Hope is found in actions. Actions create a better world; a preferred future – to quote from ACARA’s Digital Technologies curriculum. Actions build capacity and confidence on which optimism associated with ‘hope’ lies.

In a classroom, actions include performing positive self-regulation skills. Self-regulation (SR) skills are the skills students practice as they engage – or avoid – learning. Perhaps the SR skill most aligned with hope is self-efficacy – the contextual confidence in one’s ability.

In my action research project, I will be using Barry Zimmerman’s SR learning model which is an ongoing cyclical process of forethought, performance, and self-reflection….kinda like the action research model… kinda like the design process we use in the computing curriculum.

Barry Zimmerman's Self-Regulated Learning (SRL) model

Barry Zimmerman’s Self-Regulated Learning (SRL) model

I’m still in the planning phase of the action research. As mentioned in my lit review, I have to design my teaching and learning program to incorporate teaching SR skills (promoting wellbeing is integrated vs an adjunct to academic learning) – and then measure and analyse and evaluate. There is so much to do yet!

However, I am excited. I hope (ha!) that this action research project will see some growth in hope in my students.

I reckon hope might as well be my one word this year.

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Teaching Thinking

There are currently a couple of initiatives at my school that target thinking as a skill; I’ve been fortunate enough to be somewhat involved in both..

One of these is using the Philosophy framework, i.e. Socrates’ “Logos, Pathos, Ethos” to unpack how we think when faced with situations where we need to make decisions or we need to be persuasive. In a nutshell, what is at the forefront is logical reasoning for Logos, emotions for pathos and ethics, character and wisdom drawn from experiences for ethos. This is a simple framework that is very accessible for year 9s to whom this initiative is targeted.

Another one uses the neuroscience framework, i.e. “Pre-frontal Cortex (PFC), amygdala and hippocampus” – parts of the brain. In a nutshell, amygdala is responsible for our ‘flight or fight’ response or when we allow our impulses and emotions to rule our behaviour and thoughts. The hippocampus is in charge of storing our memories, like a scrapbook of our lives. The PFC – which is not fully developed in adolescent brains – takes care of thinking and decision-making and so, moderating our behaviour. This framework is very accessible for year 8s to whom this is targeted.

In Software Design and Development – and really many (all?) subjects, students need to think logically particularly when critically analysing, evaluating and making recommendations. In SDD, we look at software from the perspective of users and developers and yet I’m finding that my students are not leveraging their extensive experience using software to inform their thinking. Seems like such a waste of resource, right?

So, I told them about the 2 frameworks above. The idea is that the frameworks provide them with another way to view contexts. For example, when they struggled to name features of a banking system, a prompt using their own experience in banking opened a flood of features in far greater detail…and stories (gotta love those). A student who often struggles with staying on-task and is regularly disruptive was also quick to change when prompted with “you’re letting your amygdala rule; try a bit more PFC”.

In our last lesson discussing software installation methods, a richer discussion was had as students were challenged to think of examples drawing from their experience and how they may have felt (connecting to another syllabus content: impact of software to users). And so then, the logic of choosing one method over another makes more sense, from a social-ethical perspective. It may well merit adding to my list of ways to teach empathy.

I’m under no illusions of the impact or permanence of these changes.  What I’ve done is planted seeds that I hope to nourish in the next few terms as I help my students face the HSC and the wider world beyond. I’m teaching them to draw deep into resources within themselves as a way to connect beyond themselves (is any other way possible?). Teaching thinking skills is all part of building student agency.

This may be an unconventional approach to teaching the syllabus but for me, it makes sense. It aligns with my own industry experience and consequently, vision of introducing more of humanities into learning about and creating digital technology.

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