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Algebra is one of those often reviled topics for students – it’s too hard, it doesn’t make sense, and what the heck are those letters doing in a maths equation! Finding ways to connect students with the concepts that underpin those seemingly meaningless questions helps them grow confidence and may even change their attitude!

Over the last few years I have played around with using Scratch to have my students engage with Algebra. Scratch is a free, online coding platform that can be used to teach a variety of subjects, including algebra.

I have developed a unit on Learning Algebra with Coding that is built around a project based approach. The unit has a progressive set of coding challenges that are rooted in an algebraic concept. The unit begins by introducing students to the basics of coding, such as variables, loops, and conditionals. Students then use these concepts to create projects that explore algebraic concepts, such as linear equations, functions, and recursion. Variables are an essential concept to understand and I often introduce this by getting students to think of where they see variables in their world.

Projects

Here is the list of project for students to complete (worked examples are also available in a Scratch studio). Please note that this list has links to worked solutions so shouldn’t be shared with students as they should figure out the solution themselves!

Pattern maker: create a project that has number patterns (odd, even, square, prime, Fibonacci…). Try to also create some sound patterns and drawing patterns using the pen tool.

Programming music patterns: create a programme for users to interact with to create or modify a musical pattern.

Cartesian plane: using the xy-backdrop, create a project where users input a co-ordinate pair which moves a sprite

Exploring Mars: follow the steps at this site to create a programme for a Mars rover

Plotting patterns: create a project where users enter a rule (e.g. + 3, – 5) or a gradient and y-intercept which the programme plots a straight line on a cartesian plane

Battle ships: create a project that is like the old school game of ‘Battleships’.

Function machine: create a project that generates a list of co-ordinate pairs and users have to input the rule

Guess my number: create a project that the user ‘guesses’ the number that the code started with

Polygon maker: create a project where the user inputs the number of sides of a polygon and the programme draws this shape showing the size of the interior angle, exterior angle, and sum of interior angles.

Pi finder: create a project where the user inputs a value for the diameter of a circle, and the programme draws the circle showing that the diameter fits about 3 times in the circumference.

Classroom noise monitor: create a project that monitors classroom noise (use the ‘loudness’ variable in the Sensing blocks)y

Finding water on Mars: make a remix of this Scratch project and programme the rover to autonomously ‘find’ the water (blue crystal).

Magic 8 Ball: Create a project for a magic 8 ball. Use a random probability (between 0-1) to return an answer relating to 8 different probability terms (unlikely, likely, possible, probable, impossible, very likely, certain, poor chance, 50-50 chance, good chance)

Calculator: Follow this tutorial to make a Scratch calculator.

Giving feedback on student projects

So you have your class working on all these different coding projects. How to see where they are all up to so that you can give them some next steps? You can use a combination of a Google Form and a shared Google Sheet. Check out this video for a walk through:

In conclusion, coding can be a fun and engaging way to teach algebra. Scratch is a visual and interactive platform that makes it easy for students to understand algebraic concepts. Students can experiment with different algebraic concepts and see how they affect the output of a program. This helps students to stay motivated and engaged in their learning.

If you are a math teacher looking for a way to make your lessons more engaging and interactive, then I encourage you to try using Scratch. It is a free, online platform that is easy to learn and use. Let me know how you get on!

I teach a year 9 and a year 10 integrated class and I’ve always had the luxury of not having to prepare students for external assessments. Not so anymore… With the introduction of the new Literacy and Numeracy standards, my Year 10 students will be sitting these two pilot assessments this year, which will be required in 2024. So how to best prepare them?

Knowing command terms is useful for success in these type of external, high stakes assessments. Command terms are active verbs that guide students in comprehending and answering an assessment question. A uniform definition and use of these terms throughout different subjects can help student achieve to their potential and so there is significant benefit in having a school wide approach to deliberately teaching these command terms (see ‘Command Terms – A Whole school approach‘)

More importance place on Command terms

It is not unusual in assessment report from various qualification authorities to see comments like this:

The difference between the key terms of describe, explain and analyse need to be clearly understood by candidates in order to meet the requirements of the
questions.

NZQA Assessment report on Geography 2018

We are also starting to see this have more importance in curriculum design. The recently released Aotearoa Histories places emphasis on “Know, Do, Understand”:

This is perhaps best explained by a practitioner:

‘Understand, Know and Do’ has always been a fundamental part of their (the students) inquiry process. Understand’, ‘know’ and ‘do’ are of equal importance; they need each other.

Any understanding, any inquiry that is absent of knowledge – the ‘know’ – runs the risk of being fluff, and any inquiry that is absent of the big and enduring and connecting ideas – the ‘understand’ – runs the risk of being irrelevant to our learners in the here and now. Any inquiry that is absent of the practices that bring rigour to learning – the ‘do’ part – runs the risk of not motivating, challenging and engaging our learners, let alone inspiring them to act on what they’ve learned.

When we deliver equally on these, our students will be informed. They will be active and passionate learners who will go on to make a difference in the world.

Barbara Ala’alatoa, Principal of Sylvia Park School in Auckland

Related to this idea in the concept of ‘capability’. A ‘capability’ is demonstrated in action. As Rose Hipkins defines, a capability is “…what the student shows they can do—and is willing to do—as a result of their learning.” We have also seen a recent shift from a focus on content to these capabilities (see ‘Growing Curiosity – Teacher Strategies to Engage Years 5 to 11 Student in Science, April 2021, Education Review Office’). We further see the need to teach these command terms with the recent change to NCEA.

Command terms in changes to NCEA

In the upcoming new NCEA Literacy and Numeracy achievement standards, there are a number of identified command words. The Literacy | Reading Assessment Specifications lists the following: locate, select, describe, recognise, identify, interpret, distinguish, predict, generalise, organise, summarise, recommend, compare, contrast. The Numeracy Pilot Common Assessment Activities (CAA) use command words such as explain (used 9 times in the September 2022 pilot CAA!), calculate, estimate. Below is a proposed list of command words that students would need to be familiar with to succeed in the NCEA Numeracy and Literacy standards:

1. Identify: recognise or name something, such as a feature or characteristic of a text or numerical problem. (similar to Locate, Select, Recognise)
2. Describe: provide a detailed account of something, including its key features and characteristics.
3. Explain: provide a clear and detailed account of something, including its underlying principles, causes, or mechanisms.
4. Compare: identify similarities and differences between two or more things, events or concepts. (similar to Organise, Contrast)
5. Interpret: explain or give meaning to something, such as a text or a numerical problem. (similar to Distinguish)
6. Apply: use their knowledge or understanding of something to solve a problem or complete a task.
7. Calculate: perform mathematical operations or computations to find a numerical solution.
8. Estimate: provide an approximate answer or value based on their knowledge or understanding. (similar to Predict)
9. Analyse: examine something in detail and break it down into its constituent parts to understand how it works.
10. Justify: provide a reasoned argument in support of a particular claim or position. (similar to Recommend)
11. Evaluate: consider the evidence and arguments presented in support of a particular claim or argument and make a judgment about its validity.

In addition to these command terms, The New Zealand National Certificate of Educational Achievement (NCEA) uses a range of command terms in their university entrance achievement standard assessments. Some of the key command terms used in these assessments include:

1. Critically evaluate: examine something in depth, identify its strengths and weaknesses, and make a judgement about its overall value or importance.
2. Discuss: consider different viewpoints on a particular issue or topic and weigh up the arguments for and against each one.
3. Evaluate: consider the evidence and arguments presented in support of a particular claim or argument, and make a judgement about its validity
4. Summarise: provide a brief outline of something, highlighting its key features or characteristics.
5. Synthesise: bring together information from different sources to create a new understanding or perspective on a particular issue or topic.

Developing coherence

When moving on to propose how we can best prepare students to understand these command terms it is important to consider the difference between progressions and coherence. Progression refers to the systematic development of knowledge and skills over time, ensuring that students are challenged appropriately as they move through the curriculum. Progression also involves a clear sense of direction and purpose, with each lesson building upon the previous one. On the other hand, coherence refers to the logical and meaningful connections between different parts of the curriculum. This involves ensuring that each component of the curriculum fits together in a way that makes sense, creating a unified and meaningful whole. In other words, progression ensures that students are consistently challenged to develop their knowledge and skills, while coherence ensures that this development is meaningful and connected to the broader goals of the curriculum. So a focus on coherence seems more useful in this context and it is one of the 8 principles of the New Zealand Curriculum.

If we take an Understanding by Design lens to how we can best teach this commend terms, Jay McTighe explains that the main goal of this approach is to teach for understanding and transfer. The approach involves two key ideas – teaching and assessing for understanding and transfer, and using backward design to plan curricula. To plan backwards, teachers start from the end, which is understanding and transfer, not content coverage. If we apply this to the narrow approach of earning a qualification, we start with NCEA University Entrance in Year 13 looking at what key command terms they need to know, and plan a coherent pathway to how these are taught across the year levels.

Deliberately teaching understanding of command terms

So after we now understand the importance of command terms, and how we can create a coherent approach by using backwards design, what are some activities that we can get student to do? How can we deliberately teach these command terms?

1. Use consistent language in tasks and assessments: For example you may create a Y9 Maths tasks that has some ‘Explain’ questions to start scaffolding that understanding in preparation for the Numeracy standard.
2. Cross curricular tasks: Look at tasks from different subjects and using the same command terms. For example an English literature task can ask “Analyse the character of Lady MacBeth in William Shakespeare’s play Macbeth” and a Science task can have “Analyse the results of the neutralisation reaction experiment and predict what will happen using acids with higher concentrations”
3. Definitions activities: Create a matching task, either with physical cards, or a digital version using a platform like Blooket, Kahoot or Quizizz. You could even have students make their own copy of flash cards using Quizlet.
4. Create a visual glossary. What do these terms look like? Have student draw their own interpretations and share with the class (see this lesson plan).

In conclusion, while there will be many more approaches to the coherent teaching of command words, these few examples should provide a start in how a secondary school can use a coherent approach.

Want to teach your students about financial literacy? Want to reinforce the importance of working hard to be successful in life? Want to have some fun with your class? Consider setting up a Classroom economy.

I came across this concept from the awesome Thom Gibson after listening to him on John Spencer’s podcast. He has created a heap of useful resources not only describing what this is and how it can work in your classroom, but also a short online training course. I completed the course and then embarked on setting up a classroom economy. Here’s how I did it:

Step 1: Set the scene

Explain to the students that the class will model itself on running as a business. I inform them that that I will be the business owner and I will employ students to do jobs, for which they will earn virtual money that they can do stuff with such as buy virtual houses, cars and use to bid for items in auctions. The reason are two fold. Firstly to reinforce class expectations including the value of working hard (the harder they work, the more money they can earn). Secondly to teach students some financial literacy skills such as managing finances, saving, and investing.

Step 2: Create a set of Class expectations

As teachers, we all have our expectations for students in our classes. Often at the beginning of the year we do an activity to have some student input into these class rules. Over the past few years I have reframed this as not only having expectations for all, but if students meet those expectations, they can have a number of privileges. This then acts as a contract where students can agree to the terms, and if they do they can participate in the classroom economy (I’ve never had any students refuse in the 4 years I have been running this in my class).

Step 3: Create a job list

Now you get your students to apply for class jobs. Rather than just make stuff up, I checked out this list from Thom Gibson’s course that I used as inspiration to make my own list. The job needs to have some authenticity to it and I’ve used some of them to ‘outsource’ some of the tasks that I do. A great example is the ‘Visual Display Artist’. This job is to design a new Google Classroom banner each week. This has turned out great as we regularly get refreshes for the digital hub of our classroom. This is something that I would do when I remembered, but now that it is a student job, it gets done more regularly and to a higher standard than me! Check out some examples below:

One thing I explain is that everyone will get an income, which I’ve called the Universal Basic Income. But I also deduct some expenses for being in the class (electricity, wifi, desk rent) so all students end up with a meagre amount left over at the end of the week. I invite all students to apply for ‘Tama tu, tama ora” or ‘Tohunga” (detailed in the job description below) that enables students to have a significantly higher income than their expenses. After that, they can apply for the variety of jobs listed. Some of my favourites are Bouncer (organised the class line for those who need to line up), Clerk (to handle any admin of giving out and collecting in resources), and Yogi (who runs a short session after returning from lunch to refocus students on their learning).

Step 4: Run your classroom economy!

I use a New Zealand based website called Banqer to handle the admin. It has two versions of class banking and I use the Primary version as it has better control over class jobs. Students can apply for the class jobs and I have enough so that any one who wants a job can get one (so even though I only have 16 listed jobs , some have 2 positions such as Bouncer). Part of the application process is to write a short CV and so we can have a class discussion around what type of information should go in this (previous work experience, characteristics such as hard worker etc). Once all the job have been allocated, I have the weekly pay to be automatically credited to student accounts on a Thursday. On a Friday, one task that Class captains need to do is deduct any wages for students who didn’t do their jobs that week. The Class captains can be made ‘Bankers’ of the website and so can manage these transactions.

Step 5: Have an auction

So now the students have earned all this cash, what do you do with it?

Firstly, have a class auction. Buy some prizes (including some mystery bags) and have students bid for each item.

Secondly, have an emoji race. Students can bet money on a particular emoji for either the pot of money bet, or a set prize.

In summary, I’ve tried this in my class over the last five years and after a number of iterations, find it really adds to the classroom culture. It’s amazing how keen students are to earn extra virtual dollars and it also serves as a great vehicle to teach financial literacy.

And if there was a problem, yo, I’ll solve it. Check out the hook while my DJ revolves it

Vanilla Ice, “Ice Ice Baby”

Teaching students how to solve problems is an important part of a 21st Century education. But what if you don’t have a hook for a DJ to revolve like that great philosopher Vanilla Ice? Is there a process we can teach students to help them solve problems? Of course there are a number of different processes but the one I will focus on here is Design Thinking.

I recently organised a teacher workshop around this called ‘Design for Success’. Supported by Dr Cathy Bunting (Director of the Science Learning Hub), we guided 25 Tauranga based educators through a sequence of activities designed to enable teachers to “use Design Thinking to unlock students’ creative problem-solving potential.” So first up, what do teachers come up with when asked to articulate a process to solve problems? Check out their responses:

Next step was to hear from people who used a process in their day to day work. I was fortunate enough to have a link with Rocket Lab through their recently announced Space Educator programme and had a one hour video call with Felicity and Alex who went into great detail of how the $4 billion aerospace company use a design thinking process to build and launch rockets. We were particularly lucky to have Alex, who is the project manager on the Neutron rocket project, describe in detail their processes. He talked about trying to solve complex problems, where the solutions are unknowable and that it is often the ‘crazy solution’ that can lead to a significant insight in to building the actual solution. He also stressed the importance, as a project leader, the importance of empathy and integrity when leading a team on such ambitious projects.

Then it was time to get into some of the nitty gritty of how to teach this process to students. When I first started this, I used the d.school Design Thinking process – you know the one with the pretty hexagons?

But I found that I had to put in a heap of time and effort to deliberately teach what those words mean to students. They weren’t that accessible to the students I was teaching, but then I discovered John Spencer’s LAUNCH cycle.

I have been using this approach over the last couple of years with much more success than the more challenging language of the the d.school steps. Over that time I’ve sourced a series of activities for students to complete as they work their way through the LAUNCH cycle and come up with a solution to their problem. I’ll go through a task for each step in more detail with each heading being a link to a web page with more activities, but feel free to make a copy of the slide deck I put together (and please share with me any awesome activities that you have come across!)

Look Listen and Learn (Empathise)

The first step is to get a problem and a user. So it’s not just enough to have a problem with Design thinking – you need a user who is experiencing that problem to come up with a solution for. A task I get my students to do is to story board for someone who is experiencing the problem:

Ask Tons of Questions (Empathise)

In this next step, we want to get a deep understanding of the problem so that when we come to identify possible solutions, we know we are solving the problem at hand. The 5 Why’s task is a great activity for getting students to consider the root cause of the problem (best explained in this video).

Understand the process of the problem (Define)

As well as researching existing solutions, technology that they could use for their solution, students should get a deep understanding of users by conducting user research. They can either conduct an interview or use a survey.

Navigate Ideas (Ideate)

One of the best activities I’ve found in this phase in Crazy 8s. There’s a great video explaining the process as well as a timer you can use when your class does this task.

Create a prototype (Prototype)

This is then fun part – creating a physical representation of the idea. This could be a scale model or a diorama that represents how the idea works. Although it would be great to have a flash as maker space with different stations such as laser cutter, 3D printing, fabrics, modelling and the like, I’ve found pretty good success with just cardboard, hot glue guns, and a couple of bins of ‘junk’ that would have just been thrown out (think Pringles cans, egg cartons, disposable cups etc).

Highlight and Fix (Test)

Now the students have something physical to communicate their idea, they can show it to someone else to get feedback. John Spencer has a really good structured activity for peer feedback and you want students to end up with some sort of summary so that they can make improvements (iterations) to their idea.

LAUNCH to an audience

So we’ve been through all those steps and your student has a kick arse idea, it’s now time to share with the world! So, get them to create a LAUNCH video – a sort of ‘elevator pitch’ where they communicate the problem, who is affects, and their solution with all the awesome features. Flipgrid is such a great tool for this. Students can record straight from their device using a web cam, or make their own video to upload. Then all student submissions are shared with the class for others to see, like and comment.

So I hope you found some of these ideas useful, check out my short video of the whole process.

Like a number of New Zealand schools, we have a wharenui on our campus. Our whare is called Aronui – named after one of the baskets of knowledge. There are number of beautiful carvings, both outside and inside, and along with a number of tukutuku panels has some rich stories to tell. We have a comprehensive document that details some of these stories but we were wanting to get students to create something that was more engaging.

Like the start of many projects, there were a few ideas bubbling away. Rach Duckworth was exploring something similar for her Google Innovator project at #SYD19, the gorgeous VR tour of the Waitangi Meeting house came through my PLN feed, and my co-teacher was keen to do something with our class on a localised curriculum bent. Sometimes you just need a spark to prod you into action!

My spark came from Raranga Matihiko – in particular the Marau Pāhekoheko Mentor Programme. At the workshop they hosted in Tauranga, one of the pieces of work was a VR / 3D tour of a class created wharenui where each student had a pepeha and pou inside (see video above). So I reached out to the team at Raranga Matikhiko for some more guidance and got a detailed reply from Kerry that I reckon is worth sharing in full here:

The virtual world you saw was made with a collection of CAD (Computer-aided Design Tools) and the virtual reality set itself (VIVE) with the use of the Tilt Brush VR app. The whare was built in Tinkercad. Worth noting, is that with Tinkercad, you are able to view as a Minecraft build and then configure block size and material before exporting as a schematic file which can then be imported into Minecraft.

The best way to experience the worlds such as we create, is to do so with a Virtual Reality interactive set. The Tiltbrush app now enables video to be imported directly into a PC world and developers are continually adding functions that allow users greater control over their own content. Unfortunately, although prices have come down significantly over the last few years, sets like VIVE are still too expensive for schools and educators to use widely and single sets only accommodate one user at a time. Alternatively, some good progress has been made with handheld viewers such as Google Cardboard.  You would possibly have to work on creating an app that supports your requirements but it may also be worth looking into what apps are already available. Some developers are open to working with users on specific requirements if that is something you think would be worth doing with your students.

If the end product of VR creation is your main focus, I would suggest the above. However, if your learning intentions are more about the content of the video or the creation of a Digital Learning Object, I would consider simply adding CAD created objects to your student videos.  For example; a student carving a pou whakairo using SculptGL and uploading to a 3D object repository, like Sketchfab. An audio recording of the student telling their story can be added to each object. You could also go on to use a screen recording of the object being rotated to see all sides in a Green screen background for their content video as they then retell their story (like a news report might do). 

From Kerry Leaf – Gallery Educator

I then reached out to Steve from Google NZ as I had a play round with Google Earth projects for another resource on Tauranga’s first migrants as part of an ancestry unit. Here’s the transcript:

The tip off to try Thinglink was the secret sauce that I wouldn’t have come to if I hadn’t been in touch.

First iteration: I used a panorama image and inserted the interactive just to test the basic concept. But I wasn’t able to embed the student video which was frustrating. So after doing some searching I came across an example of sort of what I was after so I reached out via Twitter which got a response in less that 24 hours!

YouTube embeds will not work in a Sandbox. It's a YouTube thing. You can use html5's video tag. See github https://t.co/ftuyDpcLpo for panel example. Sample Earth Project with both full and large panel html. https://t.co/WA30FSlnsT Feel free to copy project and grab html.

— jwilliams (@geteach) August 9, 2021

So after more trial and error I now have a concept that works!

After using the Streetview app to take a 360 image, this latest artefact shows the concept. Starting with a 360 Thinglink, going to the full video and then link to Google Earth Project which contains the embedded video.

So a great example of how collaboration, seeking help and having a go can lead to better outcomes. Our next step is to get our students to record high quality videos of carving stories as well as have them create their own Google Earth project of their story. Once these are done we will collate into one comprehensive resource for our school and use as an example for other story telling projects (we also have a grove of Totora tress planted on site for each of the Old Boys that fought and died in WWI).