Stories From The Field: Learning Mathematical Modelling with Desmos

 Karen Oliver

One of my teaching colleagues, Karen Oliver,  just showed me what she has been doing with  Desmos Classroom Activities and graphing linear equations. I was very impressed with their system.


Let Karen explain what she did in her class:

Other Online Mathematics Applications Like This





WALT and WILF the Easy and Rigorous Way

The QCAA has already developed the basis for WALT and WILF within the senior syllabus standards and P-10 Australian Curriculum elaborations; with cognitions and qualities for each standard A-E. Why not use them!

For example:

Cognitions are highlighted in yellow and discriminating qualities are highlighted in blue.

These standards can be used in formative assessment by modifying them to add quantity and content dimensions. In the example below, I have added the quantity of content that I am looking for.

I have students set goals and track their learning by highlighting these scales.

What about Higher Order Thinking Standards?


You probably could still add a content/quantity descriptor, for Analysis, as the standards are usually of the form:

Health Education

However, if you do want to provide more rigor, then I suggest aligning the skill of Analysis to Marzano’s Taxonomy. In this case Analysis increases in complexity from Matching at the bottom end to Specifying at the top.

[Adapted from The New Taxonomy (Marzano and Kendall, 2007) and Marzano Taxonomy – Thinking Processes with Design Verbs ]

So, using this, to be proficient with a score of 3 or at standard, students can Match or Classify. To score a 3.5, students could Generalize and Specifying could score a 4. Therefore, a student Proficiency scale for Health Education, becomes:


This is an example Proficiency Scale for the Learning Goal “I can EVALUATE..” Notice how it ‘climbs’ up Bloom’s taxonomy almost exactly.

This assessment criterion for English is not too bad as it too recognised that a poor evaluation is closer to an explanation or analysis. Most just use the qualifier discerning or thorough evaluation.

I would value add to your existing criteria by adding:

2 = explain/identify

3= evaluation

3.5 = justify decisions

4 = make recommendations


This thinking skill tends to be wide and deep and this is reflected in the range of standards across subjects:


Ancient History


So, leave these as is or use simpler language. You can then increase students’ familiarity and understanding of these by unpacking them and providing tangible examples.

How to use them

I develop these at the beginning of a topic and then just point to the place in the criteria sheet that relates to a lesson or learning activity. At the end of a unit, these also become my marking criteria (front-loaded assessment).

I have students set goals and track their learning by highlighting these scales (self feedback). I also use them when conferencing with students (feedback) and students can use them for peer feedback.

This is one I have used recently: WALT-WILF

Explicit Instruction and Not Quite Blended (NQB) Classrooms on the Road to BYOD

“BYOD” by AJ LEON is licensed under CC BY 2.0


BYOD So Far….

Federal Government funding in Australia for a 1:1 ratio of devices to students is long gone. This has left most school in the situation of having something like a 1:5 ratio, of school owned devices,  that they can barely sustain. There has been an attempt, by most schools, to address the shortfall with a Bring your Own Device (BYOD) program. This has largely been unsuccessful; a strawpoll of schools around the region suggests a less than 10% uptake. Even in places where students have multiple devices at home, they rarely bring them to school. When asked why they generally respond, “My teacher doesn’t do anything with it.”

Why is it so?

The main problem is the focus on the device and the technology, rather than the pedagogy. As articulated by Michael Fullan, “Pedagogy is the driver, technology is the accelerator.” So, when we were given devices but no training or the development of a culture of growth and reforms to our practice, we did the only thing we knew and substituted this tool for something we were already doing. Internet connected devices certainly are useful for ‘research’ or other online content. For a variety of reasons we did not engaged in practices that let us see how transformational technology can be in the process of learning. Meanwhile, students and their parents have not developed a value for technology as an indispensable device for learning.



Where to now?

The only way devices are going to make it through your classroom door is by students bringing them. Parents will not provide devices and students will not bring them until they both value them for learning. Therefore, we need to make the first moves and begin to demonstrate the value that technology adds to learning. We can do that by shifting to Blended Learning.

What Will the Shift to Blended Learning Look Like

Blended Learning is a mix of face-to-face and online learning, along a learning path or sequence. Blended Learning is also Personalized, so students have an element of agency over the pace, place and path their learning takes. Before we leap straight into this and because we don’t have devices, we need to start with ‘Not Quite Blended’. This will then be the foundation we need to journey all the way to learning opportunities afforded be Inquiry-Based Learning such as Project-Based Learning.

Not Quite Blended

The major difference with this approach is that it does not have all the systems and processes you need to Personalize learning. This is more of an explicit approach rather than an implicit one, so students are more likely to be consumers of information rather than producers of knew knowledge; you might post content online and guide students through it rather than guide students through an inquiry process. At this stage, technology is used to enhance pedagogy with Substitution and Augmentation (SAMR Model), with some creep into transformation. This may be in the form of starting to use the 4C’s of 21st Century Learning:

  • Communicate – students might blog their learning and receive feedback
  • Collaborate – students may develop shared artifacts of learning with wikis, blogs or other web 2.o technologies such as Padlet.
  • Critical Thinking – this might be made more visible in combination with Communicate and Collaborate strategies
  • Creativity – instead of the product of learning presented as text, other media may be used in creative ways. Students may also synthesize knew knowledge via inquiry learning.

How can I do This with Explicit Instruction?

If you have read this far, then you already know that it’s all about the Pedagogy! The Pedagogical Framework we use is Explicit Instruction (Archer & Hughes 2011) overlayed with the Gradual Release of Responsibility:

Explicit Instruction

Warm-up ideas

  • Play a youtube video as students enter
  • Pose a ‘Socratic’ question
  • Give a short pre-test using Kahoot
  • Have students play a game
  • Project an image at the start of a lesson
  • Demonstrate a physical behaviour such as a chemical reaction and ask ‘why is it so?’
  • Read an interesting quote from a famous person.
  • Analyse a tag cloud of the topic for high frequency words
  • Hold a Seed Discussion online
  • Have students post an Anticipation Guide


  • Always have these accessible 24/7 in your Virtual Classroom (Blackboard for senior, Edmodo for Junior).
  • Have students track their learning, either on paper or online.
  • Try using a KWL, either on paper or preferably online (have students post this in their online journals).

I Do ideas

  • Create a Virtual Classroom (Blackboard for senior, Edmodo for Junior)to curate ALL content
  • Reduce cognitive load for students by sourcing multi-modal content
  • Let the content do the “chalk and talk” for you. ie: there is probably a youtube or teacher tube clip out there that will say it better and students can watch it several times until they get it.
  • If you do “chalk and talk”, record it and upload it to provide a bank for review/revision. You can then build on this to ‘flip’ your classroom. ie: have students review the material for homework and then go straight into the ‘we do’ step.
  • There are a heap of online learning activities , around content and input experiences, that you can access.
  • Why not explain a concept with someone else’s animation.
  • Chunk‘ content into digestible bites
  • Identify critical input experiences
  • Manage response rates with Kahoot, Padlet and a host of other technologies.

WE DO ideas

YOU DO ideas



1. Develop a Growth Mindset

2. Deliberate Practice

In Hattie’s “Teachers Make a Difference What is the research evidence?”, Teachers accounted for 30% of the variance.

The research also tells us that Teacher reflective practice leads to increased pedagogical skill which results in increased student achievement.

Deliberate Practice is about refinement of practice over time:

3. Couple Deliberate Practice with a Collaborative PLC Cycle, for you and your colleagues:










Gamify Your Classroom With Kahoot and Other Online Formative Assessment & Response Systems

Why Kahoot?

Kahoot is great for:

  • Introducing new topics
  • Review, Revice & Reinforce
  • Formative Assessment and Checks for Understanding
  • Surveying to initiate discussion and debate

Kahoot is available on desktops and all mobile devices as an app, so one way or another, students have options for access to a device that they can use (BYOD). This is a great stepping stone to inspire students and parents to value technology for learning. Actually, students love this, so don’t be surprised if devices flow into your classroom if you regularly use this as part of your exit routine.

How it Works

Powerful Ways to Use Kahoot

Alternative Online Systems



5 Ways to Use Padlet In Your Blended Classroom

Why use Padlet?

Even a basic use of Padlet ticks most of the 4C’s for 21st Century Learning: Communicate, Collaborate, Critical Thinking and Creativity. In terms of integrating digital technology in your class, it is at the Transformation end of the SAMR Model. From a pragmatic point of view, it is also a great vehicle to use to inspire students and their parents to value technology for learning and start bringing in their own device (BYOD).

How does Padlet Work?

The best answer to this question is to read the Padlet FAQ. Otherwise, it can be used on desktops, android and apple platforms; so your students should have reasonable access to some kind of device for learning.

How can I use it?

1. Word Wall

Word Walls have multiple uses and pedagogical intents, such as:

When these are just in the physical classroom, then they can only be used in a synchronous way and are usually not sustained beyond the timeframe of a unit of work. There is also limited opportunities to update and refine these as learning progresses. When these are posted online, however, the reverse is true.

View this example

2. Increasing Response Rates

Normally, gaining responses from a class involves the teacher asking questions and recording responses on a whiteboard. This may be effective for you if you pair it with strategies to increase student response rates. With Padlet, you can have a response from all students.

3. Collaborative Critical Thinking

Critical Thinking is usually not a collaborative affair beyond very small groups of students. You could arm expert jigsaws with butchers paper and have them fill in a graphic organizer and then post the finished collaborative artifact of learning on a spare wall. Or, you could use Padlet.

View this compare and contrast example

View this Evaluation example

4. ePortfolios

Folio assessment tasks are great for students to collect evidence of their knowledge and skills, even when they are on paper. However, paper-based folios are difficult to share within and beyond the classroom. This means that students miss out on feedback from peers and others to inform their learning.

ePortfolios improve on this by allowing a public reflection, evaluation and sharing of learning. Students can also Personalize their learning with “voice and choice” because they can determine what they need to learn, how they will learn and present evidence of their learning. This is the main reason that ePortfolios are utilized for Problem-Based, Challenge-Based and Project-Based learning; where students determine what the problem is, decide how they will solve it and then present their solution.

Padlet has upgraded its technology and now you can drag and drop files to organise an ePortfolio.

5. Exit tickets

These are a great formative check for understanding and can be used as part of your feedback for visible learning.

View this example

Padlet Alternatives

Stories From the Field

My colleague, Wendy Coleman, uses Padlet to give her students anywhere, anytime access to learning activities and resources.  Students are then able to interact with learning resources at their own time and pace.

These Padlets are password protected, so she also sends these to parents so that they can support students at home. Further to this, they all have an associated QR code.

Wendy tells me that she likes the visual nature of padlet and the way it is so easy to post a variety of content. As you can see from the snapshot below, Padlet is quite versatile.


Proxy Fix for Raspberry Pi

When I first opened my shiny new Raspberry Pi 3, my excitement was soon dampened as I had no network or internet access; rendering my Pi at least half as useful. Luckily, my techie is a Linux wiz and he created a custom build that was able to authenticate on our network.

The build document you need is Raspberry Pi Build Doc. I suggest you give this to a tech if you have one. Once built, the Raspberry Pi SD card can be cloned. Watch the video below:


Tracking Learning in a Blended Classroom using Journals

One of the reasons I can’t live without Digital Technology is that it actually makes my job of teaching easier. Without technology, I’m not sure how I would share the responsibility for learning with my students and have them track their learning, in a place that we both can access. I have seen star charts used in Primary settings, but I’m not sure these would work in the insecure world of teenagers. This is where technology comes to the rescue and enables a strategy modified by an online world.

The video below shows one way to track learning using the journal feature of Blackboard. This can only be viewed by individual students and their teacher. The journal is being used at the beginning and end of the video. I have left the Reading To Learn strategy (the middle) in for those that may be interested.


I have previously written about this here:

But this video gives some more details about what it looks like in a Virtual Classroom.

How to use a Reading To Learn Strategy in a Blended Classroom

Below is a video showing the wonderful Bridget Williams modelling our Reading To Learn Strategy, augmented for my Blended Classroom. I have not been trained in this strategy, so Bridget is modelling it for me.

My class seems to have acquired this skill to scan, highlight, summarize and re-write, as they have been able to employ it independently. They are working through a series of text-heavy article as part of a written assignment, so I plan on using this strategy for their next article so that I can develop my skills with Reading To Learn. After that, I might experiment with incorporating some other Detailed Reading strategies (outlined below the video).

For example, I would like my students to be able to refine this process with the ability to easily identify what needs to be highlighted, without my modelling as a Que. Perhaps the GIST method can be incorporated? Another sticking point for students was the re-write. My aim is always to release responsibility so that students can use new skills and knowledge independently; so I might incorporate some of these other strategies and see which ones students are able to confidently reproduce.

Keep a lookout for my next blog about reading.

Detailed or Close Reading in a Blended Classroom
Detailed Reading techniques encourage an active engagement with text as well as providing students with a useful record of their reading. Passively reading large amounts of text is not effective, while active note taking techniques increase levels of concentration and understanding.
Detailed Reading involves:

  • underlining and highlighting to pick out what seem the most central or important words and phrases.
  • keywords to record the main headings as you read; using one or two keywords for each main point.
  • questions to encourage an active approach to reading. Recording questions as you read can also be used as prompts for follow up work;
  • summaries to check you have understood what you have read. Pause after a section of text and put what you have read in your own words. Skim over the text to check the accuracy of your summary, filling in any significant gaps.

Why Detailed Reading?

  • Stimulates critical thinking skills.
  • Helps students remember what is said in class.
  • Helps students work on assignments and prepare for tests outside of the classroom.
  • Allow students to help each other problem solve.
  • Help students organize and process data and information.
  • Helps student recall by getting them to process their notes 3 times (if SQ4R and Cornell is used)
  • Reading and Writing is a great tool for learning!

Three Strategies:

  • SQ4R Strategy Combined with Cornell Note Taking
  • GIST
  • Sum It Up

1. SQ4R Strategy Combined with Cornell Note Taking
Before you start reading:
Survey to get an overview of what you will be studying
Why Survey?
1) To give a purpose to your reading
2) To find out how difficult the material is going to be for you
3) To estimate how much time you will need to read the assignment

How to survey
1) Read the text title.
ASK: “What does it mean?”
2) Read the Introduction.
              ASK: “What will be covered in this chapter?”
3) Read the main headings and subheadings.
              ASK: “How are the main ideas going to be covered?”
4) Read the summary at the end of the text or chapter.
              ASK: “What are the chapter’s major points?”
5) Note any study aids such as pictures, charts, etc.
              ASK: “Why are these included in this chapter?”
6) Note any important and/or unfamiliar terms.
              ASK: “What might these words mean?”

How to Question?

  • Read each title or heading.
  • Turn each title or heading into a question.

Title = “How the Aztecs Adapted”
Questions = “What did the Aztecs adapt to?”
“Why did the Aztecs have to adapt?”


  • Start reading while thinking about the questions that you wrote earlier.
  • Do not move onto the next section until you have answered your questions.

Cornell Notes!
Remember, Cornell notes are not just a way to set up your paper
Cornell notes require:
– adding or deleting notes
– highlighting or underlining
– questions in the left margin
– a summary at the bottom



Class Title

Class Notes

3 to 4 sentence summary across the bottom of the day’s notes


  • Questions should elicit critical thinking skills
  • Questions should reflect:
  • Info you don’t understand or want to discuss with your teacher/tutor.
  • Info you think would go good on an essay test.
  • Gaps in your notes

Computerized Notes
These are the same but without the left hand side column. Just use underlined headings instead

Tips on Taking Text Notes
Be an Active Reader:

  • Consider how the parts relate to the whole; how the text relates to previous ideas
  • Create questions about new words/ terms, why emphasized points are important

Be Aware of Textbook Organization:

  • Look for the pattern in elements like chapter /subsection  headings, summary points, graphics

Use the text style to identify important points:

  • Become familiar with the font, symbols, borders, graphics, colors, and layout that highlight main ideas or terms
  • Be alert to the writer’s goal: highlight ideas/ references /opinions that seem significant to their                                         point of view

Take notes while reading:

  • Include headings, key terms, & graphics
  • Take down only the important ideas: brief, but clear
  • Summarize in your own words
  • Use symbols to highlight for review
  • Use textbook review questions to develop study questions


  • Summarize out loud
  • If you cannot find the right words, you probably do not have as good as a grasp of the material as you think you do.

To help you remember the key points in the chapter
Cover up your notes and quiz yourself using your Cornell note questions.


  • Immediately after completing the entire reading assignment
  • Periodically to keep the material fresh in your mind

How to Use This Strategy in a Blended Classroom?
There will be many times when students will be independently reading moderate amounts of text in learning resources. You may well have some accompanying comprehension questions or you may not. In the case where you do provide comprehension questions, this strategy is still an effective way to have students actively read and learn, so it certainly is complementary as well.
In a Personalized classroom, students may seek out their own answers in an inquiry and encounter a variety of texts that they need to read, understand and use to create their own learning and understandings.
Use Learning Logs
This technique to help students focus on what you are learning in class. Writing in a learning log is a great way to use reading and writing as a process of discovery and for clarification of ideas.
Every time a student is exposed to a moderate to large body of text, have them create a journal entry in your Virtual Classroom. This is a great formative assessment tool as you can clearly see what a student has actively read and understood. You can also adapt this so that it is collaborative by having students blog and share their notes as well.
This is a good approach to take as part of the Discover phase of Project Based Learning.
Lead-in Activities
If this is the first time your class has been exposed to this kind of strategy, then use the Gradual Release of Responsibility strategy to train them in these skills. If you have a younger grade, you may like to explore Group Reciprocal Reading strategies as a foundation.

SQ4R Worksheet
Text Title: ____________
Author (s) _____________
What major topics are included in this text?
Scan and list any major vocabulary words
Q -Question
Turn the first heading into a question. Use who, what, where, why, and how.
R-Read Actively (annotate: write in the margins, highlight, underline…)
Read the material following the first heading looking for the answer to your question.
R- wRite
Reread the heading and recall the question you asked. Use the Cornell note taking system to briefly answer this question in your own words without looking at the section. Check to see if you are correct.
Continue using the question, read and wRite steps until you have finished each part of the text. Then complete the review step. You may want to include definitions in your notes.
After completing your notes, review them by covering up the right side of your Cornell notes and trying to answer the questions on the left side. Then check to see if your answers are correct.
Take a few minutes to reflect about what you have read/ studied.
Compare new ideas to What you already know.
Ask yourself
‘ How can I use this?”


1. Scan the page and try to predict what the information is about and what comes next as you scan each paragraph
2. Read the page or section of the textbook
3. Fill in the 5Ws and 1H you found out from your reading
4. Using these facts, Write a 20-word or less GIST summary

3. Sum It Up
1. Read the page or section of the textbook
2. While you are reading, list key words or phrases in the blank space provided below. The words must convey the main idea of the passage.
3. Circle all the keywords above that are the most important in the text.
4. Use the main idea words listed above to write a 20 word summary


An Easy Way to Track Learning in a Contemporary Classroom

“The three forms” by Christopher Michel is licensed under CC BY 2.0


1.Define Learning Goals in answer to the question: “What do we want students to learn?”

For this I create a Proficiency Scale, for a topic,  so that students and I can track learning within the topic’s learning sequence. This also provides both the cognitions and qualities required for success at each stage of mastery. In practice, it looks like this:

WALT/ WILF Scale Standard 4 Standard 3.5 Standard 3 Standard 2 Standard 1
Implementation and evaluation The student work has the following characteristics:

Use of a variety of complex technical skills and resources to present an efficient and effective solution:

  • Import files
  • Strokes, fills and vectors
  • Text
  • Shape tweens
  • Symbols
  • Motion tweens
  • Publishing
The student work has the following characteristics:

Use of a variety of technical skills and resources to present an efficient solution:

  • Import files
  • Strokes, fills and vectors
  • Text
  • Shape tweens
  • Symbols
The student work has the following characteristics:

Use of technical skills and resources to present a solution:

  • Import files
  • Strokes, fills and vectors
  • Text
The student work has the following characteristics:

Use of basic technical skills and resources to present a partial solution:

The student work has the following characteristics:

Use of isolated technical skills to produce an output:

The easy part is that this is lifted straight out of the syllabus and I have just added lists of content as a way of adding a quantity dimension to the descriptors. The P-10 equivalent of this are the Standards Elaborations provided by the QCAA. So, now my scale has cognition, quality and quantity. Instead of A-E, I use a 4-point scale, with a B being roughly 3.5. The reason for this is that I want to use this for formative assessment and not as a final summative grade.

2. Design Instructional Strategies in answer to the question: “How can we design learning to support student engagement and progression?”

Both engagement and progression can be achieved with Personalized Learning strategies. At the beginning of the topic I introduce students to the WALTS and WILFs and have them set goals (feedup) in their online Learning Journals (Blackboard). They do this by copying the scale and highlighting where they wish to end up. Then, as they master the skills at each level, they highlight in a different colour (feedback/feedforward), until they reach their goal. This is mostly a self-assessment, but I facilitate by conferencing with students about how they are going and give them feedback as well.

3. Assess Learning

This is the really easy part, because students have managed this for me.  Remember, differentiation is something a teacher does (monitor learning and re-design for different learner needs), while personalization is something a student does. Technology has also enabled this process of personalized formative assessment. Then, in a PLC meeting, it is easy to flip through student journals and collaboratively evaluate the effectiveness of instructional strategies and the progress of students.

Additional Strategies

The Single Point Rubric

These are useful for students to use in order to understand and demonstrate the level of mastery they have achieved and to decide if they have achieved their goal. This could also be incorporated into a portfolio reflection and could be annotated in student learning journals in the same post as their learning goal tracking process.

Single Point rubrics work by having students create three columns, with the goal in the middle and, the evidence that they have met the goal on the left and any concerns they have on the right. Remember, this is more a self-evaluation, rather than a reflection and students need to “argue their case” for mastery based on evidence from their work.



Basic 3D Printing in Your Class

“3D Printing” by CSM Library is licensed under CC BY 2.0


This guide is intended for situations where you want to value-add to your lessons or provide inspiration to students about your content or topic. If you want to use 3D printing as part of a project where students design and make something new (create), then you also need to seek out a curriculum guide for designing and developing products that solve a problem. This guide ranges from finding a suitable 3D object and printing it, to finding a nearly suitable object and making small modifications, to customize it before printing it out. Students could extend on this themselves by making something from scratch, without the guidance of a formalized design process.

Step 1 – Find your thing

There are two resources that can be employed:

  1. – this even has a customizer
  2. – search engine for 3D Models

Whichever way you go, you can download the .STL file you need. This can be either loaded straight into a 3D printer or customized somewhere else. Much of the 3D models in thingiverse can be customized.

Step 2 – Re-mix your thing

Go no further than . Here, students can upload the .STL file they found and modify it. It’s a good idea for them to try the basic tutorials to get a feel for the tinkercad environment. There may even be a tutorial or project that is exactly what students want to make anyway.

Step 3 – Print your thing

To do this, your students just need to have the .STL file of their thing. For WHS reasons, someone else will print out their thing. If this is a regular activity for your class, then it’s a good idea to train several print monitors or technicians and then students can see this happening in your class. Either way, you will probably need to make arrangements for the manufacturing process.

Instructional Strategies

  1. Grouping – I highly recommend that students have a ‘buddy’ to work with when learning how to use tynkercad
  2. Discovery Learning – You will probably not have many of the skills needed for 3D creation and printing. Even if you do, I’m sure there will be some rare skills that you do not have. Therefore, guide students to the thingiverse site and have them explore it together and share what they have discovered. This may mean some movement around the room. Use the stategy, “ask 3 before you ask me”. Even when a student asks you a question that you can’t answer, call out and ask the class if they have a solution. Nine times out of ten, someone will. When students go to tinkercad, direct them to complete the basics tutorials first before attempting any modifications. These can also be reviewed as a reference point later. Again, have students collaborate and help each other.


From here, students may well want to delve deeper into 3D design or you may want to pursue Project-based Learning in another unit. Therefore, your next steps could be:

  1. – this has entire curricular K-8, but needs a subscription.
  2. – free design, engineering, animation, and architecture courses
  3. – very easy 3D Design software that is free for Education. It is also very well supported and has an extensive 3D Warehouse.
  4. Creo –Next level up from sketchup. Moderately easy to use 3D design app that is well supported.
  5. – look for the app
  6. – lots of projects