Free visual learning apps to support conceptual understanding

The teaching model (using materials, then screening them before progressing on to using numbers alone) is a key feature of the Highland Numeracy Progression and is used to support conceptual understanding.  Other ‘schemes’ or ‘programmes’ sometimes refer to this as CPA (Concrete-Pictorial-Abstract).

Although having something physical to manipulate is most likely more effective initially to support many children’s understanding, sometimes we don’t have the resources available or we want to show something to the whole class at one time.  These free apps from ‘The Math Learning Centre’ are a great resource that can be used to support conceptual understanding.  They can either be used as a web based app or for those who are using Chrome books, you can download the app from the Chrome Store.

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One of my favourite ones on here is the ‘Partial Product Finder’.  It’s a great resource to support children’s understanding of how you can partition numbers additively to make a multiplication problem easier to solve.

  • Children can see visual representations of different ways that numbers might be partitioned.
  • It also allows children to see clearly and easily the link between multiplication and area (hence the name ‘area model’)
  • It could support links to a more abstract ‘area model’ where every individual square didn’t need to be drawn out/represented.Screen Shot 2018-12-12 at 20.31.12.pngScreen Shot 2018-12-12 at 20.46.22.pngScreen Shot 2018-12-12 at 21.51.21.png
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Christmas Holiday Challenge

This year’s Christmas Holiday Challenge has been published and will be making its way to schools and libraries this week.  If you click on the link it will take you to a downloadable copy of the challenges.

Solutions will be published on January 4th on the Making Maths Count blog.

Enjoy!

DFM Christmas Challenge 2018

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Mindset and maths

Check out this FREE online course, presented by Dr Jo Boaler, from Stanford University, who set up the Youcubed site.

The course is aimed at pupils – best suited for P6 onwards but particularly secondary.  However, having done it myself, I found it to be incredibly useful for teachers too (there’s a more in-depth teacher version which you can pay for).

The P6 and P7 pupils from Scourie Primary School used it alongside their parents at home so that both parent and pupil could learn from and benefit from the key messages.  It sounds like the kids and parents really liked it and the kids wanted to finish it all in one go!

Click on the image below to go to the site and sign yourself up and get your pupils to sign up too.

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If you want even more content like this then check out the Youcubed site which has a wealth of great videos to promote a growth mindset for all areas of learning and life but specifically for maths.  The tasks are great too with lots of open ended ideas which support conceptual understanding.  If you haven’t already seen the site, head on over.

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Books galore… and it’s all mathematical!

Sharing of books in school and at home is often thought of as an activity related to literacy but there are a wealth of books available that have mathematical ideas that can be explored in fun ways so you can enjoy both literacy and maths at the same time!

Scottish Book Trust:
From early years to 14+

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Each book has a recommended age range and suggests a range of cross-curricular links and includes activity ideas.

Each example has a numeracy and maths link and includes the relevant experiences and outcomes.

How To STEM:

From early years to age 11+

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Each book indicates the age range it would be appropriate for and the topic it covers (e.g. geometry, place value, fractions etc.).

They also have a series for the four seasons of the year.

NRICH:
From 7+ to 17+

Each book has a lower age band based on content and language and the books are grouped into three main categories:

Screen Shot 2018-11-29 at 23.43.05.pngHistory of Maths
Recreational
Thinking Mathematically

 
I recently read The Number Devil which was a brilliant read and could spark some great discussions and explorations with pupils in P6 or 7 onwards.

Erikson Institute:
From Early years to Primary 5 (approximately)

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Each book indicates the age range it would be appropriate for, the topic it covers (e.g. spatial relationships, number sense, counting etc.) and gives suggestions of how you could use the book beyond just reading it.

Finally, also from the Erikson Institute, is a video clip of two teachers using a story to support the understanding of mathematical concepts in their classes.

Feel free to share any favourite books you’ve used within your classes that others might enjoy too.

 

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Progressions in early number and counting, addition and subtraction

Take a look at these great videos by Graham Fletcher (who I have mentioned before in the blog posts about 3 Act Tasks).  He’s created several short videos highlighting the progression in key areas.  I’ve posted the ones for ‘Early Number and Counting’ as well as ‘Addition and Subtraction’ below.  Although this is based on the US system, you’ll notice that there is a huge cross over to what is being discussed here and what is highlighted within the Highland Numeracy Progression.

Remember to keep in mind as well that these are stages of development so you may have a child who is in P6 or P7 who is still working at one of the earlier stages, if they don’t spend the time fully understanding the concepts that underpin future learning, they are going to struggle so keep it relevant for the pupils you are working with.  (If you want to draw comparisons to our Primary levels and the US grade system, you can use this document here.)

While you’re watching, try and reflect on a few key points:

  • Where/how does this link with HNP, the diagnostic assessments and the developmental stages of thinking?
  • Are there hands on materials in your setting that could be used to develop conceptual understanding of these concepts?
  • Can you identify times when he is using a hands on manipulative (concrete material) and then creating a visual representation of this using a visual diagram?  Why do you think this would be useful for pupils?
  • Can you identify how the hands on manipulatives have been adapted/progressed?  For example, items that can be unpacked in ones then moving on to items that need an exchange to happen i.e. one ten exchanged for ten ones.

Graham has another three progression videos (multiplication, division and fractions) that you might want to take a look at.  I’ll be posting more about these in another blog post as I feel they are worth watching and link in really well with the ideas around teaching maths and numeracy that we are trying to promote however, if you can’t wait for the next post, you can go to the site here and watch them now.

Enjoy!

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Careers in Maths… it’s not what you might think!

Some people, including many of our students, have a view that much of the maths that they learn at school is not really relevant in ‘the real world’ and may have quite specific ideas about the types of careers that would likely make use of maths.

Check out this wonderful Ted Talk by Pixar’s director of photography, Danielle Feinberg, and get a taste of the wonderful and inspiring ways that she uses maths, science and code as part of her job.  Consider how many people worldwide will have watched and loved these films and challenge your students to think again about the endless possibilities that pursuing an interest in maths can offer them.

 

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Using visuals and manipulatives

If you’re looking for some ideas to support your teaching so that pupils understand what’s going on conceptually take a look at Berkeley Everett’s site which has lots of short animations on a wide variety of concepts.

Here’s an example with some reflective follow up questions:

How to use: Ask: What do you notice? What do you wonder? Why did it take 2 from the 6? Could you use this strategy for 9+5?

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