From Mess to Magic !

Hands-on learning isn’t just a "nice to have" in a classroom, it’s a core pedagogical and best practise must ! In our classroom manipulatives often take centre stage allowing our students to explain their thinking or demonstrate their understanding of different mathematical concepts. 

The refreshed curriculum emphasises a Concrete-Pictorial-Abstract (CPA) sequence. This is a research-based "Science of Learning" approach where students don’t start with symbols (like 5 + 3 = 8) on a whiteboard. Instead they start with: 

• Concrete: They move physical materials, manipulatives or Numicon shapes.

• Pictorial: They draw dots or use ten-frame diagrams.

• Abstract: They finally write and use the numbers.

Here you can see one group trying to represent their thinking using numbers and drawing on the whiteboard. Lots of discussion happened around checking our thinking and helping to develop our understanding. It told us a lot about what they know and understand and what they need next.

By using physical tools, we help students build an anchor for abstract concepts. It’s much easier to understand "regrouping" when you physically swap ten tiny ones-cubes for a single "long" ten-rod.  Many of us can remember these cuisenaire rods from our school days ! 

The new curriculum is built on a model of knowledge and practise. Manipulatives sit right at the intersection of these:

• Students grasp the "Big Ideas," like the fact that a number can be partitioned (broken apart) and still represent the same total.

• They develop fluency with basic facts by seeing the patterns in bead strings or counters.

• They use these tools to solve "rich tasks"—real-world problems that require logic, not just memorisation.

Our aim is to get much better at using a variety of manipulatives or resources to support students.  Not some students but all students.  We want to get to a place where our students are free to grab what they need to help them with their learning.  

One of the best things about manipulatives in Tautoru is how they differentiate learning naturally.  We are able to support bottom line big ideas whilst providing stretch at the end where needed.  We can ask the right questions for different groups of students.  

• A student struggling with one-to-one counting can use counters, bears or buttons to stay grounded.

• An extension student can use those same materials to explore early multiplication by arranging them into arrays -  these are rows and columns.

Sometimes its utilising the other resources around.  Lego lends itself to many different ways of working and exploring in maths.  Here are a few examples.  

The goal is to move from just the answer to "exploring the concept." In maths, the hands-on mess is where the magic happens.