The 200 block misconception

numeracy leaders teachers May 17, 2023

You may be aware that my PhD research looked at designing an assessment for whole number place value. At the end of the four years I had created a valid and reliable paper and pen (and online) assessment called the Place Value Assessment Tool (PVAT). In many schools I am introduced as "This is Ange... the PVAT lady"... which always makes me laugh!

If you want to try the PVAT with your Year 3-6 students you can download it here.

One of the items in the PVAT that always generates discussion amongst teachers is this:

I developed this item after having a discussion with a student who explained to me that they couldn't understand why the block represented 1000 and not 600. After all, there were 6 x 100 block faces. It was a logical and considered thought and (as I later discovered) more common than you might imagine amongst Year 3-6 students. 

Whenever I work with schools and we look through their PVAT data, there is on average 25% of students in Year 3-6 who display this misconception.😲 You can read more about the 600 block misconception in the following blog.

Many teachers cannot believe that this misconception is so prevalent! To be honest, when I was doing my research I felt the same. I was genuinely shocked that this misconception existed.

I think this 'shock' is because we are coming from a place of expertise, and often this leads us to forget what it was like to be learning a new, abstract concept, like place value.

This phenomenon is known as the 'expertise reversal effect' (Kalyuga, 2007). Basically, this means that as we become experts in a skill, we forget how hard that concept was to learn in the first place.

I remember being made very aware of this when my 3 year old son was trying to put on gardening gloves for the first time. He was asking questions like: "why are all my fingers squashed?", and when I said "just spread them out" he said "but I can't see where they go".🤷‍♀️😂

As you can see in the photo below, we eventually got there (only for him to decide that he didn't want to garden anymore!).

I had completely forgotten the challenging combination of fine and gross motor skills and brain action required to put on gloves. As an 'expert' I had to go back and 'break it down' into explicit instructions a 'novice' could follow.  For example: "Spread out your fingers", "Put one and only one in each hole", "Start with your thumb"

This idea has really important implications for us as maths teachers, because our job constantly requires us to assist novice learners to master abstract mathematical concepts.

Not long ago, one of my good friends from my classroom teaching days (Hi Janet!) sent me through a message explaining a conversation she had shared with a Grade 2 student.

The students were required to make 3-digit numbers using base ten blocks. This particular student was making 223. This is how she represented it.


When Janet questioned about her response, the student proceeded to explain that the "big flat square was 200 because there is 100 on this side (pointing to one side) and 100 on the other side (turning the block over)”. This response blew Janet (and myself) away!

I had NEVER seen/heard a student explain/think of a hundreds block in this way! But now that I have heard it, I can completely see why!

She was thinking in 2D but we were asking her to represent the quantity in a 3D model! 

I shared this story in one of my monthly NTA member webinars and one of my members from South Australia, Margy, told me she had recently heard a child say the EXACT same thing!

I think for two children 725km away from each other to display the same thinking, suggests this 'misconception' might be more common that we think, and suggest it is definitely worthy of further investigation! So stay tuned, because I am fascinated to explore it further! (Side note: If you have ever noticed this (or any other strange place value related phenomenon) with one of your students please reach out!)

This week I encourage you to listen carefully for any insights your students provide as they come to master the concepts you are teaching. This requires us to listen carefully! My Pa used to always tell me "Ange you have two ears and one mouth, we should all try to listen twice as much as we talk"!

I think this is excellent advice! 

The questions our students ask, the explanations they provide, are truly priceless. These insights are windows into the thinking of novice learners and allow us to constantly refine our craft! Too often we are blinded by our expertise!

Have a great week!



Kalyuga, S. (2007). Expertise reversal effect and its implications for learner-tailored instruction. Educational Psychology Review, 19(4), 509-539.

Want to learn more from Dr Ange Rogers? Click here to find out about her 'Quality Place Value Assessment in Years 3-6 Mini Course'

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