Place Value Thinking Mistake: Name/RecordJun 01, 2022
Place Value Thinking Mistake: Name/Record
When I work with students, I love to celebrate mistakes and promote a growth mindset (Dweck, 2016). I encourage all students to see that through mistakes comes learning. I like to label misconceptions as ‘thinking mistakes’. ‘Thinking mistakes’ are in direct contrast to ‘silly mistakes’- ones which I want my students to consciously avoid- these are made when our brain is not ‘switched on’. In stark contrast, ‘thinking mistakes’ are made when our brain is working hard, struggling to make thoughtful and logical conclusions. It is during these times that real brain growth occurs.
This series of blog posts presents six common ‘thinking mistakes’ which have repeatedly surfaced in my research into Year 3-6 students whole number place value understanding. Along with each thinking mistake I also present a piece of teaching advice to help you address these issues.
In this blog I am looking at the ‘name/record’ aspect of place value. In my research I defined this aspect in the following way: Read and write a number in words and symbols (e.g., ‘seventy-five’ and 75). Name the place value columns (the hundreds column is next to the tens column). Round numbers to the nearest place value part (567 is closest to 6 hundreds). Determine the value of a digit (the digit 7 in 75 has the value 70)
Thinking Mistake: When students attempt to record numbers, they often completely ignore place value conventions and simply write the numbers they recognise (in this case four hundred and seventy-three).
Or as you can see in the below example, they concatenate numbers, writing each part in sequence, for example (four hundred thousand, then 73).
Teaching Tip: When we teach reading and writing numbers, we should encourage students to chunk (within the periods) and observe patterns (between the periods). Just as in literacy it is ok for students to be able to read some words they don’t understand, it is perfectly ok for students to read and write numbers they have no comprehension of… yet! This comprehension will come as we teach other aspects of place value. I like to use a ‘Place Value houses’ template (see below) to teach the structure of our number system. As soon as students can write and read a 3-digit number, they are ready to learn to read/write numbers of any magnitude. Once they see the structure and conventions of recording numbers, they rarely make the errors shown above.
Students need to appreciate that to read/write numbers we simply read the 3 digit number in each period, then say the name of the period. They need to be supported to see the repeating Hundreds, Tens, One or ‘HTO’ pattern within each period. This will help them to see that 456,789,345 would be read as: 456 million, 789 thousand, 345. As you can see once they know this structure reading numbers is so much more manageable!
One of my favourite (super simple) activities for encouraging students to practice writing and reading numbers is to have a pair of students sitting back-to-back. Player 1 inputs a 5+ digit number on the calculator and reads it to player 2. Player 2 writes the number they hear, if the numbers match the pair receives a point. First pair to reach 7 points is the winner.
Another authentic activity is to complete real estate property sale searches on the internet (particularly in Australia- where the house prices are insanely high!!). Students are encouraged to find 5 houses from the suburb their school is located in and read their price to a partner. Their partner then writes the prices (and for an added challenge, puts them in descending order).
Students find this authentic application of reading numbers surprisingly engaging and it often provides an opportunity for some impromptu financial literacy discussions too!
Next week I will be looking at another place value 'thinking mistake'... in the 'Count' aspect of place value.
P.S: Are you interested in joining my Numeracy Teachers Academy? I will be opening enrolments and welcoming a new group of 30 members in the next couple of weeks. If you want to be the first to know when the doors open, click here to join the waitlist!
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'