The birds

On the holidays we welcomed five birds into our family.

This was a big moment for the Rogers clan, as we had previously been a 'pet free' family.

I don't have anything against pets, it's just since birthing humans, I feel like they have taken up all of my feeding/caring/cleaning up after/worrying brain space. So I have avoided any discussion of pets.

My avoidance strategy was working well until we moved about 2 years ago.

When we moved into our new house, there was a inbuilt bird 'aviary'.

The first thing I thought when I saw the aviary, was ‘hmmm… down the track we can pull that out and plant a lovely garden”.

Turns out people can look at exactly the same thing and have opposite thoughts.

My husband and children all looked at the aviary and thought… “We can’t wait to get birds!”

I have managed to avoid the ‘bird’ discussion for nearly two years, but on the holidays my family organised a democratic family vote to decide whether we should have birds or not…and it is not surprising that I lost 5-1!

My aversion and fear of birds runs deep.

I can trace it back to several traumatic incidents involving a magpie's beak getting temporarily stuck in my helmet while riding my bike😯, and one memorable day as a graduate teacher where I had a bird flying around my classroom with 28 screaming children.

I had to seek help from both the principal (!) and the teacher who was in the classroom next door. They both displayed amazing bird whispering skills to somehow convince the bird to exit the room so I could continue my teaching.

Teaching is never boring, that is for sure!

While I accepted the result of the family vote, I announced that I would not be taking care of the birds in any way- it was the five ‘yes’ votes who would be required to share responsibility.

So on the holidays, I accompanied 4 excited children and 1 excited adult to purchase 5 finches.

Visiting the bird shop was not my favourite experience...hundreds of birds squawking and one canary who had escaped deciding to fly straight at me! But I put on a brave face* and we arrived home safely with our new feathered friends.

Unfortunately only 4 birds made it through the first night 😔🤷‍♀️(we are not sure what happened), but 'luckily' the pet store offered a 7 day guarantee on purchases, and with 'proof of death' (a photo of the deceased bird 😲) we were able to go back and get a 'replacement', and a ‘travelling partner’ to accompany it on the trip home (a nice upsell by the bird shop!). So now we have 6 finches!

Two months on, I must admit the birds are lovely to watch and listen to in the aviary and the children are caring for them very 'responsibly'.

As I watched the birds settle into the aviary on their first day at our house, I observed an interesting phenomena.

The first 5 birds had never been in our cage before. Inside is a tricky section where they have to fly low to get into the area where the food is located.

It took what seemed like forever for the original 5 to work out how to get to the food.

There was lots of trial and error and frustration from the birds… they could see the food, but couldn’t work out how to get to it!

Finally, one bird's experimenting paid off and he made it to the food section. He was the hero!

The technique was quickly observed and passed onto the rest of the flock.

What surprised me was when the two new birds arrived the following day, they took almost no time to work out where the food was located. They learnt very quickly from those who had already mastered the skill. 

This made me think of the maths classroom and the 'explicit vs inquiry' debate reaching fever pitch across the world.

There is no doubt that there is strong evidence to confirm that explicit teaching of mathematics for novice learners is a fast and efficient way to impart knowledge. 

However, I question whether just because a concept is 'explicitly taught', it is automatically 'best practice'.

One example that pops into my mind is place value related (of course!). 

I have seen the script below used in direct instruction text books and on 'explicit teaching' videos widely available, and it concerns me that teachers are not always being shown research-informed teaching methods and this leads to suboptimal instruction.

If a teacher is wanting to explicitly teach their students 'place value', they may write the number 325 on the board.

They may point to each column and say "there are 5 ones, 2 tens and 3 hundreds in this number". In this 'I do' stage the teacher is telling the students what they need to know and showing them the process they need to follow. They are modelling their thinking and then checking for understanding.

Next they may complete some faded worked examples on the board, where they may say "In the number 456, there are 6 ones, and ask the students to identify the number of 'tens' and 'hundreds'. This is known as the 'We do' stage.

Finally, students complete independent practice of this skill while the teacher provides the student with individual feedback. This is known as the 'You do' stage.

What concerns about this model of teaching is not so much the process (although I do think it is important to use a variety of teaching models in our maths instruction), but the content that is being presented in classrooms.

One of the most common misconceptions that students develop in place value is 'Independent Column Thinking' (you can read more about this misconception in this blog I have written).

Students with this misconception come to believe that each column is its own entity. They believe the hundreds live in the hundreds column, tens in the tens column, and ones in the ones. So when we ask: 'how many tens are in 456?', they head straight for the tens column and say '5'.

This causes issues when we try to teach the skill of renaming because students don't see the relationship between columns. We want students to 'see' that there are actually 45 tens in 456. If they have been explicitly taught that tens live in the tens column, they will have to unlearn this when we teach renaming, and thus we are slowing the learning process.

If we think back to the lesson I described above, this explicit teaching is actually creating a misconception in students. Now, don't get me wrong, I am not saying it is the 'I do, we do, you do' that is causing this misconception, it is the content that is being presented to students.

If the teacher was confident in their knowledge of how to teach place value and aware of the Independent Column Thinker misconception, they would chose their words very carefully and say "In 325 there are 2 tens in the tens column but there are also 30 tens hiding in the hundreds column". This would be much more effective way of explicitly teaching this content.

My point is... at the end of the day if teachers do not have the deep content knowledge to teach concepts, or are showing videos or reading from text books created by someone without this understanding (and they cannot recognise possible issues with these resources), the explicit teaching will be less than optimal. 

Not all explicit instruction is created equal, just like not all inquiry teaching is created equal.

The truth is that the more teachers know about maths content and instruction the better their teaching (inquiry or explicit) will be.

Teachers often ask me to make videos to show them how to best explicitly teach critical skills in place value. I have done this for a few skills, you will find these here. But for me, it is just as important to upskill the teachers in their own knowledge of how to teach mathematical concepts. This provides them with the confidence and knowledge to be critical consumers of content and have the skills to recognise and support their students at their point of need. 

This week I encourage you to engage critically with some explicit mathematics teaching content. What would you change? what do you think is missing? What could you improve on? Does it align with the research you have read about teaching that particular content area?

Our new birds learnt to get to the food faster from the 'expert', but if they learnt through a sub-optimal technique, is it really helping?!

Remember, no matter what method you use to teach maths, teacher pedagogical content knowledge that is at the heart of its success or otherwise! 

Have a great week

Ange:)

*my daughter informed me later I looked scared witless the whole time at the bird shop...so clearly my 'brave face' is not so 'brave'!

PS: If you are interested in booking me for PD at your school to help your teachers develop their pedagogical content knowledge in any area of mathematics, click on the right of the screen to find out more!