Tuesday, 16 February 2016

Dividing Your Class with Division Strategies

We all know that differentiating or the new buzz word - personalised learning is key to student engagement and mathematical development.

It can be tricky orchestrating 20 different levels of conceptual understandings and skill awareness amongst children in our classes so I've been experimenting with this strategy of flipping our classroom to enquire into multiplication strategies and now tried with division strategies.

For home learning ( a much more positive term than homework- why do we call learning work?!? ) students were given the following Google doc showing a list of different levelled division strategies I found on YouTube:

Enquiry into Division Strategies Google Doc- Feel free to copy and use :)

Division Strategies
Choose two strategies to learn.
Record on the paper provided.

They were asked to select two division strategies from the list of YouTubes by self-assessing whether they feel they might be at. The columns range from easier to more challenging.  We use this column strategy quite often in class and the children are really great to selecting a level that is suitable for them.

The process for their home learning enquiries is:

1. Select a division strategy to enquire into from a column you feel is at your level (easier to more challenging)

2. Watch the YouTube at least twice to gain a good understanding of how the strategy works.

3. Explain how the strategy works visually or in written form.

4. Test the strategy by creating 4 questions and attempt to solve them using that strategy.  (This might sound simple, but actually requires deep thinking. For many of these strategies, the children really need to think about what type of numbers will work for the strategy or not in order to by able to apply them. The trial and error strategy is often applied and this helps deep the child's awareness of number sense and the strategy)

6. Ask for feedback from parent/s about your teaching communication skills and record the feedback to share with us in class.

Some samples of recorded enquiries:

The children remark on how much they enjoy teaching their parents the strategies.  Some explain how proud they feel when they know something Mum or Dad doesn't.  Others say it helps them to really understand the strategy because they need to think of what to explain first and so on.

Today, it was time for us to share the strategies we had enquired into.

We grouped in trios or partners depending on the numbers and recorded an explanation of one of the strategies we particularly found interesting on a communal chart paper. This served three main purposes: firstly it freshened the strategy in the child's mind by revisiting how it works and secondly it gave them a opportunity to perhaps improve how they could explain it more effectively on paper than they had done the first time at home. Thirdly, they could use this explanation as a teaching tool should they want to.

Some samples:

After the groups recorded, they created a way to peer-teach those in their group the strategy in any way they felt would be the most effective.  Some chose to use manipulatives like cubes etc. Most chose to use mini whiteboards to explain. After explaining how the strategy works, they then gave questions for their peers to try to solve using that strategy and would offer help if needed.

A lot of excited questioning and mathematical reasoning skills and debating were generated whilst this peer-teaching took place of up to 8 different division strategies being explored at the same time in the room.  You can't get this type of student engagement and buzz from typical chalk-n-talk style teaching practices.

To help improve our communication skills, the children in the group gave feedback on the peer teaching by completing a rubric based on some PYP Learner Profile attributes.  Using these attributes in situations like these helps the children to internalise with direct experiences what the Learner Profile really means and why we discuss our development of them.

Peer-Teaching Division Strategies Peer Feedback

Learner: __________________

Feedback from: _________________

 Emerging Developing Consolidating Expanding Knowledgeable: Understanding of how the strategy works Communicator: Ability to clearly explain the strategy on the chart paper Communicator: Ability to clearly teach the strategy Communicator: Making regular eye contact body language positioning & whilst teaching to engage the listeners

To wrap up, in groups we discussed 'big picture' understandings we felt we gained from this enquiry and sharing. Some ideas included:

° Some division strategies are easier than others.

° The best strategy is long division because you can do it with any number no matter how big.

° Some strategies are not helpful.

° Some strategies for division are quick and some take longer time.

° Division is easier when you can recall times tables well.

° Division can include decimals!

° Halving can make division a lot easier.

We used a few of these to play 'The 5 Whys'

We started with one big picture idea.
Why?
Why?
Why?
etc etc

If the player can continue with 5 whys they succeeded.

Here is our sample we did before playing with a partner using a different big picture idea generated:

It is a really fun, deep thinking and challenging game that had us really thinking about numbers and division. :)