Digital teaching tips & tricks, ideas, examples, and general thoughts and reflections. Follow my Inquiry.

Saturday, 17 March 2018

More than a hunch

My hunch for this inquiry was that the DMIC approach could help to raise maths achievement and language acquisition with priority learners in the classroom. 

This hunch was based on previous years experience, where I had noticed that many of my learners working 'Below the National Average' would fail on questions not because of the maths itself, but their lack of understanding of what the maths was asking them to do.  Rather than wrangle with the problem, these learners would too often jump into what they thought (or guessed) the equation was and in doing so work it out incorrectly. Yet when given the equation directly they almost always had a far higher rate of success at answering the problem correctly. 

I believe that the launch aspect of the DMIC process will greatly help these learners. In particular their understanding for what each maths problem is asking them to solve, i.e. what is the story of the problem about, and what are you trying to do with it. Working in groups with learners at a higher level, and watching and listening to their strategies for unpacking the problem will hopefully help as well.

A secondary aspect to this inquiry that I wish to implement, is a stronger focus on language acquisition of technical maths language. The graphs below show that there is a larger gap for this group between the national average in Literacy than in their Maths* (*with the exception of a couple of outliers). My belief is that by increasing their arsenal of "Maths language" they will have greater success at comprehending the maths problems they are faced with. 

The Graphs

These graphs show my target group of 9 Year-Six learners working "Below" or close to "At" in maths at the End of last year. The red line shows the national average. I thought it would be interesting and revealing to show the Maths data alongside the Literacy data to see if there were any trends that I could spot. Not too surprisingly, the most obviously trend was that almost all of these 9 learners were falling behind in their literacy more than in their maths.

I think this helps to support my hypothesis that language acquisition in maths will ultimately help lift maths achievement levels, as it supports my own observations where success has been blocked due to comprehension of the problem.
* I thought it was worth noting that I don't usually consider a "Overall Gloss score" or "Global score" as it can provide quite a warped view on the individual learner if their scores aren't streamlined across the 3 fields. However for this graph it was the best way to show results.



Friday, 2 March 2018

Talk moves

crucial aspect of the DMIC approach is the successful dialogic discussion and argumentation involved in exploring the the different ways of looking at, or solving a maths problem. A useful resource for developing this culture amongst the class is through the use of Talk moves.

If you Google Talk Moves it will produce about 198,000,000 search results. The majority of the links on the first 3 search pages are useful, and will get you on the right track. However, here are 2 links that I found were really helpful for my own understanding.

First Link: What are talk moves?
A summary of the 5 Talk Moves outlined by Chapin, O'Connor, & Anderson (2003).
- Link to PDF

Mathematical Discourse
Five Talk Moves

Revoicing
The teacher tries to repeat what a
student has said, then asks the
student to respond and verify
whether or not the teacher’s
revoicing is correct.
“So you’re saying…”

Asking Students To Restate
Someone Else’s Reasoning
The teacher asks one student to
repeat or rephrase what another
student has said, then follows up
with the first student.
“Can you repeat what he just said
in your own words?”

Asking Students To Apply
Their Reasoning To
Someone Else’s Reasoning
Students make their own reasoning
explicit by applying thinking to
someone else’s contribution.
“Do you agree or disagree and
why?”

Prompting Students For
Further Participation
The teacher asks for further
commentary.
“Would someone like to add on?”

Using Wait Time
The teacher waits at least ten
seconds for students to think before
calling on someone for an answer.
“Take your time… we’ll wait.”

Second Link: Useful cards for the classroom
Some print outs/ ideas to help develop the culture of using Talk moves and 'Talk move like' discussions by the Virtual Learning Network, Ministry of Education (2014). Copyright, Ministry of Education, NZ. 


References
Chapin, S. H., O'Connor, M. C., & Anderson, N. C. (2003). Classroom discussions: Using math talk to help students learn, grades 1-6. Sausalito, CA: Math Solutions Publications.
  • Miller, L. (2004). Talk Moves (Unpublished Resources), Virtual Learning Network: Ministry of Education, NZ.

Where do I start with half-class grouping??

As I already mentioned in a previous blog post, grouping my maths class into mixed ability groups was a difficult concept to get my head around. However the concept of also splitting my class into only 2 groups (i.e. half the class in each group), left me feeling pretty clueless about where to begin. This is what I did.

First go
I decided to start by finding out what it was like to teach half the class as one group. So, instead of worrying about how to group them, and who to group them with just yet, I simply asked to see the Girls and Boys as seperate groups. The learners absolutely loved it, but in hindsight (and what a beautiful thing it is) this may not have been the best decision... BUT, it did allow me to get a feel for what it would be like to have half the class down on the mat.


What I noticed:

  • We can fit - One of my main personal resistance's to this approach was the fact that I believed I would not fit a half-class group on the mat. Well we did, and it was easy. 
  • Some learners will shine - After the initial shyness wore off, there were some clear stand outs that loved being able to share their thinking, or their "way" of doing the maths. They loved having the attention of the whole group, and this was clearly their element.
  • Some learners will freeze - Even some kids who I know will happily share their thinking in a small group froze. I believe this must of come from a place of insecurity, i.e. knowing that they were in the same group as the "smart kids", and not want to get shamed for being wrong.
  • Confident kids will convince more capable kids they are wrong - Confidence is key! I had kids working at Early Stage 5 convincing other kids working at Late Six that they themselves were right with their "guesses", while and the mathematical reasoning and computational thinking was wrong. 
  • All of us were going to take some time to get used to this - I talk too much. Both myself and the kids are going to need more practice at this approach before we have any success.
  • It was fun - All of us left the lessons buzzing. 


Second go:
After a week and a bit of staying just the boys and the girls. I finally decided to regroup. Initially I asked each group of boys and girls to split into 2 groups and then combined them from there. I later read that social groupings does not necessarily (and in most cases does not) mean "friend groups". So I rejigged some of the kids around after that. After I had done this, I looked at their current achievement data, and found that the kids had organically done a pretty decent job at mixed ability grouping all on their own! The ability spread was pretty even across both groups, and I hadn't had to do any of the work, fantastic.

What I noticed:

  • It worked a lot better - Both the boys and girls worked together well, and took the lesson far more seriously now that the genders were mixed. However, I'm not sure if this was due to being mixed, or whether it felt more like an 'official' maths group, and therefore should be taken more seriously. Either way it was good news.
  • Confidence was improving - I started seeing less of the initial "hanging back" that I noticed, and more kids were piping up. I also noticed that my higher ability learners were now backing themselves a lot more. Instead of simply trusting the "loud" kids.
  • It was still fun - Aside from a small number of resistant and/ or very quiet kids these lessons are becoming a highlight of the day for everyone. 

I'm looking forward to learning more about the DMIC approach, and getting better at it. It's exciting, and the more I experiment with it, the more confident I feel. I just hope/ fear that I'm not wasting too much precious learning time figuring it all out too much..

Monday, 12 February 2018

A lesson Outline - Bobby Hunter

Here is a brief outline for a DMIC lesson that Bobby shared with us.

10 minutes : Warm up
- Do a problem from last term

5-10 minutes : Launch/ group norms
- Work as a family not a 'team' - this is not a competition, its more like a family working together
- Cooking a feed, where everyone pitches in. No one owns it, it's a shared product
Launch needs a good story

15 minutes : Small group activity
- in small groups tackling the problem

15 minutes : Large group discussion
- Sharing Solutions
- Exploring Thinking

10 minutes : Making connections to the big idea
- Connecting the learning to the big ideas
- Explicitly pointing out what was learnt

Teacher role: anticipate, monitor, select, sequence, connect