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

Thursday, 26 April 2018

Building Vocabulary through Context

Image result for Builders
Building Vocabulary

In a previous inquiry into reading I learned that new Vocab and understandings can be built up over time successfully, when the texts and learning content are themed around a similar context for consecutive number of weeks.

Therefore it is my hypothesis that this can also be applied to maths learning. My maths planning and teaching centres around a "topic" for 3-5 consecutive weeks. In most cases this will probably be a Strand focus and all the problem solving stories and questions will centre around that strand. The multiple part problem design of the DMIC questions, seems to work perfectly with Strand and Number combined problems i.e Unit Conversion and multiplication, or finding the area of shape then subtracting.

In doing this, I am hoping to build up a vocabulary knowledge base that will build over time and mean that they are capable of more complicated problems and stories. While also having a platform on which to build or gain more concrete understanding around unfamiliar maths vocabulary.

In Term One I felt like this worked really well in the two contexts that I chose. Instead of doing a whole week or 2-weeks on Measurement, we spent 5 weeks, but only focussed on specific measurement knowledge when it came up. Otherwise it was simply was just the context in which we solved our number problems.


Thursday, 19 April 2018

The launch

The Launch is an incredibly important part of the DMIC process.

The "Launch" refers to the launch of the problem solving question that the group is going to be attempting to solve. It should be done with a large group, rather than small groups to save time. I personally split my class of 34 into roughly half, however I pull other kids down or shift them around quite fluidly.


Unpacking and understanding the story of the problem takes up a huge chunk of time. It is important to allow the students the chance to figure it out, without giving it away. This was an issue I had in the beginning where I would rush the launch so that they could get started on the maths thinking. However understanding the story, is just as important for the DMIC process as unpacking the equation. I recently had my first observed session by a DMIC mentor. They told me that the launch involves just two questions; “What is the story about?/ What do we know from the story?”  and  “What are we trying to find out?”

Once you have introduced the problem and taken a few ideas from students about what the story is about, get the large group into smaller groups of 4. Together they will figure out what they think the story is about, and whether they can agree on a strategy they could use to solve it. It is important to make sure that none of the students have a maths book in their hands at this point, and that all the discussion is verbalised amongst the group. The teacher then goes around and assesses how the group discussions are going, but does not sit and work with any one group yet. When the group has agreed on a strategy, choose one student to be the 'recorder' and let them use that persons (at only that persons) maths book and pencil.

In these groups the learners will solve the problem together and then report back, and continue with the rest of the DMIC process. To read these notes we were given in full see the document here.

An example problem that I used during my observed lesson was this:

Launch

  • Teacher (T) to read problem in full.
  • T) Question group about the problem
    • Who knows who Roger Tuivasa-Sheck is?,
    • Who watches League?
    • Who knows what the Full back does?
    • What are running meters?
    • What do you think the phrase "clocked up" means?
  • T) ask students to think about what the "story" is
    • What is the story asking us to do
The idea is that all the learners will understand what this story is about, and that they are thinking about whether or not Roger Tuivasa-Sheck will be able to run enough meters each game to meet his goal. This is crucial that they understand the story, before they start thinking about the maths. Therefore when they start thinking about the maths strategy to use they will be able to eliminate some strategies that wound't fit the problem.

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.