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

Wednesday, 30 May 2018

Learning new Vocab in a Geometry Unit

As mentioned in a previous blog post I have been attempting to build new maths vocabulary in a meaningful and authentic way. To do this I have been focussing on a particular strand in maths as a kind of "topic" to build on each lesson, for 4-5 weeks in the term.

This term I have focussed on Geometry on and Measurement. I realised from looking at their MathsWhizz results, as well as observations during our daily lessons that a large majority of my class had huge misconceptions around Geometry and Measurement. Particularly anything to do with 'shapes'. In fact when I quizzed few of my kids across all of the ability groups it was very clear that this was an area of confusion and uncertainty for our class.

Not really knowing where to start, I went straight to the curriculum expectations for Level 3.
This really threw me off if I'm being honest. It was too much, and I didn't know how to do it. 
I started with names of shapes thinking this was a logical place to start... it wasn't. In fact all I did when I reflected on my lessons was teach kids how to cram. "Lets learn a whole bunch of names and try to remember them".

I decided that this wasn't going to achieve my goal for "authentic learning". There was no real reason to learn these names other than 'the teacher told me to'. Instead I picked ONE bullet point.
  • Find areas of rectangles and volumes of cuboids by applying multiplication.
In fact I only intentionally planned to teach 3 "words":
  1. Perimeter
  2. Area
  3. Volume
Naturally*, as we battled with these three concepts using the DMIC process, there was a TONNE of vocab that we had to use and understand to be able to be successful in these problems.
*I say 'Naturally' but it wouldn't seem natural at all unless you are familiar with the DMIC process.

I didn't explicitly teach nor plan for these words, but just as you would expect new vocab to be learned in a topic surrounding 'flight' for example, we came across and had to use/ learn a whole bunch of words related to Geometry and Measurement during our problem solving questions.

~5 weeks later~

According to MathsWhizz since the beginning of Term 2, my class average has improved 11.5 weeks in "Shape and Space", 9.5 weeks in "Measures", and interestingly* 13 weeks improvement in "Multiplication Calculations".
*Actually on reflection this makes sense seen as most of the calculations over the past 5 weeks have been multiplicative.

However far more obvious in the classroom is the lift in confidence and use of vocab surrounding this topic when we work on anything related to it. There is technical and precise vocab being used by the learners to each other and in response to each other. 

Overall a really positive result and outlook for the success of this inquiry. Onto Fractions, Proportions and Ratios next :)

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:


  • 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.