What happened for the learners?
My learners had to get used to a completely new way of learning maths.
They learnt to carefully read, talk about, argue, listen to others, and communicate their ideas about a problem
...before attempting to solve it.
They learnt to attempt new problems in groups of 3-4, and insist that their group work together and share their thinking
...before finally agreeing on a solution (or an attempt at a solution)
They learnt to share their ideas and explain their thinking back to a much larger group (15-20 learners)
...before listening to those of another group (or vice versa)
And they had to learn to be able to do all of this before I (the teacher) would offer them much in the way of support with the problem.
Before considering anything else, I think that this alone is a huge thing to have happened for my learners, and I couldn't be more proud of the way they have taken these lessons on.
There are other changes to their maths learning that I will briefly list:
- Half class groups
- Mixed ability grouping
- Flexible groups (i.e. changed regularly)
- 40-60 minutes lessons
- Only 2 formal maths lessons a week
To be fair to the inquiry I think student achievement has to be talked about in two different areas. Maths achievement and Dialogic capabilities.
Maths achievement - The ultimate goal of the inquiry.
Short answer: achievement gain = yes, accelerated shift = no.
I had a target group in mind for this inquiry. 7 learners working around the same level (Late Lv 2/ Early Lv 3). Their results were mixed. These mixed results matched the rest of my class as well.
Dialogic capabilities - What was originally supposed to be the vehicle for achievement.
At the beginning of the inquiry I never thought of dialogic capabilities or skills as something that needed to be achieved, instead I thought of them as the necessary tool or vehicle that would drive the maths achievement. In most regards this holds true, however what I didn't anticipate was the amount of learning that would need to happen (dialogic learning), in order to use it as the tool for maths achievement. As stated above this learning was massive, and although was not something that I formally recorded or captured, that changes in the class behaviour and practice is very noticeable. Does this mean that every kid became capable of these skills, unfortunately no. In fact it became more and more noticeable which leaners continued to stay quiet and allow others to speak.
Short answer: Dialogic increase = BIG YES, Whole class: no
What evidence do I have of this happening?
As stated above I had a target group in mind for this inquiry. See their PAT results below
As you can see the results are positive, however mixed. What you might find interesting to know is that the learners from this group who had the most growth, also showed more development in their Dialogic capabilities. This pattern was reflected across the rest of the class, however there were many outliers that did not fit to this correlation. i.e Some of my least talkative learners still had big gains in their maths learning. So although there appears to be some evidence that good mathematical discourse and critical discussion can lead to gains in mathematical understanding and achievement, perhaps the learners who listen and reflect on the discourse internally can gain understanding just as well.
I also noted that there appeared to be a similar pattern of achievement from these learners in their literacy. How and if this inquiry is connected, or whether the literacy gain helped to lift the maths is yet to be determined...
Unfortunately this was not recorded or captured throughout the inquiry. Having seen the achievement gains in this area I wish that I had, although I'm not entirely sure what this would have looked like. Perhaps a simple audio or video recording that could have acted as a comparison could have sufficed.
The acquisition and use of precise mathematical language was an intended part of this inquiry and again unfortunately was not captured well. I battled with the best way to have achieved this but kept getting stuck. For example a pre and post vocab test would have been simple when starting a new unit. But it ran the risk of teaching to a test, rather than allowing the vocab to be learned authentically and needs based as part of their mathematical reasoning. However, anecdotally I believe that the student-talk IS helping the acquisition of language among the students. At least you can hear them questioning and correcting each others language throughout the lessons. This was most noticeable when working with decimals “wait you mean tenths, not hundredths” “its not 5 its 5 tenths” etc. I also believe that the discourse that the students engaged in greatly impacted their understanding in our geometry unit, where the students argued over whether they needed to solve the perimeter, area, or volume etc.
What did I do to make this happen?
Developing Mathematical Inquiry Communities (DMIC), is a complete overhaul of our mathematical teaching practice. It involves spending more time allowing learners to attempt problems collaboratively without teacher support, to share their thinking, and listen to each other's ideas. It involves the teacher listening to the students and identifying misconceptions that can be addressed at the end of the lesson.
This meant that in my practice I needed to adopt the use of the talk moves in maths discussions, and allow the students time to wrestle with the problems on their own. Identifying and predicting misunderstandings and misconceptions during the planning process. Then later responding to students needs during the “connect phase” of the lesson.
Instead of being grouped by level or ability, the learning groups are of mixed ability allowing students to learn from each other, and not have their learning capped by their groups achievement “level”. Lessons last 40mins to an hour, rather than 20 to 30 mins.
Instead of taking 2-3 maths groups per day, I only take 1 a day instead because of the time constraints.
Wonderings for what next?
At this point in time I’m not sure that I can claim that the inquiry has led to accelerated student achievement in maths. However there has been a growth in student dialogic capabilities in maths.
It does appear to be leading towards a growth in mathematical understanding, however I believe that because the dialogic learning needed to come first, that we won’t see the intended the results within this academic year.
A truer test will be to follow these same students next year (assuming their Year 7 teacher will continue using the DMIC approach in the classroom next year), now that their foundation dialogic skills are already there. Because there are lots of indicators to show that this inquiry is on the right track, at least in line with my initial hypothesis. I’m hearing a lot less “is it a plus” and more questions like “what is it asking us to do” “how do we do that”.
Another example has been the problem solving ability through dialogic conversations of the students in other curriculum areas. - I have been experimenting with students and different Digital coding applications. I have offered limited support and set challenges for the students to complete (in a similar fashion to their DMIC lessons). Throughout these lessons I have heard the same types of critical discourse and dialogic discussions, that the students use in their maths learning. They are solving complex problems and learning to do things far beyond the guidance I have given them. The students have been allowed to form their own groups and interestingly have followed the DMIC model and naturally formed mixed ability groups. The ‘expert’ students in the class tending to group themselves with less capable peers, rather than teaming up.
The student-talk I believe IS helping the acquisition of language among the students, at least you can hear them questioning and correcting each others language throughout the lessons. This was most noticeable when working with decimals “wait you mean tenths, not hundredths” “its not 5 its 5 tenths” etc. I also believe that the discourse that the students engaged in greatly impacted their understanding in our geometry unit, where the students argued over whether they needed to solve the perimeter, area, or volume.
This is the first time in my short career (5 years) that I have had to really “unlearn” something to change my practice. The DMIC pedagogy is so different to how I had previously been teaching maths that it took me a lot longer than I expected to become proficient at it (and I am still learning and not at the level I hoped to be). Because of this, my own learning journey affected that of the students, it felt like it wasn’t until term 3 that we really started to learn maths again, instead of learning DMIC.
This meant that I didn’t get to see the growth in language that I hoped to see in this inquiry. Yes I saw a growth in dialogic discussion and discourse skills from the students, however these skills were necessary in the first place for me to test my hypothesis. It feels like my work in this inquiry was about setting up the foundations for what I wanted to investigate, rather than actually investigating my theory.
Do I feel like my practice or professional learning has grown in this inquiry cycle - Absolutely yes. I have done lots of work around dialogic conversation before (mostly in literacy), however I have never attempted a complete overhaul of my practice in the way that I have for DMIC. My use of the talk moves, and my ability to set up and maintain group norms has grown.
There is still a tonne of work that I need to improve in my practice in DMIC, for example; accurately pitching the problems at the right level, tracking all students (including the quiet ones), assessing the students, maintaining group norms, and time management.
There are also parts DMIC pedagogy that I am still yet to fully understand, most notably the mixed ability grouping. This is an area where myself and my team have become very frustrated and stuck in how to meet the needs of all the learners in the group.