Extended Discussion and Reciprocal Maths

Why I chose this focus:

I have been working on developing numeracy for a couple of years now. I had a hunch that improving oral and read literacy would have a positive impact on numeracy, especially with comprehending word problems.

Where I am currently:

I have taught Extended Discussion through Reading. I have aligned my Reciprocal Maths roles with my Extended Discussion roles. I use both regularly in lessons.

Changes I have made to my practise:

I have built extended discussion in to my reading lessons. I have a specific lesson for working on word problems and allow students to discuss through a problem and teach each other.

Problems:

• Some students are not buying into helping others through conversation. They prefer to just solve problems. I may need to make specific groupings.

Next steps:

1. I have an idea for a more simplified Extended Discussion cue card. Hopefully this will promote more natural discussion.
2. I still need to move from Reciprocal Maths to the more open discussion format of Extended discussion.

Basic Facts Boxes v2

Basic Facts Boxes has been updated, four years after I first developed it. This version has several new features to improve the experience all coming under an altered basic facts focus and a different physical layout.

Basic Facts Boxes v2 focuses on the addition/subtraction facts to 20 and times tables, i.e. the first 100 multiplications. I work with students who have major gaps in knowledge and are often far behind expectations, so I need to figure out ways of helping them learn. The Numeracy Development Project takes children on a meandering path through number learning, which in my opinion makes children run sections of the path before they can walk. Focusing on the facts to 20 and times tables covers the main facts we English speaking people need as core maths skills.

To differentiate for those less skilled, there is now the option of choosing ordered or random. Ordered being the easier version... That's assumed, not tested. I would hope that students would be able to see a pattern forming so they can solve anything they don't know yet. Anyone who can't is likely to need a different level of education programme anyway.

The basic facts boxes that students fill in are now collated into two 10x10 grids (excluding frames). This change imparts several improvements:

• Increased practise frequency within a single "box".
• Smoother and faster number entry. Users now only need to use the tab and enter keys to move between cells.
• Improved screenshot captures.
• The ability to print to an A4 page.

Using a new format forced me to make improvements on the layout and programming. Everything except the title, grid, and buttons at the top are generated through the script. This brings everything one step closer to a "fool proof" spreadsheet where if anything (such as the grid) was deleted somehow, the whole grid would be reset/ regenerated by clicking a button.

Extended Discussion - Actual Teacher Inquiry

This year is shaping up to be a strange one. While I am still working on maths, my inquiry this year is into reading comprehension and more specifically an initiative called Extended Discussion. Extended Discussion attempts to improve reading comprehension of texts through conversation between group members. This is very different from my initial post about this year's inquiry.

The end goal of Extended Discussion is to have students discussing a text and asking questions of each other. Discussion and questioning pools students' mental resources and gives opportunities to learn from others or teach others. Effective questioning also encourages students to discover where they may not realise they have misunderstood the text.

Obviously, training students to be capable of conversation requires different amounts of work for different students. In general the students of my class tend to be on the polite side, not wanting to disagree or speak out of turn. A handful are able to comprehend texts at their chronological age or higher. Even then, they still do not have the background knowledge (derived from reading mileage) to help them overcome some language hurdles such as idioms or metaphor. A large majority of my students' reading ages are sitting just below their chronological age. On top of that, they have the same background knowledge issues as the handful mentioned above but more pronounced. While I suspect much of my students' reluctance to answer questions, or their seeming inability to answer simple questions is the result of doing nothing at home over our multitude of lockdowns, the reading mileage issue has been present since long before lockdowns started. 

A breakdown of my process follows:

The benefit of running this in my Reading programme is that it is going in the direction I wanted my Maths to go, hence the Reciprocal Maths cards I developed. I will be trying to develop this within my Maths programme as well.

Reciprocal Maths: first lesson for the year ... or not?

Week One was the intended first week of teaching Reciprocal Maths and applying it to word problems...that didn't happen, for many reasons. One such reason was my underestimation of the effect of covid based learning gaps, and the lack of formal maths education using maths exercise books.

Week Two ended up being a very brief introduction to Reciprocal Maths, while Week One ended up being a lesson on how to rule up a maths exercise book. It seemed that students took to the steps and process of Reciprocal Maths easily enough. However few groups applied the strategy taught prior to exercising Reciprocal Maths. More instruction and closer observation are needed.

This week, perhaps a choreographed demonstration is required to give an idea of how to run through the procedure.

Side note: it seems many students need more instruction on which way to begin opening an exercise book and how to find the "first" unused page.

2022 Teacher Inquiry...not

*Edit and disclaimer* The following post doesn't detail my confusion as to what the Inquiry for 2022 actually was. In subsequent posts you will see that my Inquiry was into Extended Discussion. This post was written before that decision was made. The principal talked about improving children's wellbeing and motivation to come to school in the new post lockdown era (seen in the post prior to this). That is what I got fixated on.

Post-ish Covid Teacher Inquiry...what to do? My Teacher Inquiry has already been chosen for me, but frankly, I don't see it as something I need to put too much thought into. More on that later. 

Right here I will bullet point the maths programme that I had started last year with Grant Ogilvie (Go for Teaching) but wasn't able to continue. The details are as follows:

• Number knowledge & algebra, other strands, and strategy are taught on separate days in the week.
• The above divisions are taught every week.
• Other strands are taught in detail throughout the term. This is where the blog posts come from.
• Number sequence and order, place value, fractions, basic facts, and algebra are taught in two week blocks. Currently the two weeks are consecutive weeks. Preferably the weeks would be separated to encourage retention. This will happen from T3, when my new co-teacher has developed some familiarity with the programme.
• strategy covers add/sub, mult/div, proportions/ratios, as Gloss (assessment) divides them. 
• proportions and ratios are taught more than the others due to it being the focus as decided by the Senior Management Team. Preferably I would make sure add/sub and mult/div are understood completely before teaching prop/rat, but that's not how the NZ maths curriculum works.

Reasoning from observation as follows:

• skills and knowledge across the board were low
• division of groups based on overall level was not targeting students precisely enough.
• retention was poor
• many students with capable skills were testing low, with our hunch being they didn't understand the problems.
• our subsequent decisions were: to look more closely at the data to target specific weak areas for each student, specifically in strand, to continually and repeatedly cover all knowledge, and to develop comprehension of maths problems and thinking skills to solve them.
• finding weak areas in strand and teaching it over protracted periods is an attempt to boost strand knowledge
• repeatedly covering all areas of knowledge is to build retention
• to improve maths problem comprehension, we developed our "Reciprocal Maths" programme, which we haven't had a good run at due to Covid.

Our Reciprocal Maths programme has been covered here.

So what is my Teacher Inquiry for 2022? What I can do to keep/increase student motivation post Covid... I understand the need for keeping an eye on student "wellbeing", and that children's motivation for school might be lowered... However isn't keeping students motivated part of a teacher's job anyway?

The New Normal and Student Engagement - Teacher Inquiry 2022

Teacher inquiry for 2022 is about how to gain student engagement in the wake of COVID lockdowns, isolations, and fear based absence. To keep students engaged Grant Ogilvie (GO for Teaching) and I have used more physically-based activities and included more social supports (tuakana-teina / sempai-kōhai teaching).

Although the general vibe of the classroom at the moment is keenness to get into work, there are some difficulties due to the situation. These difficulties range from not having the resources they normally would have by this time to a disparity between their keenness and actual ability. 

The main strategy Grant and I are employing, though, is keeping class running as close to normal as possible. This includes everything from keeping all expectations as they were pre-covid (while understanding that many have not had a full Year 3 or 4) to running lessons as close to "normal" as possible and not leaning too heavily into online learning. For the moment, this strategy is difficult, however it should pan out well.