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.

Explanation Writer

The Explanation Writer is up! (See below)

It's a bit late for the Inquiry units we could have used it for, but at least it's ready for the next time students need to write an explanation.

Next will be the information report version which will need to be ready by next term in a couple of weeks.

Recount Writer - test results

Background

I created the Recount Writer in an attempt to further scaffold the writing of the recount text type. Initially the roll out went to my maths groups. Within this group of children, there is a wide range of writing ability. Subsequent roll outs were to my reading groups, most of whom find writing difficult, and the whole class in Inquiry.

In our school, we teach the structure of a recount as TREE; title, reveal, events, ending. The reveal is meant to introduce the overall activity done and who was involved. The events detail separate parts of the activity. We generally aim for three events for a standard recount or one event for a quick recount. The latter are primarily used in short blog posts. Personal reflections of the activity come in the ending section.

Test Results

Following are three results from different students showing a reasonable amount of success. An interesting point to note is that while all three of the events were set to compulsory in the Recount Writer scaffold, only the topic sentence for each paragraph was compulsory. The examples below show that students have attempted to add further detail, for the most part.

This recount is from a student in my maths groups. This student is both new to the class and has difficulty with sentence structure, particularly tense.

The sample shows that while the student still has issues with tense, they have been able to separate the learning task into three separate events. Separating events is often a big hurdle in writing recounts and learning how to use paragraphs.

Animal Rescue Centres is a text I taught for reading. The student who wrote this is new to the school, new to using netbooks on the scale we do, and comes from a Te Reo Māori immersion kura so less experienced with writing English than other students.

We can see that they have not only separated events, but also started to think about where sentences start and stop. This is part of the how the Recount Writer was designed. The easiest next step for this student would be to remind them to use full stops at the end of their answer to each prompted question.

The fact that this student has written about what they did over several lessons as opposed to the reading tasks is an indication of where many students are at in terms of their understanding of the content they need to be blogging about.

Party popper Prototype is written by a more experienced writer who has worked their way up from being an unproductive student. All of the aspects of recount writing are present. The next step for a student like this could be to use the Recount Writer to develop single events that are detailed over multiple paragraphs. Alternatively the next step would be to take them off the writer after a bit more practise and have them write blog posts of this detail.

Next Step

The premise of a writer has been shown to have promise. The next step is to adapt this to the Information Report and Explanation text types.

Reciprocal Maths UPDATE

 Follow this link for an update regarding the Reciprocal Maths idea. Spoiler alert, there's been an overhaul.

Reciprocal Maths

 Read about the Reciprocal Maths idea Go for teaching and I developed here.

Recount writer - a digital scaffold

Background

Last year GO for teaching and I came up with an idea to increase writing mileage while freeing up time for more targeted teaching in writing. See our initial post and the follow-up post regarding the update. This idea was successful in having students practise writing different text structures (recount and information report mostly) semi-independently for their blog posts. Moving practise time to non-lesson time allowed us (the teachers) to focus on teaching more grammatical and stylistic points. The extra practise time was particularly needed during the various lockdowns throughout 2020, which made us lose a lot of lesson time.

Issue

This year, our class has not been completing the same volume of work despite being at school more because there are less lockdowns. There seem to be a multitude of possible reasons. One of those reasons is our class make up having expanded to include year 4's The year 4's are a small group of students who aren't used to the amount of production required for years 5 and 6. 

Fix

After throwing around a few ideas, Go for teaching and I decided on another scaffold to try speeding up the process of getting blog posts written while learning the different parts of various text structures, starting with recounts. The scaffold made (see below) is based on a survey mailing list that we came across. The Recount Writer uses prompts divided into the different sections of a recount to aid students in writing their recounts.

The Recount Writer then sends a copy of the student's responses written and formatted on a Google Doc to their inbox (see examples below). Students are then expected to copy and paste the text into Blogger to create a blog post.

The next step, aside from refining this prompt, will be to create scaffolds for the information report and explanation text types.

Blog post structure

TREE, TIIC, TIMES, the text type structure acronyms for recount, information report, and explanation respectively have been taught in my classroom for at least 3 years. So it was a bit of a shock to find that many students we have taught already (in some cases this is their third year with us) cannot remember them and how to apply them. See the blog post I have written about this here: https://ls1teaching.blogspot.com/2020/05/blog-post-structure-update.html.

Oral language and comprehension

Oral language and comprehension, check out this blog post.

Addressing the basic facts gap

How have Grant and I begun to address the basic facts gap?

Back to phonics for me

Phonics, decoding, and spelling; a brief overview of our programme being instituted in the class.

IKAN results... a small ray of hope

My pupils were tested on their knowledge earlier this term. Generally in New Zealand, this involves the IKAN test. My pupils however often need to be retested on the JAM (junior assessment for maths) to get a clearer idea of what they know as opposed to what they can hear, read, parse, recall, then write down within 3 seconds.

After seeing the results, I had a sense of a general increase in certain domains of maths, especially fractions. I have put it to the test and made a comparison.

Colour coded IKAN shift for 2018

With green being the code for an increase in level, this screenshot of my spreadsheet shows that there has indeed been a general improvement in the Overall Level out of the pupils present for both tests (there is one coding error for pupil #28, which made no overall change). IKAN's Overall Level though, is taken from the lowest score within the domain scores, so it doesn't necessarily show improvement. The large number of increases in fractions demonstrates this phenomenon.

I have taken the small win in fractions and have moved on to improving basic facts for the remainder of this term (since about Week 7), and next term I will focus on place value.

Basic Facts Boxes

Basic Facts... a gap in knowledge that I never had when I was growing up. A gap in knowledge that prevents or hinders improvement in most areas of mathematics. How can Basic Facts knowledge in children, who are in some cases quite far behind expected ability, be brought back to average and boosted further?

Here's something I developed to give it a go.


This Google Sheet populates boxes with random addition and subtraction problems to solve. On entering an answer, the sheet checks the answer and gives immediate feedback. Another sheet in this Spreadsheet does the same for times tables and the corresponding division facts.

I tested the first version of this on my own pupils to limited success. The positive is that many of the kids wanted to keep going until they got everything correct. The negative was that they didn't take screenshots of the boards that had errors, so there was no record of their improvement.

A colleague, Robyn Anderson tested version 2 (without the times tables) with her class. You can read about her success and outcomes I never expected from this tool on her blog post.

The inspiration for this tool came from two places. The first being a Japanese tool for memorising basic facts and the second being Monty Jones's (Tāmaki College) spreadsheets for practising maths problems at secondary school level.

Feel free to copy it, use it, attribute it, and tell me about the successes and challenges you have had.

Talking about capacity using Flipgrid

Capacity. What is it? How can it be measured? How is it usually measured? These are some questions for a maths concept that can develop some much needed language skills. But this is maths, how does one get children talking about maths? FlipGrid to the rescue.

In these lessons about capacity, children learned about containers and different ways of filling them up to find out how much they held. Children then learned how to talk about the comparative sizes of containers and how to measure exact capacities using a measuring cylinder and millilitres.

The capacity and verbal components to this lesson were very successful. The learners enjoyed using water and scientific instruments to find out about capacity. They also enjoyed sharing their learning by talking about it and using a simple video response recording system.

Problems arose with the word problems I had developed for them based on the learning done in the lesson. There were two main problems, both of which could be foreseen with knowledge of my learners. These problems were the inability to comprehend the problem despite being written in a simple and consistent format, and a lack of basic facts knowledge.

In subsequent lessons I structured and walked through how to understand, respond, and answer these problems with some success. I will need to continue scaffolding responses till learners become reasonably proficient before dropping the scaffold.

 

Maths Synonyms - reflection

The synonyms task I tried earlier this week was not as successful as I'd hoped. I had not anticipated two things: the learners misunderstanding the task and the learners not looking up the meanings of words they were unfamiliar with.

I still feel the vocabulary task would have been a valuable task for the learners to engage. Learners would be exposed to both the connections between everyday and mathematical vocabulary, and the nuances between synonyms such as trim and cut.

Ultimately, a positive is that the learners gained a stronger understanding of the meaning of the words addition, subtraction, multiplication, and division. However these synonyms will most likely need to be revisited someday.

Subtraction language - reflection

The subtraction language task was a almost a dismal failure. Many of  my learners were not able to unpack the language in the task. I will have to step back to more of the core concepts and build up language from there. I will also need to ensure tasks are explained and scaffolded better.