Reciprocal Maths Update

Background:

Previously GO for teaching and The Wong Teacher posted about their Reciprocal Maths idea. After a number of weeks gradually introducing the context, then the skills, the process has turned out well on at least a surface level.

Issue:

With any new technology or development, the first pass is always improved on. The Reciprocal Maths idea is no different. Several areas for improvement were found.

While the reciprocal reading concept of continual cycles for each section works for texts, it doesn't work for maths problems which tend to be only one or two sentences that need to be comprehended then acted upon. Reworking the roles with a single cycle in mind resulted in many consequent changes including altering the roles, the flow, and the example questions.

Fix:

Two of the most critical changes relate to clarifying when events happen in the cycle. Those changes were adding a "solve" step into the cycle and grouping the Questioner with the Comprehender and Clarifier is meant to clarify when they are needed.

Sentence prompts were another part adjusted.

   
                                                                                                                                                                                                                                                                                                                                                            

Reciprocal Rea...Maths!

The issue:

Comparing various data points over several years, GO for teaching and The Wong Teacher came across a trend within students' numeracy skills. Students seemed to be capable of interview style assessments and problems that were pure abstract maths, but were less capable when solving word problems.

The hunch:

Students are having difficulty comprehending word problems therefore reducing their test scores and not presenting an accurate measure of mathematical capability. This is not to say that students' numeracy skills are in fact much greater than they test or that the assessments were flawed. In fact the comprehension of word problems may be closer to a reading comprehension issue than a numeracy issue.

The proposed solution:

GO for teaching and The Wong Teacher figured that if a literacy component is required to solve mathematical problems, then literacy skills in maths should be taught. To achieve this, we took the concepts of reciprocal reading and tried to adapt them for usage in a mathematical context. See our first attempt below. This Reciprocal Maths™ is intended to leverage peer learning and increased oral language use.

Teacher Inquiry 2021

 This year we will be focusing on increase maths achievement through oral language.

Below is a brief introduction to the planning of this initiative, including a backwards map and initial data of a cross section of our classroom. 

Most changes will be implemented through a range of activities in a range of groups by both teachers at different times.

Comment Threads

 To follow on from the post in June, after several months of practicing our open and closed questions students are beginning to develop confidence and independence when trying to gather more information.

At first the first comment was the focus to engage the original blog poster to share some extra information.

The next step was the original blog poster was to engage that person after the reply to see how the relationship can lead to a shared understanding or learning activity.

Students are now explaining the purpose of this for their learning, and splitting the focus between the post itself and the comment.

The next step will be to simplify the post to share a succinct explanation, recount or report to develop longer threads to unlock information in a meaningful way.

Open and Closed Questions

 2020 has definitely been an interesting year, and that has delayed slightly a focus in to getting students to gather or obtain information from their peers.

Distance learning allow us to gauge independence when developing a blog post or a text type based on the purpose they wanted for their audience.

It was abundantly clear that consistent years of being made to assess the ability to recount had 2 negative effects. First the students seem disengaged and not really genuinely wanting to recount their learning. They also seemed to lack the ability to correctly formulate the structure of  a range of other informative text types such as information report or explanations. This is where the previous blog post on the structural prompts and help came from.

The Next step was to see how even a well written blog post can be unlocked for further information and learning. We parked the idea that by now it is well ingrained in our students that they know how to write a comment. Greeting, something nice, or learned and perhaps some next steps.

Commenting allows people to build each other up and give positive affirmation, though is that going to increase shift or knowledge! Short answer is probably not...

So to start on this journey we needed to unlock how to question to gather information, before we could even entertain the idea of threads of learning conversations. 

Open vs Closed questions is where we started.

The first piece of learning was how to start a question as that determines 95%of the time what information you will gather, and how useful it will be to you.

Once we got the hang of some simple investigation type starters we looked at the purpose of what you are trying to do. Are you trying to confirm or reaffirm something, or was there a piece of the puzzle missing that together could be unlocked.

UPDATE Blog post structure

Over the past couple of months we have noticed that student's blog structures have improved. More capable students are drafting blog posts that clearly use the correct structure for the text type. Less capable students are drafting blog posts that demonstrate at least a rudimentary understanding that there is a certain order for each kind of text.

The aspect we haven't observed yet is an increase in the use of appropriate language features. That is our next step for teaching blog post writing...or rather writing the text types recount, information report, and explanation.

To aid this process, I have updated the Blog Guide poster to include the language features and examples of those features.

Blog post structure

Recounts, information reports, explanations. How do we write them? In spite of having taught these text types in detail consistently for several years, we are still giving feedback on the same aspects of these text types. To scaffold students into self managing their usage of these text types, I (Greg) have developed a diagram/ flow chart showing the structure, and an example of recounts, information reports, and explanations in one place.

Students will be referred to this diagram for feedback on these text types for their blog posts.

Increasing learning conversation and literacy through blogging and commenting | Teacher Inquiry 2020

Accelerated learning, the holy grail being sought by schools in the Manaiakalani cluster. At Panmure Bridge School, our data has shown acceleration particularly in Writing. This acceleration has been aided in recent years thanks to a flattening of the 'Summer Slide', related to implementation of the Summer Learning Journey (SLJ). Grant Oglivie and Greg Wong's joint teacher inquiry for 2020 is to increase students' other forms of literacy, i.e. reading and oral, by leveraging learning conversations through blogging and commenting as used in the SLJ. The first step in this process is to codify and teach a system for blogging, then do the same for commenting.

The system for blog posting has been decided as using the recount, information report, and explanation text types taught in the Writing curriculum. There are several reasons for using these text types rather than developing another structure. Using these text types will compound on Writing lessons, providing students and teachers with more opportunity to refine students' writing techniques and find areas needing improvement. Working on these text types so frequently frees up Writing lessons to be dedicated to the grammar, style development, and the remaining text types (narrative, persuasion, and procedural). Finally, areas to be commented on are made available when students have written their posts in a well structured and thought out manner.

Evidence from students' drafting process will be used to inform the exact teaching points needed and when to continue to each phase. This process is likely to take a whole school year and possibly reach into 2021 to establish good routines in this year's year 5 students. Small scale improvements are likely to be seen by mid 2020, with long term improvements appearing as students reach Years 7 & 8.

Student Voice

At the conclusion of the plays the students were asked some very basic questions and put their hands up. Eye closed to allow them to be honest and not just copy their mates.

Surprisingly the larger majority of student found the 5 weeks extremely difficult. On the other hand the large majority enjoyed the process and wanted to do more.

After this students were ask several more questions to blog about. Reading the responses it was pleasing to see that overall the students perceived they had improved in their oral language. Was this necessarily true........Short answer is NO! Even though they enjoyed it, were they ready to take on Broadway?? Absolutely not, but there was enough positive energy and excitement that it will be interesting to watch their improvement over the next 5 weeks. Students wanted more so they have been given the remainder of the term to put together one last performance. Surely 4.5 weeks of practice will be better than a 2 week period......... Only time will tell.

Overall however ever student took part and didn't shy away from the challenge.

Oral language through performance

An under utilised and extremely good resource are the plays in the school journals. Why?? You can search reading level, topic and amount of parts in each play. This makes planning easier.

These were used to enable students to develop their oral language skills in a realistic setting, that they had on most cases not been exposed to.

Students started with just understanding the vocabulary in the text and how it was used to tell a story. Something they have always done through guided reading!

The next stage was to learn their part, this proved very quickly to be the challenge. They had never been asked to learn lines before. Why is this important? They quickly realised learning their part in isolation was difficult but learning as a group made the "cues" easier and soon the flow came to their reciting. Listening was a skill they didn't first think they needed, but soon it was as big a part as say their lines. Another part that helped was they also needed to have an under study partner. Once they had their lines, students were tasked with thinking about the character interactions and expression of certain lines.

Once they were learnt we could go on to expression and delivery of lines. This was the fun stuff! Students experimented with anger, sarcasm, excitement etc; Something they found they never did when reading before.

This all tied together over a 2 week period, with a "show" at the end. No lighting, no props, and costumes, just voice and body to tell the story.

Vocabulary and non-fiction texts

Across the board in LS1, but especially among the lower ability readers, there seems to be a big deficit in vocabulary (in all learning areas). To alleviate the deficit this year, Grant and I are explicitly teaching new vocabulary to students and making them use it in context to strengthen the understanding.

I have also made a push in reading to read non-fiction books on a wide range of topics. Many of the topics are ones the children have never come across or talked about in detail. Coupled with explicit vocabulary teaching, I hope this will expand the children's prior knowledge and vocabulary.

To work in conjunction with the reading of non fiction texts, I have a series of tasks for students to complete after reading a text. The tasks range from simple tasks that would be used in the junior school to more complex tasks such as creating a hierarchy graph of ideas in the text.

Boosting literacy through oral language

In an effort to boost not only reading comprehension, but also the confidence to present an answer, we are increasing the amount of oral work students are doing.

We are attempting this in multiple ways including performing plays and regular oral presentations for IRL (in real life), and screen casting and FlipGrids for the online component.

Using FlipGrid and screen casting allows students to actively consolidate their thoughts and understanding through preparation to provide a well scripted exposition.

Off the cuff oral presentations and performing in front of their peers improves the confidence to communicate ideas. At the very least, presenting and performing will help desensitise students to being in front of a crowd, which in itself can be a crushing fear.

Basic Facts gaps

And here we are talking about one of the other major gaps in our students' knowledge; basic facts. How does one address a gap in knowledge caused by lack of exposure and practise at a time when homework is considered "ineffective", there is less time for parents to be involved in their children's learning, and there are much more compelling activities than in the past?

One way of addressing the gap in basic facts knowledge is to increase exposure to everyday. This is done through use of simple flash cards and randomly going through about ten or so at a time. The series of flash cards was simple enough to produce using Google Slides.

Another way I have implemented with the higher ability learners is to do a Basic Facts quiz before every lesson. Students are automatically given immediate feedback on the correct answers, so the quiz also becomes a feedback based learning tool. After everyone has finished the quiz, I also briefly go over the questions that seemed to cause problems for many of the learners.

The quiz method had rapid increase in recall ability, initially starting with many students scoring in the low teens out of twenty and now most scoring above 25 out of 30.

Phonics, decoding, and spelling

One issue we have across the board (but especially for our target learners) in LS1 is the ability to decode and pronounce new words along with spelling already known words. In an effort to alleviate this we have instigated a phonics programme.

The phonics programme is based on Yolanda Soryl's phonics professional development course Grant and I both attended. While we have both taught phonics previously Soryl's programme consolidates many of the phonics practises and concepts into a coherent course based in New Zealand accents.

After an inconsistent start, we have found a place for a phonics lesson within our unconventional schedule. Perhaps one of the most powerful practises, though, is continual exposure and practise through the days and weeks. A particularly good strategy is bringing up phonics at random points throughout the day.

Place value rears its ugly head again.

As I suspected, Place Value became a noticeable issue again when trying to teach how to use Place Value as a subtraction strategy in week 3 of term 2.

This time, I took a different strategy with the stick counting method. I assigned each colour a particular value coinciding with the different place values from ones to 100 000s. Learners used the valued sticks to create numbers and solve increasingly difficult subtraction problems. See the task here.

Assigning sticks a different value per colour is an adaptation of an idea gained from my study of the Ancient Egyptian and Chinese Number Systems compared to other number systems including the modern Place Value system. The idea being that the colours provide a visual cue for the worth of each place value as the Chinese characters and Egyptian hieroglyphs do.

Keeping numbers organised in their discrete place values also forces the user to exchange sticks for usable sticks when subtracting beyond the means of the value being subtracted. For example when doing the subtraction 12 - 7, seven ones can't be taken from 2 ones, thus forcing the ten to be exchanged for 10 ones. Incidentally, discussing these place values, subtraction, exchanging, and breaking etc. exposes learners to the vocabulary needed to truly understand the written algorithm.

The lessons were successful with most, if not all, learners picking up enough understanding of Place Value to use it as a strategy for addition and subtraction from 3 or 4 digit numbers and higher. One of the two learners that did not pick it up to the 3 digit level is noted for their absence and lack of engagement in school.

A Gap in Knowledge

Back in Term 1 with IKAN testing finished and analysed for gaps in knowledge for the group as a whole, it was time to get into serious teaching. Unexpectedly, Place Value was the largest gap with Basic Facts close by. More on Basic Facts here and later (link retroactively added).

To address the Place Value gap in the higher ability learners, I went back to grouping sticks and recording numbers on a sheet. I made sure to have the learners add on 10 and 100 in the hopes they would notice the jump up in place value of particular numbers.

The task was mildly successful. I noticed about a half of my learners understood quite quickly, whereas the other half or so didn't. In the second week of working on Place Value, I extended those with an understanding to go down into the decimal place values. At the time I had suspicions on how well it was taken up. These suspicions turned out to be true

What the Data Says

As eluded to in the previous post we are selecting 2 groups for our collaborative inquiry this year.

Collaborative Inquiry

With the change in direction of the cluster and school with PLD, preconceived ideas and the group of student in LS1 we decided to run a collaborative inquiry this year.

What does this mean??

We will target oral language through Reading, Writing and Maths.
We are also focusing on improving Maths attainment through integrated topics using the HPE, Arts and Oral language curriculums.

The way the majority of content is covered is in differentiated groups. This will mean the target groups get "hit" from all different directions, from both teachers throughout the year.

We are also going to have 2 focus groups.  One group which teachers traditionally always focus on, the group who are "nearly" there but need a push. The second group is going to be a group that is operating ahead of where they need to be.

The rational behind this is to give a wider range of approaches a go, and to keep ourselves thinking, reflecting and planning throughout all lessons. An observation of previous years inquiries was that too much focus was put in to a specific area. This in turn frustrated us as there seemed to be no escaping the pattern of focusing below the chronological level and when shifts weren't obvious teaching self esteem suffered.

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