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.

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.

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.

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

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