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.