Today I had the pleasure of attending a course to grow my knowledge of PaCT and of the relationship between this tool and the Math Learning Progression Framework. (Here is the Website, if you wanted to have a look for yourself).
One needs to have a reasonable understanding of the Math Learning Progression Framework before you can start using the PaCT. Therefore we started the day with a deep dive into the Math Progressions, where these came from and how these can be used to strengthen teacher practice.
In order to teach an effective math programme one must have a good knowledge of math to begin with. The level that teachers need to be working at in order to teach successfully is Level Four. (Unfortunately, this does not seem to be the case for most educators).
It is important to note that the website above provides guides, videos and PLD activities that are used nationally to help support a coherent message of what achievement in Numeracy looks like and also what the PaCT supports.
Currently there are are twenty high user schools of PACT and MOE can point schools in their direction to provide support based on region.
The possible elephant in the room is... The Numeracy Progression Framework. This is the content knowledge that teachers need to know to be able to teach math. Teachers confident in their math knowledge should be able to identify what students are doing in math and therefore where they are sitting in terms of the Learning Progression Framework (LPF). Programmes like DIMIC and YouCubed provide a pedagogy around the teaching of math rather than math content.
Looking at the Learning Progression Framework:
There are eight aspects of knowledge: The reasons behind the eight explains each aspect and where the Number Framework sits.
(Side note: Fractions and proportions are integrated throughout the framework. We have not “lost” this in the final aspects.)
Looking at Sign Posts:
Sign posts for learning progress are informed by number framework. Placement of the signposts shows you comparatively when new aspects could be introduced when comparing to others. All placements have been generated by NZCER research so are evidence based. LFP were designed so that all of the meaning would be visible in the examples as words can be interpretive. (The design development in more depth). The illustrations give an example of what the description is there is a big focus on teachers going through the illustrations. TEACHERS MUST read the annotation to understand the illustration. Not just focus on the question.
The number of signposts per aspect relates to the complexity of learning the aspect and the number of illustrations is determined by the minimum illustrations required to explain that aspect at that sign post. For example: multiplicative thinking has 9 signposts because NZCER found them to be significantly different.
It is crucial to make sure a teacher understands that it is not just one thing that determines each sign post but rather the range of aspects of a learner at each point.
Teaching teachers to identify what each aspect is and what it looks like in student work. Then from this how to plan for each aspect to be taught every term rather than in siloed subjects - we know teaching this way does not work to build math knowledge.
A question that teachers could be asking is:
How much progress should I be thinking that my students will make this year?
These sign posts are not to be used as examples to teach through or as an assessment. They are used to capture the key things that go on as a student progresses in math.
NZ math - resource finder - in the future there will be a way to find resources by addressing the gap between signposts under using LPF Aspects.
An interesting note is that the Framework has removed “Stage 3” because it is a pedagogical step rather than a cognitive one. Students can move from materials to number properties without having gone through the “imaging” phase.
From the site itself:
“It is important that students develop their knowledge and skills across all aspects of the mathematics framework so that they can use mathematics and statistics confidently, within the mathematics and statistics learning area, in other learning areas, and in their everyday lives.
The strong connections that exist among the mathematics aspects mean that lack of exposure to all the big ideas in mathematics and statistics can restrict students’ progress. The framework helps you to think about the breadth of your mathematics and statistics programme and provides a way to check that you are planning for a comprehensive coverage of the learning area.”
This will only work if teachers programme has the potential to cover multiple aspects. Long term plans crucial to tie aspects into what is happening in other curriculum areas. Look at depth of the signpost. Multi problem rich tasks to support signpost learning.
The whole idea is around noticing what you have observed students doing. Do not think that you need to Gloss or Numpa, (these tests have always been to improve teacher understanding of Framework - now become overused assessment tool - STOP IT!) all students to be able to identify where they are achieving. Trust your judgement and provide examples of what the student has done in class - you could also get students to show you a problem as evidence if that was required. Student blogs are a great example of where students can provide evidence of where they are at in math.
Moving to PaCT - The Tracking Tool:
(School’s need to log in to PACT and set account if they do not have one. It uses education sector logon.)
Consistency comes from using the same illustrations rather than adapting and making your own. This creates dependable information that can be used by everyone.
This tool goes from school to school tracking student progress - it is an online digital tracking tool. So let’s get a shared understanding of what each sign post looks like with a group of students. As a Cluster this could be perfect PD - we could create a shared understand of math progress.
When we are making judgements with the tool we are looking at what students understand independently. Focus is on un-scaffolded understanding.
E.g. starting a session with a class problem and then seeing which students can move past this on their own, which need support and which need a different problem entirely.
DO NOT only use this tool for a few students! It is for a whole class. There are probably only 2 sign posts that your class sits between. (Side note: we don’t group as a result of sign posting, this is not the message we are giving here).
We aren’t looking for a perfect fit we are looking at the sign post above and below (to rule them out) and see where they fit best.
At every point it is what student CAN do. Not what they are beginning to do.
In October there will be no time windows for when data can be added it can be added authentically at the time it occurs in practise.
This is an example of a report for a class. You can also get a similar looking graph per student.
You can remove the curriculum trajectory so that the comparison is what typical students on average are achieving (the grey highlighted line).
The report allows you to add matched student data to the report from students within the school or previous classes.
The tool also allows the data to be collected at a cluster level. This could have great positive implications for our cluster to help identify pockets of promise.
There will be pdf's added within the next few months to give more information on how the reports can be used.
Final thoughts for the day:
If we can empower teachers to use this tool to inform their practice it should have a HUGE positive implication for Math Data at a WF level.
Teachers who use this tool confidently would have better content knowledge and understanding what next steps are, meaning better focused teaching.
Another implication could be less testing, it is not needed therefore students and teachers may take WF testing more seriously.
