By now you might feel that you’re an old hand at mapping. Or at least, you might feel that you have an idea about how the process works. Here’s something to remember:
- All you’re doing is applying what you know about your own subject as an expert in your own field.
The only thing that might be new is that you’re using the progressions as a kind of lens to filter your judgements through.
If you know what you’re doing, just get on with the assessment task. If you’re not sure or you feel less confident about mapping numeracy then don’t worry. We’re going to go through it in detail next.
1. Print out the Make Sense of Number strand.
Make sure you have the Make Sense of Number strand in front of you so you can refer to the details for each step. Sometimes, we’ll just refer to this as the Number strand.
It looks like this, but it will have descriptions of skills and knowledge in all of the steps. You can download the Number strand here if you need to.
There are six progressions in this strand. The first three are about how to do things (strategies) and the second three about what you need to know to do those things (knowledge).
You only need to think about the first three when you map demands. What you need to know (the second three) will sit one step behind the highest step of the first three
2. Choose a specific sample calculation or task involving number work from your teaching programme.
Choose some kind of teaching material that your learners have to work with, not NZQA unit standard descriptions. Choose a task where your learners have to do a basic calculation or work with numbers in some way. This might include reading some material, but the focus should be on using basic maths.
Here are some examples of samples that you could choose where your learners have to use number skills:
- Working out the percentage of something For example, calculating a 20% discount or working out GST on an amount of money.
- Working out how long it takes to travel somewhere.
- Adding up hours worked for a timesheet.
- Costing a job.
- Adding together measurements such as weights or lengths including decimals.
- A task where it’s necessary to converting fractions into decimals or vice versa.
- Working out how much fertiliser to use on a garden.
- How to work out the average weight of a mob of stock.
3. Have clear reasons for choosing the sample
In the assessment template, as with all of your samples, you’ll need to say why you chose to analyse this calculation or task. There are lots of reasons. Here are some:
- You might have chosen a calculation that you already know causes difficulties for your learners.
- You might already know that you need to create some new material to teach a calculation in a new part of your programme.
- Your supervisor or manager may have asked you to focus on a particular calculation or task.
4. Start your mapping with the strategy progressions
At every stage, we refer to the relevant Strand charts and progressions and then you shade in your own chart down to the relevant step.
This time, the best place to start mapping the number demands is with the three strategy progressions on the left-hand side of the chart. The ones on the right are the knowledge progressions and we can leave those for now.
Unless you are teaching a very low level foundation class, the number demands for your programme are likely to be at step 3 or above. Steps 1 and 2 are very much developmental.
You’re the expert though. Remember: you know your subject. The framework is just a lens or tool to look at your programme.
Here’s what you’ll see in the number strategy progressions:
Before we go any further, what’s a partitioning strategy?
That’s an excellent question…! Partitioning is splitting numbers into parts, for example, by place value. Here’s an example.
- 365 is three hundreds, six tens and five ones.
Partitioning strategies are strategies that are based on splitting numbers into two or more parts and then recombining them in a different way. This is how people in the real world do maths. For example:
- 26 + 9 can be split up (or partitioned) into 26 + 4 + 5 and then 30 + 5.
Writing out the explanation for this makes it sound more complicated than it is. But here have a think about this:
- Working out 26 + 9 is hard for some learners. But splitting up 9 into 4 + 5 is easy.
- Then adding 4 to 26 to get 30 is also easy if you know your number facts that add up to multiples of 10.
- After that it’s also straightforward to add on the other 5 to get 35.
5. Use what you know about your own subject
Use your own knowledge of your training material or calculations to decide which step applies for each of the strategy progressions.
Here are some things to think about. Does the calculation require:
- Addition or subtraction? Use the Additive Strategies progression.
- Multi-digit problems? Then look at step 4.
- Adding or subtracting decimals as well? Then look at step 5
- Multiplication or division? Use the Multiplicative Strategies progression.
- Multi-digit problems? Then look at step 5
- Multiplying or dividing decimals, fractions and percentages as well? Look at step 6
- Fractions, decimals and percentages? Use the Proportional Reasoning Strategies progression
- Converting between fractions, decimals, and percentages? Look at step 5.
- Working with proportions, rates and ratios? Look at step 6.
Keep in mind at all times that when we’re working out the demands of a task or calculation in this case, we are only interested in the task or calculation. We’ll get to what your learners can actually do later on.
If you work in trades or do any kind of vocational training, the calculations that you have to work with are probably at least at step 3 or 4 and most likely at steps 5 or 6.
As always, if you’re not sure about what step, do this mapping together with a colleague.
6. Map the demands for the three strategies progressions first
If you’re working on paper, get a highlighter and shade down from the top until you’ve included the highest step that you identified for each of Additive Strategies, Multiplicative Strategies, and Proportional Reasoning Strategies.
You can download a chart and worksheet here for mapping your own sample calculation on the Number strand. It’s exactly the same as section 3.5 of your assessment task. Print this out and you can use it as a rough draft and for notes.
Once you’ve mapped the three strategies progressions, you’ll end up with something like this:
7. Map your calculation against the rest of the progressions in the strand.
There’s a quick way to do this. It only works with this strand. But it goes like this:
- Map the three knowledge progressions at one step less than the highest strategy progression.
So in our example above, the highest step mapped on the strategy side is step 6 for Additive Strategies. This means that we can map all of the knowledge progressions at step 5. Like this:
The reason we can do this is that the three strategy progressions require that all of the knowledge is place at the previous step.
In other words, you need to know things at step 5 in Place Value, for example, in order to do things at step 6 in Additive Strategies.
Once you have mapped your calculation visually, you need to be able to talk about your results and what they mean.
As with your literacy samples, you’ll need to answer a series of questions to show that you understand what you’ve just done.
These questions are in the assessment template and in the worksheet if you download it:
- What text or task did you use?
- Why did you choose this as your sample?
- Out of everything here, what are the most important progressions and steps?
- What about planning for assessment and teaching?
If you can map a sample calculation or other task involving numbers and answer the questions, you can move onto the next module.
Make sure you keep your sample handy, though. You’ll need to scan it and upload it when you submit your completed assessment task. If it’s a calculation, you can write out an example and scan this.