# Numeracy profile example - Year 2

This numeracy profile is a student example for ages 5–8 (Mahli). The advice and strategies in this example are also applicable for ages 13–16. This example includes conclusions and next steps to better support learning moving forward.

Mahli's profile was constructed at the end of Term 1 and focuses on the first two strands of the Victorian Curriculum F–10: Mathematics:

• Number and Algebra
• Measurement and Geometry.

The teacher has organised the numeracy profile using growth points or key steps to mathematical understanding in the Mathematics Online Interview that the school uses to measure the existing maths knowledge of its students.

## Growth points

### Counting

Mahli understands the numerosity (number) of sets of up to 20 items. They can count smaller numerosities more accurately than larger sets. Mahli can count sets of up to 20 items by touching each item while saying its name. Their linking of number names and items is not automatic.

Mahli can read and write one-digit numbers and can assemble a set of items to match a spoken number up to 20 and a written number to 10. Mahli recalls some sequences of numbers up to 100.

### Subitising

Subsisting is the ability to instantly recognise the number of objects in a small group without the need to count them. Magnitude comparison is a student's ability to compare different quantities or amounts . Deficiencies in these areas may indicate the presence of a learning disability, such as dyscalculia.

Mahli can subitise sets of up to four. They can identify sets with more items when the sets are matched. Otherwise, Mahli counts each set. Mahli can reason 1:1 correspondence. They can use ordinal numbers up to 10 with confidence.

### Place value

When Mahli sees a ten-grouped quantity they know to count in tens. Mahli can count in tens and recall the name of each decade number (10, 20, 30) but cannot easily count up or down a quantity of tens and ones (16, 26, 36). Mahli can group sets of units into tens.

### Addition and subtraction

Mahli understands adding as 'getting more' items and 'taking away' as losing items from a set. They can add items and remove items from a set, and count to get the final amount. Mahli has linked 'getting more' with the plus symbol (+) and 'losing some' with the minus symbol (-). Mahli can solve simple addition and subtraction sums when these problems are presented with concrete materials. They perform the relevant action and then count the amount remaining at the end.

Mahli still finds it difficult to count backwards from any number and to count up by more than one step (such as counting in twos, threes, …).

### Multiplication and division

Mahli can distinguish between sets of grouped and un-grouped quantities. They can work out the number of items in a grouped set of less than 20 by counting each item. They can also use the term 'group' to describe various grouped quantities (such as 'three groups of two'). Mahli can assemble different grouped quantities, for example, making three groups of four tokens. They are also capable of replicating and extending grouped patterns.

### Times

Mahli recognises that everyday occurrences happen at specific times. They can sequence events over the course of a day, for example, 'I got dressed, I had breakfast, I went to school. We had reading and then playtime'. Mahli can identify the correct sequence of events when asked, for example, 'lunchtime is after playtime'. They know that a second is shorter than a minute, and a minute is shorter than an hour. Mahli uses words like 'first', 'after', and 'while' in relation to everyday events.

### Length

Mahli can confidently select and group long items and short items. They can manipulate shapes to lengthen or shorten them, for example, a plasticine worm.

Mahli uses words like 'big', 'long', 'little', 'short', 'tiny' and 'small' to refer to the length of objects.

### Mass

Mahli knows that some items are heavy, and some are light. They can accurately select an item that is heavy versus light by lifting them. Mahli still has some difficulty distinguishing between size and mass, for example, thinking a hot air balloon weighs more than a car because it is 'bigger'. Mahli can use words like 'heavy' and 'light' to describe the mass of objects.

### Spatial concepts

Mahli can organise and group items based on their shape and different attributes. They can recognise that different shapes are 'straight', 'round', 'pointy' etc. They are very good at using their body to illustrate these attributes, for example, moving their hands, arms and legs to show what 'pointy' means. Mahli can use spatial words like 'behind', 'under', 'next to', and 'above'. Mahli can select items that match a target object shape and other features, for example, other triangles or round objects.

### Language development

This includes languages spoken at home, development of language, identified language issues, reading practices at home, communication skill.

Mahli's home language is Arabic, but the family are fluent English speakers. Mahli came to the school in Year 1, so there are no school records on their developmental benchmarks in language. However, Mahli has reached the developmental benchmarks in language and communication at the same rate as most students in Year 2.

### Sensory issues

Sensory issues include earlier visual and auditory perceptual problems.

School records and conversations with Mahli's family indicate that Mahli does not have a history of visual-perceptual or auditory issues.

### Emotional and social issues

Emotional and social issues include emotional management ability and social interaction difficulties.

Mahli is a well-liked student who socialises easily with peers and without difficulties. Mahli can at times become frustrated and less cooperative during maths and when engaging with numeracy activities (such as counting games).

### Physical issues

Mahli has no known physical development and motor co-ordination issues.

### Intellectual development and skills

This includes general reasoning ability, developmental milestones, conceptual maturity, ability to remember, retain ideas in short-term memory.

There is no indication that Mahli has delayed or impaired intellectual development and or skills. Their short-term and general memory appear adequate and on par with most peers.

### Medical issues

Medical issues include early medical issues that impacted on readiness for numeracy learning.

No medical known medical issues.

## Early access to teaching

### Interventions

Previously, Mahli has not received additional numeracy support or intervention beyond the differentiated, evidence-based delivery of curriculum.

### Periods of successful learning

Mahli's Year 1 teacher did not have data about this. However, Mahli does tend to enjoy more success when working one-on-one with a teacher.

### Breaks in attendance

Mahli has not had any significant breaks in attendance.

### Family history

Mahli's parents have reported no family history of numeracy difficulties or delayed development.

### Attitude toward mathematics

Mahli does not enjoy maths and will often 'zone out' or talk to friends during class. Mahli is reluctant to begin numeracy activities and needs to be continually encouraged to engage and complete tasks.

### Self-efficacy

Mahli has a low opinion of their abilities when it comes to maths. While they do not explicitly use negative language, Mahli will often say things like 'I don't get it' or 'I don't want to' or 'I don't want to play', for example, when the class is playing a numeracy-based game. Mahli is usually an enthusiastic student unafraid of taking risks in learning, however, becomes very reserved during maths and rarely volunteers or actively participates.

### Use of appropriate task-organisational strategies

Mahli is usually capable of thinking ahead and planning how to approach tasks. However, during maths they have trouble maintaining their attention and staying on-task. Mahli has also started distracting others during independent tasks in maths.

## Planning a teaching program

### Conclusions

Mahli's numeracy profile provides a base for planning a program of learning and relevant interventions. Across all numeracy knowledge areas, their existing skills are roughly at Foundation to Level 1.

Mahli's ability to reason and think about mathematical concepts suggests they can recognise patterns. Mahli has begun learning the number names up to 100. The difficulty seems to be in learning the appropriate mathematical procedures and linking these with the correct language.

Mahli's engagement with and attitudes toward numeracy learning are not positive. Mahli experiences frustration and is reluctant when required to work independently. Mahli does not hold a high opinion of their own numeracy abilities and potential. Mahli will benefit from additional encouragement and recognition of their progress. Mahli's teacher should draw on reflective questions during interactions.

For example:

• What do you know now that you didn't know before? What can you do now that you couldn't do before?
• How do you think you might use what you have learned in the future?

It's important to help students like Mahli see that numeracy is something that we use every day in all areas of our lives. Encourage students to talk about examples of numeracy and maths that they might use at home, such as when cooking or counting money.

Mahli's existing numeracy skills are in the first six months of Level 1, so the early goals of intervention should target the knowledge, understandings and skills that are typically developed during the second half of Level 1.

### Next steps

Mahli needs to learn more sophisticated procedures for counting. For example, counting backwards, counting on and then back from any number and enumerating ten-grouped quantities.

Mahli also needs to learn how to link knowledge of number names for two-digit numbers with the matching quantities, and to use them in a coordinated way when enumerating them. Mahli needs to learn how to enumerate a quantity that comprises two different groupings.

Encourage these more sophisticated procedures by differentiating and building on those Mahli already knows.

Consider the following questions when planning for interventions or adjustments to support students' learning:

• What does the student need to learn next? Use developmental pathways (for example, the Victorian Curriculum F–10: Mathematics, the Numeracy Learning Progressions) that can locate students and their existing knowledge and skills as a guide for what to teach.
• How will you sequence what they need to learn? Certain knowledge and skills may need to be developed before the student can demonstrate others or meet numeracy goals.
• How will you develop their attitudes toward numeracy and themselves as learners and users of numeracy and mathematics?
• What organisational skills will you teach students to develop their capacity to teach themselves?
• How will you adapt your classroom to be a better environment or culture for learning?
• What will continue to require scaffolding? How will you gradually release responsibility for learning back to the student?  For more information, visit Helping students to become independent learners.