Written reporting in plain language in mathematics and statistics is likely to include information about the student’s ability to solve number problems, and in a non-number related aspect of mathematics (geometry, measurement or statistics), concisely. Strong emphasis is placed on students’ ability to solve problems and model situations in a range of meaningful contexts by selecting and applying appropriate knowledge, skills, and strategies.
Reporting in plain language can be challenging for teachers as we use complex education language routinely. In addition, as students progress through school, the mathematics and statistics knowledge and the tasks with which they engage become more complex.
The following table provides examples of "education language" the language teachers use routinely, and then an example of how this might be rephrased as plain language. Teachers gather a range of information when forming an overall teacher judgment and there are many resources, such as The New Zealand Curriculum, Mathematics Standards and the Number Framework, that provide characteristics of the stages students move through. The examples follow a broad progression from after one year at school until after year eight. In mathematics, a written report comment is likely to cover:
| Written Report Comments – Mathematics and statistics
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| Level
| Education language
| Rephrased in plain language
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| In the first year of school
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- Scott can copy a repeating pattern and enjoys working with his group to create a new pattern for others to copy. He enjoyed answering questions during our statistical investigation on favourite foods and his next step is to be able to explain his reasoning for his findings. Scott is working in the early stages of level one of the NZ Curriculum.
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| After one year at school
| Compares volume of objects directly. Applies counting-all strategies.
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- Hirini is always keen to work on maths activities, and particularly enjoys activities involving water and comparing liquid measurements. He has made very good progress and can now add two groups of fewer than ten objects together. He uses counters and his fingers. Hirini is learning to count backwards from a given number. He has consolidated level one of the maths curriculum and is beginning to explore the objectives at level two.
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| Investigates questions using the statistical inquiry cycle. Creates and continues sequential patterns.
| Jo:
- is working in the early stages of level one of the NZ Curriculum, this is slightly below where she should be
- is able to say and write numbers up to 5 and is now learning to say and write numbers up to 10
- enjoys making patterns and putting objects into ‘big and biggest’, ‘small’ and ‘smallest’ groups.
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| After two years at school
| Describes the likelihood of outcomes involving chance. Uses simple grouping strategies to combine and partition numbers.
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- Turki is working within level two of the NZ Curriculum. This is above where he should be for his year level. Turki understands new ideas quickly. He enjoys working on more difficult and challenging activities, but needs encouragement to get started. He makes good guesses about the numbers on the dice when we roll these in class. His next step when adding and subtracting numbers is to use his good knowledge of counting in 10's.
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- Uses equal sharing to find fractions of sets, and measure duration.
| Nico:
- has made steady progress with counting to and from 100
- is on the Maths Recovery programme
- can use halving of objects as a way to share evenly.
- can group objects into even groups up to 20
- is learning how to tell the time, and can say the time to half hours
- is working within level one of the NZ Curriculum.
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| After three years at school
| Applies basic addition fact and knowledge of place value to combining and partitioning numbers. Measures using linear scales.
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- Rota has a very good understanding of basic addition facts and this is helping his progress. He can add numbers quickly in his head. Rota has learned how to count in Māori from his Koro and is helping the class with learning bigger numbers. He showed us that Rua tekau mā rima = Rua Tekau (20) Mā (+) Rima (5) = 25.
- Rota has a good understanding of length and is able to measure accurately. He is working within level two of the NZ Curriculum, this is above the expected level for his year.
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| Uses knowledge to think mathematically when modelling situations. Continues spatial and number patterns.
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- Leilani has worked extremely hard this year on recalling her basic facts. She has made progress with counting, and can add numbers from any number between one and one hundred. In class Leilani is learning to add numbers in her head. Leilani is able to sort objects and shapes. She has worked hard to make progress and is now working within level two of the NZ Curriculum.
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| By the end of year 4
| Applies knowledge of place value to combine or partition whole numbers. Gathers and displays category and simple whole number data.
| Su Wei:
- has made great progress learning maths words in English
- knows and uses her times tables and makes few errors in her addition or subtraction
- has achieved the expected curriculum level for her year.
Her next step is to practise using Excel on the computer for her graph work.
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| Special needs student
| Applies basic addition and subtraction facts to combine or partition numbers, or find fractions of sets.
| Jonnie:
- has received additional mathematics support this year which has strengthened his number knowledge
- is working within level one of the NZ Curriculum
- is beginning to recall addition facts to twenty
- is now learning to count from one when adding numbers.
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| By the end of year 5
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- Applies multiplicative strategies, and measures time.
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- Maddie has identified a number of areas in which she has improved this year. She loves working in her group and helping her friends when they are having problems in maths. She is especially pleased with her faster times tables speed. She can now use multiplication and division to solve problems involving fractions. She is particularly pleased that she can now add and subtract time. Maddie is working at the expected curriculum level for her year.
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| Describes locations and gives directions using grid references and points of the compass. Applies simple multiplicative strategies to combine or partition whole numbers.
| Bella:
- can correctly name locations on a map using co-ordinates
- is able to multiply numbers by 10, 100, and 1000
- says her next step is to solve more difficult problems using more than two steps
- uses her fractions knowledge in technology
- is not working at the expected curriculum level for her year.
One of the things Bella and I have discussed is that she would progress more quickly by learning fast recall of times tables. Bella’s next step is to memorise the times tables.
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| By the end of year 6
| Performs mixed operations using addition and subtraction as inverse operations. Gathers or accesses multivariate category and whole-number data.
| Oliver
- works out answers to problems accurately using his knowledge of addition and subtraction
- continues to make very good progress with understanding the features of two and three dimensional shapes
- identified that his next step is to improve on simplifying and rounding decimals
- is working within level three of the NZ Curriculum, this is the expected level for his year.
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| Applies additive strategies to decimals. Creates or identifies nets for rectangular prisms and other simple solids.
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- Findlay has made progress this year with learning to add decimal numbers, and can add money. He was able to use these skills working on his enterprise inquiry. With extra help from the teacher Findlay can draw outlines for solid shapes, and he takes care to make his models accurately, like the stars he made for the Matariki display. He is working at level two of the NZ Curriculum, this is below the expected level for his year.
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| By the end of year 7
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- Applies additive and multiplicative strategies flexibly to decimals and integers.
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- I finally understand how to work with fractions, percentages and decimals. I am still working on ratios. I understand BODMAS. My biggest success this year was creating a project with my group for the year 7 Maths Competition. My group learned a lot about working with data (and working together!). I have achieved the expected curriculum level for year 7.
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| Identifies patterns and displays it in different ways. Applies additive and multiplicative strategies flexibly.
| Jesse:
- is working at the expected curriculum level for his year
- can sort information and talk about what he has learned
- uses his knowledge of geometry on the DesignIT programme to model his plans for hard tech
- has made sound progress at reading and ordering large numbers
- is now learning to convert length to smaller or larger amounts (mm, cm, m).
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| By the end of year 8
| Applies additive strategies flexibly to decimals and integers. Using the statistical inquiry cycle, sorts and displays data identifying patterns, variations and relationships.
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- Karl understands decimals and place value and this helps him to answer problems. He uses a range of ways to work out harder problems, including division. He successfully uses information from graphs to help his problem solving and is very quick to spot any errors. His next step is to use his maths understanding more consistently in his science and technology work. Karl is working at level 4 of the NZ Curriculum, this is the expected level for his year.
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| Finds and represents relationships in spatial and number patterns using recursive rules for non-linear relationships. Identifies and describes the features of shapes or patterns than change or do not change under transformation.
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- Siobhan is working at the expected curriculum level for her year (level 4) and she can discuss the areas in which she has made the most improvements this year. She indicated that she particularly enjoys algebra and working with equations. Her next goal is to master addition and subtraction of negative and positive numbers. Siobhan is to be congratulated for the work she put into her digital maths artwork that used tessellating shapes. She successfully included her maths work as part of her art portfolio.
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