PAT Maths and KeyMaths data indicate that Rahul is well behind his peers at their year level. Outcomes on both assessments place Rahul consistently in the lowest percentiles when compared to their cohort.
The items that Rahul was able to answer during the PAT Maths test for Geometry, Measurement, Statistics, and Probability either involved the manipulation of numbers less than 10 or did not require the use of numerosity about understanding the other strands. This suggests that Rahul is confident solving single-digit problems but is not equipped with the knowledge of, or understanding to use, more complex numerosity skills in these strands.
The item that Rahul answered correctly in the Number strand involved the addition of two negative numbers, each less than 10. Each item on the PAT Maths assessment is linked with a standard from the Victorian F–10 Curriculum: Mathematics. The items that Rahul answered correctly, and their matching content descriptors, are listed below.
- Measurement – item 21 (VCMMG141) at Level 3 and 22 (VCMMG259) at Level 7.
- Statistics – item 27 (VCMSP235) at Level 6.
- Probability – items 32 (VCMSP267) and 33 (VCMSP266) at Level 7, item 34 (VCMSP177) at Level 4.
- Number – item 39 (VCMNA241) at Level 7.
Levels 5 to 7 require a knowledge of numerosity that covers whole numbers generally, proportional reasoning, directed numbers and algebra. PAT Maths items only provide a partial assessment of each standard.
Rahul completed most tasks in the KeyMaths assessment slowly, suggesting they were not able to recall relevant numeracy knowledge fluently. Rahul's difficulties with enumeration likely contributed to their mental computation, addition/subtraction and multiplication/division outcomes and their application of maths in problem-solving. Rahul's performance on the KeyMaths sub-tests showed a consistent pattern; their outcomes were in the lowest 10 percentile range for tasks that required the application or use of maths comprehension and skill.
Dynamic assessment is a procedure for investigating a narrow maths learning domain by constructing a mini-learning progression.
The steps required to solve a problem are specified to the student, and the teacher and student collaborate to solve the problem. The student may not be able to solve the entire problem independently, but with help from the teacher, they can complete the steps one by one to solve the problem. The teacher might use prompts such as, 'Okay, what do we do now?' or 'What do you think we need to do next?', handing the student responsibility to then solve like problems.
During this exercise, the teacher can also gauge the student's learning needs, specifically, the nature and amount of help needed to solve problems independently. Dynamic assessments can help students to internalise problem-solving concepts and procedures.
The following example is a dynamic assessment that might be used to support Rahul.
Rahul's teacher could use vocabulary for symbols to help Rahul to solve this problem a² + b² = c². The teacher might ask prompting questions such as, 'What do we call these symbols?' (for example, plus, add, minus), and 'What's another word for them?
When prompted, Rahul remembered 'add' and knew 'minus' but not 'takeaway'. They were unfamiliar with 'addition' and 'subtraction'
Further prompting, such as 'When the two is small and above a number or letter, what do we call it?', revealed Rahul knew 'square' and 'squared' and that they meant for something to be multiplied by itself. Rahul was unfamiliar with the term 'to the power of' and still seemed a little unsure after it was explained.
To further support Rahul to solve the problem, the teacher could:
- Ask Rahul to describe the concept in their own words
- Explain the task and what is required
- Make connections between the current topic and prior learning
- Break the task down into smaller steps
- Test numeracy idea(s) with friendlier numbers
- Represent information visually
- Interpret information by manipulating concrete materials (such as MAB blocks).
While it is clear from these data that Rahul requires significant support in their numeracy knowledge, understanding and skills, it is also important that the teacher's observations and the possibility of a literacy learning difficulty are also considered.
Rahul's family emigrated from Sri Lanka in the middle of last year. Rahul attends a supplementary English as an Additional Language class once a week. Rahul's teacher has noticed that they have difficulty with long-form maths questions but is reluctant to seek help. When questioned further, Rahul admitted that this is because at times they do not completely understand the language of the question or what it is asking for. This may indicate
literacy learning difficulties.