Monitoring students' numeracy progress

This page describes different ways to monitor the effectiveness of your teaching and how to make adjustments when necessary.

Frameworks of academic support (such as Response to Intervention) require continuous monitoring of student progress and ongoing adjustments based on these observations, to be effective. It's not only the interventions that teachers employ, but students' responses to these interventions that are important.

For students with specific maths learning difficulties, interventions should be based on a student's cognitive strengths to ensure maximum benefit. These decisions can only be made through the ongoing collection of data.

Data collection

It's essential that you plan the types of data you intend to gather and for what purpose. Your plan should clearly indicate:

  • Your purposes for monitoring students and the types of questions you want to answer about their learning or your teaching. Frame your responses using the curriculum or learning goals you have for your students.
  • How you will gather this data and what form it will take (formative, summative). For example, the time taken for a student to learn a skill and the skills they can use independently. The computational strategies the student uses and the errors they make are very informative about number understanding and skills.
  • How you intend to modify your teaching and how you expect these changes to influence numeracy outcomes.
  • The types of activities students will engage in and how you will evaluate their performance. For example, dynamic assessments, working with concrete materials or number lines. These are critical for students with maths learning difficulties or learning disabilities such as dyscalculia, particularly dynamic assessments and working with concrete materials.
  • How you will monitor students' attitudes toward these activities in class.
  • What you would expect students to know, understand or be able to do if adjustments were successful. This should include short-term expectations (week to week) as well as long-term (month to month).

Student observation

You have likely already created a numeracy profile for students you suspect may have learning difficulties. It's important to remember that this is an evolving document.

How students learn changes over time and previous challenges may not be relevant later. This is often true for behavioural difficulties.

As students feel increasingly supported and grow more positive and independent in their learning, challenging behaviours will often become less frequent and acute.

Monitoring a student's progress through regular observation will help keep their numeracy profile current and provide you with moment-to-moment information about how they learn and respond to a particular approach. Aim to monitor students for a short period (for example, one month) before trialling adjustments. This will help you to identify when and why they improve.

Begin by making only two or three changes. Too many changes at once can be overwhelming for you and for your students and will make it difficult to isolate what led to improvement and what didn't.

Observe numeracy learning

As well as providing you with data about your teaching, your observations should also add additional information to your students' numeracy profiles.

For a student in the ages 5–8 range, you can observe if they have:

  • Normal vision acuity. Does the student's posture during class suggest they find text difficult to keep in focus? Does the student try to move forward or leave their chair to read what is written on the board?
  • Adequate oral language and communication strategies. Does the student struggle to recall mathematical terms or have a limited vocabulary? Is the student able to wait their turn to speak? Do they raise their hand? Do they interrupt others regularly?
  • Typical cognitive ability. Can the student recall information and retain ideas in their short-term memory during classroom activities? Can they make predictions, recognise cause and effect, reason by analogy and form abstract concepts?
  • Organisational strategies. Can the student plan for how they will complete a task? Can they maintain focus and attention and ignore distractions?
  • Attention. Is the student able to maintain focus during the class or small group instruction? Are they displaying disruptive behaviour or lack of engagement (such as zoning out)?
  • Positive attitudes toward maths, and about themselves as users of numeracy.
  • Learning difficulties in other areas, such as literacy or social-emotional difficulties.

Decide on indicators for student growth

While planning what adjustments you will make in your teaching, it's also necessary to select tasks and measures to help assess the effectiveness of instruction, as well as clear criteria for mastery. This will help you to better judge not only if students are making progress, but also the rate at which students make progress.

Depending on what outcomes you are targeting, you may have indicators or tasks for measuring:

Conceptual understanding

This could measure how easily a student can explain a task and what's required, or else describe a concept in their own words.

Interpreting information

This might measure whether a student can use concrete materials to represent problems or how well they can represent this information visually.

Knowledge of symbols and mathematical vocabulary

Can the student recognise different symbols and explain what meaning they have numerically?

It's important to keep consistent records of a student's performance on these measures and refer to them when updating their numeracy profile. 

Make adjustments in your teaching

You can make adjustments to your teaching in several ways, including making use of number lines or concrete materials. Adjustments will vary from teacher to teacher and classroom to classroom. It's important to observe how these changes impact the learning of students with learning difficulties.

With mathematics, observe how progress changes when you:

  • target engagement and a student's motivation to do maths. You can encourage students by linking their interests to class activities and helping them to see how numeracy is relevant to these.
  • For example, a student who enjoys camping might be interested to learn about the numeracy involved in logistics (planning how much food to take, how long it will last), distance (how far a journey is, how far can a person travel in one day or one hour), mass (how much does camping gear weigh), orienteering (what bearings or angles are needed to locate a position, determining the type of terrain by reading and interpreting contour maps).

    Making these types of connections will also help students to see the relevance of what they are learning and how it relates to the real world. You can also build a student's motivation by discussing their thoughts and thinking about maths, and by giving positive feedback that relates to their outcomes

  • model or teach ideas through actions first or with multiple exposures (for example, using concrete materials to represent the problem or skill in addition to explaining it or using symbolic notation)
  • scaffold organisational strategies, for example:
    • break larger tasks down into smaller steps
    • plan how to use what a student already knows (drawing on prior learning)
    • guide a student to use specific strategies
    • help a student to review what information is present in the question and recall examples of similar questions they have answered previously.
  • manage factors that impede learning. Measuring a student's ability to learn in situations where there are fewer distractions (such as one-on-one), grouping students with peers they work well with.

Monitor the effects of these changes on a student's maths abilities and engagement and the extent to which these changes lead to improved outcomes. Specifying progress indicators at the start of the intervention will help you more accurately measure improvement.

It's important when making new adjustments to trial and monitor them separately. This is essential to measure their effects and determine which adjustment has led to improvement.

Review and evaluate

Following a set period (for example, four to six weeks) evaluate a student's progress using your chosen indicators. Make a judgement about the modified teaching and whether the student has improved due to these changes. If it has helped, identify which changes led to the improvement and continue with these adjustments for another four to six weeks.

If these adjustments do not appear to be helping a student to improve, and all other factors that could impede learning are being managed, do not feel obligated to persist with them. The strength of approaches like Response to Intervention lie in their flexibility (Hattie 2015). Return to a student's numeracy profile to see if there are any clues that might help direct future instruction to better support the way the student learns.

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