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Maths Mastery & Formative and Summative Assessments: a Guide for NQT.

formative and summative assessments
Formative assessments are integrated into the classroom to track the progress of students. Summative, on the other hand, focus on the overall journey of the student's mastery...

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Formative and Summative assessments have been part of every student’s education since 1970. 

In this article, we will focus on the assessments and how it ties into the maths mastery approach teachers use to educate their students.

What is the Mastery approach?

The mastery approach is the belief that no student should be left behind through their learning progress. The National Centre for Excellence in the Teaching of Maths (NCETM) breaks the mastery approach into five big ideas:

  1. Coherence – Lessons are broken down into connected steps that gradually unfold the concept – this supplies access to all children which later leads to a generalisation of the concept and the ability to apply it.
  2. Representation and structure – representations expose the mathematical structure being taught, this helps students be able to do the maths without the aid of representation.
  3. Mathematical thinking – to understand something deeply, it must be worked on by the students, thought about and discussed with others.
  4. Fluency – the quick and efficient recall of facts to develop the flexibility to move between subjects.
  5. Variation – this is twofold – it is about how the teacher represents the concept after being taught and the sequencing of the activities used in the lesson/follow-ups to connect mathematics.

These five key ideas help the understanding of mastery.

Mastery has many benefits case study performed in 2018 at Elmhurst Primary school compared their 2017 results to their 2018 to see how the ‘mastery’ approached had aided students to progress. It was found that 41% of students achieved greater depth and 97% of students met expected standards. See the case study here.

The Assessments:

Many people assume taking an assessment is the same as taking a test, however, assessments are bigger than that. In primary school, there are two types of assessment which are known as a formative and summative assessments.

These assessments are not like SAT’s, GCSE’s, or A-levels. The formative assessment is a low-stake test while the summative is a high-stake test. These tests are not to pressure students but to understand their learning progress and their mastery journey.

Formative and Summative assessments are started from year one up until the end of a student’s education. Even in university, students will be allowed to express their learning progress through assignments and coursework.

The assessments help contribute towards the idea of mastery for teachers to support each student where necessary and how it ties into everything teachers do. Here, teachers understand that a whole school commitment is vital for student success. This also promotes the principle of keeping up instead of catching up removing any negative language that might delay or affect a student’s learning progress.  

Formative Assessments:

A formative assessment refers to a wide variety of methods that teachers use to conduct in-process evaluations of students learning – here they will see how their mastery journey is going!

Many teachers believe that formative assessments are an essential part of effective mastery teaching. Compared to other assessments, formative assessments are integrated into teaching and they can be as simple as asking students to raise their hand if they have understood a subject.

Before formative assessments are integrated, teachers must begin with a diagnostic assessment, which will educate them on what students may already know, or what skills exist.

Summative Assessments:

Also known as the end of term or end of block assessment. These serve the purpose to evaluate a student’s learning at the end of term or year. They sum up what a pupil has achieved at the end of a period of time.

Summative assessments can be written observations, conversation, or task tests. The tests allow teachers to track progress and be able to communicate with others on how each student needs to be supported.

Many teachers believe that formative assessments are an essential part of effective mastery teaching. Compared to other assessments, formative assessments are integrated into teaching and they can be as simple as asking students to raise their hand if they have understood a subject.

Before formative assessments are integrated, teachers must begin with a diagnostic assessment, which will educate them on what students may already know, or what skills exist.

The difference between formative and summative assessments are that one is integrated while the other is performed at the end of a block or term. But overall, the main difference between these two assessments according to the Education Reform is that formative assessments are for learning, while summative assessments are of learning.

10 times table

What do the assessments look like?

As said above, formative assessments and summative assessments are quite similar but different in their way. But what makes them stand out from one another?

The Formative Assessment:

A good formative assessment is one that also allows students to learn independently, are mindful of the relationship between teaching and learning, covers small content areas, monitors the students learning and focuses on the progress.

There are many ways you can integrate these assessments, but if you can’t think of any here are our top five formative assessment examples that promote educational growth and mastery:

  1. In-lesson quizzes
  2. Journaling – top five favourite ideas they learn during the lesson.
  3. Write postcards as if they were a historical figure summarising an event or concept
  4. Talking about it
  5. Poster making
  6. The popular exit cards

The Summative Assessment

These assessments are vaster due to being a high-stake test. However, there are many ways you can approach these assessments without removing the fun in the learning progress of your class.

Great examples of summative assessments are those that:

  • Motivate students to study and pay close attention
  • Allow students to apply what they have been learning
  • Give space to see gaps in learning
  • Gives space to see gaps in teaching
  • Contribute positively to learning outcomes

An article for Corwin suggested crafting your summative assessment with seven aims in mind.

  1. Accompanied with enough time and management
  2. Achievable like in and out of class activities
  3. Active involvement in the planning of it
  4. Applicable to the standards and expectations of the national curriculum
  5. Appropriate to your teaching style and your students learning style
  6. Attractive to your students, does the assessment look engaging?
  7. Authentic to learning outcomes and curricular context.

How do we make summative assessments fun?

These are some ideas to make your summative assessments less daunting and more fun for students. Enjoyment creates passion which can lead to a better understanding of concepts and eventually mastery!

  1. Write a script and chose a creative approach to assess a concept or a strategy. For an example, check out the fun video at the bottom of this paragraph!
  2.  Conversations with other students, explaining how complex maths concepts work.
  3. A living museum – this is like the first idea only students must give 2–3-minute presentations on the “exhibits” which can be concepts learnt.
  4.  The use of Venn diagrams. These are quite old however they are the perfect tool to help visualise the relationship between different things.
  5.  Ed-Tech Games – students in this generation are used to phones, tablets, and computers. For some, video gaming is a hobby. Therefore, it can be a good idea to incorporate game-based learning into classes. Learning with Emile is the perfect tool for summative assessment (and even formative assessments), it tracks and rewards students’ progress reducing marking time for teachers allowing them to fully focus on the importance of these tests.

What do we do when students need support throughout their mastery journey?

We understand that time is vital in a teaching approach to a student’s mastery journey. The national curriculum is vast therefore realistically there is not enough time to fully complete the journey of mastery. Therefore, other interventions are used to support their progress.

If students do not fully understand a concept, teachers do not see this as a failure but simply an area that needs to be worked on further by providing support such as activities, home learning and out of school clubs.

It is always having to reflect and analyse the assessment itself. Within a formative or summative assessment, you might consider the following:

  • Format – is it tricky? Do students have experience in this format? For example, a multiple-choice test might throw students off causing them to get overwhelmed. For next time, a different approach would be needed such as not use a format that is so formal.
  • Vocabulary: Do students fully grasp the idea behind vocabulary?
  • Aligned: does the assessment align perfectly with your instruction?
  • Similarities: Which students struggled the most? Do they have something in common? Which content was missed the most? What areas need looking at with more time?

Other ways in which a teacher might support their students is:


  • Allowing them to expand their knowledge in maths club.
  • Praising their efforts as any progress in the right step towards mastery.
  • Developing an action plan with SLT, other educators and guardians/parents to meet the student’s needs.
  • Allow students to also give you feedback, what did they understand? What didn’t they understand? This is a great idea for engaging conversations in classes.
  • Regularly do formative assessments to see if students are beginning to pick the ideologies up.

Overall, formative and summative assessments are to keep track of how each student is progressing in order to offer interventions as soon as student’s feel like they require it. These assessments will help students get used to the notion of progress and growth in their studies, motivating them to always give their best whilst having fun all at the same time.

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