How do we improve maths teaching, learning and assessment for 7-14 year olds?

Thanks to John Dabell for the following article.

Is it better to ‘predict and prevent’ or ‘fix and find’ or do we do both?

There are thousands of studies available that make claims about impact but how can teachers separate the wheat from the chaff and know what really works and what to avoid.

We know that the effects of high quality teaching are especially significant for pupils from disadvantaged backgrounds. If only we had some discerning and pragmatic guidance to point us in the right direction based on secure and reliable evidence.   

The good news is, we do have help and this draws on the best available international research and expertise of respected teachers and academics.

The Education Endowment Foundation (EEF) report  ‘Improving Mathematics in Key Stages 2 and 3’ has plenty of razor-sharp insights and ideas to share including eight practical and evidence-based recommendations for making a difference to all students but particularly to those struggling with their maths.

One of the key principles for effective teaching the EEF report makes is to ‘Use assessment to build on pupils’ existing knowledge and understanding’. In other words, if you want to build higher, then dig deeper, find out what students already know and teach accordingly.

High-quality maths assessment must focus on the interaction of assessment with learning and teaching rather than just tracking. The goal isn’t simply to unearth what students know but also what they don’t know and perhaps, more significantly, what they partly know including any misconceptions they hold and why they may persist with errors.

In short, assessment has to be informative, unambiguous and supportive in order to facilitate an upgrade in partial-understanding to a fuller understanding and significant learning.

Time spent on assessment contributes to the goal of improving the mathematics learning of all students and any assessment event can be used to satisfy formative and summative ends.

The EEF report reminds us that “formal tests can be useful” for providing current and accurate intelligence about what students know so we can plan next steps in learning but where do we look?

Selecting reliable summative assessments to power efficient formative feedback and drive improvement is key and this is where Progress in Understanding Mathematics Assessment for Key Stage 3 (PUMA KS3) can help.

PUMA KS3 is a collection of finely-tuned standardised termly tests that empower schools to analyse the cracks, cavities and craters in students’ knowledge and understanding and authentically measure and predict their progress in maths.

Feedback will only have large effects on learning if the quality of the test data is reliable and diagnostically sound. Assessment in support of learning is key to unlocking mathematical progress and this is what PUMA KS3 is designed to do with flair and precision providing standardised scores, age-standardised scores, performance indicators, maths ages and the monitoring of progress and the prediction of future performance.

There are three tests per year group from Year 7 to Year 9 which ideally would be given around the second half of each term. Curriculum maps summarise which topics are covered in each test. (For through-schools, the range of also available for Years 1 to 6.)

As each question is coded by curriculum area this allows teachers to easily profile a student’s performance by objective then calibrate teaching responses and develop meaningful interventions for any areas that represent an Achilles heel.

All too often a sharp line is drawn between assessment and teaching. Teachers teach, then teaching stops and assessment occurs. Worthy testing devices are also worthy teaching devices and with PUMA KS3, teaching, learning and assessment are integrated and seamless so they feed each other.

PUMA KS3 illustrates how all three can be fully combined by design and how teachers can modify how they teach and make informed decisions about what learning activities best support how their students’ learn.

Schools need to provide support for teachers to access appropriate resources that are fair and inclusive, appropriate and inform learning and action. PUMA KS3 covers all bases. They up-skill teachers in diagnosing weaknesses and interpreting results and they provide clear signposts for teachers to plan, implement and review strategies for future learning.

PUMA KS3 promotes high-equity and maths education for all because the information it provides helps teachers adapt their teaching to address identified needs and nurture high quality outcomes.

The PUMA KS3 tests are a way to track learners – but they go much further than that because they make assessment an interactive process and feedback to feed forward so students can build up their skills, knowledge and understanding.

Find out more about PUMA KS3, view curriculum maps and  download sample PUMA KS3 tests.







key stage 3, maths, summative assessment

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