Educators are exploring new methods to support students affected by interrupted learning, making Assessment for Learning (AfL) strategies increasingly vital. AfL facilitates feedback exchanges between learners and teachers to organize and direct educational progress. This feedback can be formal or informal, incorporating peer and self-assessment practices.
AfL strategies aim to help students understand their learning objective, take responsibility for it, and plan how they might move forward. In the context of maths lessons, integrating AfL techniques can be particularly beneficial. A key aspect of AfL is listening closely to what learners say, as this often reveals more about their mathematical thinking than their written work.
Integrating AfL into Maths Lessons
One approach to integrating AfL into maths lessons is to focus on constructive comments rather than grades. By avoiding exact marks or grades and instead writing comments that encourage reflection, educators can help learners understand their strengths and weaknesses. For example, a comment like “I can see five errors in the work you’ve done. Can you find them and try to fix them?” encourages learners to engage with their mistakes and think critically about their work.
Feedback should be active, not passive. Educators can give comments that encourage learners to engage with feedback and with each other. Discussion is sometimes overlooked in maths, but sharing solution strategies is key. By asking open questions that explore how learners know something, rather than just whether they know it, educators can help learners develop a deeper understanding of mathematical concepts.
Listening Reveals Mathematical Thinking
In maths, it’s easy to try to interpret what learners know by what they’ve written down. However, the marks learners make on paper are not necessarily what they always mean and can hide the mathematical thinking that’s going on. Listening carefully to what they say, both to each other and to the educator, can reveal more about how they are making sense of concepts. This is particularly important in Early Years, where learners may not have the language or writing skills to express their thoughts clearly.
Planning ahead for common misconceptions can also help prevent the wrong thinking from becoming ingrained. When students have a lot of time off school, as they have in many countries over the past year, this becomes even more important. Misconceptions in maths usually happen when students try to solve a problem by doing something that they think is perfectly logical – it’s not a guess, it’s not a mistake, they just have the wrong thinking behind it. The more they do it wrong, the more it becomes ingrained.
Setting problems with more than one possible answer can also help to reveal misconceptions and encourage deeper thinking. This approach can be particularly useful for AfL, as it encourages learners to think critically and develop their problem-solving skills.
Principles of Assessment for Learning
A key principle of AfL is that teachers can use assessments to form students’ learning and look forward to what they will learn afterwards. This approach has been influenced by the work of Paul Black and Dylan Wiliam, who suggested embedding formative assessment by helping learners understand exactly what they must do to succeed. Their pamphlet, Inside the Black Box, published in 1998, helped to establish AfL as a key approach to teaching and learning.
According to Dylan Wiliam, formative assessment can achieve success equivalent to a 50 to 70 percent increase in the rate of student learning. This approach emphasizes the importance of helping learners understand exactly what they must do to succeed, encouraging productive classroom discussions, and providing feedback that helps students to move on in their learning. By training learners in self and peer-assessment, educators can provide opportunities for them to be learning resources for each other.
The Cambridge Mathematics website provides more information on the Cambridge approach to AfL. By exploring this approach, educators can develop a deeper understanding of how to integrate AfL into their maths lessons and support their students‘ learning.
Building Classroom Culture
In maths, peer-to-peer work is key to building a classroom culture that encourages learners to question, explain, and challenge mathematical ideas together. By posing provocative statements, such as “1/10 is double 1/5”, and asking the class to think and talk about it, educators can encourage learners to engage with mathematical ideas and develop their critical thinking skills. As learners talk about and explain their own ideas, they often reveal a lot of strengths and weaknesses, providing valuable insights for educators.
For more information on maths research, including the importance of feedback in maths, educators can explore the Cambridge Mathematics website. By staying up-to-date with the latest research and developments in maths education, educators can continue to refine their practice and support their students in achieving their full potential. The pamphlet Inside the Black Box by Paul Black and Dylan Wiliam is also a valuable resource for educators looking to develop their understanding of AfL and its application in maths lessons.
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