Editorial
The landscape of education and…
by Lee Keat Peng & Grace Koh
Introduction
Students struggling with Mathematics often need help identifying what they do not know. While teachers often encourage these students to approach them for individual consultation, when asked what they need help with, we often hear students saying “Everything!”. In this article, we hope to share how we redesign the feedback cycle in Secondary Mathematics lessons, to increase students’ feedback literacy so that they can appreciate feedback, make judgements of their progress, manage affect related to feedback and eventually take actions to close their learning gaps (Carless & Boud, 2018).
Koh & Tan (2024) shared an example of how a series of feedback cycles would look in the teaching of the Chinese Language. However, they also highlighted the idea of “signature feedback pedagogy” (Pitt & Quinlin, 2021) that a disciplinary approach to feedback would be necessary to help students better understand and take action on feedback. The article inspired us to think deeply about how the feedback cycle would look in a content subject like Mathematics where teachers not only need to deal with skills but also content matter.
As part of our school’s Professional Learning Team (PLT) project, we decided to review the feedback cycle in teaching “Differentiation of Trigonometric Functions,” as many students struggled with it even with much feedback from teachers. Taking reference from the Feedback Pedagogy Cycle (Koh & Tan, 2024), we reviewed our current practices in terms of Feed Up, Feedback and Feed Forward. We identified that it was necessary for teachers to see feedback as a process and to intentionally design for feed up and feed forward to make our feedback more meaningful for our students.
Feed Up Stage
In the past, teachers used general learning outcomes for this topic such as:
Students will:
- learn how to differentiate trigonometric functions.
- need to understand the general rules of differentiation, for example chain, product and quotient rules
- learn how to apply to specific trigonometric functions like sine, cosine, tangent and others.
Students in general needed help with this topic as it is very abstract. As they did not have a deep understanding of the concepts, they were often confused and applied the wrong rules to differentiate the functions. In some cases, students did not know what to apply and hence could not even start on the question.
Without a clear understanding of the topic, the low-progress students did not know how to articulate specifically what they did not know. Therefore, they concluded that they did not understand anything at all.
We realised that our initial learning outcomes described what students are expected to know, understand or be able to do after learning the topic. They focus on the end goal of learning. To help students fill the gap, we decided to add in success criteria in our lessons. Success criteria are more specific and measurable indicators that show whether students have achieved the learning outcomes. In other words, learning outcomes define the destination, while success criteria provide a map to gauge whether the destination has been reached successfully.
As the topic is both abstract and complex, we decided to use a tiered success criteria (Table 1). Tiered success criteria offer a few levels of expectations for students’ performance, allowing for differentiation based on their varying abilities, learning needs, and progress. This approach can be particularly beneficial in classrooms with diverse learners.
By providing different levels of success criteria, students can work towards attainable goals before moving on to more challenging tasks. In addition, by defining clear success criteria that students can understand easily, they can monitor their own progress. This helps them identify their strengths and areas for improvement, fostering independence and self-regulation. They can pinpoint and articulate what they understand and what they do not understand using the proper mathematical terms. This is a metacognitive approach that can help students learn to take control of their own learning.
Teachers also realised that it is not only about listing success criteria, but it is also important to help students make sense of the success criteria (To, Tan, & Lim, 2023). To ensure that students understand the success criteria so that they know what is expected of them and how to achieve their learning goals, teachers model the use of the criteria by providing examples and demonstrate the process of using those criteria to identify different levels of success in class. During this time, teachers can engage students in discussions to check their understanding and clarify their questions about the success criteria.
Changes were also made to our current department resource to make the success criteria explicit to students. Each of the practice questions that were used in our notes was explicitly tagged to each success criterion (See diagram 1). This enabled students to articulate their learning gaps if they were not able to understand or independently complete the practice questions.
Feed Back Stage
Previously, teachers would randomly assign homework questions from the textbook. Students would submit their work two days after for teachers to mark. As teachers marked the students’ work, we would give feedback by circling their mistakes or writing the correct method beside the wrong steps. Although teachers go through the solutions in class, there was no follow-up work given for students to demonstrate learning after feedback was given.
In the newly designed feedback stage, teachers were more intentional in the homework assigned and students are more involved in the feedback stage as well. After the lesson in class, students are assigned similar practice questions which were intentionally chosen and tagged according to the tiered success criteria (See diagram 2). As these questions are short, students will be able to complete and submit to their teachers for feedback the next day. They are encouraged to refer to the tiered success criteria when attempting the practice questions and complete the self-assessment checklist on paper (See diagram 3).
When assessing students’ work, teachers will ensure that our feedback referenced the success criteria. We will identify the areas where students have succeeded based on the criteria, and then provide constructive suggestions for improvement so that students understand how to improve their performance. Teachers will also check students’ self-assessment checklist and provide feedback on the accuracy of the students’ self-assessment (See diagram 4). This will also help to reinforce students’ understanding of the success criteria.
Besides giving students personalised feedback on paper, teachers will also go through the solutions in class. During this time, teachers will revisit the criteria that students are unclear about based on their work to reinforce understanding. Students will be given the time in class to review their work and reflect on their strengths and areas for improvement (See diagrams 5 & 6).
Feed Forward Stage
In our previous practices, we did not plan for feedforward and thus students did not have much opportunity to apply the feedback given by teachers. In the new design, after receiving teachers’ feedback and doing self-assessments, students are given quick formative assessments like exit tickets in class to gauge whether students achieved the success criteria. The exit tickets will be differentiated based on the class’s areas for improvement. At this stage, teachers encouraged students to use the success criteria to evaluate a peer’s work (See diagram 7 & 8). This not only reinforces their understanding of the criteria but also helps them see examples of other students’ work. This approach of using student self-assessment and peer assessment helped develop students’ self-regulation and metacognition
In summary, diagram 9 and diagram 10 show the teachers’ and students’ point of view of the whole feedback cycle/process respectively.
Why did we want to change?
Tiered success criteria allow for gradual progression and individual growth. Students can build their knowledge and skills step by step, moving from simpler tasks to more complex ones as they master each level. As they meet each level of criteria, they will be motivated as they gain confidence and competence to strive for the next, fostering a growth mindset.
This change in the teaching approach encourages students’ deeper engagement with the success criteria. As students move through the tiers, they are likely to develop a more comprehensive understanding of the subject matter.
With tiered success criteria, teachers can more accurately assess students’ progress by the varying levels. As such, teachers can better identify which students need additional support and in which specific areas, allowing for more targeted interventions.
Students’ Feedback
In general, the students feedback that the tiered success criteria was clear and useful as they were able to use it to check their progress and whether they were on the right track. The sorting of the questions into the different levels of success was also useful. It allowed both teachers and students to identify the specific area of weakness to work on. The tiered success criteria provided a common language for both teachers and students.
It was observed that the higher ability students did not use the tiered success criteria as they had understood the topic during the lesson. This was more beneficial for the weaker students as they now could articulate what they understood and what they did not understand. The tiered success criteria also served as a guide for weaker students when they did not know how to start solving the question.
Since the Exit Pass questions were differentiated based on the class’s need. Therefore, it was a good way to check if the students learnt from their mistakes and for them to further practice the concept they were unsure of. It was noticed that there was an improvement from homework to Exit Pass and students gave positive feedback to their peers when they marked the Exit Pass.
Areas for improvement
Some areas for improvement will be to adjust the success criteria to reduce the number of levels – Level 1 to Level 4. Simplification will be inclusive for all 4 levels, since students are expected to simplify the answer after doing differentiation.
Next, students were not very well-trained at identifying their own mistakes and as such self-assessment and peer-assessment. This can be improved with more practice.
Lastly, students generally respond well to the tiered success criteria and feedback from others. To maximise the effectiveness, feedback should be specific and clear, actionable, and framed positively, with an emphasis on improvement. Tailoring feedback to individual needs and creating a supportive classroom environment can significantly enhance students’ learning.
Conclusion
In this project, we could really see that the impact of good feed up processes, to help students make sense of what good learning is, could promote students’ feedback literacy and help them better help themselves. With clear articulation of success criteria and the intentional design of feed forward tasks that are linked to the success criteria, lower progress students could better understand where their learning gaps are, in fact, they no longer feel that they know nothing about the topic, but could articulate it was the higher difficulty success criteria that they had issues with and would need more time to work on. By gaining knowledge of their own understanding, they felt more confident in tackling the issues they face.
Reference
Carless, D., & Boud, D. (2018). The development of student feedback literacy: enabling uptake of feedback. Assessment & Evaluation in Higher Education, 43(8), 1315-1325.
Edd Pitt & Kathleen M. Quinlan (2021) Signature assessment and feedback practices in the disciplines, Assessment in Education: Principles, Policy & Practice, 28:2, 97-100, DOI: 10.1080/0969594X.2021.1930444
To. J., Tan, K.H.K. & Lim, M. (2023) Student-centered feedback pedagogy: Implications for feedback partnerships. In Lipnevich, A., To, J., & Tan, K.H.K. (Eds.) Unpacking students’ engagement with feedback (pp. 59 – 84) Routledge.