Observing students at work is an important part of your role as a teacher. It is important to look at more than what students are doing to establish how engaged they are, or whether they have completed a task. Teacher attention should be focused on the mathematical ideas that students are exploring, the thinking they are engaging in and where they are going next.
To effectively observe students, you need to:
- know the development of understanding in the content area that you are teaching.
- probe to better understand students’ thinking (assessing questions).
- push students towards the mathematical goal of the lesson (advancing questions).
- help inconsistencies in the students’ thinking to become apparent.
- encourage deeper inquiry and looking for generalisations and proof.
Purposeful conversations as part of student observation
It is always tempting to start questioning students as soon as you begin to observe their mathematical activity. However, first spend time listening to the students as they discuss their thinking in small groups. You will be more likely to ask relevant questions because you will hear the mathematical ideas that the students are discussing and see the strategies that students are using. Teachers can probe deeper into student understanding, by using prepared questions to assess students understanding and to advance them towards the mathematical goal of the lesson (see Pedagogical tool: Anticipate).
Effective observation
Teacher observation requires expertise in teacher noticing, which is more specialised than your everyday noticing. You need a clear understanding of the mathematical learning goal that students are exploring to be able to notice the mathematical significance in what they say and do. Teachers can learn a lot about students’ mathematical thinking by paying attention to:
- how they use representations.
- the logic of their reasoning.
- the mathematical meaning implied in their gestures.
Teachers should record evidence of these kinds of observations to inform your interpretations of students’ mathematical understandings. Your observations afford you deeper insight into what a student currently understands and make you more aware of emergent mathematical ideas which may be just out of their reach.
An observation chart may be useful to keep track of what you notice and consider as relevant to the lesson’s mathematical learning goal. Learn more about observation charts at Pedagogical tool: Observation chart.
Discuss with your colleagues:
- Are there any ideas which are new to you here? What are they?
- What strategies do you currently use to observe students?
- Reflect on what you focus on and what you notice when you observe students during a mathematical task.
References
Imm, K. L., Fosnot, C. T., Dolk, M., Jacob, B., & Stylianou, D. (2012). Learning to support young mathematicians at work: An early algebra resource for professional development. Heinemann.
Mason, J. (2021). Learning about noticing, by, and through, noticing. ZDM Mathematics Education, 53(1), 231-243.