There are many different methods of assessment, both summative and formative. Summative can be considered the assessment of learning, usually taking place at the end of a period of teaching to establish the pupils’ performance. Whereas formative is often referred to as assessment for learning and continually takes place in the classroom (Bourdillon and Storey 2002). Effective formative assessment involves the student and teacher in a dialogue and exchange of reflection and feedback, which allows the teacher to identify understanding and provide the students with the means to make progress (Hodgen and Wiliam, 2006).
Questioning is a method of formative assessment, and it is a method I use regularly with all my classes. Questions can be either open or closed, and both have their merits. Closed questions can be asked to individuals or a whole class. They can provide teachers with a snapshot of the students’ ability to answer a question, and can be used to discover how well they can recall facts and processes. However, closed questions can be limiting for students and teachers alike. Less confident students are unlikely to volunteer answers where there is a wrong or right answer. The use of mini white boards for whole class participation can negate this issue, whilst also enabling the teacher to check everyone’s understanding and I have found repeated closed questions can help to build confidence in students. However, teacher often perceive correctly answered closed questions as evidence that students have understood the learning objective. Whereas, in fact students can answer questions correctly, through a learnt process, whilst still having misconceptions within their understanding (Wiliam, 2002), and it is through open questions that teachers can uncover, and then address these.
Although closed questioning can enable me to gauge if students can respond correctly to a particular style of question, I find open questions more effective in uncovering misconceptions. During a lesson on linear graphs, a student could correctly identify the equation of a line. However, when I asked her to explain how she knew the equation, her explanation was mathematically inaccurate and in time this would have hindered her progress. Through deeper questioning and allowing the class to become involved in a discussion surrounding her ideas, the whole class was then able to share ideas and re-evaluate their understanding. This example highlights the importance of open questions, where deeper thought is necessary. However, open questions require teachers to be responsive in their questioning in order that they provide the necessary feedback to students’ current understanding (Hodgen and Wiliam, 2006). This can pose a difficulty in that each student and class will vary and therefore, to ensure teachers respond effectively their subject knowledge and awareness of possible misconceptions must be strong, but, although they cannot be sure of exactly what to expect, this level of questioning can be planned for (Hodgen and Wiliam, 2006).
Most students consider mathematics and discussions to be mutually exclusive, which has meant some students have been reluctant to discuss their ideas in class. This has changed over time, and I intend to develop better discussions by using questions that have more than one answer to encourage class debates, as this can be beneficial to the development of students’ mathematical literacy (Hodgen and Wiliam, 2006).
Kirsty Clarke- Howard