Relational Understanding and Formative assessment
Article: Relational Understanding by Richard Skemp
Video: Formative assessment and feedback by Dilan Wiliam
In his article Richard Skemp leads us to think about the meaning of ‘understanding.’ In French a faux ami (false friend) is where a word in a person’s first language can mislead them to believe a similar looking word in another language can mean the same thing. For example, in Spanish the word ‘televisión’ means the same as ‘television’ in English. However, ‘Estoy embarazado’ does not mean ‘I am embarrassed,’ but ‘I am pregnant.’ His point is that two meanings of ‘understanding’ can be:
- Instrumental understanding
- Relational understanding
By ‘instrumental understanding’ or ‘rules without reason’ we accept things like that A=bxh (A= area of a rectangle; b is the length of the base; h is the height of the rectangle). In mathematics students are often given information such as this and then told to do an exercises from a textbook showing that this indeed is true. Subsequently, if a student is challenged to consider that this is true it may lead to an attitude, ’of course it is true; all of my answers are correct according to the book.’ I have experienced this personally working as a Maths T.A. where a student insisted the way his teacher had showed him how to use Pythagoras’ theorem was the correct way; despite the fact that he needed to rearrange the formula to find the length of the side of a right-angled triangle that was not the hypotenuse.
A ‘relational understanding’ is where we know what to do and why. A more rigorous approach to investigating how to find the area of a rectangle or the length of a right-angled triangle, etc requires a greater investment in time. It may require thinking that is outside the immediate confines of the syllabus and challenging what is already accepted as the given method.
In the end Skemp decides meanings of the word ‘understanding’ are important and have their place. For example, explaining -1x-1=1 is very difficult to explain in terms of ‘relational understanding,’ but as ‘instrumental understanding’ moving forward will bring its rewards.
In a wide-ranging video Prof Wiliam outlines aspects of formative assessments. Sometimes telling the student where we are going spoils the journey. Telling the students an answer to a question before they have been provoked into thinking about it may make the investigation less appealing and take away from the engagement in a lesson as teachers we are trying to foster.
His work describes how feedback can be constructive in improving learning. His research and reading of research articles advises constant adjustment of teaching to meet the needs of students’ learning. ‘Feedback’ that is forward looking is based on assessment will achieve better learning outcomes. Evidence from assessment should be used to plan the learning path suited to the students and not blindly plough on to the end of the syllabus regardless of any assessments that have been done.
Both the video and article were thought provoking and informative. In Richard Skemp’s article it encourages teachers to value relational understanding although not really explaining what needs to be sacrificed in order to complete a syllabus. The reader is basically told that there are two approaches. I can only conclude that time will be the determining factor in deciding upon an approach.
Dylan Wiliam suggests that learning should be adjusted depending on the evidence of any assessments. This makes sense. A student will progress given constructive feedback. However, I found it is difficult to believe that adjustments could be made to an entire class of students before they leave a class or by the time they next return. Teaching will always be a compromise between how much time is dedicated towards a certain aim in the time available against the ideal of making sure a certain level has been achieved in a topic by all.