Students understand mathematics in many complex ways. Students ask questions, see ideas, draw representations, connect methods, justify, and reason in all sorts of different ways. But recent years have seen all of these different nuanced complexities of student understanding reduced to single numbers and letters that are used to judge students’ worth. Teachers are encouraged to test and grade students, to a ridiculous and damaging degree; and students start to define themselves – and mathematics – in terms of letters and numbers. Such crude representations of understanding not only fail to adequately describe children’s knowledge, in many cases they misrepresent it.
This chapter deals with the growth in standardised testing and that often in mathematics classes this practice is mimicked through the delivery of low-quality standardised tests. This is despite the knowledge that these tests only assess a narrow focus within mathematics.
The testing regime of the last decade has had a large negative impact on students, but it does no end with testing; the communication of grades to students is similarly negative. When students are given a percentage or grade, they do little else besides compare it to others around them, with half or more deciding that they are not as good as others. Commonly students describe themselves by saying “I am an A student” or “I’m a D student”.
So this is where FEEDBACK comes into it…the reason it is in the top 10 of strategies to improve learning.
The students receiving comments (not grades) learned twice as fast as the control group, the achievement gap between male and female students disappeared, and student attitudes improved.
This is the response to a mathematics homework study where half the group were given grades and half the group were given diagnostic comments and no grades.
Race to Nowhere
An American documentary that addresses the stress upon today’s students:
Assessment for Learning
Paul Black and Dylan Wiliam provide some valuable insights into the use of assessment for learning.
Teachers who use A4L spend less time telling students their achievement and more time empowering student to take control of their learning pathways.
The 3 vital questions:
- Where students are now
- Where students need to be
- Ways to close the gap
Developing Student Self-Awareness and Responsibility
The most powerful learners are those who are reflective, who engage in metacognition – thinking about what they know – and who take control of their own learning. A major failure of traditional mathematics classes is that students rarely have much idea of what they are learning or where they are in the broader learning landscape. They focus on methods to remember but often do not even know what area of mathematics they are working on.
There are many strategies for encouraging students to become more aware of the mathematics they are learning and their place in the learning process. Here are 9 favourites of the author of Mathematical Mindsets:
- Peer Assessment
- Reflective Time
- Traffic Lighting (understand (green), partially understand (yellow) and need help (red) – some Teachers hand out coloured paper cups)
- Jigsaw Groups (work together to become experts on a particular area and then split and join new groups to share information)
- Exit Tickets
- Online Forms
- Students write questions and tests
Advice on Grading
Many teachers, unfortunately, are forced into grading, as it is a requirement of their school district or the administrators of their school. The following lists compiles advice on ways to grade fairly and to continue communicating positive growth messages even when faced with a grading requirements:
- Always allow students to resubmit any work or test for a higher grade;
- Share grades with school administrators but not with the students;
- Use multidimensional grading
- Do not use a 100-point scale
- Do not include early assignments from mathematics class in the end-of-class grade
- Do not include homework, if given, as any part of grading
Not all practical but worth thinking about and discussing at another time. Some of our feedback work should be designed to provide students with opportunities to improve on drafts and early tests.