Written by Eliza Stine and Joan Whittaker, Riverside International School
Are you good at Maths?
We all remember the moment when we first found out that we were “good” or “bad” at maths. As some point as a child, it might have hit you that you were bad when you longingly looked across at your friend flying through a page of multiplication problems as you chewed on the end of your pencil and the numbers seemed to swim meaninglessly in your vision. Perhaps, for you it was confirmation that you were good when you solved a word problem before anyone else in the class and your teacher called you up to show your solution on the board. You might have even categorised yourself vicariously, as your mother sighed over your homework and said that she had never been able to do maths either.
For some reason, seeing yourself as good at maths or bad at maths sticks with children in a way that can last all the way into adulthood. Most adults still judge themselves as being good or bad at maths in the same way that they did as children. At a young age, students are already developing this perception that can affect their sense of self-efficacy for the rest of their lives.
The Reality: We are all learners
However, the reality we know as teachers is that children aren’t universally good or bad at maths. Students with a strong number sense may find telling time confusing. Students who struggle to recall multiplication tables are sometimes the most confident solving a spatial reasoning problem. Often, there is no relation to a students’ understanding of shape and measures and their ability to add large numbers systematically.
For example, in Year 4 there are 63 maths objectives we assess children for. In our cohort of 39 students, is it possible they will all be working at a similar level on all of those objectives? Of course not! As any maths teachers know, students join your class with a huge range of understandings and confusions. International schools can often see this even more clearly since students may have moved between schools, curriculums and countries multiple times in their education leaving them with a set of unique gaps.
The fixed maths groupings that our school was using were not taking this diversity into account. Furthermore, dividing students into “high ability” and “low ability” groups was also undermining our school’s culture of growth mindset and negatively affecting students’ self-efficacy and their perceptions of themselves as learners. Lower attaining pupils in the “Top group” felt constantly demoralised by simple comparison against peers, even though they were actually within the top third overall in the year group for maths attainment. Teachers were also finding it difficult to teach one group exclusively for the year: constantly trying to challenge and extend, or to re-explain basic maths concepts could be tiring, and not necessarily using teachers to their strengths.
Making fluid grouping work
As teachers sat down to reconsider this system, a simple but radical solution was offered. What would happen if we were able to regroup students every week based on a pre-assessment of the specific area of maths that would be taught that week? Students would still be able to be taught in groups that could focus on their specific needs and teachers would know exactly which objectives a group needed to focus on. Teachers were also keen to teach different groups each week so children wouldn’t know who was the “high” maths teacher and continue to build their self-conception through comparing themselves to other students.
We moved into this way of teaching (not without a little apprehension!). We decided to structure each week with a Monday pre-assessment activity, 3 days of targeted skill-based teaching planned according to the needs that were shown in the assessment, and then a final day of Application and Problem solving in class groups. The final lesson would allow teachers to pull the weekly skills together, develop problem solving skills and promote the use of maths in a real-world situation. It would also allow teachers to spend two days of the week with their own classes to be able to understand their mathematical development even if other members of the team had been working with their students on their skills that week.
The benefits of fluid groupings:
- These fluid groups allow teachers to teach to their strengths e.g. I have a great practical model for teaching division so I will teach the group that needs to learn the basics of division this week; or I have a great idea for a complex problem-solving task using timetables so I will take a group that needs to extend their problem solving skills this week.
- Children are constantly working with different adults and children which they enjoy and helps them to see themselves and their peers all as learners who need to focus on developing different skills.
- A growth-mindset is promoted beyond catch-phrases and posters. Students start to develop their self-efficacy and see themselves more accurately as learners, not “good” or “bad” at maths.
- Students know they will continue to have the opportunity to be in different groups, nothing is fixed. Parents also benefit from knowing that their child has not been pigeon-holed into a rank or place within the cohort.
- There are opportunities for students to be the best in their group, rather than struggling in a group with children who are finding the activities easier.
- Teachers are prepared to provide targeted support and differentiation for individuals who need to meet specific objectives.
It has been exciting to see students who might struggle in different systems develop their confidence in maths, as well as hear the excited buzz as students find out which students and teacher they will be working with each week. It has also been exciting to teach a greater variety of students and look into the eyes of your class each week, knowing that you have prepared activities that will support the exact skills these children need to develop.
Eliza Stine is a Primary School Teacher and Curriculum Coordinator at Riverside International School in Prague. There, she has taught everything from Year 1-6 (K-5). She has worked in international schools for 15 years in Bangkok and Prague and continues to love working with curriculum to help meet the needs of students coming from around the world. She received her BA and MA from Colorado College where she first fell in love with the idea of students learning through inquiry. She loves that teaching primary school children gives her the opportunity to see students develop new ideas and for her to see the world a little bit differently every day as well.
Joan Whittaker is a Primary School teacher at Riverside International School in Prague. She holds a Bsc in Archaeology, and a Post-Graduate Certificate in Education. Prior to teaching internationally, she taught in the UK for five years at a small rural school. A life-long lover of learning, she particularly enjoys the diversity of primary teaching, because she is passionate about so many different subjects, and couldn’t possibly choose her favourite.
