Low Floor High Ceiling or Differentiation through the use of Te Tau o te Rā/Number of the Day & See Think Wonder
The two approaches that are the basis for Tahi Maths which allow for differentiation are; See Think Wonder and Te Tau o te Rā/Number of the Day.
See Think Wonder comes from Harvard Graduate School of Education. When presenting a See Think Wonder, the teacher puts an image on the screen and allows time for learners to share their thinking about what they see, think or wonder about the image. The teacher can participate in the dialogue. All ideas are accepted and this sets the tone for maths time; freedom for creative thinking.
Te Tau o te Rā/Number of the Day is having a number as the focus for maths time. The Scope & Sequence used in Tahi Maths has numbers arranged in sequence from 1-10 for Year 0 then 1-20 for our Year 1, all the way through to 6 digit numbers in Year 6 and hundredths in Year 8. Having a Scope & Sequence reduces the cognitive load for both teachers and learners, knowing what will be coming in future lessons.
The first step of Te Tau o te Rā/Number of the Day is having concrete materials for learners to manipulate and find the different components of the focus number. Double-sided counters work well for single digit numbers then the use of place value blocks for the exploration of larger numbers is recommended. The teacher shows, or models, some of the ways the number can be decomposed, writing them on the board. Different concepts about number can be explored; fact families, repeated addition, adding on 10 to a number, subtracting 1 or 2.
At the beginning of a lesson the teacher writes equations to match the material objects and learners are given time to practise writing the number on a whiteboard and then recording something of their choice such as a picture to represent the number or equations. The following day the teacher repeats writing equations and learners record their thinking in an exercise book (simple notebook).
Differentiation occurs through the different levels in which learners enter into their participation with the See Think Wonder, and through their different recordings of their mathematical thinking within Te Tau o te Rā/Number of the Day.
The teacher is able to scaffold learning at an individual level when the learner shares their recording with the teacher. The teacher is able to bridge any gaps from any attempts that have been made that are not completely accurate.
For instance a learner may have attempted to write an equation that is not completely correct so the teacher is able to teach the conventional way of writing the equation. Or, if a child has not yet secured counting one to one, the teacher is able to work with that child and practise one to one correspondence.
Low Floor High Ceiling originated from the work of Seymour Papert and the central design of the Logo programming language in the 1970s which was referred to as “Low Threshold High Ceiling”. “Low threshold” means that anyone can get started and the “high ceiling” meaning that advanced users shouldn’t be limited by the programming language.
Low Floor is beneficial to all learners as they can see themselves as capable and competent. Te Tau o te Rā/Number of the Day has a low floor because everyone is capable of doing something with the focus number. It could simply be drawing the particular number of lines or circles corresponding to the number, or counting stickers (for those reluctant to draw). It could be drawing a favourite picture and representing the number within the picture and writing some equations. It could be listing equations based on a pattern or based on something that is of particular interest to the learner such as subtracting 2 or adding on 20 to the number.
Learners can challenge themselves. They can have a go at something that they are not completely mastered such as subtraction, writing 6-9=3, and the teacher can provide them with a quick lesson in what the numbers mean and how an equation is read from left of right.
Maths anxiety is reduced and learners have a sense of agency over the direction of their mathematical representations. They can explore many different components of the number and make attempts at doing something they are not completely competent with but knowing that the teacher is able to provide input if needed.
Using Te Tau o te Rā/Number of the Day & See Think Wonder means that all learners are doing the same thing, but in their own way, at their own level and achieving success. Teachers are not required to develop different tasks for the different abilities of the learners in the class, instead, the teacher provides individual support to meet the needs of each of the learners.
The use of Te Tau o te Rā/Number of the Day & See Think Wonder as a Low Floor High Ceiling task allows learners to show what they can do and are attempting to do. It allows for learning to happen through discussions with the teacher, or with other learners, and means that all learners can enter into the maths task at their own, individual level.
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