Mental routines are ten-minute segments at the beginning of the maths
lesson. A routine may be repeated with slight variations over a one to
two week period. Throughout that time a pattern of questions,
behaviours, responses and strategies is repeated. The repetition
encourages students to anticipate what is coming and to prepare to
participate fully in them. As the days go by extra levels of complexity
and challenge can be developed without changing the basic nature and
structure of the routine. Mental routines are designed to promote an
active thoughtful approach to number and also as a tool to developing
automaticity with number facts based on deep understanding of the
underlying principles and concepts.
Are mental routines pencil and paper tests?
The routines are not paper and pencil tests, in fact most of them are
carried out without a pencil and paper at all. They are questions that
develop strategic thinking, number sense, estimation, games, everyday
problem solving situations. During mental routines all the different
strategies used are shown mutual respect so that the children feel
confident to have a go, to use trial and error, take a risk and develop
awareness that there may be many approaches to a question and also that
they all arrive at the same answer (if carried out correctly). Errors
that may occur are not penalised, rather they are used as opportunities
to explore what went wrong and why. Using errors as learning
opportunities often leads to a deeper understanding for all children not
just the child whose work is being reviewed. Fix up strategies are
developed through this process, so too, are complex thinking and the
desire to look for smarter ways to work things out.
Structuring a mental routine
In mental routines, questions are aimed at three different levels. We
begin with closed questions to which there is one
right answer. At first we tried to bypass these questions in favour of
the open-ended questions. This was a mistake on our part. The closed
questions (e.g. what is 3 + 4 or what is 13 + 14) certainly ground the
children setting them up for the open questions that follow. They also
provide a comfort zone where children do not have to think too hard and
where they can activate prior knowledge before the questions increase in
challenge level.
Next, the open questions require more thought and often
require the explanation of strategies or decision making (e.g. What
different strategies can be used to work out 3 + 4 or show me an even
number between 4 and 10). The latter of course has more than one
possible answer.
And then come the flip questions. Flip means that the
role of the children is now reversed and they get to ask questions or
apply the ideas in a different way. Guess my Number is a typical
example of a flip question. During the flip questions, the
children have to think differently, use the language and strategies
developed earlier and generally take more responsibility as learners.
Flip questions are often game like or in the form of
"guess my…" and require the children (not the teacher) to
use the mathematical language and strategies being developed. They also
develop adaptive reasoning, which is central to mathematical thinking.
"In mathematics, adaptive reasoning is the glue that holds
everything together, the lodestar that guides learning. "
(Kilpatrick 2001)
It is always beneficial to close the mental activity with one or more
reflective questions. These are used to reflect on what strategies were
used, what were most effective, which were most popular and what to do
next. They may also be used to make links with the real world and the
classroom maths world, an example of this is when the children are asked
to explain when they might use the strategy to help them in an everyday
situation or in their problem solving activities.
Guide for Planning Mental Routines
Although there are many mental routines included in this book you
will want to plan your own as you become confident in using them. The
following guidelines provide the framework for creating mental routines:
- Select a topic suited to your range of learners.
- Identify the strategies, and concepts you want the children to
learn.
- Think about the meta-language of those strategies and concepts,
perhaps listing key words or developmental levels (e.g. count all,
count on, skip count)
- Consider what concrete materials might make the routine
interesting and engaging for your learners.
- Pose three closed questions, one at each of the three broad levels
matched to your learners. Decide who you will target with each
question.
- Plan a flip activity that will make the children apply their
mathematical thinking in different ways.
- Plan reflection questions to ensure that the children see
connections and purpose in what they are learning as well as to
identify how they are processing.
- Review the questions to identify a possible routine.
While this may sound like a lot of effort you will find that it
allows for easy innovation and the creation of mental routines that can
last for several days and be returned to throughout the school year.
Bibliography
Kilpatrick, J., Swafford, J., and Bradford, F.,(2001) Adding
it Up: Helping Children Learn Mathematics National
Academy Press.
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