The New Curriculum – An opportunity for creativity
Learning
Overview
When talking about the new curriculum, Mick Waters of QCA contrasts deep
learning with lily-pad learning (in which learners skim across the surface and
eventually sink). This unit invites you to consider your own beliefs about
learning mathematics and the role of the teacher in facilitating deep learning.
Where are you now?
In Improving learning in Mathematics: Challenges and Strategies (part of the
Improving Learning in Mathematics pack by the Standards Unit, available from
the NCETM), Malcolm Swan identifies two opposing beliefs about learning in
mathematics.
In pairs, first, describe a lesson you’ve seen or taught that exemplifies first
one, then the other of these beliefs.
Then, using appendix 2, mark on the first scale where a student in your
classroom would assume your beliefs about learning in mathematics to be
given their experience in your lessons. Mark on the second scale where your
belief about learning in mathematics is at the moment
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Activities
Watch the video.
Activity A
In the video, George says that his aim is to ’get the students being
independent learners, thinking for themselves, asking questions they wouldn’t
actually think of if you just gave them a traditional, book-led lesson’.
In Improving learning in mathematics, Malcolm Swan states:
Our model of learning should not be confused with that of
‘discovery’ teaching, where the teacher simply presents tasks and
expects learners to explore and discover the ideas for themselves.
We see the teacher as having a much more pro-active role than
this.
In pairs or as a small group, discuss the role of the teacher in the activities on
the video.
Activity B
Malcolm Swan states:
The teacher’s role in our model is to:
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assess learners and make constructive use of prior knowledg
choose appropriate challenges for learners
make the purposes of activities clear
help learners to see how they should work together in profitable
ways
encourage learners to explore and exchange ideas in an unhurried,
reflective atmosphere
encourage the discussion of alternative methods and
understandings, examining their strengths and weaknesses
remove the ‘fear of failure’ by welcoming mistakes as learning
opportunities rather than problems to avoid
challenge learners through effective, probing questions
manage small group and whole group discussions
draw out the important ideas in each session
help learners to make connections between their ideas.
(These are also listed in appendix 3.)
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In pairs, allocate one person to be Person X and one to be Person Y.
Person X should choose one of the above aspects of the teacher’s role and
argue that this is not beneficial for students. Person Y argues that it is
beneficial.
If time permits, you might choose to swap roles and argue for and against a
different aspect of the teacher’s role in learning mathematics.
Activity C
In the video, George says:
You can’t just dive into this sort of freedom . . . you have to
wean them into it.
In pairs or small groups consider strategies that you can use in your everyday
teaching that will help students to develop independence, discussion and group
work skills. You might find it useful to consider a favourite textbook exercise or
activity and think of ways to adapt this.
Reflection
Look back at the way you marked your beliefs about learning in mathematics
and the way that your students would perceive your beliefs to be. Is there a
difference? How will your discussion today help you to address any difference?
Implementing and continuing to learn
Think about a lesson you’re going to teach tomorrow. Consider a short episode
of this lesson; what will you do to promote the independent thinking and deep
learning discussed in the video?
Web links
QCA programme of study (www.curriculum.qca.org.uk)
Improving Teaching and Learning in Mathematics: Challenges and Strategies
by Malcolm Swan
(http://www.maths4life.org/uploads/documents/doc_187.pdf)
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Appendix 1: Resume of lessons
George Hardy (The Northampton Academy) works on a project with his Year
10 class that focuses on students finding the volume and surface area of
composite shapes using the cone and sphere.
Amy Rouse (West Park School, Derby) runs a project with her Year 10 class,
who are required to plan a healthy week for themselves or for a partner.
Karen Hancock (Oriel High School, Crawley) uses the context of the
frequencies of musical notes to encourage her Year 10 class to develop a
deeper understanding of ratios, powers and roots.
Dominic Hudson (West Park School, Derby) introduces his Year 7 class to an
annual unit of work called ‘The Great West Park Getaway’, in which students
plan how to get as far as possible from their school while spending only £50.
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Appendix 2: Learning in mathematics is . . .
From their experiences of my lessons a student in my class would mark my
belief as (mark a point on the scale):
I believe learning in mathematics is (mark a point on the scale):
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Appendix 3: The role of the teacher
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