Problem Solving and Reasoning CDP DVD For Years 1 to 6 Developing a reasoning classroom Written by...
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Problem Solving and Reasoning CDP DVD For Years 1 to 6 Developing a reasoning classroom Written by Tim Handley (Mathematics Specialist Teacher, NCETM Professional
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Written by Tim Handley
(Mathematics Specialist Teacher, NCETM Professional Development
Lead and author of Problem Solving and Reasoning)
Slide 2
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Aims Understand what reasoning is
and why it is important. Explore some reasoning activities. Explore
ways in which reasoning can become part of day-to-day
teaching.
Slide 3
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Running order Introduction: What
do our children already do? Taking a slice: a non-numerical
activity What is reasoning and why is it important? Reasoning in
the past week Graffiti Maths with Chicken Nuggets: a numerical
activity Break Childrens mathematical superpowers Key strategies to
make reasoning part of day-to-day life in our classrooms Planning a
reasoning activity Next steps
Slide 4
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom What do children in our school
already do? Have a look at the statements on the progression cards
from http://nrich.maths.org/6105. http://nrich.maths.org/6105
Highlight them green if children in your year group do these
regularly and independently. Highlight them orange if children in
your year group do these regularly but require support. Leave them
blank if children in your year group struggle to do these, or only
do them infrequently. Then identify the 4 statements which you
consider to be age appropriate, but which children in your year
group struggle with the most and mark these with a star.
Slide 5
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom What can children do
independently? What do they find difficult?
Slide 6
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Take a slice: a non-numerical
activity Here is one way of splitting a 4 x 4 board into 2
identical pieces: How many other ways can you find?
Slide 7
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Take a slice: a non-numerical
activity So, what were you doing? What key phrases were you using?
What were you thinking? We were all reasoning! Things to think
about
Slide 8
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom So, what is reasoning? Some things
reasoning can be seen as: Thinking about mathematics Making
connections Application of facts and knowledge either explicitly or
implicitly Justifying Convincing yourself and others
Slide 9
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Why is reasoning important ? What
do you think?
Slide 10
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom What OTHERS say...
Slide 11
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Academics In our understanding, we
have two components the range of mental representations and the
reasoning linking them together. Therefore we must also develop the
reasoning that we carry out between representations. Barnaby et al,
Primary Mathematics, Teaching for understanding. And lots, lots
more
Slide 12
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Examiners Just some of the
questions that require children to reason from the 2009 KS1 + 2012
KS2 SATs tests.
Slide 13
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Ofsted The reports Mathematics:
made to measure (Ofsted, 2012) and Good practice in primary
mathematics: evidence from 20 successful schools (Ofsted, 2011)
make clear that: Real mathematical thinking lies at the heart of
learning mathematics. It involves making sense of mathematics
through engagement, reasoning and making connections. Sometimes
this may involve significant challenge in terms of the requirement
to think. But it is only through their own thinking that children
will develop real depth of learning.
Slide 14
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Ofsted Maths subject-specific
criteria Outstanding Pupils understand core concepts and make
connections. They think for themselves. They show exceptional
independence when solving problems in a range of contexts. They
think for themselves and persevere with challenges, knowing they
will succeed. They embrace the value of learning from mistakes and
false starts. They reason, generalise and make sense of solutions.
Requires improvement Children use techniques correctly. They have
an insecure understanding of concepts. They solve routine problems
in known contexts. They follow the teachers example. They avoid
making mistakes.
Slide 15
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom The DfE: 2014 National Curriculum
Aims It is expected that these aims are applied throughout the
programmes of study.
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Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom How have our children been
reasoning over the past week? Share with your table!
Slide 17
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Graffiti maths is an approach to
problem solving and reasoning tasks which encourages children to
think and work big. See page 12 of the Introduction in the Problem
Solving and Reasoning books for an explanation of how it works. See
the Key Strategies Maths Stories section on the DVD for footage of
Graffiti maths in action. Graffiti maths Now use the graffiti maths
approach to try out the Chicken nuggets problem from Problem
Solving and Reasoning Year 5.
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Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom BREAK!
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Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Mathematical Superpowers All
children have them!
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Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Conjecturing and Convincing
Specialising and Generalising Imagining and Expressing Organising
and Classifying See page 8 of the Introduction in the Problem
Solving and Reasoning books for more details. Mathematical
superpowers John Mason identified a set of 8 Mathematical Powers
that all children posses. They come in pairs:
Slide 21
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom The Story of a Number An easy way
to get children reasoning, pattern spotting and generalising. Watch
the Maths Stories clip on the DVD.
Slide 22
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Money boxes Try the Money boxes
problem from Problem Solving and Reasoning Year 3. Can you work out
how much money could be in each money box? If we know that half of
the coins are 1, what else do we know? Which of these clues are
hard/easy to solve? Why? Which of the clues is the odd one out why?
Add in questions to draw out the reasoning
Slide 23
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Key strategies To help include
reasoning as part of our day-to-day teaching. The Problem Solving
and Reasoning books include 14 key strategies. Watch the clips on
the DVD.
Slide 24
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Always, sometimes, never Always,
sometimes, never can also be used as part of shared learning. Can
you come up with some always, sometimes, never statements for your
year group? Look at the statements from the Number Knowledge
problem Resource Sheet 13.1 from Problem Solving and Reasoning Year
6. Discuss with your partner. Are they always, sometimes or never
true? Make sure you give examples.
Slide 25
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Other examples for always,
sometimes, never The picture on a pictogram represents one piece of
data. If the answer is in cm 2 you are measuring area. The
diagonals of a quadrilateral bisect each other. Two negatives make
a positive. All multiples of 3 have a digital root of 3, 6 or
9.
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Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Another, another, another An even
number Number with the product of 60 Factors of 36 A triangle A
prime number Draw out the links and generalisations between the
sets generated.
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Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Convince me... All angles in a
triangle always add up to 180 degrees. That the next whole number
after 119 will be 120. That coordinates are useful for identifying
points. An odd number plus an odd number always equals an even
number. That the area of a rectangle divided by the length of one
side gives the length of the other side.
Slide 28
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Hard and easy A calculation whose
answer is 7 A three digit subtraction A word problem A region made
up of rectangles whose area and perimeter are to be found A
calculation to be carried out on a calculator
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Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom If this is the answer, whats the
question? 24 Impossible No Square numbers 15.3
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Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Odd one out (and why?) 3, 6, 9 3 x
10 = 30, 31 x 10 = 310, 423 x 10 = 4230, 0.3 x 10 = 3, 1111 x 10 =
11 110 1 / 4, 8 / 36, 6 / 32, 10 / 40 11, 101, 1001, 101
Slide 31
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom POGs: Peculiar, Obvious, General A
quadrilateral A multiple of 2 A factor of 36 A fraction equivalent
to A number A set of 3 numbers with a product of 10
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Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom What do you notice? 2, 4, 6, 8,
10, 12, 14, 16 2, 3, 5, 7, 11,13 (Can you give me more in this
set?) 1 / 2, 2 / 4, 3 / 6, 4 / 8 4, 9, 16, 25, 36,
Slide 33
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom What else do we know? (and why?) 5
x 8 = 40 3 + 4 =7 1 cm = 10 mm, 2 cm = 20 mm All even numbers end
in an even digit: give me an even number over 1000. 50 is 5 lots of
10, 40 is 4 lots of 10, 1 / 2 = 2 / 4 = 4 / 8 = 3 / 6
Slide 34
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Whats the same? Whats different?
One and 1 9 and 18 Multiples of 3 and Multiples of 6 1 / 2, 0.5,
50%, 4:8, 3 / 6, 1:2 Square numbers and numbers that are not
square
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Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Whats the same? Whats different ?
Choose any two of the three. In what way are they the same as each
other and different from the third?
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Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Zooming in Write down a: Multiple
of 4... ... that is greater than 30... ... that is also square...
... where both digits are even. Draw a: Quadrilateral... ... that
has at least one line of symmetry... ... and only one pair of
parallel sides... ... and at least one acute angle.
Slide 37
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Is it a good explanation of? Is
having three sides a good explanation of a triangle? Is adding a
zero a good explanation of multiplying by 10? Is a shape with 4
sides a good explanation of a square? Is moving the digits 3 places
to the left a good explanation of multiplying 1.3 by 1000?
Slide 38
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Planning a reasoning activity In
your year group, plan a reasoning activity that you could use next
week. This could be a key question, it could use one of the
strategies weve just looked at, or be a full lesson activity.
Slide 39
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Next steps Encourage and support
our children to reason! Over the next 2 weeks, ensure there are at
least 6 opportunities for your children to reason. Try also to
include reasoning and some of the key strategies in other
subjects.
Slide 40
Problem Solving and Reasoning CDP DVD For Years 1 to 6
Developing a reasoning classroom Resources to help 14 key
strategies with example questions for each year 18 activities and
investigations per year level