2. • Learning mathematics: the PYP philosophy
• How children learn mathematics
• The written curriculum
• The taught curriculum
• The assessed curriculum
Primary Parent Workshop
5. The power of mathematics for describing and
analysing the world around us is such that it has
become a highly effective tool for solving
problems. It is also recognized that students can
appreciate the intrinsic fascination of
mathematics and explore the world through its
unique perceptions.
Learning Mathematics – The PYP Philosophy
6. In the same way that students describe
themselves as “authors” or “artists”, a school’s
programme should also provide students with
the opportunity to see themselves as
“mathematicians”, where they enjoy and are
enthusiastic when exploring and learning about
mathematics.
Learning Mathematics – The PYP Philosophy
7. It is important that learners acquire
mathematical understanding by constructing
their own meaning through ever-increasing
levels of abstraction, starting with exploring
their own personal experiences, understandings
and knowledge.
How children learn mathematics
8. Additionally, it is fundamental to the philosophy
of the PYP that, since it is to be used in real-life
situations, mathematics needs to be taught in
relevant, realistic contexts, rather than by
attempting to impart a fixed body of knowledge
directly to students. How children learn
mathematics can be described using the
following stages (see figure 1).
How children learn mathematics
17. Learning Outcome: Understand what each digit represents in two and three digit numbers; partition
into hundreds, tens and ones.
18. Learning Outcome: Find halves, quarters, thirds, fifths, eighths and tenths of shapes and numbers.
19. Learning Outcome: Find halves, quarters, thirds, fifths, eighths and tenths of shapes and numbers.
20. Learning Outcome: Find halves, quarters, thirds, fifths, eighths and tenths of shapes and numbers.
21. Learning Outcome: Measure angles; describe and estimate the size of angles and classify them as
acute, right or obtuse
22. Learning Outcome: Measure angles; describe and estimate the size of angles and classify them as
acute, right or obtuse
23. Learning Outcome: Identify relationships between numbers and make generalized statements using
words, symbols and letters, e.g. the second number is twice the first number plus 5 (n, 2n +5)
37. Learning Outcome: Compare lengths and weights by direct comparison, then by using uniform non-
standard units. Use comparative language, e.g. longer, shorter, heavier and lighter.
39. Diagnostic
Diagnostic assessment can help identify
students’ current knowledge of a subject, their
skill sets and capabilities, and to clarify
misconceptions before teaching takes place
Knowing students’ strengths and weaknesses
can helps teachers better plan what to teach and
how to teach it.
Assessment
40. Formative
Formative assessment provides feedback and
information during the instructional process,
while learning is taking place, and while learning
is occurring.
Assessment
41. Summative
Summative assessment takes place after the
learning has been completed and provides
information and feedback that sums up the
teaching and learning process. Typically, no
more formal learning is taking place at this
stage, other than incidental learning which
might take place through the completion of
projects and assignments.
Assessment
43. ‘Testing is a small part of assessment. It needs to
be part of the picture. A good test has a role to
play. The language that we like to use is, it's an
audit. It's a snapshot. You don't run your
business for the audit. You want more than a
snapshot, you want a whole family album. But
the audit and the snapshot have a place in the
larger picture.’
Grant Wiggins - Defining Assessment
Distinction between ‘testing’ and ‘assessment’
44. • Standardised testing is one small part of a
comprehensive process of assessment
• We use standardised tests with the
understanding that they are simplistic and
generic but they also provide quick and easy
way to measure basic skills in core subjects
• Teachers do not ‘teach to the test’
Assessment at KICS
45. • For tracking student progress over time
• To highlight strengths and weaknesses in
curricular provision
• As a performance indicator of teaching and
learning – class, year group or school
• To compare cohorts of students (EAL, gender,
nationality etc.)
• To provide an external benchmark for the
purposes of quality assurance
How test data is used
46. • Provide standardised score and percentile
ranking
• Completed at beginning and end of year
• Results are automatically delivered as soon as
tests are complete
• Instant detailed diagnostic reports
GL Online Assessments
51. Standardised Results indicating Value Added from class mean average scores
Class September 2010 June 2011 Value Added
A 89 101 +12
B 99 111 +12
C 93 103 +10
D 98 107 +9
E 100 107 +7
F 102 108 +6
G 94 100 +6
H 91 95 +4
I 94 97 +3
J 103 105 +2
55. 85
90
95
100
105
110
115
Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8
StandardisedScore
Year Level
UK
Expected
Expected IS Results with high EAL Population