This document discusses mathematics education in the Primary Years Programme (PYP). It covers the PYP philosophy of mathematics, how children learn mathematics through constructing meaning, and the written, taught, and assessed curriculums. The PYP views mathematics as a tool for problem solving and sees it as intrinsically fascinating. Children should see themselves as mathematicians and construct their own understanding starting from personal experiences. Mathematics is best taught through relevant, real-life contexts. Assessment includes diagnostic, formative, and summative strategies to provide feedback during and after the learning process. Standardized tests are just one part of assessment and not meant to be taught to directly.

1. April 2014
Every Child Counts
Mathematics in the PYP

2. • Learning mathematics: the PYP philosophy
• How children learn mathematics
• The written curriculum
• The taught curriculum
• The assessed curriculum
Primary Parent Workshop

3. The PYP Definition of Curriculum

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

9. How children learn mathematics

10. constructing meaning
transferring meaning
applying with understanding
*See handout
How children learn mathematics

11. The PYP Definition of Curriculum

12. *Please see handout – Primary Mathematics Scope and Sequence

13. The PYP Definition of Curriculum

15. Learning Outcomes: Sort or match objects and talk about sorting. Explore the language and value of
numbers 1 to 10 using concrete materials

16. Learning Outcome: Relate addition to combining two groups and subtraction to taking away

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)

24. Learning Outcome: Read and plot coordinates in all four quadrants

25. Learning Outcome: Record using non standard units of measure

26. Learning Outcome: Record using non standard units of measure

27. Learning Outcome: Record using non standard units of measure

28. Learning Outcome: Sort and describe the properties of 2D shapes.

29. Learning Outcome: Sort and describe the properties of 2D shapes.

30. Learning Outcome: Record using non standard units of measure

31. Learning Outcome: Sort and re-sort objects using one attribute at a time. Sort a random collection and
explain own sorting.

32. Learning Outcome: Use concrete materials to demonstrate understanding of the language and value of
numbers 1-20

33. Learning Outcome: Estimate, measure and compare lengths, weights and capacities using standard
units

34. Learning Outcome: Understand what each digit represents in two and three digit numbers; partition
into hundreds, tens and ones.

35. Learning Outcome: Use Carroll, Venn and Tree diagrams to sort numbers or objects using one
criterion.

36. Learning Outcome: Add and subtract a single digit to and from a two-digit number.

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.

38. The PYP Definition of Curriculum

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

42. Assessment Strategies and Tools

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

48. Standardised
Score

49. Percentile Rank

50. UK National
Curriculum
Level

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

52. Data can be
used to
monitor EAL
groupings

53. Data can be
broken down
into
nationalities

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

56. Raising the profile of Mathematics at KICS

57. Raising the profile – ECIS Maths Quest Berlin