How Children Learn Mathematics

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. 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.

Constructing Meaning: Students construct meaning from direct experiences such as using equipment or materials and explaining or exploring.

Transferring Meaning: Students begin to connect symbols with objects and mathematical processes.

Understanding and Applying: Through authentic activities, students independently select and use appropriate symbols and processes to record their thinking.

Overall Mathematics Expectations
At YIS the students will be taking part in learning experiences that encompass five strands of mathematics: data handling, shape and space, pattern and function, measurement, and number.

Kindergarten - Grade 2

Across the five strands of mathematics, students will be doing the following:

Data handling
  • Expressing how information can be as organized and structured as data and that this can occur in a range of ways.
  • Collecting and representing data in different types of graphs.
  • Interpreting the resulting information for the purpose of answering questions.
  • Developing an understanding that some events in daily life are more likely to happen than others identifying and describing likelihood using appropriate vocabulary.
  • Measuring and describing objects and events using standard units.
  • Using both estimation for approximating measurements, and particular tools for measuring and describing attributes of objects and events with more accuracy.
  • Developing an understanding of length, mass, capacity, money, temperature and time.
Shape and space
  • Classifying and naming 2D and 3D shapes according to their properties.
  • Identifying symmetry and transformations in the immediate environment.
  • Interpreting, creating and using simple directions and specific vocabulary to describe paths, regions, positions and boundaries of the immediate environment.
Pattern and function
  • Observing and describing patterns and relationships that whole numbers exhibit.
  • Using numbers and other symbol to represent patterns.
  • Investigating the inverse relationship between addition and subtraction, and the associative and commutative properties of addition.
  • Representing and making sense of real-life situations.
  • Solving problems involving addition and subtraction.
  • Developing their understanding of the base 10 place value system.
  • Modelling, reading, writing, estimating, comparing and ordering numbers to hundreds or beyond.
  • Recalling addition and subtraction facts.
  • Modelling addition and subtraction of whole numbers using the appropriate mathematical language to describe their mental and written strategies.
  • Understanding fractions as representations of whole-part relationships and using fraction names in real-life situations.

Grades 3 - 5

Across the five strands of mathematics, students will be doing the following:

Data handling
  • Collecting, organizing and displaying data for the purposes of valid interpretation and communication.
  • Using the mode, median, mean and range to summarize a set of data.
  • Creating and manipulating an electronic database for their own purposes, including setting up spreadsheets and using simple formulas to create graphs.
  • Understanding that probability can be expressed on a scale (0–1 or 0%–100%) and that the probability of an event can be predicted theoretically.
  • Understanding that a range of procedures exists to measure different attributes of objects and events, for example, the use of formulas for finding area, perimeter and volume.
  • Deciding on the level of accuracy required for measuring and using decimal and fraction notation when precise measurements are necessary.
  • Demonstrating their understanding of angles as a measure of rotation, by measuring and constructing angles.
Shape and space
  • Understanding the properties of regular and irregular polyhedra.
  • Understanding the properties of 2D shapes
  • Understanding that 2D representations of 3D objects can be used to visualize and solve problems in the r eal world, for example, through the use of drawing and modelling.
  • Developing their understanding of the use of scale (ratio) to enlarge and reduce shapes.
  • Applying the language and notation of bearing to describe direction and position.
Pattern and function
  • Understanding that patterns can be represented, analysed and generalized using algebraic expressions, equations or functions.
  • Using words, tables, graphs and, where possible, symbolic rules to analyse and represent patterns.
  • Developing an understanding of exponential notation as a way to express repeated produc ts, and of the inverse relationship that exists between exponents and roots.
  • Using their understanding of pattern and function to represent and make sense of real-life situations and to solve problems involving the four operations.
  • Understanding that the base 10 place value system extends infinitely in two directions
  • Modelling, comparing, reading, writing and ordering numbers to millions or beyond, as well as model integers.
  • Developing an understanding of ratios.
  • Understanding that fractions, decimals and percentages are ways of representing whole-part relationships
  • Modelling, comparing, reading, writing, ordering and converting fractions, decimals and percentages.
  • Using mental and written strategies to solve problems involving whole numbers, fractions and decimals in real-life situations.

The above is an extract taken from the IB Mathematics Scope and Sequence (2009) that explains how children learn mathematics in the PYP.