Multiple Ways of Knowing - The IT Education Company

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The best practices in developmental psychology and cognitive science are the cornerstones of Symphony Math®. The uniquely designed delivery methods ensure that students – regardless of learning styles or knowledge levels – fully grasp fundamental mathematical ideas, even for difficult-to-explain and abstract concepts.

Multiple representations of each concept, including: story problems, auditory sentences, and visual models, integrate with a structured conceptual sequence to help students visualise, reinforce, and apply ideas quickly and accurately.

The result is a solid foundation for acquiring higher math skills, as well as a positive learning experience.

Conceptually understand what the concept "looks like"
Explicitly connect symbols to visual representations
Understand concepts at abstract levels
Auditory Sentences
Learn the formal language of math
Apply learning to real life problem solving
Develop cluncy in recall of number relationships


Math is learned in a structured approach, that bridges each concept to the previous one.

These underlying “big ideas” provide the foundation for mathematical learning. As students master each big idea before moving on to the next, they learn to succeed with more complicated math later on.

Mathematical TopicUnderlying Big Ideas
Hierarchical grouping
Repeated equal grouping
Hierarchical grouping coordinated with parts-to-whole
Repeated equal grouping coordinated with parts-to-whole


Models aren’t just kids play! The visual math that students learn in their early years can support math success well into their adult lives.

Visual models used in Symphony math include:
ModelUsage Examples
Number Bars
Number bars are a tool to represent magnitude. Students will progress to connect their understanding of magnitude to Parts-to-Whole, and Addition, and actively construct number sentences.
Dot Cards
Number sequence can be represented through models that show groups of discrete objects such as the dots on dot cards. Students will progress from counting dots to ‘subitising’ (or looking at cards and instantly tell ‘how many’ the card represents), and actively construct number sentences.
Number Lines
As students begin to become more comfortable with numbers, the Number Line is introduced. As with Number Bars and Dot Cards, Number Lines are used to construct number sentences. The Number Line is a very common model in math.
Fraction Bars
Students are introduced to fractions with simple models that can be divided into equal parts and filled. Students will progress to create the whole that will result from the sum of their parts. Later students will use only symbols, and then word problems, to demonstrate their mastery of addition with fractions.
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