Develop an understanding of the foundational building blocks of math, taking knowledge beyond procedures and formulas.
Conceptual Understanding is the linking of separate elements of mathematical knowledge into a holistic comprehension of a specific topic. In a nutshell, it’s the why behind an answer.
We underpin our focus on developing conceptual understanding with five principles.
Progressing from Concrete to Abstract
Mathematics is a world of abstractions, but in order to develop real, authentic conceptual understanding and not just follow algorithms, we need to go through all levels of abstractions, from the very concrete, to the very abstract. Matific’s activities are developed in such a way, that children are taken on a path from the very real, and concrete representations of mathematics, through gradual steps through symbolism, to an end where a child can solve a problem even in the abstract. This progression ensures children aren’t just memorising a procedure but actually understanding what the procedure means.
The Need for Multiple Metaphors
When teaching a mathematical concept, to develop true understanding we must use multiple metaphors. By using multiple metaphors we help children generalise mathematical models, and recognise the suitable mathematical model of unfamiliar problems they encounter.
Spiral Learning and Seeding Ahead
We put great emphasis on seeding ahead to lay foundations prior to formal teaching. Whenever possible we try to demonstrate more intuitive variations of a concept to help children understand the essence of it. This strengthens the child’s confidence, helps with their problem solving skills, and buttresses against mathematics anxiety.
Making Connections across Subjects
Mathematics books and curricula break learning material into a collection of skills. This classification of topics helps us build a learning progression, but we need to remind ourselves that things are interconnected and topics don’t stand in isolation. At Matific, we embrace the interconnectedness between the topics because to develop deep understanding, it’s important to understand not just the what, but the why, when and how.
Effective and Informative Feedback
Matific uses a 3 step, wrong answer sequence to provide just-in-time intervention that encourages children to review their mistake and try again. We provide illustrated suggestions, and if needed, provide the suggested steps to solve a problem. This gives children the tools to answer the next problem correctly.