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 memorizing 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 generalize mathematical models, and recognize 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.

Matific fosters Critical Thinking by encouraging children to challenge definitions and conclusions. We push them to ask things such “When does this apply?” “What is necessary to make this statement”. We encourage children to need to be convinced, rather than accept rules at face value.

We build Critical Thinking skills with the following four pillars.

Developing Problem Solving Skills

Problem solving is at the heart of mathematics. It’s featured in curricula around the world, but teaching problem solving is difficult as there’s a fine line between challenge and frustration. Matific activities are specially designed to allow children to approach new problems and find new ways to solve problems, especially when there’s no clear algorithm.

Ensuring Accountability

The ability to monitor, and understand yourself is fundamental to the development of a child’s educational independence. Matific gives children an environment where they are able to understand their mistakes. We follow their mistakes to logical conclusions so they can see how and where they went wrong.

Identifying with the Mathematical Community

The Mathematical community can feel quite abstract from a children everyday life, but we want children to see the beauty in mathematics. At Matific we have created an environment where children feel comfortable asking questions, taking actions, and importantly as a contributor to mathematics.

Multiple Strategies, Multiple Solutions

In real life, problems have multiple solutions, and the same is true of mathematics. Infact, multiple strategies are a characteristic of complex problems. By enabling multiple strategies and solutions, we encourage creativity and the playfulness of mathematics. Matific presents problems with multiple ways to answer a problem, allowing children to reveal new insights, reach their own conclusions, and deepen their understanding of problems.

By placing mathematics in an authentic context that feels real to children, we allow them to see the importance of different mathematical concepts to their everyday life. This authenticity ensures that as greater and greater abstractions are introduced, children feel confident knowing how they fit in with their day to day lives.

Relevance to Children

Ensuring relevance is fundamental to ensuring ongoing engagement and motivation in mathematics. Too often mathematics comes across as an abstraction, divorces from children's everyday life. At Matific, we provide a continent that is intrinsically interesting to children. The content can be related to the movies they watch, the games they play, or the world around them. Our mathematics is relevant to their everyday life. We also create worlds and problems where children can use their imagination and playfulness. They should be able to imagine the world we are trying to show.

Authentic Settings

A key focus of Matific’s activities is to give intuition to the mathematical concept. The best way to do this is to rely on the intuitions that the children already have. We do this by relying on children’s natural, real life experiences. Our problems have been thoughtfully designed, and selected for children to learn, develop, and consolidate new ideas across a range of realistic situations. We avoid contrived situations where the examples don’t reflect real life such as if talking about the number 6, we’ll show six eggs in a carton as opposed to 6 mushrooms in a forest.

Intrinsic Feedback

Traditional feedback in education is an external force telling the child “You’re wrong”, but providing meaningful context also means providing intrinsic, contextual feedback. At Matific we provide intrinsic feedback that is inherent to the environment of the problem. The feedback is directly derived from the actions the child took and it is not an outside verdict.

Each child learns in unique ways, from different learning speeds, to different learning styles. By providing the right question at the right time we are able to let every child follow their own learning pathway. By providing a learning environment where children are able to take ownership of their learning, we not only foster independence, but also ensure that, whatever their learning needs, children can approach each question in the way that suits their ability.

Individualized Journeys

Matific’s activities have been carefully designed to ensure children are able to complete at their own pace and in their own manner. This means, unless we’re asking children to practice their fluency we don’t use time constraints. We allow children to return to an activity as many times as they want to improve their score. We believe children need time and place to absorb the subjects, and conquer the challenges they face.

Thriving in a Heterogenous Classroom

Thriving in a multi-ability classroom is tough at the best of times for both children and teachers. Matific provides a number of different tools to not just manage but flourish in these classroom environments.

Personalized Feedback and Hints

Feedback is a fundamental part of the learning process, but too little or too much information in the feedback doesn’t help the child understand their mistake nor the problem. At Matific, we use the answers the child gives to provide effective, and personalized feedback that takes into account the child’s actual answer ensuring just-in-time intervention.

Ensuring children are authentically engaged with mathematics is the fundamental to building the foundations to a lifetime of mathematics. At Matific, we challenge ourselves to create fun content. You might say that Matific is a place where children want to hang out. The characters are enticing, the situations are intriguing, and the problems are accessible. You want to stick around to see the end of the story. At the same time, we are always cautious to ensure that this engaging user experience does not overshadow the pedagogy.

Reduce Anxiety

When there is only one answer, it is glaringly clear when an answer is wrong. This, coupled with a culture where failure is linked to low intelligence, causes mathematics anxiety in children; in turn leading them to abstain from mathematics in higher years.
A sense of competence and confidence is crucial for learning, at Matific we use a gamified environment to provide an environment for exploration, reducing anxiety.

Arouse Curiosity and Letting Perseverance Flourish

Fostering an environment where children are free to exercise their curiosity and galvanize their perseverance is an important part of ensuring a nurturing educational environment. We do this by giving children a large degree of control over their progress, giving them the freedom to explore, to decide what to do, and how to progress. We also make our activities challenging, yet engaging. We provide multiple chances to answer and encourage children to want to see through to the end.

Provide Freedom to Fail

True learning is only realized through productive struggle, where one is confronted with a challenge, you fail several times, and then overcome it.
At Matific, we use the metaphor of the gamified environment to ensure children are not afraid to fail. Just like in the games they play, failure is part of the process of overcoming and progressing through problems. By using Matific, children see that errors are no longer a threat, but a natural learning process.

Exploit the Technology to Achieve Inherent Engagement

Technology gives us so much opportunity to enhance the educational experience but most commercial providers supply no more than digital worksheets. At Matific, we push technology to the limits to provide thousands of teaching aids, virtual laboratories, and interactive environments.

Learn by Doing

The quote from Confucius, “What I hear I forget, what I see I remember, what I do I understand” applies so much to modern instruction. Studies have shown that active, hands-on learning is far more effective than passive learning.
At Matific, we provide problems with interactive components allowing children to acquire knowledge for themselves, allowing “Aha” moments to emerge.