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Innovamat’s didactic sequence and each of our activities are based on principles drawn from the most rigorous educational research. We have centralized all this research in the White Paper, a document where we dive into key concepts such as mathematical richness, learning trajectories, the use of manipulatives, the importance of addressing diversity, and assessment as a tool to improve the educational experience in the math classroom.
Mathematical knowledge must be built from understanding, through exploration, manipulation, experimentation, and discovery, with the teacher as a guide. In particular, manipulation and experimentation are essential components of the learning process, regardless of the student’s age.
Social interaction and conversation are essential to build conceptual understanding, at any stage.
All mathematical knowledge is interconnected, and these connections need to be encouraged. Content must be discovered following a spiral sequence of rich activities and practiced to develop fluency. Then, knowledge must be consolidated to move towards abstraction.
A context is relevant for the student when a challenging situation arises, sparking curiosity without the need to focus on personal interests. Connections between math and other areas can build meaning and relevance.
Arithmetic fluency, understood as efficiency, flexibility, and accuracy when dealing with numbers and performing operations, is key to students’ mathematical success. It is essential to invest time in the classroom to clearly explain different strategies and practice them in various contexts, in order to automate the basic facts for each stage. Practice is necessary for the development of fluency. Also, it is important not to introduce algorithms prematurely, to prevent cognitive passivity.
Math is for everyone; anyone can do math and feel satisfied as a result. Activities should be designed from a “low threshold, high ceiling, wide walls” perspective to provide differentiated instruction in the classroom, giving everyone the opportunity to take part and make progress.
Assessment should be a means to regulate the teaching and learning processes, to identify successes, difficulties, and mistakes, and to find ways to move forward. While it is necessary to focus assessment efforts on learning content, it is equally important to pay attention to processes or competencies as well as socioemotional skills. Assessment is an ongoing attitude that combines the collection of enduring evidence with the gathering of ephemeral evidence.
When technology is used to promote learning, it adds differential value to the personalization and generation of valuable data. In turn, these data help educators to adapt their teaching to better support their students. It plays a key role in systematic and reproductive practice, enabling personalization and autonomous work.
Teachers play a crucial role in guiding and assessing students throughout their education. It is essential for them to view mistakes as a learning opportunity and value them as such. They should also foster an environment in which students feel challenged and learn how to handle their mistakes without getting frustrated. Finally, teachers need to engage in constant training and must transmit a passion for math.
Achieving competency-based math learning requires a shift in perspective, as well as the active and collaborative participation of the entire educational community: teachers, students, and families.
All the resources we offer are based on existing theoretical research frameworks in the field of math education and validated in the classroom. We continuously conduct rigorous research to test, improve, and iterate the resources we develop.
