The iLEAD math rational is based on cognitive psychology which states that students best learn by first constructing meaning, then transferring the meaning into signs and symbols, and finally applying and showing understanding. This means that teachers need to first create that hands on learning where they construct meaning from direct experiences using manipulatives, then transfer these into the algorithms, which then lead to students learning how to explain their answers explain the process and apply these processes.

Singapore math follows this exact philosophy. It is all about the teacher creating meaningful hands-on experiences that build the concrete concepts in math. This is followed by the pictorial representation which develops the math vocabulary and furthers the students understanding of the concepts. Students are then led to the abstract representation and are required to solve problems using a variety of methods. Furthermore Singapore math focuses on the reasoning and explanations which is the basis of all common core standards.

Learning does not mean simply receiving and remembering a transmitted message; instead, “educational research offers compelling evidence that students learn mathematics well only when they construct their own mathematical understanding” (Mathematical Sciences Education Board, 1989, p. 58). When educators begin to see learning as knowledge construction, they change their thinking about curriculum, instruction, and assessment, developing more powerful approaches to connecting thinking and mathematics and designing more mathematically significant instructional learning experiences. Such learning experiences are:

  • Hands-on, involving students in really doing mathematics – experimenting first-hand with physical objects in the environment and having concrete experience before learning abstract mathematical concepts;
  • Minds-on, focusing on the core concepts and critical thinking processes needed for students to create and re-create mathematical concepts and relationships in their own minds;
  • Authentic, allowing students to explore, discover, discuss, and meaningfully construct mathematical concepts and relationships in contexts that involve real-world problems and projects that are relevant and interesting to the learner.