Pedagogy: Conceptual Learning vs. Memorization

Conceptual learning in mathematics focuses on teaching math by concepts rather than asking students to memorize isolated facts, methods, or formulas. Concepts are the big ideas or the "why's" related to solving math problems. Addition/subtraction and decimals/fractions are both recognizable examples.

Another way to look at conceptual learning is that it means teaching math as a language. If you have ever learned another language, you know that the best approach is to experience speaking in the context of that language. With Elephant Learning, we provide your students with mathematical experiences that we can place language around. These activities build intuition in mathematics by providing a safe space for children to play with the concepts using the puzzles on the screen.

The philosophy behind teaching conceptually is that students who learn this way understand mathematical ideas and then transfer their understanding to new contexts and problems.

As a teacher, you know that as children learn concepts and develop intuition, the classroom experience is enhanced with a deeper understanding of the concepts. Math time becomes enjoyable when students are not memorizing procedures but learning a new way to solve problems. We like to say: Empowerment is understanding the concepts. Enjoyment in a classroom setting is understanding the teacher. Elephant Learning can help you achieve both in your classroom.

Elephant Learning helps you lift your students beyond mere memorization and makes it far easier for you, as a classroom teacher, to move onto more challenging concepts. The app focuses on ensuring your child fully understands each concept. This is critical because, in mathematics, these concepts build on each other. You need to master the first set of concepts to progress to the next set. For example, your child needs to understand addition before they learn multiplication.

Take the concept of multiplication, for example. The memorization of multiplication tables does not demonstrate mastery of the concept. Students who merely memorize multiplication may later struggle with exponents, area, or volume. If you show a student four groups of five things and ask them how many, can they provide the answer, or do they have to count? The student who provides the solution immediately understands the concept of multiplication. The student who counts may quickly give the right answer if instead, they are asked what four times five equals. But this student has only memorized the answer. They don't truly understand the concept of multiplication.

We see this problem very often. It is why children struggle with word problems and experience difficulties when they get to algebra. Math class becomes a stressful exercise in memorizing random facts. That is the reality for many of our children, and it is a cruel situation to be in. It is why almost half of the first and second graders report having math anxiety. They tell themselves they are not a "numbers person" and decide not to learn math.

Children understand later in life how to use multiplication to solve these problems, and that is the saddest part: they did not know when it could have made a difference. These concepts are not difficult to grasp (nor are they innate), and our software presents activities that are known to teach these concepts in a safe environment where there is no judgment or biases. We allow children to develop an intuition for mathematics.

Elephant Learning also makes it easy for you, as the classroom teacher, to understand which concepts your students are struggling with, collectively or individually. You can drill down to individual questions and even try them for yourself or with the student to find out exactly where their understanding is faltering. Teachers find this ability to drill down particularly helpful in assessing a student's strengths and weaknesses but also in determining the next steps for assisting each student. We also provide printable worksheets that you can use to reinforce each concept further.

The philosophy behind teaching conceptually is that students who learn this way understand mathematical ideas and then transfer their understanding of these ideas to new contexts and problems. This same philosophy of definition, recognition, and production continues through higher levels of mathematics.

In other words, conceptualized learning prepares children for long-term success in mathematics.