According to Piaget, exploration of color, size, shape, and texture can help to build a child’s “logico-mathematical” knowledge. This knowledge is used as the building blocks of early mathematical thinking. Piaget’s theory of development through well defined stages is based upon children developing concepts through their own interaction with the environment. So, for young children learning about math, this exploration takes place with everyday objects and everyday events. Teachers of young children are cautioned to use this understanding of knowledge building when teaching math and to develop a curriculum that involves “challenging problem-solving activities” so that children are not rushed through rote learning skills.

Piaget’s Concept of Conservation: The theory follows that each child must understand a concept before moving on toward understanding of the next. Piaget’s seven tasks of conservation are: number, length, liquid, mass, area, weight, volume. This theory is demonstrated in the above video. With this thinking, children must master the concept of conservation before they can use the abstract thinking needed to make complex comparisons. Piaget’s theory is that CLASSIFICATION, ORDER, AND SERIATION are good for instruction in the younger classrooms.

Ordering or Seriation: Piaget’s three stages of growth with ordering: 1 – random ordering, 2 – trial and error, and 3 – systematic, theorizes that children must progress through these stages before true ordering can be mastered. Number work and counting are “mechanical” but comparing sets (how many more, how many fewer) is only achievable after children can “conserve” numbers (theory of conservation).

Conversely, Montessori schools believe that giving children self-correcting ordering manipulatives to work with will improve their ordering abilities. And, that this skill can be learned at an earlier age with practice. Upon quickly studying some sites about Montessori theory, I found: “Maria Montessori said that a mathematical mind was “a sort of mind which is built up with exactity.” The mathematical mind tends to estimate, needs to quantify, to see identity, similarity, difference, and patterns, to make order and sequence and to control error.” (http://www.infomontessori.com/mathematics/introduction.htm) Materials used in the Montessori classroom support sensory experiences with math concepts. Working with these materials helps children “construct precise order” and make sense of it.

Even though there seem to be some differences in the pace at which children develop their math understandings, both Piaget and Montessori believe that manipulatives are necessary to make the learning concrete and more understandable.

**Katie – Even though there seem to be some differences in opinion with pacing and children’s development of math understandings, I think that both Piaget and Montessori believe that manipulatives are necessary to make the learning concrete and more understandable. **

**What did you note as significant differences or similarities? **