Developing math skills is constantly at the center of concern for many educators and parents. The content area is like a new language with rules to apply in unknown contexts. Providing children with precise and accurate language while working on math skills is crucial in developing their confidence, capacity to compound knowledge, and healthily progress.
Arithmetic, the study of properties and manipulation of numbers, is the entry point to computation, which is approached around age five. Our Research Development team has determined that children would highly benefit from explicitly learning the terminology of the four operation processes (addition, subtraction, multiplication, and division). When children are offered an opportunity to learn through the use of concrete manipulatives, such as those we created for our Wooden Mathematical Terms material, they stay active in their learning and can retrieve their knowledge by remembering this experience.
Mathematical Terms – Wooden Material
Our new material, Wooden Mathematical Terms and Nomenclatures Cards 6-9, is a way for learners to organize knowledge as one always does in Montessori settings. Our set consists of wooden tiles with arithmetic terms and signs, and nomenclature cards with definitions and illustrations. Learners use the wooden tiles in the form of a mind map to reconstruct and recall the order in which equations are laid out. They develop a deeper understanding of the relationship between numbers with an equation and how certain equations relate to others. For example, by comparing and contrasting multiplication and division, children understand inversed operations such as 3 x 4 = 12 and 12 ÷ 4 = 3. They can also comprehend math properties such as commutative law. For example, in addition, multiplication, addends, and factors are interchangeable (4 x 3 or 4 x 3 always equals 12). The same is not true for subtraction and division. We cannot interchange a minuend and a subtrahend (4 – 2 or 2 – 4) or a divisor and a dividend (8 ÷ 2 or 2 ÷ 8) and expect the same result. By working with Mathematical Terms and wooden parts, children develop a semantic map upon which they can mentally rely when working with equations.
Mathematical Terms – Nomenclature
We have provided a set of 6-part nomenclature cards to go along with the wooden materials. The nomenclature contains 20 definitions and serves to explain the function of each part of an equation. The illustrations indicate where each part is located in relation to the equation. Children can use the nomenclature cards to build the equation layouts with the wooden tiles. The Nomenclatures Cards set contains 6 parts for each term. At first, use the Control Cards (picture & label and description & label) to learn the precise language tied to the process studied. Once children are familiar with the definitions, they can test their knowledge by using only the Control Cards and matching a description card or picture card to them. Your learners should practice with the set several times independently to ensure long-term retention.
Mathematical Terms – Support Material
Working with equations becomes much more meaningful once the vocabulary has been established and children developed a mental image of how equations function. There are several Montessori materials that can follow the use of Mathematical Terms 6-9: the Decanomial Bead Box, the Montessori math charts for memorization, the Multiplication Board, the Division Board, the Stamp Game, etc. Once a classic Montessori material has been introduced and practiced, it would be appropriate and meaningful to add parts of Mathematical Terms to children’s learning experience. As an example below, children can lay out Mathematical Terms wooden tiles above the Division Board to keep in mind that all division equations consist of a dividend, a divisor, a quotient, and sometimes a remainder. The parts of the Mathematical Terms set reminds the learner how to write the equation and provides a description for each part. This way, children can see that each part of an equation has its own entity and function, rather than seeing a long series of numbers and signs. This process is comparable to Parts of Speech in grammar where each word can be attributed to a name and a function!
We believe this new material is going to improve your learners’ confidence when working with arithmetic problems. We want to encourage you to add this set to your math area a specific place for concept enrichment which will support all learners and ensure that foundational knowledge isn’t overlooked and forgotten. As we continuously create support materials to respond to all various learners’ needs, we invite you to keep visiting our section “Curriculum Materials” at www.alisonsmontessori.com,
