Glossary 

📘 Glossary of Terms (Work in Progress)

Base Ten Blocks

Mortensen Math "Combo Kit" brightly colored manipulatives representing one through nine (1–9), blue rods (10 or ×), red flats (100 or ײ). They help children understand place value and operations visually and tangibly through color-coded, proportional pieces.

Montessori Principles

Core ideas guiding Montessori education, including: respect for the child, prepared environment, self-directed activity, hands-on learning, mixed-age classrooms, sensitive periods of development, and intrinsic motivation.

Concrete–Pictorial–Abstract (CPA) Progression

A method where learners start with hands-on materials, transition to drawings, and finally to numerical symbols.

Control of Error

Materials are designed to help children identify and correct their own mistakes independently.

Directed Discovery

Children explore and uncover mathematical truths with teacher guidance, not direct instruction—supporting ownership of learning.

Degree of Difficulty

A way to scale lessons to a child’s readiness, gradually increasing complexity as mastery grows.

Exhibition of Mastery

A child shows understanding through independent use, creative problem-solving, or teaching the concept to others.

Five Basic Concepts

1. Math is Counting
2. The Concept of SAME – We must count like things.
3. Rectangles Facilitate Counting
4. Hero Zero (0)
5. 1 – No Fun, Get Back to One (NFGBTO)

Golden Beads

Montessori decimal system material using gold-colored beads to teach units, tens, hundreds, and thousands.

Hero Zero

A child-friendly way to teach the value and power of zero, especially in place value.

Math Rich Environment 

Similar to the Montessori structured, prepared environment Maria believed was best for learning. Giving the child freedom to learn within a structured framework where through socratic method and directed discovery the thirst for knowledge is ignited. A place where there are blocks and whiteboards and pens or pencil and paper generally the living room or kitchen floor or table top or wat have you.

Number Sense

An intuitive understanding of numbers, relationships, and the effects of operations. The sense is greatly increased when students are exposed to manipulatives.

Pattern Recognition

Spotting and using regularities in numbers, such as multiples or visual arrangements, to deepen mathematical understanding.

Pedagogy

The art and science of teaching—Montessori pedagogy values hands-on, child-centered, exploratory learning.

Place Value

The idea that a digit’s value is determined by its position in a number, foundational to understanding our number system.

Positive Reinforcement

Encouraging correct responses through praise, success, and enthusiasm instead of correction or punishment.

Prepared Environment

A structured learning space where everything is designed to support independent learning and developmental needs.

Rectangle Formation

Using blocks to form rectangles (arrays) that make arithmetic visually obvious and support conceptual learning.

Removal of “No” from the Lesson

A strategy to keep exploration positive—redirect mistakes without using negative language like “no” or “wrong.”

Scaffolding

Supporting learners at their current level and gradually removing help as they develop competence.

Self-Correction

Encouraging learners to independently find and fix mistakes through feedback embedded in materials.

Sensorial Learning

Engaging multiple senses to support deep learning—especially through touch, sight, and movement.

Skip Counting

Counting by intervals (e.g., by 2s, 5s, or 10s), laying groundwork for multiplication and division fluency.

Three-Period Lesson

A Montessori Method for introducing new, concepts, language, or ideas:

1. Naming – “This is a ten.”
2. Recognition – “Point to the ten.”
3. Recall – “What is this?”

Vertical Alignment

Ensuring that math concepts are introduced early and then revisited and expanded in a logical sequence over time. Combine with degree of difficulty for baby steps from counting through calculus. 

Visually Obvious

A principle where materials or layouts immediately reveal the concept—no lengthy explanation needed.

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