Absorbent Mind
A term used by Maria Montessori to describe the young child's ability to absorb knowledge and experiences from their environment. Brain state from birth to approximately seven years old when the brain is mostly making Delta and Theta Waves, Alpha waves are made on a regular basis starting around the age of seven. The absorbent mind corresponds to the grammar stage in the trivium and the Brain's Delta & Theta stage.
Age Appropriate Instruction / Learning
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.
Brainwave Stages
Different frequencies of brain activity associated with various stages of cognitive development, including delta, theta, alpha, beta, and gamma waves.
Control Of Error
Place the child i a situation where they can not fail. The child is placed in a position where failure is either impossible or easily recognizable and self correctable. The child needs no help from instructor to recognize errors.
Developmentally Appropriate
Directed Discovery
DOE Department Of Education. A Federal for Profit taxable Corporation DUNS#944419592. Or one of 50 STATE OF taxable for profit corporations which are tasked with dumbing down American Citizens, and aiding in their naturalization into the US corporation as resident US citizens through omission and fraud. links not built yet
Economy Of Symbol
Fewest symbols possible to express an idea or expression. The mathematics is succinct & precise without superfluous and unnecessary symbols. All mathematical formulae are examples of economy of symbol from the area of a circle to Einstein's famous equation. This is mathematical rhetoric. The language is easy to read when you can see it. Those symbols represent a lot of math.
A method where learners start with hands-on materials, transition to drawings, and finally to numerical symbols.
Materials are designed to help children identify and correct their own mistakes independently.
Children explore and uncover mathematical truths with teacher guidance, not direct instruction—supporting ownership of learning.
A way to scale lessons to a child’s readiness, gradually increasing complexity as mastery grows.
A child shows understanding through independent use, creative problem-solving, or teaching the concept to others.
Etymology
Five Basic Concepts
Five Basic Concepts: A framework for understanding mathematical concepts, emphasizing the interconnectedness of mathematical ideas and relationships.
Golden Beads
Montessori decimal system material using gold-colored beads to teach units, tens, hundreds, and thousands.
A child-friendly way to teach the value and power of zero, especially in place value and problem solving. Zero is your hero because he does so much for you. WHen things get negative or when you need to discover x, zero is your hero.
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.
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.
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
he art, science, or profession of teaching, including the methods, techniques, and philosophies used in educational settings. Montessori pedagogy values hands-on, child-centered, exploratory learning. The Mortensen Method is the Montessori Method focused on math.
The idea that a digit’s value is determined by its position in a number, foundational to understanding the base number system. In base ten 111 is one hundred, one ten, and one unit. In base two or binary it is 7, one four, one two, and one unit. x² + x¹ + x⁰.
Encouraging correct responses through praise, success, and enthusiasm instead of correction or punishment.
A structured learning space where everything is designed to support independent learning and developmental needs.
Using blocks to form rectangles (arrays) that make arithmetic visually obvious and support conceptual learning.
A strategy to keep exploration positive—redirect mistakes without using negative language like “no” or “wrong.”
Supporting learners at their current level and gradually removing help as they develop competence.
Encouraging learners to independently find and fix mistakes through feedback embedded in materials.
Engaging multiple senses to support deep learning—especially through touch, sight, and movement.
Counting by intervals (e.g., by 2s, 5s, or 10s), laying groundwork for multiplication and division fluency.
Self Directed Learning
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
The deliberate sequencing of curriculum and skills from one educational level to the next, ensuring coherence and continuity across grades or advancing tiers, and mirroring the natural growth of the human mind.
Thus 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. Examples of vertical alignment regarding algebra:
x² + 3x + 2
Beginner. 3 - 7
toddlers just build rectangles, count and multiply, they learn the names of the pieces. Grammar. link not built yet
x² + 3x + 2 = 0
Intermediate. 7 - 12
we can factor and solve for x. We can divide, multiply and factor. We can evaluate for various values of x, (and have fun doing it). Negative expressions. Logic.
x² + 3x + 2 = 0
Allegedly Advanced 12 - 18+
we can graph, find x and y intercepts, convert to vertex form by completing the square after we've learned to square numbers ending in five. Negative expressions are easy too because they can see them. They know what the symbols represent. They no longer require the blocks the same way you no longer require a picture of a cow when decoding C-O-W. Rhetoric. link not built yet
Visually Obvious
A principle where materials or layouts immediately reveal the concept—no lengthy explanation needed.
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For $1 per month (the lowest level subscription) you get access to
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You'll find hours and hours of videos with base ten blocks and information you won't find anywhere else not even on this website there. i often post video tutoring sessions there. Other people post vids and links there too. Lessons cost the people doing them minimum $60.00 and hour. You can watch 2 to 10 of them a month for a dollar...Do the math. Currently 127 people are there. About half of them are active.
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Note: from time to time the passwords change. Simply e-mail me for a new one or a new passport as the case may be. Annual passes are good for one year, lifetime passes are good for as long as the site remains up, (site has been up for eight years now). All single page passwords have lifetime renewal.
Note: Mortensen Product Ordering Buttons Have Been Removed Due To Shipping/Inventory Issues. i basically DO NOT sell product for them anymore. Use eBay or other sources for base ten blocks. Check with Anna's Math Page.
Want to see more free pages & lessons & other free stuff on this site?
Consider a dollar a month.
For $1 per month (the lowest level subscription) you get access to
The
Super Duper Super Secret Facebook Page.
You'll find hours and hours of videos with base ten blocks and information you won't find anywhere else not even on this website there. i often post video tutoring sessions there. Other people post vids and links there too. Lessons cost the people doing them minimum $60.00 and hour. You can watch 2 to 10 of them a month for a dollar...Do the math. Currently 127 people are there. About half of them are active.
You basically get a support group for a buck a month.
Here's My Patreon:
https://www.patreon.com/CrewtonRamone