Montessori Elementary Homeschool Blog - with documentation of our infant Montessori, toddler Montessori, and primary Montessori experiences; as well as preparation for the upcoming adolescent Montessori homeschool years.

Thursday, September 17, 2015

Longevity of Montessori: Mathematics

The Montessori approach meets the needs of children where they are at - both collectively and individually. Therefore, it is an approach that meets the needs of ALL children. The only limitation is the preparedness of the adult to meet those needs ;)

A recent post at introduces this concept as it applies to primary (3-6) and elementary (6-12). Montessori is Developmental

Even in our material,

Let's look at math specifically - just some highlights: 

With infants and toddlers, we do a lot of natural one-to-one correspondence. Few toys, each that belongs in a particular place. Matching activities in sizes, shapes, colors. Helping to set the meal-table using a diagram of what goes where.

We can also give the language of numbers (counting), and children love language at this age, so most do pick up on counting numbers, although they typically skip a few numbers or repeat a few sequences ;)

Primary Mathematics:
While we don't typically start math in primary until around age 4, we begin with a few materials that extend into primary mathematics as well as into use at elementary and adolescence. Sensorial and Mathematics materials are both noted here:
  • Red rods - extend into the number rods 
  • All the groups of ten we have extend into the decimal system
  • Pink Tower and Brown Stair can be used in geometry at elementary
  • Binomial Cube and Trinomial Cube (elementary and adolescence)
  • Geometry Cabinet and Solids (elementary)
  • Golden beads (elementary and adolescence)
  • Bead Cabinet and contents (elementary and portions in adolescence)
  • Snake games (if you purchase the negative snake game, it includes all you need for primary as well as elementary and adolescence)
  • Decanomial bead bar box (elementary and adolescence)
  • Stamp game (elementary and adolescence)
  • Short Division with Racks and Tubes becomes Long Division with Racks and Tubes (elementary)

Common Threads: 
  • Place value color-coding remains consistent throughout all levels - into the checkerboards that are the visualization of the multiplication process, the bank game (just numbered cards, no beads), and more.
  • The bead cabinet colors also remain consistent through all levels - even into the solid wood blocks of the cubing material that is used in elementary and adolescence. 

Additional posts of interest:

Toddler Exercises of Practical Life

All Montessori Trails posts on Mathematics

Mathematics Logic Game from Wff'n Proof

Review post on Adolescent Algebra Album

And that, dear friends, is today's show ;) 

Monday, September 14, 2015

Getting Started with Elementary Montessori Homeschooling - 10 Steps

Getting Started with Elementary Montessori Homeschooling

Useful tips for starting a new classroom or transitioning in new-to-Montessori children as well.
Over the years, there have been numerous blog posts and other articles helping parents get started with Montessori homeschooling; most of these articles are addressed to the primary (ages 3-6) level; a very few to elementary (ages 6-12). None really get to the heart of the matter. Dr. Montessori intensely observed the child and his inner workings, observing what has been there since the moment of creation - and found a way to provide for what she discovered. On the one hand, nothing magical; on the other hand, so profound that it affects our very being - because that is what she observed - the depth of the human soul. Thus Montessori is about so much more than materials and lesson plans (album pages), more than the academics... it gets down deep into the child's being, thus the environment MUST reflect this depth in order to achieve the true fulfillment of the child.
Elementary is compatible with primary, if you have children of both ages in your home; but it is NOT the same. The needs and tendencies are the same, the core response is the same (respect, follow the child), but the outward signs are different. Why? Because the elementary child is now in the second plane of development, which brings about a set of changes. A need for order? Yes! but order has now been internalized and the child no longer feels the need to keep order in his outer environment - now we must be very conscious about keeping our space cleaned up out of respect for the other persons in the environment and not for our own internal development. Among many other examples.
So how do we get started with Montessori homeschooling at the elementary level? What if your child has had no Montessori background or is even approaching the adolescent years. Let's take a look at what remains the same. First some previously posted articles of interest that remain pertinent to our needs in this article - these apply to both primary and elementary, with my elementary additions:
Thoughts to keep in mind as you FOCUS ON THE KEYS: 
    • A set of Montessori albums (manuals, lesson plans) will be your "keys" - your academic teasers to get the children working on their own interests. 
    • The children should be exploring their own interests; and you will need to pull in resources according to those interests.
    • You do NOT need the most expensive manuals with every possible interest included. You want something reasonably-priced with the *keys* so that you have both time and money to do what you need to do with your child's interests.
    • You WANT a theory album to explain all the background in every day applicable terms.
    • The elementary level is OPPOSITE the primary level in the following key ways:
        1. If the child is not yet reading/writing, reading will typically come first. (in primary, writing was first)
        2. We will now provide the BIG picture first; then go back and fill in the details. We will provide that big picture every single year of elementary - so there is plenty of time to come back to it; they don't need to get everything the first year. (in primary, we start with the most basic) - Cosmic Education (everything is inter-connected) - the big picture is told via stories called the Great Lessons. 
        3. It is NOT necessary to finish the primary albums before moving into elementary, if you have AMI (keys) albums that provide for what to do with children who didn't finish or didn't do primary Montessori.
So how do I suggest getting started with elementary Montessori homeschooling?
(these tips are good regardless if you are new to Montessori altogether or are transitioning from primary to elementary or even if your children are nearing or even in adolescence)
  1. Follow the steps in the two articles above - and READ. This is just to get started in laying the foundation. Add in the book Volume 2 of The Advanced Montessori Method (available free online through Google Books) - just the background portions to get a feel for things. Also add in Child of the World from Susan Stephenson. Purchase your core set of albums, or at least the "theory" album. Hint: if the set of albums does not contain theory, it probably won't suit your homeschool needs at this time; these other album options can be added later if you find your child has particular interests. 
  2. Focus on de-cluttering your home. Don't get rid of anything just yet (you'll end up wanting some of that stuff back) - just clear it out of the main living areas. Do get it out of the way - what is the purpose(s) of each room, just have what you need there. You do not need 5 tools to do the same job. You do want your children to have access to the tools they need. Consider placing strong chemicals in a high-up cabinet so that the accessible cabinets contain safe items. Consider replacing your cleaning chemicals with safe substances your children can use with you.
  3. IF you are transitioning from primary, you will be removing a LOT of trays (or keep the trays for your other littles). The elementary child now has things he needs in more logical places. Science experiments are only trays for the teacher demonstration, and when the child goes to the supply shelf to gather his needed supplies. He does NOT need everything laid out for him on a tray anymore. Trays at the elementary age, for the most part, are an insult to his intelligence. Yes, a nice basket of interesting items, requested by the child or presented once in a while by the adult is a great way to entice an interest, but that doesn't look like primary ;)
  4. WITH your children, make any necessary repairs on found items. These practical life skills are HUGE to the foundation of an elementary child's education. And a very strong preparation for a fantastic adolescent experience.
  5. WITH your children, truly clean the house. Same idea with the practical life skills. Use those safe cleaners (white vinegar, baking soda and citric acid go a LONG way; add some washing soda and borax and 99% of your cleaning is done). Use those large muscles and those tiny muscles. CARE about the environment and show them how to do so as well.
  6. On your cleaning breaks: Begin telling the Great Lessons. Just the stories, with the included experiments. You'll pull your supplies from what you have, only buy what you  need for these lessons.
  7. Work on remedial language skills IF needed. 5 minutes at a time, interspersed throughout the day - the needed keys should be in your elementary Montessori language album. The ideal is that a 1st grader can read at what the public schools consider a 3rd grade reading level. By 2nd grade, a Montessori child utilizing KEYS, will be reading at middle/high school level and your only concern from there is keeping up with maturity in regards to topics.
  8. Where do your children's interests lead? Establish the pattern of hearing a story, exploring what we think about it, what entices us, what questions do we have (write those questions down and expect them to find answers, sometimes with your help), what do we want to DO with this new knowledge (write that down too). The children can copy the chart, re-create the charts in another way, repeat experiments, seek out further information on a key point of interest.... If they have more than one idea, write down the other ideas to save for another day. Encourage a point of completion - write down the question and the answer found; draw pictures; collect ideas in a notebook; create a poster; etc. Around this time you will also be starting to work on work plans and journals - as you are comfortable and find the need for accountability, it will come more naturally. Not every story or presentation will lead to self-designed follow-up; be ok with that, but also be encouraging of the child asking questions, going further, and EXPLORING. 
  9. (this step might be a month or more in) With your chosen set of albums, go through the early math lessons to find where your child is. Keep it fun and interesting - let your child show you what they know. Let them know this is what you are doing (show a material, state its purpose and say, "show me what you know, I'll fill in the rest"). Do NOT worry about the age on the album pages when you are starting - just focus on finding where your child is since the sequence is very different from every other math option out there. Begin where needed and move forward from there. Hint: Good elementary math albums include a section on what to do with children who have had no (or limited) primary experience. Do not start a typically developing elementary child in the primary math album.
  10. Getting into the rest of the albums. By now, you should find that you are using most or at least half of the subject albums based on the child's interests (geography, music, biology, history) and the basic skills (math, language, geometry). Add in the remaining subjects when appropriate for your family.
There you have it: 10 Steps to Elementary Montessori Homeschooling.

Sunday, September 6, 2015

Montessori Memory Development

Memory – something so many of us struggle with, despite 13 years of a traditional school model which required us to memorize pieces of information to regurgitate at test time. Shouldn’t we all have perfect memories by now?

In contrast, a Montessori education has no testing of those memory skills, no straight-forward regurgitation of facts; yet Montessori graduates go on to continue their lives with excellent mental skills, including in the area of memory.

Don’t we need tests to prove memory skills? Don’t we want to be able to remember a string of unrelated facts without any context? Well… yes… and no.

Montessori allows memory skills to develop by connecting the memorization of a particular fact to so many other areas simultaneously that almost *anything* can be a trigger for a needed memory.

Probably many of my readers here will entirely agree with that fact without me saying another word. But please allow me to extrapolate for a moment.

A child in the primary (ages 3-6) class is working on memorization of math facts – those equations based on adding, subtracting, multiplying and dividing the numbers of 1-9. This typically kindergarten (age 5-6) child is probably quite adept at the following:

  • performing all four operations utilizing the golden bead material as well as the stamp game – both are kinesthetic to varying degrees, the golden beads require collecting material by walking and the stamp game requires fine motor movement and introduces writing out the operations;
  • this child has also probably worked on counting up and down the short and long chains, representing the squares and cubes of the numbers 1-10, introducing skip-counting and multiples (and indirect introduction to factors). Some Montessori environments include a writing-related extension for the chains. Many children turn the skip counting up and down into something of a chant, all on their own. 
  • the child may be using the snake game for addition and subtraction, which include a verification stage that utilizes multiplication.
  • the multiplication material itself involves some bead boards, strip boards and charts – before even getting to the writing portion with the booklets.

Thus this child has already worked with the math facts in the whole body; in the arms/hands; in some writing; and finally in the mind and fingers with the beads where the child isn’t moving just as much in the whole body. So as the child moves into the charts, we can say, “Check into your mind first – see if the answer is already there, before you use whatever material you want or need to verify your answer.”

Montessori develops memory skills in a variety of areas.

Memory isn’t just in math, but that is the first place we think of.

Order in the environment – Sensorial and Exercises of Practical Life:

From the child’s beginning days in the primary level environment, we invite them to think through their tasks. “As you put away the wood polishing tray, think to yourself, ‘What else needs to be replaced so it is ready for the next person?’” Not only that, but where does the tray even go? If it is put away incorrectly, someone will fix and may gently point it out the child.

Indeed, we set up our environments so that there is a place for everything and everything in its place. Establishing this sense of order is key to developing the child’s memory skills on an ongoing basis. It encourages the use of memory (“where does this go?”) and using context clues to locate the correct spot. It also helps the child when he is elsewhere and thinks about his learning environment, when everything is essentially in the same place, he can visualize it to make his plans for the next day or to tell someone else about his work. Or to wonder what will be new in an area the teacher/parent has said the day before “We have something new coming tomorrow! And I will place it in this spot when it arrives!”

Within the sensorial area in particular, the child see several groups of “ten”, the basis for our decimal system: the pink tower, the brown stair, the red rods, the knobbed cylinders, the knobless cylinders. What doesn’t come in tens, comes in pairs for the sake of matching and some items later for grading. There is a consistent order to things for the children to explore while experiencing an isolation of concepts with our “keys to the world” as Montessori called the sensorial materials. We have the materials on display in a way that highlights the item’s main attribute or teaching point. This aids the child in finding patterns in the world around him which only aids in memory skills as new experiences are ordered to the variety of patterns the child finds in his mind, organizing information in a variety of ways (this information I am learning is like the pink tower in this way; and like the bells in this other way; etc. – meaning that name of something new might sound like particular notes on the bells; or be equally as pleasant to hear).

Maintaining this order, causes us adults to consider making any major (and many minor) changes to the environment with the children present, so that the child can make the mental shift at the same time.

Nothing like a constantly changing environment to make memory development trickier! Those of us who have to change environment routinely with our children, should consider this need for order and look to what we *can* maintain. Whether it be routines around mealtimes and bedtimes, worship practices, consistent behavior expectations, family traditions, or other areas, children are not harmed in any way by moving a lot or long-term travelling, when they find consistent order in other areas of life.


We utilize three-period lessons to introduce new nomenclature to the children. We give the name in the first period, do a lot of action with the nomenclature in the second period, and when the child is successful at the second period (either in the first session or a future session), we move to the third period of asking the child for the name of the object or quality at hand. We can add more objects/qualities right away if the child was easily successful or we can review another time or day, and add more then.

We strive to use whole language (complete sentences, full words, real words), an extensive vocabulary (children can soak in any word of any length when used in context – we do not need to simplify our vocabulary for young children!), and full interaction with the children on a variety of topics (look them in the eye while having a conversation). It is a stronger impression on the child’s mind when we share in and discuss real life experiences. Instead of just watching a video about gardening and having pretend gardening tools and items, to actually garden, grow one’s own treats, have fun getting dirty – and talking about it, sharing ideas, trying out new things. These things provide a multi-sensory approach to learning that aids in memory development.


Beyond the 3-period lessons we use with the children to teach nomenclature in all areas, we also ask the children to tell us what they are going to bring after we tell them a quantity of beads or cards to bring to the mat. “Please bring me four thousands and 3 tens. (pause) What are you going to bring me?” (the child repeats – if they miss it, repeat the request and ask them to repeat it again; until they get it – please note if you are using two or more categories and a child cannot say it back, back down one less category and strengthen those memory skills first ;) ).

As the child works through math problems throughout primary and elementary, the child should be verbalizing the process. This helps to internalize the skills at hand - saying, hearing it, finding words to explain it, the physical manipulation, the visual acuity. 


The sensorial materials for matching are awesome memory developers because are intentionally spreading the experience out. The sound cylinders: shake a red one (switching hands and doing it in both ears), shake a blue one (both ears as well). Not sure if it matched? Listen again. If a “no”, the blue one is set aside; re-shake the red one before listening to the next blue one. Reinforcing that sound. Later, a challenge is to shake the red one, listen to the all the blue ones and select the one that matches.

With the bells, we have distance matching and distance grading. One of the extensions of this distance work is to listen to a bell, then go have a short conversation with someone before proceeding to the bells cabinet to find the match (or next in grading series).

And remember! The control of error is in one's own senses - there is NO OTHER control of error here! 

This memory work area is one area where the children do not ever really age out of the sensorial materials. A 4 year old might be done with the main ways to build the pink tower and may have mastered all the language by age 5; but can they feel a cube while blindfolded, go chat with a friend (having removed the blindfold but not looked at the cube), and only then find the next cube in the series when all the cubes have been scattered around the room. This challenge combines many of the extensions and is a fun challenge for most 5 and 6 year olds (and elementary children!). 

But it is never too late to get started.

Start using these same techniques at any age to get started, either for yourself or with an older child. Recent brain research shows the brain remains pliable throughout life, for as long as it is used. The only time things are truly lost is when one or more areas of the brain are left so inactive for so long, generally from so early childhood that the area was never activated to begin with. We used to think that the brain couldn’t learn much after so long because of the experiences with children found feral and without language in the wilderness. What we have found is that if those areas were activated at all in childhood they can be stimulated – perhaps not to the same extent as if they’d been active all along, but certainly something can develop under the proper circumstances! has an article on using the Montessori approach for people with Alzheimers. 

So what do we do to develop our own memory skills?
  • Eat right. Limit sugar intake which causes huge fluctuations in the blood and brain.
  • You learn something new, use it right away – many times over. You meet someone new, use their name several times in the next few minutes, while looking that person in the eye.
  • When you are going into another room to get or do something, repeat the plan several times in your mind or out loud.
  • Need to memorize something important? Make up a song for it.
  • If you are looking for a nutritional method of memory assistance, rosemary is an excellent herb of choice; if you don’t like the flavor, the rosemary essential oil can be utilized via aromatherapy to stimulate the memory centers of the brain.
  • If you have access to the Montessori materials, do the primary level exercises yourself! Challenge yourself!
  • Get up and move! Circulating blood brings more oxygen to all areas of your body, connecting multiple types of experiences to information you want to remember, and generally having more energy – all aid in memory retention. 

Now, please share some of your ideas – where have you seen memory practice in the Montessori environment (any age: infant, toddler, primary, elementary, adolescence) – and what others ways can adults enhance memory skills?