Teaching Elementary Math with Montessori Materials
Updated: Mar 17, 2022
Of all the materials used in the Montessori Method, those designed for the introduction of math concepts are my favorite, and why, even as a current traditional public school teacher, I incorporate as many as possible into my classroom. It doesn't matter if you are a homeschooler, or a teacher at a typical public or private school. You don't have to be a certified Montessorian for your students to benefit from research based tools. (Dr. Montessori was a trained scientists with degrees and experience in Medicine, Psychology, Pedagogy, and what we now call Special Education, and developed her methods and materials in a school setting with real children). Dr. Montessori designed her math materials to isolate the difficulty, so a child only needs to focus on one thing at a time when learning something new. She also designed them to be visually simple, yet beautiful, and often include a secondary purpose such as development of fine motor skills.
In this post, I will focus on Montessori math materials I use or have used to teach four core topics in math: counting, base ten & place value, operations & math facts, ranging from Pre-School to 3rd grade content.
One Important point I must make is that Dr. Montessori garnered international attention for the miraculous progress her impoverished students made, partly due to discoveries she made about optimal ways that children learn. This includes short windows of time in every human child's development known as "Sensetive Periods", that enable a child to learn a great deal of information with little effort, or consciousness. She named the sensetive period in child development from age 0-6, "The Absorbent Mind" phase. We all know that a young child can learn any language by mere exposure. Dr. Montessori designed her math materials to take advantage of this. This is why children in Montessori pre-schools often easily learn multiplication, and can add, subtract, and divide four digit numbers with hands-on materials. These same skills are not even introduced in the typical school system until 3rd grade, and often with much effort and mental strain on the part of child and teacher. This is a bit of a disclaimer, because I am recommending the use of concrete Montessori math materials for concepts that would be introduced at a much earlier time in an authentic Montessori school, and therefore, will not have the same deep impact when introduced after the absorbent mind stage. Montessori is a cohesive method, philosophy, and curriculum, with a complete suite of tools designed to all work together in harmony. This doesn't mean these materials are not beneficial however in a non-Montessori setting.
I am advocating that educators and parents take elements of Montessori math that can easily be incorporated into our current educational framework, while having a positive impact on student learning.
To illustrate my point, when I was a child, I still remember my teacher introducing place value and base ten on the chalk board. She gave a wonderful, but abstract lesson. I had absolutely no idea what she was talking about. Had she used the Montessori golden beads, and let me build and exchange groups of ten, I would have understood. Nowadays math "manipulatives" are more common in elementary schools, but there is still much room for improvement. While some Montessori materials, such as the golden beads have made their way into our education system as plastic base ten blocks, other powerful tools, such as the addition strip board, the colored bead bars, and the Seguin boards have not. I think that should change! Montessori math tools are concrete, precise, beautiful, developmental, self-teaching, systematic, focused, purposfully designed, and come with over 100 years of results!
I have used many of the following materials in both Montessori lessons, and as a supplement to conventional curriculum. I have found that using Montessori materials is especially beneficial for struggling students and students with learning differences. The best part is they help these children to love math! If you want to learn the exact Montessori lessons that go with these materials (which I highly recommend), there are a ton of online and in person training programs available. There are also tons of free videos on youtube showing various ways to present all of the materials listed here. Just remember to include "Montessori" in your search. I am also developing a series of short demo videos on my youtube channel, so stay tuned!
Red & Blue Rods + Sand Paper Numbers - I love these because they offer a visual, tactile, and kinesthetic introduction to numbers and counting. The red and blue rods represent a fixed quantity, while the sand paper numbers give children a tactile impression of each numeral. They are introduced separately, then used together. The genious of Dr. Montessori also incorporated the child's natural tendancy to play with blocks and want to touch everything into the design of these two materials! CLICK HERE for a free printable template for the sand paper numbers.
Spindle Box - The spindle box capitalizes on the child's natural tendency to sort objects. This material is designed so the numbers are in fixed order, but the objects are loose, isolating just this skill.
Colored Bead Bars - With this material, a child can touch each bead as they count, helping them develop a one-to-one correspondance. Because each quantity is always represented by the same color, children automatically begin to recognize each quantity by color. The children will see the beads again later in the curriculum in a variety of ingeneous ways. I personally think this material should be standard in every elementary classroom, and look forward to the day that they appear in manipulative kits for conventional teacher text books and in mainstream supply catalogues! If I had any business or marketing sense, I would market them direct to teachers myself!
Red Cards + Counters - Almost all Montessori materials have a primary and secondary purpose. This simple material has a primary purpose of helping children match loose number cards to loose counters as a primary purpose, and as a secondary purpose, children will literally see the difference between even and odd (when one counter does not have a match)! CLICK HERE for a free printable version.
Seguin Teen & Ten Boards + Beads - The teen and ten boards were developed by a French educator, Edouard Seguin, who opened schools for people with learning differences in the 1800's. Dr. Montessori studied his work, and incorporated these materials into her work with children. With the seguin boards, a child can systematically go through the number sequence past nine by physically placing a single digit on top of another. For example, when they place the number 5 on top of 10, they make 15! Every year, I have several 8 year old students who either cannot count to 100, do not know their teens, or lack number sense. That is when I break out the Seguin boards! For younger children learning to count, they help lay a solid foundation.
100 & 1000 Chain + Tickets - I still remember the sense of wonder and awe I felt in my Montessori training, when I got to stretch out a chain of ten linked golden bead ten bars! A little ticket with numbers written on it marked each new group of ten. What a cool visual and kinesthetic way to show children how much 100 is, while reinforcing skip counting by tens. Then came out the 1,000 chain, and I was floored! We learned that in a Montessori classroom, the children often take this chain out into the hallway to stretch it all the way out. Besides all of the lessons that can be done with this to reinforce counting (by ones, tens, & hundreds), there is the sheer amazement when you see the 100 chain side by side with the 1,000 chain. Can you see how Montessori can bring joy to learning math with the simplest of materials and lessons, and cause children to wonder things like, "What would a one million chain look like?" I do not have these chains in my current classroom, but I have replicated this lesson by pre-counting out a container of enough base ten bars to show 100, and 1000. Just remember, the children should build it, and the bars should ideally be all the same color if golden bead chains are not available.
100 Board - This material is made up of 100 loose, numbered chips and a grid board. After many previous lessons on counting, children practice sequencing the numbers 1-100 in order. In Montessori, there is someting called a control chart, showing what the correct arrangement looks like. With the 100 board, the control chart is simply a printed 100 chart. This allows children to check and correct their own mistakes during the learning process, thus increasing independence (an important aspect of the Montessori philosophy). CLICK HERE for a printable version of the 100 board.
BASE TEN SYSTEM | PLACE VALUE
Golden Beads - I introduce base ten and place value to my students with a series of Montessori mini-lessons using the golden beads. My students can see, hold, and understand the difference between one unit, and one thousand, and they are always impressed! Because golden beads are pretty expensive, I only have one golden bead tray with one of each: thousand cube, hundred square, ten bar, and one unit. I do follow up lessons with yellow base ten blocks found in almost every elementary classroom (now you know who inspired these, ahem, Dr. Montessori!!!).
Large Number Cards - There are plenty of number cards out there in conventional education catalogues, but the reason I love the Montessori design, is that they are consistently color coded for place value with the same three colors: green, blue, and red. This helps children to make lots of connections, as these same colors appear throughout all of the Montessori place value and base ten materials, and help to reveal interesting patterns in our number system! CLICK HERE for a printable version of the large number cards.
THE FOUR OPERATIONS
Golden Beads or Base Ten Blocks - When teaching the four operations of addition, subtraction, multiplicaiton and division of multi-digit numbers, I always start with the concrete (golden beads or base ten blocks). Students use reusable, color coded command cards (turns out Dr. Montessori made the original task cards), with problems on them and a control chart to check their work. CLICK HERE to grab a printable bundle of command cards for all four operations.
The Stamp Game - When children have had plenty of practice usigng the large blocks to do their math, and understand the concept, they can move on to the smaller and more abstract color coded number chips that represent the quantities of golden beads, called the stamp game. Dr. Montessori called this the passage to abstraction. She found it important to help children move from concrete materials to purley abstract symbols on a page with tools such as the stamp game. CLICK HERE for a printable version of the stamp game.
The Bead Frame - Every year, my students are drawn to this tool, and ask me to show them how to use it. There are actually several bead frames in Montessori (small, large, and golden), used for different purposes. The bead frame looks like a triditional abacus, only it is color coded in the same green, blue, and red place value colors as the number cards and stamp game stamps. This material is another bridge to abstraction, but can be a bit tricky for studends. I find my advanced students love to use this tool, as it enables them (after much practice), to quickly calculate very large numbers!
The Checkerboard - This is another hands-on color coded material used to help children learn to calulate large numbers in a more abstract way. It also uses the colored bead bars. Dr. Montessori discovered that although young children like to repeat the same activity over and over, older children enjoy novelty. To take advantage of this, she designed many tools for older children that allow them to practice the same skills and concepts in a different, but still hands-on way. Although I learned how to use this material in my Montessori training, I do not have one in my classroom, and have not actually used it with students, although I would like to.
Colored Bead Bars - This is the only way I will introduce multiplicaiton facts in my classroom! Even before doing any activity or exercise with our adopted curriculum, my students complete a little booklet of multiplicaiton tables with the colored bead bars. All they have to do is grab the colored bead bars one at a time, and count the beads. My students always go home with big smiles that day, becasue they learned how to multiply! I could almost teach the entire concept without talking this tool is so powerfu! CLICK HERE for a printable set of the little books I use in my classroom.
Boards - There are four different Montessori boards to help children calculate math facts more absractly, while still being hands-on. There is one for addition,called the Addition Strip Board, one for subtraction called the Subtraction Strip Board, one for multiplication, called the Multiplication Bead Board and one for division called the Division Bead Board. These boards are ingeniously designed so children can visually see and build things such as counting on, arrays, and distribution by building with their hands. This enables students to understand these concepts without a teacher having to explain them. Dr. Montessori discovered that children learn through the hand far better than through listening. As a secondary purpose, using these boards helps to develop fine motor skills needed for writing. This is another set of materials that I wish came standard in conventional teacher catalogues and curriculum, but are totally missing. Some day, right?! Click on the links to ge printable versions of the: Addition Strip Board, Multiplication Bead Board, Subtraction Strip Board, and the Division Bead Board.
Charts + Equation Slips - It is quite common to see the multiplication chart being used as part of a typical elementary math curriculum. Montessori takes it a step further of course by using purposeful color coding, self correcting, hands-on versions of the typical paper chart (there are also charts for addition, division and subtraction facts). In addition there are sets of equation slips and matching answers to be used with each chart in various ways. Most children start to see patterns emerge with repeated use! These charts also allow children who have had lots of practice with the more hands on materials mentioned above, to move towards abstraction and memorization. Click the links for printable versions of the charts and equation slips: Addition, Multiplication, Subtraction, Division.
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