How to Ensure Students are Repeating Math Materials and Concepts to Attain Proficiency

by Letty Rising

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When considering both the hallmarks and benefits of the Montessori elementary classroom, one of the first things that generally comes to mind is the idea of freedom to choose work.  This is one of the aspects of a Montessori environment that sets us apart from other pedagogies and approaches.  It is also true that certain kinds of learning need repeated exposure in order for the information or skill to be attained, and one area where this is most obvious is math.  

Math is kind of like a foreign language…unlike reading, we don’t see numbers and equations continuously throughout our day, and because of this, there needs to be a conscious and deliberate effort, as well as continuous and regular practice, for math facts and concepts to be retained and applied. 

Sometimes the Montessori environment feels like an ever moving pendulum, swinging from freedom on one side, to the accountability measures we put into place to ensure mastery and growth on the other side.  How do we find this balance of freedom and responsibility when it comes to math? 

Maria Montessori looked at math from a developmental perspective. She was a scientist who approached education with observation, and learned how children best absorb the world around them.  When considering math in a Montessori context, we are not only developing a skill, but the human personality as well.  Maria Montessori observed some universal human tendencies that people across the world share, and some of these tendencies are: order, precision, and exactness. Math is an area that addresses these tendencies.  

Knowing this, you will want to start with the assumption that children are interested and curious about numbers, and that they want to know more.  Start from a place of assuming that they will be excited and grasp concepts quickly, and be hungry for more.  This is a better orientation than beginning from a place where you believe that math is hard, needlessly repetitive, boring, and unimaginative. 

When you draw upon you internal wellspring of inspiration, the children will not only be enthusiastic about math lessons, but will also feel motivated to repeat to proficiency, and feel eager to move forward through each lesson as they are presented. 

How do we present Montessori math lessons?

One thing you’ll want to keep in mind is that the math materials are the primary teacher, and you are their assistant, so to speak. You as the guide are presenting the math materials, and they are using their minds to grasp concepts.

During the presentation, you will first show them how to use the material, then you will do a problem or two with them. Then, you can sit and watch as they complete a couple of problems and guide them if they run into roadblocks.  Then, you release them to the environment to engage with the materials independently.  Eventually, they move away from the material and towards abstraction, which means they can perform calculations mentally or on paper.  

In order to give a high quality presentation that children will easily be able to repeat, you will want to practice the lesson beforehand.  The more prepared you are, the more confident you will be, and the more likely the children will be able to engage with the materials independently after the lesson.  

How do we ensure that math practice happens regularly?

The easiest way to ensure repeated usage of math materials is to create assignments and deadlines.  However, this comes up in opposition of the spirit of the Montessori approach.  And knowing this, teachers often will then go the opposite direction, which is to not assign and “hope” that the children will pick up the large bead frame or checkerboard and practice after you’ve given a lesson.  But that would take a highly self-directed child to be able to do that.  

Let’s say that you’ve presented the lesson clearly and correctly, and the children have a clear understanding of how to use the material, but after the lesson, or maybe after one or two times of practicing the lesson, they stop.  This could happen for a number of reasons, and particularly due to the following: 

The presentation wasn’t clear enough, and the children aren’t yet comfortable with the material.

There will be some times when presenting a lesson once, even with scaffolding and practicing with the children, is not going to be enough.  If this happens, you will want to re-present the lesson again! It might be that you invite the child to a lesson, but really you are just repeating the lesson and practicing with them. Some children need 2-3 times of scaffolded support before they feel comfortable going on their own.  

The child doesn’t understand the cycle of work.

This is especially true for young elementary children who have first come into the environment, and also for older children entering into the Montessori classroom for the first time.  You might need to model to the child how to pull the work off of the shelf, where they can sit, how to lay out the material, where to get a paper, a pencil, a clipboard. 

These things may seem very basic if you’ve been in the environment, but if you are with children who have never been in a Montessori environment, the executive functioning aspect of selecting work, doing work, and putting work away is a skill in and of itself.  

There isn’t enough variety.

If you have a child working on the stamp game over and over again, or the large bead frame, and you haven’t introduced them to other math materials that address the same concept you are teaching, then you might want to try something new! Remember that with elementary children, repetition happens through variety, and so offering a variety of materials can help increase levels of motivation.  

They aren’t seeing where math is relevant in their daily lives.

Remember that most elementary children want to know the reason “why” they are doing something.  They aren’t going to wash a table or mop a floor just for the sake of doing so, as they would have in the first plane of development.  Elementary children seek meaning and relevance.  You can make math more relevant for them by giving them word problems using themes related to the child’s interests or names of friends or classmates. You can also have them help plan events and calculate costs, measure the volume of objects in the room, use fractions via recipe creations, and so forth.  

They have mastered a good portion of the material but need an additional challenge.

Give them large numbers into the millions. As this age is drawn to “big work,” they often prefer to do one large problem rather than several smaller ones.  Also, you will want to look at special cases, such as zeros in the divisor or dividend, this gives an extra point of interest to the work, and can revive their interest in continuing forth.  

They don’t have a solid work partner.

According to the psychological characteristics of the elementary child as described by Maria Montessori, elementary children often don’t enjoy working in isolation. And while math doesn’t lend itself to larger group work, it is great for children to work in pairs or groups of 3.  Children are much more likely to practice regularly if they have a practice partner to work with.  You might want to help a child who is resistant to practice identify someone in the class that they would enjoy working with, so that when it comes time to practice the material, they feel more excitement around doing so.  

The “third” way

We’ve just covered numerous reasons why children might not be repeating math work.  But how do we encourage this repetition?

When approaching this challenge, besides swinging from one end of the pendulum (assigning math work for practice) or the other (leaving it to chance that children will regularly practice materials to learn new concepts), there is another way!

Remember that the Montessori elementary environment is an environment brimming with opportunities to collaborate.  It is often the case that the guide comes together with a student or group of students to collaborate, negotiate and create agreements. 

Approaching the idea of math practice is no different.  If a child isn’t practicing math concepts from a previously introduced lesson, invite them into a discussion about it during your weekly one-on-one conference. The following steps can serve as a guideline as you have these conversations: 

• Ask them how many days a week they think would be good to practice the checkerboard presentation they learned last week. 3, 4, 5?  
• Remind them that you have some really cool lessons that you want to give that come after this one, and you hope that they can practice and master this presentation so that you can give them the next one soon! 
• Have them commit to how often they will be practicing.  Let them know that your experience has shown them that practicing at least 3 times a week will be most effective, and you haven’t seen progress when children practice once a week.  
• Check in on them at the next conference, and ask them if the amount they practiced felt like too little, too much, or just right, and adjust accordingly.  
• If they feel like they’ve practiced enough to be proficient, ask them to show you a couple of problems. If you observe them using the materials with ease, and in fact it possibly seems like the materials are slowing them down, then you know they are ready for the next step.  

An environment where students are able to have voice and choice, along with an understanding of the accountability measures in place to ensure repeated practice with materials, will result in lots more regular math practice happening in the classroom. 

Children ultimately want to learn, want to refine, and want to perfect.  They are constructing themselves through their own inner drives towards growth. When we are there to support them by sparking their interest, giving them freedom and at the same time helping them set and define practice goals for themselves and helping them be accountable to these goals, we are then creating an environment ripe for mathematical minds to flourish.