November 2023

Welcome to EFM's November Newsletter!

It is essential that every family and caregiver in the world read books and do math with their young children!

EFM believes in every child’s mathematical right to equity, opportunity, and personal fulfillment.


News

Playing Cards for Educators K-3 – Our playing cards have been too big a success. We have sent them all out. However, we will be making more in a few months. If you are interested in a large order, please let us know in advance so we can allow for that in our ordering. Even if you don’t have one of the physical decks, there are great free resources associated with them on the Playing Cards Page on our site.

Donations – With the end of the year coming up, perhaps you are looking for a year-end tax-deductible charitable donation. Look no further! Join the two people who gave us $5000 and $100 this month. We have improved our Donation Page to make it easy to use credit cards or PayPal. We are all unpaid volunteers, so 100% of your donation goes to providing free materials and services to families and schools.


Reggio Emilia, Montessori, and EFM

Reggio Emilia and Montessori are educational programs started in Italy in the 1900’s. This article is not intended to be a full overview of their programs. Rather, I’m interested in their use of manipulatives and how that translates to EFM and our wish to create rich math environments in homes and schools around the world, particularly in low-resource communities. If you spend a lot of money on books, toys, games, and educational kits, it is easy to create an educationally nurturing environment for a child. The challenge is to do it effectively with less!

Montessori

Maria Montessori (1870 – 1952) believed in providing kits where a child may choose any kit (as long as it is at the right level) and experiment with it by themselves, or sometimes in small groups, as much as they wanted. The kits were carefully crafted so that play in that environment would guide a child, without outside interference, to learn some skill or concept. If the materials were used in the wrong way, feedback was built into the materials to make them self-correcting for the child. After a brief introduction to a kit, a teacher was not needed to teach a concept or correct a child’s mistakes.

An example of a self-correcting kit is a collection of five rods of lengths 1 to 5 together with a series of 5 slots in a piece of wood, where each rod exactly fits a corresponding slot. If a child puts a smaller rod into a larger slot, they will find that they cannot put all the rods into all the slots. Thus, they will be forced to put the rods in order exactly matching the sizes of the slots.

Montessori believed that a very young child has an “absorbent mind” that is happy to do repetitive activities whose only point is the challenge of completing the activity. Her math activities often involve beads and rods and sometimes numerals, are very tactile and repetitive, and do not involve any difficult problem solving.

Having a young child playing almost entirely by themself is antithetical to EFM’s goal of involving caregiver and child in math play together. Fortunately, it is not difficult to repurpose Montessori’s materials and ideas for our more social goals.

The website Sugar, Spice, and Glitter has a list of some Montessori materials. For each one, the site describes the pros and cons of creating your own version versus buying commercial ones. Most of these are either expensive or require a fair bit of effort and resources to make.

Here are some basic kits that are producible with very simple materials.

Rods of length 1 to 10. These have alternating colors (perhaps red/blue or black/white), always starting with the same color on one end. If the length of each color is a basic unit (say 1 inch or 1 decimeter), these can be used for measurement and counting. One task would be to mix up the rods, and have the child place the rods in order, in a triangle or pyramid on the ground, as shown above.

In another task, these rods can be used to practice creating all sums that add up to a number, such as 7. Putting together the rods of length 1 and 6, or 2 and 5, or 3 and 4, creates a pleasing picture of combined rods of constant length 7. This exercise will also point out even versus odd numbers – even numbers will have one rod that must be paired with itself. This practice with number bonds is particularly helpful for number bonds of 10.

Cards with numerals or collections of dots from 0 to 10. Use these cards on their own, with the rods, or with any collection of small objects to practice with quantities.

Bins of pebbles. For example, use 15 pebbles for the numbers 1 to 5. The child’s task is to remove from the bin the right number of pebbles and put them with the rod of the right length or the numeral on a card. If they use the wrong number of pebbles for one number, the pebbles won’t work out evenly. One options is to display the pebbles in two columns, with any extra odd pebbles put at the bottom in between the two columns. 0 can be included once the activity is familiar.

Outlines of shapes. Identify a collection of shapes you want practiced. These could be triangles, squares, and circles, or they could be everyday objects like forks and spoons, or they could be shapes of letters or numbers. Cut out shaped slots in a box top, or make outlines of these shapes on paper or on the ground. Have your child practice matching the objects with the holes or the outlines.

Beads and String. Use beads, nuts, tubular pasta, or anything else that could be put on a string and not fall apart easily. Put these objects on string in various ways. Have one collection of 10 strings where the strings have 1 to 10 beads on them. Have another collection where all the strings have exactly 10 beads. Montessori also has a 100-square of 10 strings of 10 beads tied together, and even a 1000-cube of 10 groups of 100-squares tied together – but that requires more patience than I would have.

Reggio Emilia

This method of teaching traces its origin to shortly after World War II, to the town of Reggio Emilia. Its guiding principles and general methods are somewhat vaguely defined and are interpreted and implemented with many variations in schools throughout the world.

In common with Montessori, Reggio believes that a young child’s learning activities should be strongly directed by the child’s own interests, and the learning should be discovery and experientially based. In contrast to Montessori, Reggio projects are not as structured and predefined, are open ended, tend to be more group oriented, and the teacher follows wherever the children’s interests lead the project.

They like to use two keywords to describe types of their activities: invitations and provocations. An invitation is a collected group of objects that invite children to explore some materials or activities, such as a collection of rocks or leaves. A provocation is a response to seeing interest in an activity and seeks to provoke the children to doing further exploration.

A consequence of their flexibility is that if you search on the web for Reggio-math invitations or provocations you will find a very wide variety of materials and manipulatives, most of which are not commercial products – they are either homemade or gathered from the local environment. These groups of objects are kitted together and support exploration around a central theme from which further projects and exploration occurs. These kits are similar to resources you might see sold to homeschoolers, but the kits typically have a larger group of objects more thoughtfully organized around a common theme, and many of the objects are everyday things you might find lying around.

Rather than trying for an overview of the sea of kits out there, I will look at just one source. Janice Novakowski has done a lot of work with Reggio Emilia, and she has a blog on the Richmond School District site with many entries about Reggio Emilia. As a result of searching for “Reggio-Inspired Kit” on that site, a Page of References to Kits was generated, with examples of kits for geometry, measurement, number, and patterning.

The DIY part of the geometry kit uses sticks with Velcro dots glued to the ends – this makes it easy to play around with making figures by sticking the sticks together.

The measurement kit has cups for measuring volume. It has different shaped cups that have the same volume – this helps a child learn that different looking things can have the same size. The kit also has curved objects that challenge children to figure out their length. It also has sand timers that children can time.

The number kit has a bag of pebbles, a bag of beads, a bag of sticks, a spool of thread, sticks that have been glued together to form ten-frames with ten empty slots in the frame, dice, dominoes, and large wooden numerals.

The patterning kit is filled with small objects of lots of different colors and shapes. There are multi-colored beads with holes, and there are also washers, nuts, wing-nuts, and bolts. It also has colored crayons and pencils. All of these are great for letting the child create a sequence of physical or drawn objects to use for exploring patterns.

Montessori and Reggio Emilia

The key for creating inexpensive kits is to be on the lookout for materials around you that can be repurposed, and to be patient and long-term in your collecting. This is a well-developed skill among underfunded elementary school teachers. Whether it is pebbles, cereal boxes, buttons, twigs, leaves, pine cones, sand, cups, empty toilet paper rolls, egg cartons, or string, be on the lookout for simple and inexpensive resources to create educational kits for Reggio Emilia or Montessori.


If you have any questions or comments, please send them my way. I would enjoy the opportunity to chat with you. Also, if you are interested in collaborating with us or supporting us in any fashion, I would love to talk with you about ways we can work together!

Chris Wright
November 18, 2023

Chris@EarlyFamilyMath.org
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Early Family Math is a California 501(c)(3) nonprofit corporation, #87-4441486.

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