What the heck is Rekenrek ?

It was designed by a Dutch man – Adrian Treffers, a mathematics curriculum researcher at the Freudenthal Institute in the Netherlands – to support the natural development of number sense in children. Dutch word “reken” shares the same root as the English word “reckon” – to count or calculate. The word “rek” means rack. Therefore a “rekenrek” is a counting rack or a calculating rack – not an abacus. It builds numbersense in children. Amy gives more than a dozen reasons for using Rekenrek in a classroom setting or home schooling setting

It is visual and clear.
It is a concrete tool.
It is interactive and hands-on.
It requires almost no time to distribute and put away.
It is versatile, covering many mathematical concepts.
It is a one-time, cost-efficient purchase.
It is mess-free (no parts to lose or replace).
It allows for a variety of problem solving methods.
It can help you to quickly assess children’s understanding and misconceptions.
It encourages and simplifies math talk.
It encourages math reasoning.
It enables students to show their understanding.
It can be visually understood by all – regardless of what language you speak.
It allows for maximum practice of the “no-excuse” mental math facts.

20 Bead Rekenrek

100 Bead Rekenrek

Manipulatives - no more excuses

I learnt a new word “manipulative”. All the math toys that aim children to learn math are called manipulative.

From Wiki:

In mathematics education, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts through developmentally appropriate hands-on experience.

Amy makes a case for using 20 bead and 100 bead Rekenrek in all the schools. She lists out all the excuses that a teacher might have in using any manipulative in an academic curriculum and then gives arguments of how Rekenrek makes all those excuses irrelevant.

Should one buy a 20 bead or a 100 bead Rekenrek ? Both says, Amy

The 20 rekenrek is the perfect tool for learning, practicing and solidifying facts (or number bonds) to 20. I do not like to use the large rack for teaching the mental math strategies. I also feel that the 20-bead is the best one for younger-grade students that need to have a solid understanding of numbers up to 10 and 20. Okay, I also like the fact that when you begin with the 20-bead and then “upgrade” to the 100-bead, students will gasp and get excited about using the “big” ones. I crave the gasps and enthusiasm as students in my class grow to love math. I cannot help it. The 100-bead rekenrek is for addition/subtraction up to 100, fractions, decimals, percentages, rounding numbers and multiplication facts. Once you learn how use the 100 rekenrek you will wonder how you ever taught these concepts before without it!

Basics

Two rules of Rekenrek

Ensure that Rekenrek beads are all positioned in such a way that red beads are ready to go to left. We read from left to right and hence when the beads are moved, our eyes should read numbers from left to right
One finger, One push: The students should told to push a number all at once with one finger, rather than pushing one at a time.

Math Talk

Verbalize or Math talk:are. Math talk is key to assessing what students know and what they are confused about, but many students often struggle to explain their thoughts.
- Rekenrek can be used an anchor to start students verbalize about numbers by asking questions such as “How to build 6 using Rekenrek?”
  - Gamification : Call students on thumb and baby finger phone and ask them to verbalize construction of some number of Rekenrek
- Useful prompts for math talk with students
  - What was the first thing you did?
  - How did you figure out your answer?
  - Can you show me/us?
  - Can you prove it to me/us?
  - Can you explain your thinking?
  - Are you sure?
  - How do you know?
  - Did anyone do it a different way?
- Stem sentences to encourage reasoning: “If I know 5 + 5 is 10, and 5 + 1 is 6, then I know 6 + 6 = 12, because I can see 5 red beads and another 5 red beads and 2 white beads. 5 + 5 + 2 = 12.”
- Prompts
  - If I know…
  - I know this because…
  - The strategy I used was…
  - I started by…
  - I noticed that…
  - I checked by…
  - I can prove my thinking by…
  - I thought about it in a different way…
  - This is confusing to me because…
  - This makes sense to me because…

Skills for the early learner

If a child can count till 20, that does not mean he/she understands numbers. We know that children need many, many opportunities to solidify number sense. They need to partition numbers in a variety of ways, count on, count back, subitize and most importantly understand place value by knowing that ten 1s is the same as one 10.

The skills that can be taught to early learner are:

Subitizing : Knowing an amount without counting
One more or one less: Get the student to build a number and then have them move one more bead
Ten more or ten less: “Ten more” is another huge feat. Previously, I always used the hundred chart for this strategy. Now I use the hundred chart along with the 100-bead rekenrek. If you build 23 and ask students to show ten more, the idea of what changes and what stays the same becomes clear. Students begin by building 23 on the top three rows: two complete rows and three beads on the third row. By adding another full row (the fourth row), they are able to see how the 1s stay the same and the change is in the 10s.
Teen numbers: The problem with teen numbers is in the way we say them. It would be more logical to write “sixteen” as “61”. I mean, what do children hear first? “Six” – so they write a 6 down. If only we called it “teensix”, students might actually scribe it correctly as “16”!
Skip counting: Hand out the rekenreks. Ask students to mirror what you do. Tell them to say “push” as they push over two beads, then say “2” when the beads have stopped on the other side. It is important for them to say “push” rather than saying the number before pushing. You want them to see the total number rather than guess. They can practice this silently at their desks after modeling and calling out the answers together as a class.
Skip count backwards
Turnaround facts – commutativity
Number bonds let students split numbers in useful ways. They show how numbers join together, and how they break down into component parts.
Recording findings pictorially

Introductory Games

Amy gives a list of games that can be used to make the class interesting and fun

Can you build what I have built ?
My way: Build a number using top and bottom beads, announce the sum and ask the students to guess the way it has been done

Mental Math strategies

Amy gives a list of activities that can be used to teach mental math strategies. She provides prompts and examples for teachers to quickly incorporate them in their lesson plans

Doubling numbers : Using Rekenrek to induce strategy of partitioning a number to easier numbers so that doubling can be fast and accurate
Near doubles addition
Two apart strategy
Briding to 10 or making 10
Number bonds to 10 and 20
Advanced number bonds with 100 bead Rekenrek
Making 100

Addition

Try to use multiple representations of the word “addition” while describing the problem such as as “altogether”, “both”, “combined”, “how many”, “increase”, “join”, “sum”, “together”, “total”.

The advantage of using Rekenrek to teach addition is that you are helping the child decompose numbers and add it up.

Amy also suggests using story problems to make addition concepts more sticky

I begin the story problems and word problems using very clear examples. In the lower grades, students are most successful when they can visualize the problem and therefore I start with stories on the 20 rekenrek. I choose examples such as the following: There are 11 books on a bookshelf. Some are on the top shelf and some are on the bottom shelf. How many could be on the top and bottom? It is open ended with many possibilities. Clearly, I want students to build these numbers thinking of the rekenrek’s rods as shelves that the books are placed on. I can then give examples of closed questions. There are 8 books on the top shelf and 5 books on the bottom shelf. What is the total number of books on the bookshelf?

Rest

There are chapters on Subtraction, Multiplication, Fractions, Decimals and Percentages, Rounding numbers in the book that can be used by teachers to illustrate via Rekenrek. In a way it is fascinating that a single manipulative can be used to teach all the concepts that build numbersense in children.

Useful links for teachers

Takeaway

The book is a great resource for teachers looking to use Rekenrek to teach numbersense to children. The fact that a single tool can teach almost all the mathematical operations around numbers should make it an appealing alternative to all the other set of tools that a teacher might be using in a class. If you are parent, just buying a Rekenrek and letting your kids play with them might be a good idea to inculcate numbersense in them.