## In Teaching And Learning

Mathematical manipulatives play a key role in young children’s mathematics understanding and development. These concrete objects facilitate children’s understanding of important math concepts, then later help them link these ideas to representations and abstract ideas. For example, there are manipulatives specifically designed to help students learn fractions, geometry and algebra. Here we will look at pattern blocks, interlocking cubes, and tiles and the various concepts taught through using them. This is by no means an exhaustive list , rather, these descriptions will provide just a few ideas for how these manipulatives can be used.

## Using Virtual Manipulatives To Teach Math

**Using manipulatives in mathematics instruction can help you to address state standards for mathematical practice.**

Abstract concepts are essential to understanding and doing mathematics. They are also a source of difficulty for students who struggle with mathematics, many of whom find even basic mathematics concepts hard to understand. Teachers often use tangible materialsreferred to as manipulativesto concretely represent these abstract concepts and help their students understand them. Manipulatives can also be used to help students link these concepts with prior knowledge. Using manipulatives in mathematics instruction can help you to address math standards, particularly standards related to making sense of problems and;abstract reasoning.

In the past, most classrooms only had physical manipulatives. Today, however, more classrooms have improved access to computers and the Internet, and virtual manipulatives are becoming increasingly common. Virtual manipulatives can be useful tools for students, and they can help them learn how to use;appropriate technology tools for mathematics.

Virtual manipulatives can benefit your students in several ways. Using these tools in your classroom can:

- Help students understand abstract mathematics concepts
- Lead to a richer and more complex understanding of concepts
- Help clarify student misconceptions and build connections between concepts and representations

## The Importance And Benefits Of Math Manipulatives In Elementary Students

Boggan explained the importance and benefits of math manipulatives. The value of manipulatives has been recognized for many years, but some teachers are unwilling to use them in teaching. Elementary teachers who use manipulatives to teach mathematics can positively affect student learning. Students at all levels and of all abilities can benefit from manipulatives.Bradley et.al. examined teachers attempt to improve instructional strategies for teaching mathematics in an elementary

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## Brought To You By Teacher Created Resources

Teacher Created Resources produces;high quality educational materials for PreKGrade 8. They also help teachers create stimulating learning environments by producing colorful decorations, manipulatives, and organizers. Learn more about their products on their website.

Students learn better when theyre engaged, and manipulatives in the classroom make it easy for kids to get excited. We recently asked a group of elementary school teachers to come up with unique ways to use manipulatives in the classroom to teach math. They definitely delivered by sharing some awesome ideas!

**FOAM DICE***This 20-dice set** is a mixed set: Half have numbers 16 on them and the other half have 712. Who doesnt like to roll dice? The physicality and the suspense instantly make learning more fun.*

**1. Teach place value.** Give each student a handful of dice and have them roll. Then have them randomly arrange the numbers they rolled on their desk. Have them write down which number is in the hundreds place, tens place, ones place and so on. Its a simple activity, but its lots of fun. *Karen Crawford, second grade, Houston, Texas*

**4. Practice makes permanent.** Foam dice are wonderful for developing fact fluency in primary students. The kids can use them to practice addition and subtraction facts within 20. Use them in conjunction with the sand timer or with recording sheets. *Liz Rauls, K2 special education teacher, Hillsboro, Missouri*

## Math Manipulatives During Lessons

I use math manipulatives for almost every math lesson I teach. When planning my lessons, I think of ways that the concepts can be explained using visuals, as well as orally or on a chart. I prep tools ahead of time so they are ready for our lessons. I vary the tools for;students to get practice using different types. During our lessons, math manipulatives are used usually during or after the initial lesson is taught. I will explain a;concept, give examples on a chart, practice orally, and demonstrate with math manipulatives. Students use those manipulatives to practice the concept or solve a problem.

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## Kids Dont Learn Math Because They Use Manipulatives; They Learn Because They Think About The Manipulatives

Simply demonstrating a concept with manipulatives doesnt guarantee that a child will understand the concept. For manipulatives to be effective, kids need time to **think** about what the manipulatives show.

One of the best ways to help your kids think about manipulatives to **ask lots of questions** as you teach. How do you know? is an especially powerful question. It allows you to check that your child really understands the concept and isnt just guessing or following a pattern that he doesnt really understand.

For example, lets say youre using bundles of straws to teach place value.

You might ask:

- How many straws are there?
*39* - How can you tell without counting every straw one-by-one?
*There are three bundles of ten straws, so thats thirty. There are nine loose straws, so thats nine more. So, there are 39.* - If I took a straw away, how many would there be?
*38* - If I took a bundle of straws away, how many would there be?
*29* - If I added a straw, how many would there be?
*40* - If I added a bundle of straws, how many would there be?
*49* - How could you use dimes and pennies to show the same number of cents? How are the dimes like the bundles? How are the pennies like the loose straws?
*I could use 3 dimes and 9 pennies. The dimes are each worth ten cents, just like each bundle has ten straws. The pennies are each worth one cent, just like each loose straw is one straw.*

## Elementary Methods : Teaching Mathematics

Teaching MathematicsSummary:With the implementation of Common Core, there is a misconception that students are learning ?new math.? However, students are not learning new concepts, just a new way of thinking about those concepts. In this unit, you will explore some effective instructional strategies and approaches to teaching students, way to get them to think mathematically, how to bridge the gap between concrete and abstract and incorporate technology to allow for more instructional time in the classroom

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## Why Does This Strategy Work

Its a twist on linking concrete, representational, and abstract together! Often we work *forward* with our students beginning with a concrete or representational model and then writing an equation or statement that matches their model.

This approach considers how to use math manipulatives in a supportive way to teach our students! But when its time to take the supports away, working backward forces our students to attempt the work at a higher level while still offering the supports as needed to check their understanding.

## Free Number Sense Email Series

Sign up for the building number sense email series filled with effective strategies, must try activities, and FREE resources to build routines in your classroom. Everything you need to help kids grow their number sense and have fun at the same time!

Success! Now check your email to confirm your subscription to the FREE email series. Stay tuned for the number sense email series coming your way soon! -Elyse

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## Three Steps To Avoid Over

#### Step 1: Hands On

When you first introduce a concept or strategy to your child, you want your child to have his *hands on* the manipulatives. He should often touch and move the manipulatives as he grapples with the concept that youre teaching.

#### Step 2: Hands Off

But once your child can easily and confidently solve problems with the manipulatives, let him set up the problem with manipulatives, but then take his *hands off*. Have him visualize moving the objects rather than physically touching them.

#### Step 3: Eyes Closed

When your child can solve problems without touching the manipulatives, encourage him to begin to visualize the manipulatives. Have him *close his eyes* and imagine moving the manipulatives around to solve the problem.

**In this 3-minute video, youll see what the three steps look like in action when applied to simple addition.**

Once your child can solve problems by visualizing manipulatives, hes ready to solve problems with pencil and paper. Allow him to go back to the manipulatives if he really gets stuck or confused, but encourage him to visualize the manipulatives as much as possible. With some practice, hell rely on the visuals less and less as he solves problems.

## Moving From The Concrete To The Abstract

Research suggests that the use of manipulatives in math instruction is particularly helpful in getting children to move from concrete to abstract understanding. For place value lessons moving from the concrete to the abstract could include pebbles, bundled straws, base-ten blocks, chip trading, and the abacus. Hilde Howden reminds teachers to pay careful attention to the bridge between concrete and abstract. Even with scaffolding, students who can solve a problem at the concrete

level, may not be able to solve the same problem at the abstract level. Howden notes that the bridge must be created by careful choices of manipulatives.18

For example, The Middle Grades Mathematics Project is an activitybased program that uses manipulatives such as tiles, cubes, geoboards, dice, and counters. Using these materials, students can explore various math challenges by building, drawing, and problem-solving with their peers. In middle or high school algebra, using tiles can help students better make the transition to the abstract level of algebra. Connecting geometry to algebra allows students to apply previous knowledge to new topics. While working with the tiles, students are encouraged to draw pictures and to see mental images which helps them understand an application of abstract math.19

New brain research reveals the importance of visual thinking to all levels of math… Visual mathematics problems help students and raise achievement.

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## Using Manipulatives To Support Math Learning At Home

Many students struggle with math. The thought of juggling arithmetic, algebra, geometry, and fractions is enough to make them anxious. But for the **estimated 3 -9% of students with learning disabilities in mathematics** , math may be even more challenging. Students with LDs may have trouble learning number facts, doing calculations, understanding visual-spatial relationships, or solving math problems. These difficulties mean that on paper, math often looks like a bunch of abstract symbols.

## Benefits Of Virtual Manipulatives

Virtual manipulatives can benefit your students in several ways. Using these tools in your classroom can:

- Help students understand abstract math concepts.
- Lead to richer and more complex understandings of concepts.
- Help clarify student misconceptions and build connections between concepts and representations.

These tools can be especially helpful for students with disabilities. Virtual manipulatives can improve their understanding of the abstract symbolic language of math. Students who struggle in math often find it hard to connect visual and symbolic representations. Virtual manipulatives can help make these connections clear.

In addition, virtual objects can be altered in ways that concrete ones cannot. For example, the size, shape, and color of a block can be changed. This means that, in many cases, students can create more examples using virtual versus physical objects. An added benefit of virtual manipulatives is that many of them give students hints and feedback, which allows them to practice on their own, without teacher assistance.

Due to these features, virtual manipulatives may be especially helpful to students with language difficulties, including English Language Learners. These students often have trouble explaining what they are learning in math. Virtual manipulatives may help them clarify their thinking and share it with others.

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## A Benefits Of Using Manipulatives

benefit of using manipulatives is that it helps children to understand mathematical concepts as they can physically move the object around. Especially with young children when they are being introduced to new maths topics, these children will struggle to just sit and watch a teacher talk, due to their concentration being poor. Learning through observation will mean that children will be at all different levels due to students preferred learning styles. If they are able to see how it works by watching

## Ten Steps To Teaching With Math Manipulatives

Steps 1 5 are all about establishing boundaries when using math manipulatives so the classroom does not end up in a chaotic mess everyday! Steps 6-10 are about using them as learning tools.

Step 1. Although its tempting to have all your;math manipulatives set up and ready to go in September, its easier to train your students to clean up and learn routines when you put out a few tubs at a time.;;As children learn to care for each set of materials. then introduce more.

Step 2. When teaching with hands-on materials, teach the children the correct names for them;and the classroom category they belong with. For example, These are pattern blocks and they are part of the math materials. All the math materials are in blue tubs.

Step 3.;Teach the boundaries for each new set of materials you present. These blocks are not for throwing or smashing against each other. They stay on the math carpet.

Remember, you dont teach all of this in one day! The first month of school is training time.

Step 4. Teach the children how to clean up. You have to spell out the process for most kids and repeat it often! See a sample dialogue below

Step 6. ;Young children need to play with each math manipulatives for at least two weeks before you attempt to use the manipulative for a structured activity. This gives children a chance to explore the objects, find out what each item can and cant do, and gives them time to learn new vocabulary.

And finally, Step 10!!

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## Connect: Link School To Home

Families can practice these counting strategies at home with their kids. Because families may not be familiar with counting all and counting on, its important to explain the strategies to them. Consider creating and sharing a video to demonstrate the strategies. Provide a list of ideas for counting manipulatives that families may have at home .;;

Board games like Hi Ho Cherry-O are also a great way for families to practice counting together. Additionally, kids can practice at home with online learning games or apps. Some games that are free to try are Tiggly Chef: Preschool Math Cooking Game or Moose Math by Duck Duck Moose.

## For The Sake Of Your Sanity: Explore Then Teach

Any time you first introduce your child to a new manipulative, **make sure you allow some free play and exploration time before trying to teach a focused lesson.** Otherwise, youll spend the whole lesson trying to get your child to stop arranging the plastic teddy bears for a tea party or building a Jenga-style tower out of the Cuisenaire rods.

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## Considerations For Effective Use Of Manipulatives

Finally, there are several key considerations that can assist teachers with utilising manipulatives.

**Have a clear rationale**

Ensure that there is a clear rationale for using a particular manipulative or representation to teach a specific mathematical concept. Manipulatives should be used to provide insights into increasingly sophisticated maths.

**Make connections between manipulatives and mathematical ideas**

Enable students to understand the links between the manipulatives and the mathematical ideas they represent. This requires teachers to encourage students to link the materials to the maths of the situation, to appreciate the limitations of concrete materials, and to develop related mathematical images, representations, and symbols.

**Avoid reliance**

Try to avoid students becoming reliant on manipulatives to do a type of task or question. A manipulative should enable a student to understand maths by illuminating the underlying general relationships, not just getting them to the right answer’ to a specific problem.

**Use manipulatives as a scaffold**

Manipulatives should act as a scaffold’, which can be removed once independence is achieved. Before using a manipulative, it is important to consider how it can enable students to eventually do the maths without it. When moving away from manipulatives, students may find it helpful to draw diagrams or imagine using the manipulatives.

**Use manipulatives across all ages**

**References**

## How To Use The Math

Many people wonder how they should use the Math-U-See manipulatives to teach math. If you dont use them properly, they are not going to be very helpful. They are such an integral part of the Math-U-See program that it might be useful to understand Steve Demmes intention in creating them in the first place.

Steve believes that math is a topic that is learned to be applied in real life. This real-life application is usually demonstrated in curriculum in the form of word problems. In order to use math in real life, its important that students not only know formulas and procedures, but that they also know the concepts behind the procedures, and the formulas. In other words, to understand how to solve a problem, but also why we solve it that way, and even when the solution requires multiplication, division, even algebra.

Steve and Math-U-See use a number of little tricks that help students memorize math facts, such as acronyms, mnemonics, and visualizations. But if the student doesnt have a healthy grasp of the whole concept of math, they are unable to be good problem solvers when faced with real life scenarios.

**Related blog post:**__Make Memorizing Math Facts Fun With These 10 Activities__

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## Younger Children Need More Manipulatives

Little children are very concrete learners. They can reason about real objects, but they have trouble;thinking abstractly about numbers.

My 5-year-old is very much in this concrete stage right now. If I show her 5 blocks and ask how many will be left if I take away 2, she knows;that 3 blocks will be left. But if I *write* 5 2, she immediately gets confused and frustrated. No matter how much I explain what the minus symbol means, her brain just isnt ready to handle it.**;**

Once children are about 10, they learn to reason more abstractly, and so they start to need fewer manipulatives.

No matter how old your children, always remember that manipulatives are there to serve a purpose. Gradually encourage your children to visualize the manipulatives and use the manipulatives less until they no longer need them.

- Related: How to Use Math Manipulatives