Teaching with math manipulatives
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Teaching with math manipulatives helps children understand math concepts. Hands on learning or learning by doing keeps the students' attention as they naturally want to play with and explore objects.
When children can touch and move manipulatives or real things when learning new skills, their senses are involved in the learning experience. Children benefit when they are able to fully understand new concepts with concrete materials before they are expected to understand the same ideas with symbols.
Hands on Math 1, 2, 3s
Stages of hands on learning in math are often called:
- concrete
- representational or connecting
- abstract
The terms "concrete materials" and "manipulatives" are most often used to describe educational learning materials that are real or physical and tangible, for example, blocks, counters, popsicle sticks, pattern blocks, and base ten blocks.
The "concrete stage" occurs when children use only real objects to demonstrate an idea.
The "representational, connecting or pictorial stage" happens when children work with concrete objects as well as drawing pictures or diagrams to record their learning.
The "abstract" stage is when children use only symbols - numbers, words, pictures, or diagrams to represent their thinking.
10 steps to teaching with math manipulatives
1. Although it is tempting to have everything set up and ready to go in September, it is better to only put some of the math materials out to begin with. As children learn to care for each set of materials then introduce more.
2. When teaching with math manipulatives, tell the children the correct names for classroom materials and the categories they belong with. For example, "These are pattern blocks and they are part of the math equipment."
3. Teach the play boundaries for each new set of materials you present.
"These blocks are not for throwing or smashing against each other."
4. Teach the children how to clean up after teaching with math manipulatives. You have to spell it out for most kids.
"The pattern blocks are part of our math materials so we will store them in one of the blue tubs. Look at the picture on the front of the tub; it shows the pattern blocks. The words underneath the picture say pattern blocks. This is where you put the pattern blocks after you are finished with them..."
Remember, you don't teach all of this in one day.
5. When it’s time to clean up after teaching with math manipulatives, don't assume that your students are aware of safety issues. Children will throw objects across the carpet into a tub and accidentally hit another child. Many kindergarten children have only played with a few other children at a time and have to learn the dynamics of working within a larger group of people.
6. Always let young children play with the math manipulatives for at least two weeks before using them in a structured activity. This gives children a chance to explore the objects, find out what the manipulatives can and can't do, and gives them time to learn new vocabulary.
At this stage of teaching with manipulatives, sit with the children and add to their vocabulary as they play.
"Look, you are balancing the thicker, hexagon block on its side, but the thinner hexagon block falls over.. You can roll the cylinders and spheres easily, but not the cubes."
7. Finally you get to teach with the math manipulatives! Make sure each child has enough space to work. Individual plain plastic table mats or pieces of plain white card spread out in a circle on the carpet work well.
First teach kindergarten children (and older) new skills using only the math manipulatives. This is the concrete stage.
The children build sets of 4 objects many times with various blocks and objects. Give them plenty of time and opportunities to learn concepts at this stage. Only when they appear to successfully understand an idea with math manipulatives, is it time to move on to the representational or connecting stage.
8. Representational Stage
Next, introduce the same activity, only this time after you teach with the math manipulatives, model a pictorial representation of the skill. Model the process, verbalize your thinking as you do it and invite the children to participate. Have the children try the process and guide them to success.
Here, the children have built sets of 4 with blocks and then traced around the blocks to make pictures that represent their sets.
If any children seem ready they can add symbols (1,2,3, +,=) to their pictures.
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Symbolic stage
Only after a thorough understanding of the connection between math manipulatives and pictures or diagrams are children ready to work with symbols alone. Don’t rush things.
10. Surprise… just because a child seems to understand, what does "4" represent, at a symbolic level, don’t assume that they will understand "5". Start all over at the concrete stage, teaching with math manipulatives only.
TEACHER TIPIt is advisable to have a variety of materials when teaching with math manipulatives |
Printing symbols
Children need time to practice printing the digits 0 - 10, in order to be ready to use them later on. Start early in the year so children will not be struggling to print the numbers when they are recording their learning.
Children like to paint numbers with their fingers or brushes, to form numbers out of play dough, or to make numbers with a variety of art materials. When they have mastered the formation of numbers, then they can practice printing numbers and symbols smaller.
All math pages:
Teaching kindergarten & preschool math - how to teach kindergarten and preschool math concepts, sample step-by-step teach measurement, activities and games
Teaching with math manipulatives - how to teach with math manipulatives to help children understand math concepts
Best math manipulatives - choose materials that are useful for more than one math concept, work well for problem solving activities and are tough enough to withstand constant play
Teaching math vocabulary - learn how to teach math vocabulary and specific words as you demonstrate math activities and talk to your students about their math experiences.
Attribute blocks - how to use these math manipulatives for different features: shape, color, size and thickness to help promote logical thinking
Graphing 1 - how to teach graphing to preschool and kindergarten children, includes collecting data and organizing it in a variety of ways
Graphing 2 - more graphing ideas for young children
Measurement - how to find measurement to young children, find opportunities for students to order objects by size, color, shape...
Number Activities - how to provide experiences that build number sense
Number Games - how to improve children's number sense with easy games
Number Skills - what number skills do children need to know?
Pattern 1- how to teach children pattern concepts
Pattern 2 - ideas and games to teach children to recognize, create, copy and extend patterns
Pattern 3 - teach patterning skills to early childhood and preschool students
Sorting and classifying- how to teach children the important skills of sorting, comparing and classifying objects
Math & Literature Connections - how to combine math and literature, learn how to promote math skills as you share good literature
Ten Apples Up on Top - open-ended math activity with Dr. Suess
10 Little Rubber Ducks - ideas to promote math with this wonderful Eric Carle story
1, 2, 3 to the Zoo - another great Eric Carle book, practice counting, making number sets, ordinal numbers and more