Manipulatives are hands-on learning tools that help students learn concepts concretely before moving to more abstract understandings. They allow students to explore ideas through active manipulation, helping cement understandings in ways that passive learning cannot. There are concrete, abstract, and virtual forms of manipulatives, each with advantages and disadvantages. Integrating different types of age-appropriate manipulatives into lessons can benefit student learning across subjects by appealing to different learning styles and building concrete foundations for abstract concepts according to Piaget's theories of cognitive development.

1. MANIPULATIVES DONE BY: KELLY-ANN CAMPO

2. WHAT ARE MANIPULATIVES?
The purpose of the manipulative is to assist children in
discovering their abilities that they would not discover
on their own and this aids in the learning process. The
manipulatives are provided by teachers and parents
with basic instructions, while students are allowed to
explore and ask questions as they feel the need to.

3. IMPOTRANCE OF MANIPUTALIVES
The purpose of the manipulative is to assist children in
discovering their abilities that they would not discover
on their own and this aids in the learning process. The
manipulatives are provided by teachers and parents
with basic instructions, while students are allowed to
explore and ask questions as they feel the need to.

4. IMPORTANCE CONT’D
 According to Piaget “children are active learners who
master concepts by progressing through three levels of
knowledge--concrete, pictorial, and abstract. The use
of manipulatives enables students to explore concepts
at the first, or concrete, level of understanding. When
students manipulate objects, they are taking the
necessary first steps toward building understanding
and internalizing processes and procedures.”

5. FROMS OF MANIPULATIVES

6. CONCRETE MANIPULATIVES
A mathematical concept is introduced with
manipulatives; students explore the concept using the
manipulatives in purposeful activity.

7. ABSTRACT MANIPULATIVES
Mathematical symbols (numerals, operation signs, etc.)
are used to express the concept in symbolic language;
students demonstrate their understanding of the
mathematical concept using the language of
mathematics.

8. VIRTUAL MANIPULATIVE
Virtual manipulative is defined as "an interactive,
Web-based visual representation of a dynamic object
that presents opportunities for constructing
mathematical knowledge. Virtual manipulatives have a
range of characteristics, such as pictorial images only,
combined pictorial and numeric images, simulations,
and concept tutorials, which include pictorial and
numeric images with directions and feedback.

9. ADVANTAGES OF CONCRETE
MANIPULATIVES
~ Simpler, more moveable
~ Tactile experience adds a dimension of learning
~ Allows student to be more creative selecting pieces
~ Student has more control
~ Process is traceable
~ Allows trial and error
~ Units are easier to distinguish, make the whole easier to
see
~ Easier to relate to real-world applications
~ Less expensive than technology
~ Allows me to be more cognitive of the operations I am
performing
~ Requires more thinking
~ Do not make me feel rushed
~ I was able to think about what it actually means to
multiply and divide fractions

10. ~ Students can be more creative
~ Allows teacher to involve the whole class in an
interactive lesson
~ It broke the concepts down for me in a way that I will
never forget.
~ Makes the concept stick better
~ Allow information to be received visually and
kinesthetically
~ Helps me understand the concepts better
~ “Clarifies misconceptions and builds connections
between mathematical concepts and representations,
encouraging more precise and richer understandings”

11. ADVANTAGES OF VIRTUAL
MANIPULATIVES
~ Immediate feedback—you know when it’s right or
wrong
~ Easier to maneuver and keep together
~ A lot quicker to grasp the concept
~ Offer a larger variety of experiences
~ Allow more complex operations to be learned
~ Catches the attention of the “technology generation”
~ Actually have to relate (what you’re doing with the
manipulatives) to the numbers
~ More accessible at home than the concrete ones
~ Gives step-by-step instruction, making me see what I
was really doing
~ Makes integer subtraction a lot more clear
~ Gives hints if you get the answers wrong
~ Would keep students’ attention
~ Often provides explicit connections between visual and
symbolic representations

12. DISADVANTAGES OF CONCRETE
MANIPULATIVES
~ Limited in the fractions that can be used (i.e., you
have
only a few denominators)
~ Can’t actually see the numbers on the manipulatives
so you may miss the concept
~ Requires internal affirmation rather than external*
~ No feedback on whether you are right or wrong**
~ Not very challenging
~ Doesn’t allow you to add or subtract fractions in your
head

13. DISADVANTAGES OF VIRTUAL
MANIPULATIVES
~ Can’t actually touch them
~ No instructions on how to enter a problem
~ Models for some content not yet available
~ Sometimes forces you to think abstractly
~ More suitable for use after a student who’s already
mastered the concept
~ Some make it too easy
~ Computers do the work for the students so they are
able to guess the correct answer
~ May limit the teacher’s ability to follow the students’
thought processes
~ I sometimes take the technology for granted and don’t
obtain a full understanding as to why a problem is
solved a certain way
~ It sometimes forces you to think abstractly
~ Takes away for the “hands and mind to work together”
~ Might feel like “do” vs. “learn/explore”
~ Doesn’t allow you to layer pieces to see equivalences
~ Doesn’t really make you find the answer on your own

14. INTEGRATION

15. INTEGRATION
Manipulatives can be integrated into any subject area,
student must be taken into consideration and their
learning abilities. Teachers should not force students, but
encourage them into accepting the manipulatives and
inform the students of the benefits of the manipulatives.
For example mathematics most of the time can be a
troublesome area of learning for students. Teachers can
associate different types of manipulatives for the students
so that they would have a better understanding of the
topics.

16. TYPES OF MANIPULATIVES
BASE TEN BLOCKS 2 COLOR COUNTERS

17. TYPES
UNIFIX CUBES PATTERN BLOCKS

18. TYPES
GEOBOARDS PIPE CLEANERS

19. CONCLUSION
According to learning theory based on psychologist
Jean Piaget's research, children are active learners who
master concepts by progressing through three levels of
knowledge--concrete, pictorial, and abstract. The use
of manipulatives enables students to explore concepts
at the first, or concrete, level of understanding. When
students manipulate objects, they are taking the
necessary first steps toward building understanding
and internalizing math processes and procedures.

20. REFERENCES
 www.hand2mind.com
 www.manipulativelearning.blogspot.com
 www.technology4all.uregina.wikispaces.net
 www.teachervision.com