This link has been bookmarked by 80 people . It was first bookmarked on 25 May 2008, by Erin Remple.
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Manipulatives enable students and teachers to represent concretely the abstract concepts that they are learning in mathematics class and to link these concepts to prior knowledge.
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Virtual versions of concrete manipulatives typically used in mathematics education, such as Base 10 Blocks, Cuisenaire Rods, and Tangrams, are available at no cost online.
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Concrete manipulatives help students with disabilities improve their understanding of the abstract symbolic language of mathematics.
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Virtual manipulatives may be particularly helpful to students with language difficulties, including English Language Learners.
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Many virtual manipulative activities give students hints and feedback, something that the more traditional concrete manipulatives cannot do without teacher assistance.
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They can also be used with interactive whiteboards, so that the teacher can involve the whole class in an interactive lesson (Mildenhall, Swan, Northcote, & Marshall, 2008).
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29 Jan 15
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05 Jan 15
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17 Dec 14
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16 Dec 14
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15 Dec 14
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alexis alexander"Learning Mathematics with Virtual Manipulatives
Abstract concepts are essential to understanding and performing mathematics. They are also a source of difficulty for many students who struggle with mathematics, many of whom find even basic mathematics concepts difficult to understand." -
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JoAnn ButtsIncludes an overview of the use of virtual manipulatives as well as links to examples.
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Carl Davis"Learning Mathematics with Virtual Manipulatives
Abstract concepts are essential to understanding and performing mathematics. They are also a source of difficulty for many students who struggle with mathematics, many of whom find even basic mathematics concepts difficult to understand" -
13 Nov 14
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Manipulatives enable students and teachers to represent concretely the abstract concepts that they are learning in mathematics class and to link these concepts to prior knowledge.
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Virtual manipulatives are basically digital “objects” that resemble physical objects and can be manipulated, usually with a mouse, in the same ways as their authentic counterparts
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no cost online
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limited research
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research into concrete manipulatives provides insight into their possible uses and benefits to learning
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resources
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research
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Using Manipulatives to Support Mathematics
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help students with disabilities improve their understanding of the abstract
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virtual manipulatives can make such connections explicit to students. For example, Pan Balance – Numbers
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concept of equality
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If the two expressions are equivalent, the pans are shown balanced (visual representation),
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(e.g., 6+8 and 7+7)
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symbolic representation)
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equation is presented
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classroom-based action research shows that student use of virtual manipulatives is sometimes more complex than their use of concrete manipulatives
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availability of unlimited objects—versus a finite set
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size, shape, and color of a block can be changed
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create more examples
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Because the time students would spend aligning and trading blocks is eliminated, there is more time for exploration.
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students may also develop more complex understandings of concepts
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helpful to students with language difficulties
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manipulative is that the student can select English, French, or Spanish for the display
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guidance in understanding the concepts that manipulatives represent
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Manipulatives by themselves have no inherent meaning
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help students build connections between the concrete materials and the abstract symbols
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Many virtual manipulative activities give students hints and feedback, something that the more traditional concrete manipulatives cannot do without teacher assistance
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hint function
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explicit connections between visual and symbolic representations
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easy to use and as engaging as concrete ones
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students benefit from teacher guidance to help them use the manipulative correctly and connect to the underlying math
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involve the whole class in an interactive lesson
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Choosing a Virtual Manipulative
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they need to be integrated into the curriculum and not just used as an adjunct activity
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opportunities for guided exploration
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level of difficulty be adjusted
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feedback do they provide
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teachers need to provide feedback and suppor
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clear are the instructions
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concept of equivalence.
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blocks can be dragged, rotated, and flipped in order to copy designs.
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elementary grades,
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Cuisenaire rods, base 10 blocks, pattern blocks, and fraction bars
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Tools are categorized by grade level.
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Manipulatives are sorted by grade level and math content area, and each manipulative includes instructions, suggested activities, lesson plans, and connection to relevant NCTM standards.
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base 10 blocks, pattern blocks, and algebra blocks)
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developing valid models to support understanding
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number and operations, geometry and measurement, function and algebra, and data analysis and probability
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how to use them in teaching and why the activity is useful
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of tools, lessons, and activities that are categorized and searchable by grade level and content
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free and open to all)
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Research Support
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sequence of instruction
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Concrete-Representational-Abstract (CRA)
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explicit instruction that moves students from concrete manipulatives to pictorial representations of those manipulatives and finally to abstract concepts
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compared the effectiveness
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using a CRA approach versus a Representational-Abstract (RA) approach
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While both groups improved their understanding of fractions, the CRA group had overall higher scores than the RA group.
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solve algebraic equations using
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CRA approach or a traditional
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After a 4-week intervention, both groups showed improvement, but those taught with the CRA group significantly outperformed those who had received traditional instruction.
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but continued to improve after the manipulatives were withdrawn
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19 second grade
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nabled students to demonstrate more sophisticated strategies and explanations of place value
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treatment group improved significantly on both the Grade One and Grade Two tests
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control group showed significant improvement only on the Grade One test
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showed increased motivation and increased time on task
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using the virtual blocks, most students created more complex patterns and used more total blocks.
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showed more sophisticated strategies after using the virtual manipulatives
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English Language Learners were able to demonstrate their understanding of place-value concepts even though they could not explain them verbally
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The CRA studies described above also demonstrate the importance of structure and guidance in linking concrete materials to abstract concepts.
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feedback
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appreciation for the immediate feedback possible with the computer-based manipulatives.
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09 Oct 14
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23 Sep 14
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24 Jun 14
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05 May 14
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10 Jan 14
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20 Dec 12
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A popular approach to help students understand abstract concepts is the use of manipulatives.
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Concrete manipulatives help students with disabilities improve their understanding of the abstract symbolic language of mathematics
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clarify misconceptions and build connections between mathematical concepts and representations, fostering more precise and richer understandings
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trouble connecting visual and symbolic representations
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virtual objects can be altered in ways that concrete ones cannot, for example, the size, shape, and color of a block can be changed.
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With virtual manipulatives, they may be better able to clarify their thinking and demonstrate it to others
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It is important for teachers to make this meaning explicit and help students build connections between the concrete materials and the abstract symbols that they represent.
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Many virtual manipulative activities give students hints and feedback, something that the more traditional concrete manipulatives cannot do without teacher assistance.
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They can also be used with interactive whiteboards, so that the teacher can involve the whole class in an interactive lesson
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- Can the level of difficulty be adjusted for different students?
- What type of feedback do they provide?
- Will teachers need to provide feedback and support?
- How clear are the instructions for use?
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08 Oct 12
Danielle Bryantresearch
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01 Oct 12
Katie HarrisThis site gives an academic overview of virtual manipulatives. What they are and supporting research. There are also many links to further support and websites with manipulatives available.
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05 Sep 12
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26 Aug 12
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19 Jun 12
Carley SchopfThis website provides a description of how to use virtual manipulatives in the classroom and websites that you can use to access virtual manipulatives. Each link has a brief description of what type of manipulatives are available for the students.
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12 Jun 12
Cynthia FeistCenter for Implementing Technology in Education resources for virtual math manipulative
18oct2012 math virtual manipulatives mathematics assistivetechnology cindy
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22 Apr 12
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19 Mar 12
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10 Jan 12
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01 Jan 12
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14 Dec 11
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01 Dec 11
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26 Nov 11
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21 Sep 11
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28 Jun 11
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20 Mar 11
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Manipulatives enable students and teachers to represent concretely the abstract concepts that they are learning in mathematics class and to link these concepts to prior knowledge.
-
As virtual manipulatives are relatively new, there is limited research on their effectiveness. However, research into concrete manipulatives provides insight into their possible uses and benefits to learning.
-
Concrete manipulatives help students with disabilities improve their understanding of the abstract symbolic language of mathematics.
-
abstract symbolic language
-
Students who struggle in mathematics often have trouble connecting visual and symbolic representations
-
availability of unlimited objects—versus a finite set
-
Thus, in many instances, students can create more examples using virtual versus physical objects.
-
Virtual manipulatives may be particularly helpful to students with language difficulties, including English Language Learners.
-
With virtual manipulatives, they may be better able to clarify their thinking and demonstrate it to others.
-
Manipulatives by themselves have no inherent meaning.
-
make this meaning explicit and help students build connections between the concrete materials and the abstract symbols that they represent.
-
Many virtual manipulative activities give students hints and feedback, something that the more traditional concrete manipulatives cannot do without teacher assistance.
-
students benefit from teacher guidance to help them use the manipulative correctly and connect to the underlying math.
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20 Feb 11
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21 Sep 10
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Resources
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03 Sep 10
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16 Aug 10
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06 Aug 10
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15 Jun 10
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08 Apr 10
Anna-Marie RobertsonCenter for implementing technology in education: Multimedia Technologies
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Virtual manipulatives may be particularly helpful to students with language difficulties, including English Language Learners. These students often have trouble explaining what they are learning in math. With virtual manipulatives, they may be better able to clarify their thinking and demonstrate it to others.
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10 Mar 10
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26 Feb 10
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11 Nov 09
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11 Mar 09
Lee-Anne PattersonAbstract concepts are essential to understanding and performing mathematics. They are also a source of difficulty for many students who struggle with mathematics, many of whom find even basic mathematics concepts difficult to understand. A popular approach to help students understand abstract concepts is the use of manipulatives. Manipulatives enable students and teachers to represent concretely the abstract concepts that they are learning in mathematics class and to link these concepts to prior knowledge. Although they are used primarily in the elementary grades, they offer a useful means to introduce new concepts to all students.
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15 Feb 09
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25 May 08
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