VIRTUAL VS HANDSON MANIPULATIVES IN TEACHER EDUCATION: Is one type more effective than the other

1
VIRTUAL VS HANDS-ON MANIPULATIVES IN TEACHER
EDUCATIONIs one type more effective than the
other?

• Annita W. Hunt
• Linda E. Nash
• Kelli L. Nipper
• Clayton State University

2
INITIAL ACTIVITY

• Perform the indicated operation in base 5 using
  Color Tiles and paper Chip Abacus
• 415
• 245
• Repeat using NLVMs Base Blocks
• Which do you prefer? Why?

3
RATIONALE

• The teacher education classroom is the ideal
  setting in which to investigate the effectiveness
  of virtual manipulatives to teach conceptual
  understanding. In the process, preservice
  teachers build a deeper understanding of
  mathematics while participating in pedagogical
  research.

4
RESEARCH QUESTIONS

• What do teachers perceive as the advantages and
  disadvantages of each format?
• What role should each type play in mathematics
  teacher education?
• Might virtual manipulatives be more motivating to
  some students?
• Is there a difference in the effectiveness of
  the two formats in bridging to the abstract?

5
RESEARCH TELLS US

• Relationships formed by the use
• of manipulatives incorporate visual, tactile,
  and kinesthetic experiences.
• Adding cooperative learning and reflective
  discussion further enhances depth of
  understanding and the likelihood of retention.
• (Daniels et al., 1993 Garrity, 1998)

6
AND RESEARCH TELLS US

• Conceptual understanding is knowledge that is
  rich in relationshipsall pieces of information
  are linked to some network. (Hiebert Lefevre,
  1996)
• It is important for teachers to build their own
  conceptual understanding to enable them to
  identify and correct their students
  misconceptions and to learn to incorporate
  bridging construction into the course. (An,
  2005)

7
RESEARCH ALSO TELLS US

• In concurrence with many other researchers, Moyer
  et al. (2002) state,
• Because it is advantageous for students to
  internalize their own representations of
  mathematics concepts, interacting with a dynamic
  tool during mathematics experiences may be much
  more powerful for internalizing those
  abstractions.

8
ADVANTAGES?

• Various researchers have listed the following
  advantages for virtual manipulatives. They are
• Availablequantities and types of concrete
  materials may not be as available as virtual.
• Time-saving (1)teachers may not have time to
  make their own concrete manipulatives.
• Time-saving (2)virtual manipulatives take less
  time to manipulate
• Motivatingmiddle and high school students may
  find virtual manipulatives more desirable.
• Better connectorsvirtual manipulatives dynamic
  images may foster easier connections with
  abstract symbols.

9
THEORETICAL FRAMEWORK

• The incorporation of manipulatives in teacher
  education has a two-fold purpose
• to aid in preservice teachers having a better
  understanding of the mathematical concepts and
  purposes for procedures and
• to assist them in learning how to teach with
  more than just modeling a procedure on the
  chalkboard.
• (Vinson et al., 1997)

10
THE PROJECT

• Participants 26 middle grades preservice
  mathematics teachers
• Procedure Participants used both concrete and
  virtual manipulatives to explore operations on
  real numbers and compared the two types with
  respect to
• Ease of use
• Helpfulness for understanding the concept
• Other advantages and disadvantages

11
THE PARTICIPANTS

• The 26 middle grades preservice teachers
  consisted of
• 4 males and 22 females
• Age range 20 to 48 mean age of 32.8
• 13 African Americans, 12 Caucasian, and 1
  Hispanic
• Third-year students, Bachelor Degree program
• Mathematics concentration

12
PROCEDURE

• Participants used manipulatives to investigate
• FractionsEquivalence, addition, subtraction,
  multiplication and division
• IntegersAddition, subtraction and multiplication
• Prime NumbersSieve of Eratosthenes
• Non-decimal BasesAddition and subtraction
• Participants completed a survey comparing their
  experiences using both formats.

13
SETTING A

• In the classroom, students
• received instruction in using each concrete
  model.
• worked collaboratively to investigate concepts.
• discussed a variety of strategies.
• received feedback.
• were motivated by a looming performance
  assessment.

14
CONCRETE MANIPULATIVES

• Pattern Blocks
• Fraction Circles
• Cuisenaire Rods
• Two-color Counters
• Color Tiles
• Chip Abacus
• Decimal Mods
• Sieve of Eratosthenes

15
SETTING B

• Outside the classroom, students
• explored virtual manipulative models.
• worked independently to investigate concepts.
• were motivated by participation points for
  completing a survey of their experiences.

16
VIRTUAL MANIPULATIVES

• Pattern Blocks (NLVM)
• Fraction Circles (NLVM)
• Base Blocks Addition Subtraction (NLVM)
• Color Chips (NLVM)
• Sieve of Eratosthenes (NLVM)
• Fraction Models ICircles (NCTM Illuminations)
• Fraction Models IIRectangles (NCTM
  Illuminations)
• Fraction Models IIISets (NCTM Illuminations)

17
PRELIMINARY RESULTS

• Perceived Advantages of Concrete Manipulatives
• Simpler, more moveablemore manipulability
• Tactile experience adds a dimension of learning
• Allows student to be more creative, selecting
  pieces
• Student has more control
• Process is traceable
• Option of Trial and Error-Allowed to make
  mistakes

18
PRELIMINARY RESULTS

• Units are clearer, easier to distinguishparts
  that make the whole easier to see
• Easier to relate to real-world applications
  (e.g., cooking)
• Less expensive than technology
• Allow me to be more cognitive of the operations
  I am performing.

19
PRELIMINARY RESULTS

• Perceived Disadvantages of Concrete
• Limited in the fractions that can be used (i.e.,
  you have only a few denominators available)
• Cant actually see the numbers on the
  manipulatives so you may miss the concept
• No feedback on whether you are right or wrong
  (One student said, You have to figure it out for
  yourself!).
• Requires internal affirmation rather than
  external.

20
PRELIMINARY RESULTS

• Perceived Advantages of Virtual Manipulatives
• Immediate feedbackyou know when its right or
  wrong
• Easier to maneuver and keep together
• A lot quicker to grasp the concept
• Offer a larger variety of experiences

21
PRELIMINARY RESULTS

• Allow more complex operations to be learned
• Less messeasier to focus on
• Catches the attention of the technology
  generation
• Actually have to relate (what youre doing with
  the manipulatives) to the numbers

22
PRELIMINARY RESULTS

• Perceived Disadvantages of Virtual Manipulatives
• Cant actually touch them
• No instructions on how to enter a problem
• Models for some content not yet available
• Sometimes forces you to think abstractly

23
DATA ANALYSIS

• Comparison of Ease of Use and Helpfulness for
  Understanding by Format across Models
• ?63 of participants found concrete manipulatives
  easier to use than virtual.
• ?79 of participants found concrete manipulatives
  more helpful than virtual for understanding the
  concept

24
CONFOUNDING VARIABLES

• Order of experience
• Teacher facilitation vs. independent exploration
• Collaboration vs. isolation
• Accountability

25
REFINING EXPANDING

• Clarify terminology (concete, hands-on, virtual,
  manipulatives, visual)
• Control for confounding variables by refining
  procedures, clarifying surveys, equalizing
  accountability
• Broaden investigation to include other levels of
  teacher development

26
LOOKING FORWARD

• There is some indication that using virtual
  manipulatives as a follow-up to concrete ones may
  aid in bridging to the algorithms. More research
  needs to be done in Teacher Education settings.
• More research needs to be done to determine which
  work best for pre-K12 students so that our
  teachers are well prepared to teach.