could be used to assist students in the learning basic algebra. Student could use geoboards when
trying to identify simple geometric shapes. They could also use geometric solid models when
learning about spatial reasoning. Teachers could use standard and non-standard rulers and
measuring cups to represent length or volume in measurement lessons. The students could also
use tiles when trying to find the area or perimeter of an object. When it comes to data analysis
and probability, students could use spinners to find the probability of landing on a designated
area. They could also use number cases or dice to find the probability of rolling a certain
number or combination of numbers (“Using manipulatives”, 2009). The numbers of ways that
manipulatives can be used are limitless. In fact, some schools use math manipulatives as a way
to get parents involved. Stephen Currie, math specialist for grades Kindergarten through fourth
grade at Poughkeespsie Day School in New York, created ‘mathtubs’ to pique math interest for
both kids and their parents. Each Friday several students are selected to receive a mathtub,
which are not due back until the next Wednesday. The mathtubs are filled with “math games
and puzzles, two or more different kinds of manipulatives such as number cubes or tangrams and
math challenges—questions which required no materials but creative brain power” (Currie,
2005, p. 52). Feedback from the parents was both positive and helpful. “In general, the parents
appreciated the activities and were please to see their child engaged in mathematical thinking”
(Currie, 2005, p. 53).
USING MANIPULATIVES CORRECTLY
Manipulatives can be extremely helpful young children, but they must be used correctly.
Children must understand the mathematical concept being taught rather than simply moving the
manipulatives around. Smith (2009) stated that there are probably as many wrong ways to teach
with manipulatives as there are to teach without them. The math manipulatives should be
appropriate for the students and chosen to meet the specific goals and objectives of the
mathematical program. “The complexity of the materials provided will increase as children’s
thinking and understanding of mathematical concepts increase” (Seefeldt & Wasik, 2006, p. 93).
It is also important for teachers to allow their students to have free time to play with the
manipulatives. After the students have explored the manipulatives, “the materials cease to be
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Using manipulatives to teach, Page 4
toys and assume their rightful place in the curriculum” (Smith, 2009, p.17). Carol Seefeldt and
Barbara Wasik also think that teachers should provide children with opportunities to work with
materials with open-ended objectives that have no specific preset goals. These opportunities
allow the children the chance to explore their own questions and generate a variety of answers.
“These experiences help children think about their world in alternative ways and help them
understand that there are multiple ways to solve problems. Generating multiple solutions to
problems in an essential strategy in mathematics” (Seefeldt & Wasik, 2006, p. 250).
RESEARCH AND BENEFITS OF MANIPULATIVES
The use of manipulatives is recommended by the NCTM because it is supported by both
learning theory and educational research in the classroom. “Manipulatives help students learn by
allowing them to move from concrete experiences to abstract reasoning” (“Research on the”
n.d.). When students manipulate objects, they are taking the first steps toward understanding
math processes and procedures. “The effective use of manipulatives can help students connect
ideas and integrate their knowledge so that they gain a deep understanding of mathematical
concepts” (“Research on the, “ n.d.).
Over the past few decades, researchers have studied the use of manipulatives in several
different grade levels and in several different countries. The majority of the studies indicate that
mathematics achievement increases when manipulatives are put to good use. Many studies also
suggest that manipulatives improve children’s long-term and short-term retention of math.
Cain-Caston’s (1996) research indicates that using manipulatives helps improve the environment
in math classrooms. When students work with manipulatives and then are given a chance to
reflect on their experiences, not only is mathematical learning enhanced, but math anxiety is also
greatly reduced. Kenneth Chang (2008) examined the work of research scientist Jennifer
Kaminski and he found that children better understand math when they use concrete examples.
Puchner, Taylor, O’Donnell, and Fick (2008) conducted a case study which analyzed the
use of manipulatives in math lessons developed and taught by four groups of elementary
teachers. There four researchers decided to study the way teachers use the manipulatives rather
than studying the outcomes of the students. “The study found that in three of four lessons
studied manipulative use was turned into an end in and of itself rather than a tool, and that in the
fourth lesson manipulative use hindered rather than helped the student learning” (Puchner,
Taylor, O’Donnell, & Fick, 2008, n.p.). The researchers believe this occurred because of the
“deeply embedded focus in U.S. mathematics teaching on the procedure and the product” (2008,
n.p.). In a few of the lessons, the manipulative use became an exercise separated from the
solving of the problem. In the second grade lesson, the students simply copied the teacher’s
example and never attached meaning to the manipulatives. The teacher’s manipulative use and
misuse provided the researchers with a focus for further study. The researchers also realized that
“teachers need support making decisions regarding manipulative use, including when and how to
use manipulatives to help them and their students think about mathematical ideas more closely”
(Puchner, Taylor, O’Donnell, & Fick, 2008, n.p.). Catherine Kelly, a member of the Montana
Council of Teachers of Mathematics, stated that “teachers need to know when, why, and how to
use manipulatives effectively in the classroom as well as opportunities to observe, first-hand, the
impact of allowing learning through exploration with concrete objects” (Kelly, 2006, p.188).
Dave Munger, author of Researching Online, reported the results of a study designed to
describe the benefits of manipulatives. The sample consisted to two third-grade classes with
Journal of Instructional Pedagogies
Using manipulatives to teach, Page 5
twenty-six students. A two-week geometry unit from the Silver Burdett textbook was
administered in both classes. The experimental group teacher used mathematical manipulatives
to teach the concepts presented in the unit, and the control group teacher used only drawings and
diagrams to teach the concepts. “Analysis of covariance revealed that the experimental group
using mathematical manipulatives scored significantly higher in mathematical achievement on
the posttest scores than the control group” (Munger, 2007, n.p.).
Additional studies have shown that students who use “manipulatives in specific
mathematical subjects are more likely to achieve success than students who don’t have the
opportunity to work with manipulatives” (“Research on the,” n.d.). Some children need to use
manipulatives to learn to count, while other students’ understanding of place value increases with
the use of manipulatives. Research also indicates that using manipulatives is especially useful
for teaching low-achievers, students with learning disabilities, and English language learners.
CONCLUSION
Elementary teachers who use manipulatives to help teach math can positively affect
student learning. Students at all levels and of all abilities can benefit from manipulatives.
Mathematician, Seymour Papert, believes manipulatives are ‘objects to think with’.
“Incorporating manipulatives into mathematics lessons in meaningful ways helps students grasp
concepts with greater ease, making teaching most effective” (“Research on the, “ n.d.).
REFERENCES
Cain-Caston, M. (1996). Manipulative queen [Electronic version]. Journal of Instructional
Psychology 23(4), 270-274. Retrieved December 10, 2009 from Ebscohost database.
Chang, K. (2008, April 25). Study suggests math teachers scrap balls and slices. New York
Times. Retrieved December 10, 2009, from
http: //www.nytimes.com/2008/04/25/science/25math.html
Currie, S. (2005). The mathtubs are coming! Teaching PreK-8 35(4), 52-53.
Friedrich Frobel (2009, March 28). In Wikipedia, the free encyclopedia. Retrieved December
9, 2009, from http://en.wikipedia.org/wiki/Friedrich_Fr%C3%B6bel
Kelly, C.A. (2006). Using manipulatives in mathematical problem solving: A performance
Based analysis [Electronic version]. The Montana Mathematics Enthusiast 3(2), 184-
193.
Munger, D. (2007, October 9). Children learn and retain math better using manipulatives
[Msg.1]. Message posted to
http://scienceblogs.com/cognitivedaily/2007/10/children_learn_and_retain_math.php
Puchner, L., Taylor A., O’Donnell, B., & Fick, K. (2008). Teacher learning and mathematics
manipulatives: A collective case study about teacher use of manipulatives in elementary
and middle school mathematics lessons. School Science and Mathematics. Retrieved
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http://www.accessmylibrary.com/coms2/summary_0286-35888184_ITEM
Research on the benefits of manipulatives (n.d.). Retrieved December 9, 2009, from:
http://www.etacuisenaire.com/pdf/benefits_of_manipulatives.pdf
Seefeldt, C., & Wasik, B.A. (2006). Early education: three-, four-, and five-year-olds go to
School (2nd ed.). Upper Saddle River: Pearson Education.
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Smith, S.S. (2009). Early Childhood Mathematics (4th ed.) Boston: Pearson Education
Using manipulatives (2009). Retrieved December 10, 2009, from :
http://www.teachervision.fen.com/pro-dev/teaching-methods/48934.html |