Academic Exchange Quarterly Spring 2002 ISSN 1096-1453 Volume 6, Issue 1
Teaching
Math Effectively to Elementary Students
Karen Burke, Ed. D.
and
Rita Dunn, Ed. D.
KAREN BURKE is assistant professor, Child Study
Department and director,
RITA DUNN is professor, Division of Administrative
and Instructional Leadership and director, Center for the Study of Learning and
Teaching Styles,
Dr.
Dunn, author of 23 textbooks and more than 300 published articles, chapters, and research reports, also is the recipient
of more than 20 recognitions/citations for the quality of her research.
Abstract
This article describes why
certain students achieve poorly in conventional classes and the need to teach
global, tactual, and/or kinesthetic elementary- school learners with
instructional resources that complement their identified learning-style
strengths. It provides practical guidelines for redesigning traditional
classrooms to increase their responsiveness to such students and outlines
practical curriculum applications and the research basis for this position.
Descriptive
Keyword: Learning Styles
Teaching
Math Effectively to Elementary Students
·
Eliza’s big
brown eyes filled with translucent tears as she raised her head from the top of
her desk and looked square into Mrs. Scheiring’s face. “I don’t know,” she whimpered. “I really
don’t know! And even if you say100 times more that I do, I still
don’t know! No ma’am! I sho’ ‘nuff don’t!”
·
Raphael followed
his teacher’s directions. He placed the crayon into its box, stopped tapping
the ruler, sat up in his seat, and pulled his feet in under his desk. However,
even with nothing in his hand and the feet out of sight, every inch of the
child vibrated with an electric energy that emanated from the depth of his soul
rather than from the activities in which he periodically engaged during each
lesson. If it could have been harnessed, there might have been enough energy to
fuel a motor! The child just could not sit still!
·
The substitute
was obviously exasperated! “How many times do I have to explain the same
thing?” she asked. Josie wilted. “I only asked you twice, “ she answered. “Yes,
but if you only would listen, you wouldn’t have to ask at all,” the sub
scolded. “Josie does listen,”
one of the boys called out. “She just can’t remember what she hears!” “Why not?” the sub questioned. “Josie’s
defender responded, “She just doesn’t!
Write it on the board. After she copies and illustrates it, she
remembers!” The sub couldn’t wait for the day to end!
……………………………………………………
Most teachers cannot
pinpoint exactly why certain children do not understand
clearly-delivered sequential lessons, do not “sit still and pay attention,” and
do not remember what they hear. However, teachers with learning-style
backgrounds recognize those traits immediately and know how to help those
youngsters. Rita and Kenneth Dunn (1992) describe 21 variables that
significantly impact how people learn. Included in that number are children who
process information globally and others who may be tactual or kinesthetic
learners.
Teaching
Global Learners
Mager (1967)
and Hunter (1990) urged teachers to introduce lessons with
clearly-stated behavioral
objectives; they insisted that students must be made aware of exactly what they
need to learn and how they can show that they have mastered it. They were
correct—but only for analytic processors, the minority who learns in a
step-by-step sequenced series of facts. Global students, the majority of
elementary school students, learn differently from their analytic counterparts.
They need to understand why they must learn specific content before they are
exposed to the details and facts related to it.
To teach global processors, we
need to:
(1) introduce
each lesson by relating its content to our students’ lives. Thus we should
begin the lesson with a short (a single paragraph or two) dramatic anecdote
that describes how, what the youngsters need to learn, directly applies to
their lives. Then we should identify the objectives
for that lesson;
(2) teach
with humor, songs, poetry, drama, and color. You quickly will see how many
youngsters who rarely paid attention suddenly become—and remain—involved in
what we are teaching when we teach it differently;
(3) incorporate
lots of pictures, drawings, graphics, and charts into our explanations;
(4) permit
some flexibility in how and where students learn. For example, global learners
tend to concentrate best: (a) in soft, rather than bright, lighting; (b) while
seated causally in a relaxed environment rather than at their wooden, steel, or
plastic desks and chairs; (c) with soft music without lyrics; (d) when permitted short
60-second breaks to review--with a classmate or two, the content they were
taught during the previous15 minutes; and (e) when allowed to learn while snacking
(Dunn & Dunn, 1992). Although these guidelines defy conventional classroom
practice, they produced statistically higher standardized achievement test
scores in poverty, minority, poorly-achieving schools throughout the
(Alberg, et al., 19 92; Andrews, 1990; Brunner & Majewski, 1990; Dunn, 2000: Dunn &
DeBello, 1999; Dunn, et al., 1995; Klavas,
1994: Koshuta & Koshuta, 1993; Kyriacou & Dunn, 1994; Lemmon, 1985; McManus,
2000; Neely &
Alm, 1992, 1993; Orsak, 1990: Quinn,
1993; Stone, 1992).
Teaching with Tactual and
Kinesthetic Resources
Students who frequently tap their fingers, play with objects, wiggle, rock back and forth, get out of their seats, or move their feet incessantly need to understand that they either are tactual and/or kinesthetic and usually have too much energy to sit still. They need to have something to do while concentrating. Such students should be shown how to create their own instructional resources (Dunn & Dunn, 1992). When we teach mathematics to tactual and/or kinesthetic youngsters by talking, they focus for only a brief amount of time and then wander off into their own thoughts and quickly forget (Burke, 2000). When these learners create their own instructional resources, their long-term memory is stimulated (MacManus, 2000; Raupers, 2000-2001).
Redesigning
the Classroom a Little
Accommodate global students' needs
for informal seating and soft lighting. You will be surprised at how few (a)
tolerate florescent lighting and (b) sit at their desks comfortably for more
than 10-15 minutes. As students become increasingly uncomfortable, they stop
concentrating!
Allow children to sit informally, as
long as they sit like ladies and gentlemen, distract no one, and evidence better
grades each week. Not hassling them when they squirm and stretch will
improve their behavior and the classroom climate (Oberer, 1999; Solomon, 2000).
Elementary school teaching practices constantly are being re-evaluated and revised. Many movements, such as the: experimental curricular projects of the 1950s and 1960s; back-to-basics movement that has been regenerated every other decade or two; “new” math, integrated curricula, Cooperative Learning, and “thinking skills”, have each attempted to change basic math programs by inserting innovative aspects (Burke, 2000). Now the new National Council of Teachers of Mathematics, 2000: Principles and Standards for School Mathematics (NCTM, 2000) is the most recent call for improved math strategies.
At the same time that major emphasis has been on increased student engagement and the use of improved math strategies, various curriculum standards have been condensed from an original list of 13 to10-- of which 5 describe the math content that students should learn. These include:
· numbers and operations;
· patterns, functions, and algebra;
· geometry and spatial sense;
· measurements; and
· data analysis, statistics, and probability.
Hands-On Strategies That Make Sense to Global, Tactual, and
Kinesthetic Learners
Numbers and operations. It is important that students understand number concepts and how these relate to their everyday experiences-- not merely recite them by rote. Using hands-on models like counters, Cuisenaire rods, multibase blocks, chips, abaci, wooden cubes, and counting sticks would be perfect for students like Raphael—the boy who vibrated with an continuous energy. After Raphael masters computation concretely, he then can use semi-concrete and abstract resources with number lines, charts, computers, calculators, and other activities such as card and board games that you, he, and other similar students can create. Tactual students often design better and more intricate tactual instructional resources that we teachers! Give them a concrete model and easy-to-follow, illustrated directions and give their imagination free rein!
Many teachers introduce algorithms with proportional materials. Then, after a few days, they distribute worksheets of problems to be answered. Many global students find this transfer to symbolic levels difficult. They need extended experiences in making trades with various objects and/or working in paired learning situations in which one classmate manages the tactual resources while another does the symbolic recording of numbers. Children also should be encouraged to create word problems to accompany the computations and to provide a contextual setting.
Patterns, functions, and algebra. When math teachers bring abstract symbols and generalizations to elementary-school students, they need to explain the concept through real life situations to which a child like Eliza can relate. How can she use these systems to solve problems? What does “x” and “y” variables in a row mean to her? What is the point of Eliza learning about algebraic equations?
Elementary students need problem solving in the context of their own personal situations. They need to generate tables and graphs and name variables for a purpose. For example, they can create bar graphs to determine the number of students who prefer various flavors of ice cream in preparation for a class party.
Functions that began as attribute relationships in the early grades continue to be extended to algebra and formula concepts. For example, develop a list of products that could be purchased in a local store at a specific percentage reduction. Develop a series of items that the students might purchase as holiday gifts for each other and have them generate the actual costs of buying those gifts. Use Cuisenaire rods to see function relationships recorded in a table and generalized to any number rod.
Geometry and spatial sense. Geometric models are used to introduce and illustrate a variety of mathematical topics. The geoboard is a helpful tool for tactual students to investigate polygons. Rectangular dot paper can be used for both sketching and recording shapes. Materials such as pattern blocks, attribute blocks, geoblocks, tiles, tangrams, and mirrors play an important role in enabling students to illustrate basic geometric figures.
The skills of geometry include naming figures, defining them, and describing their various properties. Josie would have a really tough time with this content if the definitions were presented to her verbally. Instead, get her involved with geometric ideas so that when a definition is needed, it will relate to an experience she has had. For example, have kinesthetic students form angles with their arms. The elbow becomes the vertex; the forearm is one ray while the upper arm forms the second ray. In this way, kinesthetic youngsters can form acute, obtuse, and right angles with their bodies. They also can pair with a classmate and form complementary and supplementary angles in ways that defy forgetting.
Measurement. Most measurements require tools and the materials for teaching them include the standard measuring instruments. Have children use rulers, meter sticks, tape measures, trundle wheels, graduated beakers, measuring cups and spoons, bathroom scales, thermometers, timers, and protractors. Place assignments on the board, allow them to work either alone or in a pair to complete the tasks, and walk among them to assist. You will not have many children who either do not pay attention or do not learn. Encourage students to: talk about their findings; compare what they did to find answers; get and give feedback regarding the various things they did and used; and apply their new knowledge to their everyday experiences.
Use children’s storybooks to teach global students math concepts such as time, money, measurement, and problem-solving techniques. Make math games and quizzes as an outcome of story lines or happenings. Pose questions related to multiplying or subtracting the number of characters or incidents.
Data analysis, statistics, and probability. Nowhere does the concept of real world mathematics show up more predominantly than in the concepts of graphing, statistics, and probability. Many professions and businesses are dependent on these concepts. Technology makes the exploration and application of these topics an integral part of our life through newspaper graphics, tables, and charts.
Like other topics, this content area should be taught with manipulative resources. Some of these materials include dice, coins, cards, colored cubes, chips, spinners, graph paper, squares, and objects for making concrete graphs and, of course, calculators and computers.
How Do We
Know These Strategies Work?
(1)
A meta-analysis of 42 experimental studies conducted at 13 different
universities with the Dunn and Dunn Learning-Style Model between 1980-1990,
revealed that eight variables coded for each study produced 65 individual
effect sizes (Dunn, Griggs, Olson, Gorman, & Beasley, 1995). The overall,
unweighted group effect size value (r) was .384 and the weighted effect size
value was .353, with a mean difference (d) of .755. Referring to the standard
normal curve, students whose learning styles were accommodated could be
expected to achieve 75% of a standard deviation higher than
students who had not had their learning styles accommodated.
(2)
According to the Center for Research in Education (CRE), the 20-year
period of extensive federal funding (1970-1990) produced very few programs that
consistently resulted in statistically higher standardized achievement test
scores for Special Education students (Alberg, Cook, Fiore, Friend, Spano, et
al. 1992). Among the few that did, was the Dunn and Dunn Learning-Style Model.
(3)
Putting It
All Together
To respond to global, tactual, and/or kinesthetic students, math teachers should make fundamental changes in their instructional methods and resources. Children should use tactual materials to learn and practice math in a section of the classroom and a social pattern in which they feel most comfortable. Assign tactual resources as homework and allow them to work and study together when doing assignments.
Compare students’ grades before and after you begin responding to their learning styles. Within six weeks of short-story beginnings to lessons and hands-on and kinesthetic activities, students like Eliza, Raphael, and Josie will produce and behave better with these approaches to math. When that happens, read a book (Dunn & Dunn, 1992, 1993, 1999; Dunn, Dunn, & Perrin, 1994) that can show you more about this learning-style approach and take the next easy steps!
References
Alberg, J. L., Cook, L.,
Fiore, T., Friend, M., Spano, S., Lillie, D.,
Andrews, R.
H. (1990). The development of a
learning styles program in a low socio-economic, underachieving
Brunner, C. E. & Majewski, W. S. (1990). Mildly
handicapped students can succeed with learning styles. Educational
Leadership, 48, 21-23.
Burke, K. (2000).
Math education, learning styles, and the standards: The winning tri-MATHLON. NY: ASCD. Impact on Instructional Improvement
29, 9-11.
Dunn,
R. (2000). The standards won’t work without learning styles. NY: ASCD. Impact
on Instructional Improvement, 29, iii-ix.
Dunn, R. & DeBello, T. (1999). Improved
test scores, attitudes, and behaviors in
Dunn, R. & Dunn,
K. (1992). Teaching elementary students through their learning styles.
Dunn, R. & Dunn,
K. (1993). Teaching secondary students through their learning styles.
Dunn, R., Griggs, S.,
Olson, J., Gorman, B., & Beasley, M. (1995). A meta-analytic validation of
the Dunn and Dunn learning styles model. Journal of Educational Research, 88,
353-361.
Dunn, R., Dunn, K.,
& Perrin, J. (1994). Teaching primary students through their learning
styles.
Hunter,
M. (1990). Mastery teaching. El
Segundo, CA: TIP Publications.
Klavas, A.
(1994). In Greensboro, North Carolina: Learning style program boosts
achievement and test scores. The Clearing House, 67, 149-151.
Koshuta, V.
& Koshuta,
P. (1993). Learning styles in a one-room school. Educational
Leadership, 50, 87.
Kyriacou, M. & Dunn, R. (1994). Synthesis of
research: Learning styles of students with learning disabilities. National
Forum of Special Education Journal, 4, 3-9.
Lemmon, P. (1985). A school where learning styles
make a difference. Principal 64,
26-28.
Mager, R. S.
(1967). Preparing instructional
objectives. Palo, Alto, California:
Fearon Publications.
McManus, D. O. (2000)
Students climbing the steps to reform: One standard at a time, with style! NY: ASCD. Impact on Instructional Improvement,
29 (spring), iii-ix.
Neely, R., & Alm, D.
(1992). Meeting individual needs: A learning styles success story. The
Clearing House, 66, 109-113.
Neely, R., & Alm, D.
(1993). Empowering students with style. Principal 72, 32-35.
Oberer, J. (1999). Practical application of Thies'
philosophical and theoretical interpretation of the biological basis of
learning style and brain behavior and their effects on the academic
achievement, attitudes, and behaviors of fourth-grade students in a suburban
school district. Unpublished Doctoral Dissertation,
Orsak, L.
(1990). Learning styles versus the Rip Van Winkle syndrome. Educational
Leadership, 4, 19-20.
Quinn, R. (1993)
The New York State compact for learning and learning styles. Learning
Styles Network Newsletter,15, 1-2.
Raupers, P. M. (2000-2001). Effects of
accommodating learning-style
preferences on long-term retention of technology training content.
National Forum of Applied Educational Research Journal, 13(2), 23-26.
Solomon, S. M. (2000).
Learning styles and languages-other-than-English: Una combinacion efectivea! Impact, 29, 47-56.
Stone, P. (1992). How we turned around a problem
school. Principal, 71, 34-36.