Teaching math effectively to elementary students. (The scholarship of teaching and learning).

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.

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* Student 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 say 100 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:

* 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;

* 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;

* incorporate lots of pictures, drawings, graphics, and charts into our explanations;

* 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 United States (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 longterm 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).

Teaching Strategies for Global, Tactual, and Kinesthetic Learners in the Content Areas

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 to 10-- 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?

Administrators repeatedly advocate strategies and models that rarely produce across-the-board grade improvement--essentially because nothing works for both global and analytic processors. Does teaching globally to global learners and using tactual and kinesthetic resources significantly improve standardized test scores?

* 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.

* 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.

* New York's Buffalo City Schools' elementary and secondary supervisors experimented with the Dunn's learning-style approaches and significantly increased the standardized achievement test scores of Special Education students after only one year of implementation (Kyriacou & Dunn, 1994).

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

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Karen Burke, St. Joseph's College, NY Rita Dunn, St. John's University, NY

Karen is assistant professor, Child Study Department and director, Learning Style Center. Dr. Burke is the author of 20 published articles and book chapters. Rita is professor, Division of Administrative and Instructional Leadership and director, Center for the Study of Learning and Teaching Styles. Dr. Dunn is the author of 23 textbooks and more than 300 published articles and research reports.