The purpose of this research is to examine and analyze the uses of mathematics in bilingual/bicultural environments, with specific applications as well as in specific communities.
Because of the Supreme Court decision (1974 Lau vs. Nichols) bilingual education is now mandatory (McNichols 111-15). Mathematics is an ever present, recurring part of daily life. This provides an excellent opportunity for the inclusion of bilingual/bicultural aspects in mathematics.
Because of this decision it now becomes essential to train bilingual teachers in all academic subjects and at all academic levels, including preschool. The states of California, New Mexico, Florida, Pennsylvania, Alaska, Arizona, Illinois, New York, Maine, Connecticut, and Colorado are “working toward improved courses leading to bilingual teacher certification” (Crespin 96-7). Teachers must be trained who will be committed to a “culturally different model” as proposed by Puglisi and Hoffman, which acknowledges that the values, cognitive patterns and language of the Mexican-American child to be evidence of a valuable culture (Puglisi and Hoffman 495-498).
At the start of formal schooling, as required by law, the trained teacher takes over the instruction of the individual started in the home by parents. Even at the preschool level mathematics is an essential part of the learning process and must be presented bilingually.
The preschool child who enjoys watching vehicles can keep count by collecting blocks of a specific color. Naming the vehicles and counting them in both languages will show how many and what types he has seen during a specified period of time and becomes a simple bilingual experience. The time allotted may also be designated and responded to in a bilingual manner. These concepts are easily continued in later grades.
Cleaning up after an activity may include counting the blocks used to build a bridge (Tucker 21-4), just as paints, paper and paint brushes may be counted while being given out by a monitor to make certain each child has a brush and paper and the correct number of paints are distributed. Each time, both languages can be used for the counting process as well as naming the items, or the languages may be used alternately. Sets can be demonstrated with the inclusion of collections kept by the children of pebbles, pine cones, or leaves. Leaves and pine cones, at a later date, provide an opportunity to learn perimeter and area by comparing the various leaves or pine cones in size and mass (Tucker 21-4). Concepts of size and shape can be questioned in one language and answered in the second language, alternating the use of the languages. By comparing the height and weight of the children in class, their shoe sizes, hand sizes, differences in sweater or jackets worn, comparisons in size and shape can be determined.
Bilingual presentation of time can occur naturally while counting the minutes until lunch time, or the arrival of the bus. It expands to the use of a calendar for months, for days of the week in school, holidays that come, vacations in the future. Presentation is continuously bilingual. Holidays become an excellent bicultural opportunity whereby Anglos become knowledgeable of the customs of others.
A cooking experience permits use of measuring which will include fractions as well as counting to be sure enough cookies or cupcakes are made for each class member. Time required to mix, to bake, to cool, even to distribute the item baked can all be included. The entire experience becomes bilingual by the use of both languages to identify the equipment used and the quantities. It also becomes bicultural when the item made has an ethnic origin, by making quesadillas or albondigas one time and cookies or cupcakes another. Concepts of more and less, and proportions can be integrated into the cooking experience while measuring and distributing.
Daily living skills provide an opportunity to improve counting, adding, and comparisons. A party permits additional experience when counting out favors, candles and balloons (Tucker 21-4). Each one of these opportunities also creates a chance to increase the bilingual knowledge of the class.
The chance to learn money concepts is presented when collecting milk money, or donations to UNICEF or United Way (Tucker 21-4). Information on the purpose of the collection as well as counting the monies should be presented in both languages.
The construction of a store in a part of the classroom can pravide experience in estimation, calculation, measurement, and quantity. Once constructed the store continues to facilitate the learning of size, by the inclusion of clothing items; of shapes, with boxes and cans; and weights as printed on the labels or determined by using a scale. It also continues the monetary learning process. Continually reinforced is the bilingual/bicultural exposure. Signs and labels appear in both languages. Food from various cultures are offered thereby expanding the shopping concept to a multicultural experience.
In addition to these experiences, a store project provides opportunities in bookkeeping, taking stock, making discounts, and even writing advertisements. The bilingual/bicultural aspect is enhanced by discussing the approaches and methods used by different segments of the population.
Other multiple experiences are setting up a post office or a travel agency. In the post office children learn to pay, make change (Tucker 21-4), determine how many stamps can be purchased for a given amount, and weigh packages. A travel agency provides means of computing costs per mile, buying tickets, choosing mode of transportation. All of these can be done in the primary and/or secondary language. The post office provides cultural enrichment by illustrating countries to which letters may be sent. The travel agency is also culturally enriching by incorporating historical as well as geographical information.
An additional experience is obtained by recording the information and writing number stories in both languages. The act of writing reinforces the mathematical concepts learned and further demonstrates the accurate use of language. Introduction to shapes can be another continuous bilingual experience. A short walk around the block will introduce squares in the sidewalk, rectangular doors and windows, hexagonal stop signs, triangular roofs, cylindrical posts.
An outdoor construction site facilitates discussions on estimated capacities and volumes (Tucker 21-4) as the dump trucks are loaded and moved out. This can lead to an exchange of ideas on time before the truck returns, possible distance travelled within that time and even gas consumption involved. Differences in construction methods and materials which bring out cultural differences can also be discussed. Numerous games which are part of Anglo life, e.g., hopscotch, jacks, scissors-stone-paper, help reinforce computation skills as well as developing motor skills (Herold 12). These can be played in a bilingual manner. Games like backgammon and Parchesi use dice; card games give practice in addition. The bilingual/bicultural aspect is reinforced with the introduction of games from other ethnic groups and in a second language.
The state of Colorado has passed its own law (Hall 519-22) requiring bilingual/bicultural schools. After one year in practice there has been a noticeable decrease in absentee rates among Hispanic students. In one community the rate has decreased from 9% to 2%. In another, which had earlier instituted its own bilingual/bicultural schools, the rate has decreased from 50% to 20%. The Colorado law states that subjects must be taught in the student’s native tongue while English is taught as the target tongue. This means that it will now be necessary to have bilingual mathematics teachers at all grade levels in Colorado school districts where 50 students of 10% of the student population have a first language other than English (Hall 519-22).
Dade County, Florida, has “become committed to bilingualism for the total community” (Bequer 644-8). The Dade County curriculum consists of five areas: Spanish language arts; social science; science, including math; fine arts; and English language arts. In the latter, the Hispanic learns of the Anglo and Black, while the Anglo and Black learn of the Hispanic. In the past non-Anglo-American children were considered to be culturally disadvantaged because of evaluating them by dominant group norms (Puglisi and Hoffman 495-8). This has been largely disproved. Children of Hispanic background have been found to be “field-independent” (Puglisi and Hoffman (495-8) and as such do well on analytical tasks. Math is one field in which analytical abilities are a great asset.
The knowledge of more than one word for an entity enables bilingual children to think more easily in the abstract. In a monolingual school abstract thinking skills are generally reinforced through mathematics. The bilingual child has an advantage in being able to acquire such abstract thinking skills by a second method (Arenas 2-6). Starting at the preschool level it is necessary to provide an environment for children to function at their highest level and develop to their full potential (Arenas 2-6). For the Mexican-American child this requires a bilingual teacher. The movement from home to school is difficult for any child. The sudden change from home environment to school is intensified in the Mexican-American child. Where the teacher is bilingual, communication is possible. If the teacher and student cannot communicate difficulties arise in the simple following of instructions, and become greater in degree when socialization is attempted.
Bicultural experiences must permeate the school environment. Story books which show various cultural groups should be available in both languages. Ethnic foods should be prepared. Holidays should be discussed in the widest possible range to give greater exposure to members of both cultures. When a holiday is anticipated all age groups enjoy counting the days to its arrival. Date, month, and day are all mathematical concepts to be emphasized bilingually. Holidays coincide and differ in various cultures, permitting not only a bicultural, but a multicultural approach to be used. Constant emphasis must be put on using both languages. “Saying ‘Buenos dias’ in the morning and ‘Hasta mañana’ in the afternoon is not bilingualism” (Arenas 2-6).
Games may consist of questioning in one language and answering in a second. Areas of the classroom can be labelled in both languages. The continuous use of one language and then another will facilitate the use of both languages by both elements. There is an absurdity in eliminating linguistic variety at the elementary level only to demand it at the high school and university level (Puglisi and Hoffman 495-8). How much more economical and intelligent to foster it from the very start of the school program.
The encouragement of native language allows an interchange at the cultural level as well. Each child enters school with a rich background of values, expectations, and three to five years’ experience which varies from that of any other child at the same time. These values and experiences can provide for the Anglo and the Chicano a broadening base from which to expand knowledge. Particularly at the early–preschool and elementary–stages, acquisition of a second language is not a difficult task.
Working side by side a child of Anglo and a child of Hispanic background can do a math problem, each in his/her own language and share the experience with the other, to their mutual advantage. They share their combined languages, their methods of approach, as well as their final answers. This concept will seem strange to the competitively-oriented Anglo child, but the Hispanic child, raised in a generally more cooperative, less competitive atmosphere will find it quite natural.