How can we improve the way mathematics is taught to Native American students?

 

·        Similar to Aboriginal students in Australia, Native American students are more visual learners.

 

Traditional approach to mathematics teaching

·        Math has no relationship to culture

·        There is no connection between real life and math.  Math exists in the classroom and in textbooks.

 

Multicultural approach

·        Teachers instruct using activities and games

·        Students work independently in groups

·        Activities are often out of context

·        Math has little personal meaning or relevance

·        Math remains something other people do

 

Culturally relevant approach

·        Math is a vital aspect of culture

·        Teachers stimulate students to create mathematical activities using situations and materials easily found in the environments where the students live. 

·        The teacher facilitates and extends students investigations. 

·        Students share their discoveries.

·        Multiple concepts are simultaneously explored as students invent their own procedures.

·        The result: students realize they possess an innate ability to think and become creatively involved in mathematical activities.  Math becomes something which surrounds them.  Math is everywhere and part of everything.

 

A.J.Bishop wrote in his book, mathematical Enculturation (1991, Kluwer Academic Publishers) that Mathematics occurs across cultures in six aspects of human activity.  No human culture has ever been without mathematics although frequently informal in nature.

 

1.     COUNTING – one to one correspondence - keep track of possessions

2.     MEASURING – comparisons according to attributes – common units for length, area, volume, weight, temperature, speed and time.

3.     DESIGNING AND BUILDING – shapes of buildings, tall, low, exploring for strength in structures, use of Lego in elementary school, explore patterns

4.     LOCATING – finding position, compass direction, points of reference

5.     EXPLAINING – Informally and formally making sense depends on organizing and interpreting data.  Graphs, diagrams, charts, tables e.g. TV viewing habits, fast food preferences, earth’s temperature, use of symbols in equations

6.     PLAYING – exploring informally – having fun.  Many games use a geometrical field such as a diamond, rectangle etc.  Many games involve chance – cribbage, solitaire, chess.  The mathematical concepts are prediction, strategic thinking and anticipation.

 

Examples in Native American culture where math is used in a culturally relevant manner the result being that math is one of the favorite subjects in these schools.

 

Mathematical and cultural insights associated with beadwork:

·        Choice of color and design

·        Shirley explains “when you do loom work, it is important to know that you always must string your loom so that you have an odd number of beads in each (horizontal) row.  This is because the median (bead) acts as the center point.  You need it to flip your pattern so that one side will mirror (reflect) the other.”

·        Counting and computation skills are very important in beadwork and the geometric patterns developed.

·        According to Shirley almost all mathematical concepts  in elementary school can be taught through beadwork – basic operations, measurement, perimeter, area, fractions, decimals, ratios, percentages, symmetry, geometry transformations – flips, rotations, slides.  Computer software can be used for design

·        “Beadwork teaches me organization, discipline and observation.  It makes me stop and look at things a little longer.”

·        The hand is man’s greatest tool. We have two of them that are identical.  So we can measure in two different places at the same time.  We can move them everywhere.

 

Developing Culturally relevant Mathematics Instruction and Activities

 

The basic developmental steps are:

1.     Interview Elders/cultural representatives who will describe a particular activity important to the tribal community.  One should seek not just content knowledge but also related beliefs, values and traditions related to the doing of the activity.  Elders often maintain a special respect in native communities and their words and presence can establish motivation as well as credibility for what is taught.

2.     The teacher examines the knowledge gained for curricular connections to the core standards.  A list is made of mathematical principles/concepts to teach.

3.     A lesson or series of lessons is designed around the concept or principle.  The lesson could contain physical, emotional, and spiritual objectives in addition to the usual cognitive objectives.  Information is presented using a variety of techniques but the main instructional emphasis should be on cooperative problem solving using materials/models and hands-on interaction.  The context of the culturally relevant application provides additional opportunities to share and discuss the values, beliefs and traditions inherent in the application.  Students should be encouraged to establish a personal understanding of what is studied and share their newly gained knowledge/wisdom in circles of sharing during the activity.

4.     Assessment is typically performance based.  Attitudinal as well as cognitive evaluation can be established.  The process a student has exhibited in the completion of an activity will often be as good if not better demonstration of learning as that of the final product. Primary in the learning is the degree to which the learner establishes personal meaning for use in ones life and for the benefit of the community.

 

The basis developmental steps are:

1.     Collect examples of Indigenous Cultural applications.

2.     Examine the applications for embedded concepts and principles

3.     Implement lessons – encourage individual meaning making

4.     Assess using a variety of techniques.