Ethnomathematics & Ethnocomputing Chart for California Standards

By Dr. Faviana Hirsch-Dubin

CSDT	Sources of Data	Math Skills/Algorithms	Math Vocabulary	Standards
Virtual Bead Loom (VBL)	Various teaching experiences using VBL Including: *Grades 3-5 Dr. Jim Barta at Ute Schools and Shoshone-Bannock reservation. Use of pre and post tests show some statistical improvement * 4^th grade at ARC Community School in Troy, NY * Joyce Lewis Middle School class grades 6-8 * Adriana Magallenes 7^th grade pre-Algebra class in CA. quantitative data from quasi-experimental study of VBL. Statistically significant improvement using VBL of (p<. 01) * Mimi Thomas, art teacher at Ute Reservation school, used various assessments * Amber Michaelsen at Utah State University used narrative of lesson as evaluative. * Linda Rodrigues at HS in CA used pre and posttests and drew the math out of VBL at each stage.	1. Explore patterns w. beads and color, number sentences. 2. Explore shapes, geometric inquiry 3. Explore symmetry 4. Basic operations of addition, subtraction, multiplication & division 5. Write number sentences with variables to represent colors 6. Ratios of color beads to white beads 7. Explore fractions using bead color 8. Math properties 9. Explore perimeter, area, and geometric shapes. 10. Use of Cartesian coordinate system in Native American designs, four-fold symmetry, fluid algorithms based on designs (like pattern of removing or adding beads to each line). 11. Algorithms from iterative rules on drop-down menu, like “subtract 3 beads from the left each time you move up one row.” 12. Problem solving, math reasoning 13. From virtual bead patterns to physical bead patterns; art and mathematics connections 14. Develop skills with electronic medium (computer) as a way of expressing mathematical ideas of pattern and design.	1. Pattern, design, number sentence 2. Name, classify & sort shapes 3. Line, point, mirror images 4. Number operations 5. Variables 6. Ratios & method of finding them 7. Fractional parts in relation to whole 8. Commutative, associative, distributive 9. Perimeter, area, Triangles, rectangles, and geometric shapes. 10. Cartesian coordinate system, grid, linear of shape iterations, graphing, ordered pairs (x, y), number line, positive and negative numbers, point of origin, axes, quadrants, axis of symmetry 11. Iterative rules and pattern generation 12. Problem solving, reasoning in mathematics 13. Pattern transfer, grid, dimensions; virtual designs, physical designs 14. Virtual tools, virtual grid and coordinate system, maneuver design system, applets, drop down menu, etc.	Grade Two Grade Five 1. Number Sense 1.1, 1.2 1.3, 1.5, 2.1 2. Geometry 2.1, 2.2 3. Geometry 2.2 4. Number Sense 2.1, 2.3, 3.1. 1.3, 2.1 5. Algebra 1.2 6. Number Sense 4.2, 4.3 1.2, 2.5 7. Fractions 4.1, 4.2 8. Algebra & Functions 1.1, 1.2, 1.3 1.1, 1.2, 1.4 9. Measurement & Geo. 1.1, 2.1, 2.2 2.1, 2.2 10. Stats, Data Analysis & Probability 1.1, 1.4, 2.1, 2.2 1.3, 1.4, 1.5 11. Measurement and Geo 2.1, 2.2 12. Math Reasoning 1.1, 1.2, 2.1, 2.2, 3.0 1.1, 1.2, 2.2, 2.3, 2.4, 3.1, 3.2, 3.3 13. Stats, Data Anal & Probability 1.2, 1.4 Math Reasoning 1.1, 1.2 2.3, 2.4, 3.3 Note: In the Introduction to the CA Standards, there are six goals for mathematics education. The VBL investigations and lessons meet all six goals, which are: 1. Develop fluency in basic computational skills. 2. Develop an understanding of math concepts 3. Become mathematical problem solvers who can recognize and solve routine problems readily and can find ways to reach a solution or goal where no routine path is apparent. 4. Communicate precisely about quantities, logical relationships, and unknown values through the use of signs, symbols, models, graphs and mathematical terms. 5. Reason mathematically by gathering data, analyzing evidence, and building arguments to support or refute hypothesis. 6. Make connections between mathematical ideas and between mathematics and other disciplines.