Perimeter, Area, Volume, and All That: A Study of Measurement

CONTENTS OF CURRICULUM UNIT 19.05.03

  1. Unit Guide
  1. Introduction
  2. Background
  3. Content
  4. Native Dwellings
  5. Perimeter and Area
  6. Perimeter 
  7. Area
  8. Surface Area
  9. Strategies
  10. Vocabulary
  11. Visuals
  12. Math Discourse
  13. Hands on Activities
  14. Teaching Activities
  15. Architecture Activity
  16. Resources
  17. Websites
  18. Appendix

Native American Geometric Community

Marnita A. Chischilly

Published September 2019

Tools for this Unit:

Background

Our school is under the Bureau of Indian Education (BIE), classified as a K-8th Elementary School located in a rural area, about 17 miles east of the nearest city. Our student population is 100% Native American in ethnicity, coming predominantly from the Navajo or Dine’ tribe, a few from other tribes such as Zuni, Apache and Sioux. As for our student body academically, we have 18% Special Education students, 98% designated English Language Learners (ELL), 10% Gifted and Talented (GT) students, with majority of 8% GT students placed on referrals for Leadership, leaving only 2% placed by Academic Achievements. All our students are receive free/reduced lunch, which indicates a majority of the student population is from low socio-economic backgrounds.

The assessment tools used by our school for evaluating Math area are from local teacher developed formative and summative assessments, resource material unit assessments and daily monitoring techniques, the standardized assessment of Partnership for Assessment of Readiness for College and Careers (PARCC) for Grades 3rd – 8th, and the Northwest Evaluation Assessment (NWEA) Measures of Academic Progress (MAP) tool for Reading, Mathematics, Language Arts and Science.

A majority of the students are identified as ELL according to the results of the state sponsored ACCESS/WIDA, given to grades K-8th to evaluate the five English Language Development standards. Currently, the demographic data of my upcoming 8th grade Math class consist of 58 students, ages 12 -15, comprised of 3 Inclusion Special Education students, 55 students classified as English Language Learners. There are 15 residential students and 43 day students. Six of the students are Gifted and Talented students eligible by the Leadership strand, and 2 by academic achievement. Five students are new, having transferred from other schools. The NWEA Fall 2018 overall Math scores indicate a high percentage of my students were in the lowest division of Levels - 23% being in the Basic Low level, 50% in the Average Low level, and 23% are in the Hi Low level; leaving the remaining 4% in the higher levels or proficient level.

Another important factor regarding my students is their cultural background. We are at a point where our youth are losing their cultural knowledge, language, clan system, and identity. As educators how do we bring our children back into learning their cultural heritage and their self-identity? How can we plant the seed of pride and passion back into them so they can understand the importance of their language and culture? What can we do to bring back the pride of living in a world of the beauty way (hozho)?

In researching this phenomenon, I feel a need for a different approach of instruction. To address this issue, it is the basis of my unit to instruct this math domain of geometry using cultural relevancy to deepen the understanding of math concepts and in the process bridging the knowledge of cultural heritage.

As part of our school district mandates, mathematics teachers are asked to seek activities that “model real-world phenomena to include cultural relevancy” and “represent and analyze relationships using mathematical concepts, verbal rules, geometric strands, and common core standards”.  By utilizing the common core standards, teachers generally give students the opportunity to be actively involved in math through mathematical analysis and correlations that are integrated into cross-curricular lessons.  I intend to demonstrate how these types of activities can be incorporated into a geometry unit as a way of conveying that history can have a strong impact on motivating students in learning math.

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