SUPPORTING LEARNING FOR NAVAJO STUDENTS THROUGH ETHNOMATHEMATICS

The purpose of this research was to address how culturally informed ethnomathematical methods of teaching can be utilized to support the learning of Navajo students in mathematics. The study was conducted over the course of four years on the Navajo Reservations at Tohatchi Middle School in Tohatchi New Mexico. The students involved in the study were all in 8th grade and were enrolled either in Algebra 1 or a Response to Intervention, RTI, class. The data collected came in the form of a student survey, student observation and student assessment. The teacher written survey, a math textbook word problem, and two original math textbook problems along with their rewritten version were the sources of these three studies. The first year of the study consisted of a math attitude survey and how Navajo students perceived math as a subject of interest. The students answered four questions pertaining to their thoughts about mathematics. The students’ responses were positive according to their written answers. The second year of the study involved the observation of how students worked through a math word problem as a group. This method tested how the students culturally interacted in order to solve a math problem. Their questions and reasoning to solve the problem were shared with peers and the teacher. The teacher supported the students in understanding and solving the problem by asking questions that kept the students focused on the goal of solving the problem. The students worked collaboratively and openly in order to complete the activity. During the iv study, the teacher was more able to notice the students’ deficiencies individually or as a group, therefore was able to support them in a more specific manner. The last study was conducted over a period of two different years. This study was used to determine how textbook bias in the form of its sentence structure or word choice affects the performance of students who are not culturally familiar with one or both. It was found that the students performed better and took less time on the rewritten problem than on the original problem. The data suggests that focusing on the culture, language and education of Navajo students can affect how the students learn and understand math.

MITEP: REFLECTIVE JOURNEY

This research looks at the use of the Interactive Student Notebook (ISN) in the math classroom and the impact on student achievement as part of the MiTEP program. A reflective critical analysis of the MiTEP program discusses impact on teacher pedagogy, leadership, and connections to people and resources. The purpose of the study stemmed from the lack of student retention, poor organizational skills, and the students’ inability to demonstrate college readiness skills such as how to study, completing homework, and thinking independently. Motivation also stemmed from teacher frustration. The research was conducted at Linden Grove Middle School in Kalamazoo Michigan in a strategic math class. Twenty-two sixth graders, thirty-two seventh graders, and forty eighth graders were part of the study.Students were given the Strategic Math Inventory (SMI) test in week 1 of the class and again at the end of a 12 week marking period. Students participated in an attitude survey to record their feelings about the use of the ISN in the strategic math classroom. The data compared the control group (the previous year’s [2012-2013] growth data) to the experimental group, the current year’s (2013-2014) growth data. Both groups were statistically similar in that the mean average was about a 4th grade level equivalency and the groups had similar numbers of grade level students. The significant findings were in the amount of growth made using the ISN. The control group started with a mean average of 586.6 and ended with a mean average of 697.1, making about one year’s growth from a 4th to a 5th grade level equivalency. The experimental group started with a mean average of 585.2 and ended with a mean average of 744.2, making about two years growth from a 4th to a 6th grade level equivalency. This is double the growth of the control group. The Cohen’s test resulted in a score of 0.311 which describes that the teaching method, the use of the ISN in the math classroom had a medium impact on student growth.

Pavement Engineering Problem

Work on a real life pavement engineering problem. This afternoon you will be working with Dr. Yan on the question: How do you make the most cost effective choice between two types of pavement contracting methods?

Meet Your Professors

To start the day, you will meet up with your professors Dr. Battle and Dr. Risser in the Student Union Building ("the SUB") on the main floor outside of the Copper Lounge.

Linear and Piecewise Functions

This morning Dr. Battle will review basic concepts of linear functions and piecewise functions and how they can be used as models for real-world applications. She will also introduce techniques for using a spreadsheet to analyze data.

Descriptive Statistics and Linear Regression

This morning Dr. Battle will introduce descriptive statistics and linear regression and how to apply these concepts in mathematical modeling. You will also learn how to use a spreadsheet to help with statistical analysis and to create graphs.

Health Care Cost Analysis

This afternoon you will be working on descriptive statistics, such as what is the total number of discharges in the state of Montana for a given Diagnosis Related Group (DRG), what is the average payment of a given DRG, and what is the range of payments of a given DRG. We will also formulate and solve a statistical question such as is there a relationship between the size of a hospital and the average payment of a given DRG.

Social Networks Analysis

This morning Dr. Risser will introduce you to the basic ideas of social network analysis. You will learn some history behind the study of social networks. Dr. Risser will introduce you to mathematical measures of social networks including centrality measures and measures of spread and cohesion. You will also learn how to use a computer program to analyze social network data

Social Network Problem

This afternoon you will be working on the question: How do you tell if a Facebook friend is really a friend?

Poster Session Set Up

During this time Dr. Risser and Dr. Battle will get you set up for the poster session.

How to Create Posters

This morning Ms. Hayden will introduce you to a computer program designed to help you create a poster for presentation tomorrow.

Open Tour of Poster Session

The campus community and your invited guests will have an hour and a half to tour your poster session. They will be able to hear you describe the problems you worked on this week and ask you questions about your work.

Panelist Presentations & Q&A

Immediately following lunch, our women panelists will speak about the mathematics courses they took and the role mathematics plays in their chosen career, followed by questions from the audience.

Warranty vs. Non-Warranty Road Construction

A project to show whether a Warranty or Non-Warranty option would end up cheaper in twenty years.

Healthcare Outlier Payment Costs

The purpose of this project is to determine the cost of healthcare per individual depending on the amount of care needed.