2 Y1’1t’44hHenry H FowlerI am of the Bitterwater and born for Zuni Edgewater. My maternal grandfather is Many Goat and my paternal grandfather is Red- running-into-the-Water.I am from Tonalea, Arizona.I am a math educator and have been teaching for 15 years on the Navajo Indian Reservation.
3 Collapsing the Fear of Mathematics: A Study of the Effects of Navajo Culture on Navajo Student Performance in Mathematics
4 Discussion Items INTRODUCTION - Research Location - Historical Background/Research Problem- Significance of the Problem- Research QuestionLITERATURE- Background- Shaping Schools and Education in America- Reconceptualization of Mathematics EducationMETHODOLOGYRESULTS OF THE STUDYRESEARCH CONCLUSIONSQUESTIONSCONCLUSION
6 Historical Background/Research Problem Americans were startled by the Soviet Union’s launch of Sputnik, October 4, 1957The launch indicated that Americans had been surpassed in technological advancement (Klein, 2003) and schools were blamed for having failed to teach basic academic knowledge, especially math and science (Blunting, 1999)“As a result, educators, scientists, and mathematicians broadened and accelerated educational reform” and the policy makers increased federal funding (Bybee, 1997, para. 2).
7 Historical Background/Research Problem Nation at Risk (1983)- American schools are in state of “mediocrity”.- Recommendations: measurable standards, high expectations, and increase in rigor25 years from the release of the Nation at RiskSchools are more at “risk” than before (Department of Education, 2008).
8 Historical Background/Research Problem The Navajo high school students are not proficient in mathematics (Arizona Department of Education (2009 & 2010).Reservation schools are using outside school consultants to improve student achievement.Treaty of 1868Navajo Sovereignty in Education Act (2005)
9 Significance of the Problem Native American/Alaskan Natives’ daily connection with their environment is not acknowledged as useful in education (Taylor, 1991).Improve the Western academic performance of NA/AN, the school system “must begin where they are, using materials and teaching methods relevant to their culture” (Taylor, 1991, p. 15).
10 Significance of the Problem This research explored the effects of implementing the Navajo Culture Component Math Curriculum (NCCMC).
11 Research QuestionHow does integrating Navajo cultural traditions in math curriculum impact student achievement and students’ learning?
12 Literature Review Background Shaping Schools and Education in America Reconceptualization of Mathematics Education
13 Background Mathematics is an important subject. Mathematics has been recognized as a measure and a tool for individual success in the workforce and success of the United States (Spelling, 2006).
14 Shaping Schools and Education in America Standards-based EducationThe premise of standards-based education is on measurement, standard, benchmark, and accountability (Malone & Nelson, 2006; NCLB, 2001).
15 Multicultural Education The effects of Mainstream on Students of ColorStudents of color experience difficulty achieving in Western academics because the culture of school does not represent their culture.Schools should implement and create instructions based on the cultural values and standards of people from different backgrounds (Gay, 1995; Banks, 2002).
16 Reconceptualization of Mathematics Education ConstructivismLearning is acquired by doing and developed through interaction (Brooks & Brooks, 1993).School curriculum should connect to the home life of students to provide enrichment of learning (Dewey, 1958).Transformation of cognitive structure takes places in a cultural setting (Vygotsky, 1978).
17 Reconceptualization of Mathematics Education Ethnomathematics“The term ethno describes all of the ingredients that make up the cultural identity of a group: language, codes, values, jargon, beliefs, food and dress, habits, and physical traits. Mathematics expresses a broad view of mathematics which includes ciphering, arithmetic, classifying, ordering, inferring, and modeling” (D’Ambrosio, p. 309).Math curriculum should be inclusive with ethnomathematics of all people of their cultural artifacts and practices of children’s own environment, experiences, and community (Zaslavsky, 1998).
18 Methodology Introduction There is little research specifically on Navajo high school student achievement in mathematics from a Navajo perspective.Action Research based on the teacher researcher perspective provided the framework for this research study which employed a quasi-experimental methodology using mixed methods of data collection.
19 Methodology Action Research The participants study their own problem situations and seek solutions to solve their own problems they encounter (Stringer, 1999).Engage the participants to continue to deeply study their activities in stages of observation, reflection, evaluation, and action (Mills, 2003).The participants research - The participants who are doing the research seek to improve their social setting by changing current practices toward better practices (Stringer, 1999).
20 Methodology Teacher as Researcher Individual teacher uses their own class to research. They ask meaningful questions to systematically improve student learning, operations of the school, and/or their teaching practice (Corey, 1953).A teacher researcher - the teacher becomes the agent of reform for a better practice (Corey, 1953).I used action research methodology in my teaching practice to explore ways of teaching that enhance the quality of learning math operations for the Navajo high school students and confront the achievement gap in mathematics for Navajo students.
21 Research DesignTwo classes of Navajo juniors and seniors who had not reached the proficient level for the Arizona Instrument to Measure Standards (AIMS) have been assigned to the required classes by the principal plus two sophomores.The two groups consisted of a control and treatment group.I was the teacher in both classes over an eight week period meeting daily with each group for 50 minutes from January to March, 2010 or 40 days.The treatment group received the Navajo Cultural Component Math Curriculum (NCCMC) and the control group received the Western traditional teaching.I taught the two groups during their scheduled math AIMS classes. The control group was during their 4th hour math AIMS class and the treatment group was during their 8th hour math AIMS class.
22 CurriculaCurricula utilized in this study are (a) the Western curriculum and (b) the NCCMC.The Western curriculum consisted of 11 Arizona math standards covering algebra and geometry topics using a traditional math textbook.The math lessons incorporated math objectives, pre- instruction, class guided practice activity, closing activity, homework, and assessment.The NCCMC curriculum which I designed and built to supplement the Western mathematics curriculum consisted of 10 math lessons that incorporated 11 Arizona math standards on algebra and geometry. NCCMC integrated Navajo culture and traditions and group work for the participants to learn the math benchmark standards.The NCCMC math lessons incorporated hands-on activities, probing explorations, graphic organizers, and applied projects.
23 SettingSand Stone High School (SSHS) is a Contract School. The school is locally managed and lead by the community elected school board members.SSHS has an average enrollment of 141 students.Each student needs 25 credits and is responsible to pass the AIMS in reading, writing, and math to graduate.The school offers eight classes with each class 50 minutes. School starts at 8:00 am and ends at 3:41 pm with 30-minute lunch break.
24 ParticipantsThe participants in this research consisted of 15 students.They were between 16 to19 years old.The treatment group had 6 students (4 females and 2 males) exposed to the NCCMC and the control group had 9 students (5 females and 4 males) exposed to the traditional teaching method.
25 Data CollectionThe data collection for this Action Research (AR) employed both quantitative and qualitative data.Qualitative paradigm provided the whole picture and the meaning of the information from the students’ perspective and the teacher researcher’s perspective (Creswell, 1994). The qualitative data included structured interviews, and teacher journal.Quantitative paradigm using numerical sense allowed for a test of cause and effect relationship (Creswell, 1994). Quantitative data included pre-and post-test and Likert scale questionnaire.The treatment and control group both took the pre-and post- test. The pre-and post-test were identical consisting of 22 multiple choice problems based on the Arizona standard math performance objectives on geometry and algebra, which is modeled after the AIMS practice test (40-50 minutes).
26 Data CollectionTreatment group completed the Likert scale questionnaire-18 questions (20 minutes).Treatment group completed the structured interview – four questions (30 minutes).The researcher/teacher kept a daily journal to record observations, interactions, and reflections. Particular attention was on teacher bias to ensure equitable opportunities for success in both classes.
27 Data AnalysisAll the data from the structured interview and teacher journal was transcribed, analyzed, coded, and categorized based on emerging themes and patterns (Miles & Huberman, 1984; Anderson et.al, 1994; Creswell, 1994).The Likert scale questionnaire and pre and post-test provided the numerical analysis.Likert scale questionnaire was analyzed by calculating the mean for each item response.The pre and post-test was analyzed utilizing centralized tendency, which was summarized by mean and standard deviation and represented into bar graphs and charts.
29 Result of the Study Quantitative Findings Table 1 Control Group Pre-test and Post-test Scores Participants Pre-test Percent Post-Test Percent (N = 9) Participant A 6/22 27% 15/22 68% Participant B 10/22 45% 13/22 60% Participant C 5/22 23% 7/22 32% Participant D 11/22 50% 15/22 68% Participant E 5/22 23% 11/22 50% Participant F 6/22 27% 18/22 81% Participant G 13/22 59% 17/22 77% Participant H 5/22 23% 14/22 64% Participant I 6/22 27% 7/22 32% M/SD M/SD 34%/ %/13.74 Percent of Increase 25%
30 Result of the Study Quantitative Findings Table 2 Control Group Pre-test and Post-test Scores Participants Percent of increase Percent of change(N = 9)Participant A 41%Participant B 15%Participant C 9%Participant D 18%Participant E 27%Participant F 55%Participant G 18%Participant H 41%Participant I 5%M of Change1.74
32 Result of the Study Quantitative Findings Table 3 Treatment Group Pre-Test and Post-test Scores Participants Pre-test Percent Post-Test Percent (N = 6) Participant A 4/22 18% 18/22 82% Participant B 9/22 41% 22/22 100% Participant C 14/22 64% 19/22 86% Participant D 10/22 45% 18/22 82% Participant E 5/22 23% 18/22 82% Participant F 6/22 27% 20/22 91% M/SD M/SD Percent of Increase 36%/ %/ %
33 Result of the Study Quantitative Findings Table 4 Treatment Group Pre-Test and Post-test Scores Participants Percent of increase Percent of change (N = 6) Participant A 64% 4.56 Participant B 59% 2.43 Participant C 22% 1.34 Participant D 37% 1.82 Participant E 59% 3.56 Participant F 64% 3.37 M of Change 2.40
34 Qualitative FindingsEach structured interview question was analyzed into themes according to the participants’ responses. The themes for each question are as follows:- Question one consisted of six themes: 1) Culture, 2) Fun, 3) Hands-on Activities, 4) Experience, 5) Group Work, and 6) Narration.- Question two generated three themes: 1) Extended Math Courses, 2) Post-secondary Education, and 3) Problem Solving.- Question three yielded three themes: 1) Culture, 2) Hands-on Activities, and 3) Visual Diagram.- Question four produced one theme: No Change.
35 Qualitative FindingsQuestion One: Please describe if this math class was different from your previous math classes.CultureAll six participants identified culture as a main component that was missing from their previous math classes.Participant B“The teacher added new things that helped me learn math and it had to do with my culture” “I liked the Navajo cultural math activities on the Concho Buckle, using the directions (E+S)(W+N) to learn FOIL, using the rug to learn transformations and all other math work was cool”Participant C“This class was interesting, it had cultural ideas that related to math.” “The cultural math problems helped me understand math better”Participant A“The cultural math representations helped me with my math thinking and understanding.”
36 Qualitative Findings Fun All six participants pointed out that this math class was different from other math classes because this class was entertaining with fun activities.Participant B“It was fun, it helped me improve my math skills”Participant E“The math class this year was fun and I enjoyed it because it contained math problems that I could relate to.”Fun math activities impacted the participants math learning experiences that was provided through integrating Navajo culture traditions into the mainstream math curricula.
37 Qualitative Findings Hands-on activities Five of the six participants expressed that the hands-on activities was missing from their previous math class.Participant C“The lessons contained hands on activities. The hands on activities were fun and exciting and motivated me to learn more math problems.” “Sometimes I wanted to stay in my math class and do more math problems because the hands on activities were fun.”Participant F“I enjoyed the hands on activity and this helped me learn math faster and better”
38 Qualitative Findings Group Work Three participants suggested that group work helped them to learn math by talking, sharing, and listening to their group members.Participant D“My group was good to work with, we helped each other when we got stuck in solving math problems and we used the cultural symbols like the Hogan colors and the rug frame to help us solve the math problems. Group work and the cultural symbols were cool.”ExperienceThe data revealed strong connections for the participants to the NCCMC math activities because it related to the participants background and to the world of what the participants experience everyday at home.Participant B“The cultural math lessons related to my life experiences which I could relate to math which made me understand the Arizona math standards”
39 Qualitative FindingsNarrationOne participant indicated that cultural narration was missing from his previous math class. The cultural narration stories bridged math learning and understanding with reading.Participant E“Other math books did not have Navajo narrations that related to the Navajo way of life, the narrations were fun to read and they connected to math. The narrations helped with my math thinking.”Question 2: How has this math class influenced your decisions for the future?Extended math coursesFive participants mentioned that the NCCMC had influenced them to take more math and science classes in the future.Participant A“I did not like math before, now I want to take more math classes”Participant C“This class has set the basic math skills for me to further study math and science in the future, before I was scared of math classes.”
40 Qualitative Findings Post Secondary Education Four of the six participants referenced NCCMC as an influence to pursue post secondary education. The participants stated that the qualities of NCCMC helped them see the reward of knowing math and the role of mathematics in the workplace.Participant B“And the class influenced me to study engineering someday.”Problem solvingTwo participants indicated that the NCCMC influenced them to expand their math knowledge through problem solving.Participant C“It made me think about math even more and wanting to do even more problem solving in math, so that I can pass the state math test AIMS.”
41 Qualitative Findings Question 3: Describe the strengths of the NCCMC. CultureAll six participants acknowledged that the strength of NCCMC was the Navajo culture traditions and heritage.Participant D“I never had a math class that used our culture in teaching math. There should be more of this in our math education.”
42 Qualitative Findings Hands on activities Four participants attributed the cultural hands- on activities as a strength of the NCCMC. The hands-on activities were illuminated with Navajo cultural representations.Participant C“Sometimes I wanted to stay in my math class and do more math problems because the hands on activities were fun.”Participant D“The NCCMC contained a lot of hands on activities like making the scale model Hogan, using the protractor to learn complementary and supplementary angles. These hands on activities made math fun to learn.”
43 Qualitative Findings Visual Aids Four participants identified that visual aids was the source of strength for the participants to learn the Arizona math standards. The participants indicated that cultural visual aids based on Navajo cultural traditions effectively conveyed mathematical ideas for them to actively and independently learn math.Participant C“The NCCMC displays a lot of cultural visual diagrams that can help students pass their math AIMS test.”Participant D“The strength of NCCMC provided visual learning and visual symbols of our culture which had helped me learn problems like numerical expressions, area of figures, complementary and supplementary angles, and scale model.”
44 Qualitative FindingsQuestion Four: What would you recommend for improvements to the NCCMC?No changeAll participants stated that no change was needed in the NCCMC. The qualities of NCCMC connected to the participants. The NCCMC educational materials according to the participants had accommodated their learning style and cognitive level of thinking.
45 Likert Scale Table 5 Likert Scale Strongly disagree Disagree Neutral Agree Strongly AgreeUnderstand1. The Navajo cultural component math helped me understand mathematical concepts of the Arizona Standards.5, 5,5,5,4,5 = 2929/6 = 4.832. The Navajo cultural component math lessons gave a different way to solve mathematical problems.5, 5, 5, 5, 5, 5 = 3030/6 = 53. The Navajo cultural component math lesson has improved my understanding of solving difficult math problems.5, 5, 5,5, 5, 5 = 30
46 Likert ScaleFeelings4. The Navajo cultural component math lesson has contributed to my confidence in solving math problems.5, 5, 4, 5, 5, 5 = 2929/6 = 4.835. The Navajo cultural component math lessons were fun.5, 5, 5, 5, 4, 5 = 296. The Navajo cultural component math lessons were easy.4, 5,4, 4, 3, 4 = 2424/6 = 4
47 Likert ScaleFeelings7. I was involved and excited in learning the Arizona math standards that supported the Navajo cultural and teachings.5, 5, 5, 5, 5, 4, 5 = 2929/6 = 4.838. I was comfortable in solving math problems that had components of the Navajo cultural and teachings.5, 5, 5, 5, 4, 5 = 299. The Navajo cultural component math activities have helped me realize the importance of math in my everyday life.
48 Likert ScaleAcademic10. The Navajo cultural component math activities helped me remember the steps in problem solving the Arizona standards.5, 5, 5, 5, 5, 5 = 3030/6 = 511. The Navajo cultural component math lessons made math more meaningful to me.5, 5, 5, 5, 4, 5 = 2929/6 = 4.8312. The Navajo cultural component math lessons were appropriate and created a new way for me to improve my math skills.5, 5, 4, 5, 5, 5 = 29
49 Likert ScaleAcademic13. Group supported work helped me expand my math knowledge.4,5, 5, 4, 3, 5 = 2626/6 = 4.3314. Hands-on math activities helped me expand my math knowledge.5, 5, 5, 5, 5, 5 = 3030/6 = 515. The Navajo cultural component math activities have encouraged me to take more math courses in the future.5, 5, 4, 5, 4, 5 = 2828/6 = 4.67
50 Likert Scale Opinion 16. Math should be taught using local knowledge. 5, 5, 5, 5, 5, 5 = 3030/6 = 517. Navajo culture and teaching should be a key part in learning math concepts.5, 5 , 5, 5, 5, 5 = 3018. There should be more cultural math activities based on Navajo culture.
51 RESEARCH CONCLUSIONS Recommendations How are the Navajos preparing their children for the 21st century education? The participants were relatively small with the control group of nine participants and the experimental group of six participants. This study could represent the start of creating ethno-mathematic curricula for Navajo high school students in general.The recommendation for this study is to expand the research across the Navajo Nation high schools using the Navajo Cultural Component Math Curriculum (NCCMC) with a larger number of participants so statistical comparison can be madeImplications