原住民學生數學自我概念與數學學業成就之研究

數學之重要性為吾人所皆知，其小至日常生活的應用，大至人類文明的發展，數學均扮演著重要的地位與影響力。而數學自我概念則關乎一個人對自己在數學方面之興趣與能力之綜合感覺與信念。然而多數原住民學生可能因其生活地域、家庭或文化等方面之因素，而使其此方面之學習態度或自信受影響並在學習成就方面較為弱勢。但此些部分之關係仍待我們更多關注、探究和釐清。所以本研究藉由探討原住民學生數學自我概念與數學學業成就之關係，探究影響教育成效之相關因素，以裨益於原住民教育政策與環境之修正、改善與擬定。本研究主要研究目的有下列幾項：（一）探討不同背景之原住民學生其數學自我概念之差異情形；（二）比較不同背景變項之原住民與非原住民學生數學自我概念之差異情形；（三）分析原住民學生數學自我概念與數學學業成就之差異情形；（四）比較原住民與非原住民學生數學自我概念與數學學業成就之差異情形；（五）原住民學生之不同背景因素對數學自我概念之預測情形；（六）原住民學生數學自我概念對數學學業成就之預測情形；（七）依據原住民學生數學自我概念與數學學業成就之關係，提出改善意見。本研究採次級資料庫分析方式，分析資料為「臺灣後期中等教育長期追蹤資料庫」中106學年度高一及專一學生調查問卷現場版資料。以原住民學生為研究對象，非原住民學生為比較參照對象。樣本總計22,282份，其中有效樣本為21,469份，有效樣本中，身份為原住民學生共957位。將資料分別採描述統計、t考驗、單因子變異數分析、雙因子變異數分析、皮爾森相關分析，以及多元線性迴歸分析進行統計分析。本研究之結論如下：一、原住民學生之「性別」及「家庭經濟狀況」對其數學自我概念有顯著性差異，並且男生數學自我概念高於女生；家庭經濟狀況為小康以上之原住民學生數學自我概念高於家庭經濟狀況為困難之原住民學生。二、「原住民身分」及「背景變項」於數學自我概念均無交互作用。三、原住民學生數學自我概念與其數學學業成就達顯著差異。四、「原住民身分」及「數學自我概念」於數學學業成就有交互作用存在。五、原住民學生的「整體背景變項」對於「數學自我概念」有預測力，且「性別」與「家庭經濟狀況」是預測變項，而非原住民學生則增加了「父親教育程度」及「母親教育程度」兩個預測變項。此外，「原住民身分」能顯著預測學生之數學自我概念。六、原住民學生之數學自我概念對於數學學業成就有預測力，且數學自我概念對於數學學業成就有正向影響，同於非原住民學生。本研究根據研究結論，對原住民教育政策、教育單位與教育專業人員，以及未來研究提出建議。

關鍵字

原住民學生；數學自我概念；數學學業成就

並列摘要

The importance of mathematics is well known to us, from daily life to human civilization. The mathematics self-concept is related to a person's own comprehensive feeling and self-confidence in his or her interest and ability. Most indigenous students’ academic achievement in mathematics may be affected by their learning attitude or self-confidence because of their living environment, family and culture. These differences between indigenous and non-indigenous students still need our attention, exploration and clarification. In this study, we would like to explore the relationship between indigenous students' mathematics self-concept and academic achievement in mathematics, especially to determine the important education efficacy factors, and understanding these factors may be helpful to revise and improve the indigenous education policies and environment. The research objectives of this study are as follows: 1. To explore the differences in mathematics self-concept of indigenous students from different backgrounds; 2. To compare the differences in mathematics self-concept of indigenous and non-indigenous students with different background; 3. To analyze the difference in mathematics self-concept and academic achievement of indigenous students; 4. To compare the differences of academic achievement in mathematics of indigenous and non-indigenous students with different mathematics self-concept; 5. To predict the mathematics self-concept of indigenous students with different backgrounds; 6. To predict the mathematics self-concept of indigenous students by their academic achievement in mathematics; 7. Based on realizing the relationship between indigenous student’s mathematics self-concept and academic achievement, we can make suggestions for improvement. This study uses a secondary database for analysis. This data is from “upper secondary education student survey: high school 10th grader and freshmen of junior college on site version in 106 academic years”. Indigenous students were the subject in this study and non-indigenous students are included for comparison. 22,282 samples from the survey were collected and of which 21,469 were valid. 957 of the 21,469 valid samples were indigenous students. The data was analyzed by descriptive statistics, t-test, one-way ANOVA, two-way ANOVA, Pearson correlation and multiple linear regression analysis. The conclusion of this study are as follows: 1.Indigenous students’ mathematics self-concept varies significantly based on their “gender” and “family economic status”. Boys’ mathematics self-concept is higher than girls’. Indigenous students from upper middle class have higher mathematics self-concept than those from lower class. 2."Indigenous identity" and "background variables" do not have effect nor interact on mathematics self-concept. 3.Indigenous students ' academic achievement in mathematics varies significantly according to different mathematics self-concept. 4."Indigenous identity" and "mathematics self-concept" interact with academic achievement in mathematics. 5.The "overall background variables" of indigenous students are predictive of "mathematics self-concept". "Gender" and "family economic status" are the main predictive variables. Non-indigenous students have two additional predictive variables: “paternal education level " and "maternal education level”. Furthermore, students' mathematics self-concept can be significantly predicted based on students’ "indigenous identity". 6.Mathematics self-concept of indigenous students is predictive of and has a positive impact on their academic achievement in mathematics, which is similar to the case of non-indigenous students. Based on the result of this study, recommendations were made for the policies for indigenous students, educational institutions, and professionals, as well as future research.

並列關鍵字

indigenous students ； mathematics self-concept ； mathematics academic achievement

參考文獻

譚光鼎、葉川榮（2011）。高學業成就原住民高中生學習現況之研究。嘉大教育研究學刊，27，141-169。

Marsh, H. W., & Yeung, A. S. (1997). Causal effects of academic self-concept on academic achievement: Structural equation models of longitudinal data. Journal of Educational Psychology, 89(1), 41-54.

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