本研究主要依據建構主義理論基礎，在一般教學和學習理論基礎上建構所謂的「建構主義取向的教學方法」。為探討建構取向教學法在數學學習成效的效果，乃選取國中一年級兩個班為研究對象，進行為期兩個月的教學實驗，以進行實地的建構取向教學與傳統教學之比較，並對學生在教學前後與其間所填答的問卷或資料進行分析，本研究所採的研究工具計有：(一)數學段考考卷；(二)數學學習成就測驗；(三)國中新生數學能力測驗；(四)數學學習經驗量表；(五)學習日記表格；(六)數學學習回饋問卷。使用的資料分析方法有：(一)獨立樣本單因子共變數分析；(二)質的分析。精分析結果如下： 一、建議教學組的學生與傳統教學組的學生在數學段考成績無顯著差異存在。 二、建構教學組的學生與傳統教學組的學生在數學學習成就測驗後測得分有顯著差異存在。且建構教學組顯著優於傳統教學組。 三、建構教學組的學生與傳統教學組的學生在數學焦慮量表後測得分無顯著差異存在。 四、建構教學組的學生與傳統教學組的學生在數學動機信念量表後測得分有顯著差異存在。且建構教學組顯著優於傳統教學組。 五、建構教學組的學生與傳統教學組的學生在班級氣氛量表後測得分有顯著差異存在。且建構教學組顯著優於傳統教學組。 六、建構教學組的學生與傳統教學組的學生在民主溝通態度量表後測得分無顯著差異存在。 七、由接受建議教學法的學生的數學學習回饋問卷與學習日記上可發現多數學生對建議教學持正面肯定的態度。 本研究針對上述發現加以討論，並對數學教學、行政措施與未來研究提出若干建議以供參考。 / The experiment on math achievement of the seventh grade students - the constructvist approach

Abstract In a charter school in the Southwest United States, elementary students were struggling to attain proficiency in math and have been failing to meet the standards in math on the Arizona Instrument to Measure Standards test. As a result, these students may not have been prepared for more advanced math courses as they continued their schooling, and this failure to attain proficiency in math may continue to impact the school's ability to make adequate yearly progress. The purpose of this explanatory case study was to explore the perspectives of elementary math teachers toward teaching math, their preparation to teach math, and the possible influences they may have on their students' math skills development. The theoretical framework was self-efficacy theory. Data were gathered through questionnaires completed by 5 participants teaching kindergarten through 5th grade and through the investigation of archival data of their students' achievement test scores. Emerging themes were coded to record and organize relevant information. The participants indicated that they did not feel prepared to teach elementary math when entering the classroom after their teacher preparation programs and that they want to gain more content knowledge and learn more strategies to teach math. Social change may occur as the elementary math teachers are given a voice concerning the teaching of math, and this voice could be used in producing staff development and improving instruction.

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本論文目的在分析臺灣學生學習成就評量資料庫(TASA)之新移民子女學習成就、心理、背景特質表現，及與本土子女進行比較。研究中自描述新移民族群的歷史演變、發展、可能遭遇困境與相關的研究中，進而，再搭配現行既有評量架構，以決定針對國小(四、六年級)新移民子女之數學成就、性別、家庭結構、家庭語言環境、家庭社經地位、家人、自我教育期望、親子關係、學校適應、學習策略、學習偏好、能力歸因、數學能力自我概念、內在動機、家庭作業、課業補習、課外活動等十多項心理、背景特質進行分析，而在詮釋其理論、實徵研究基礎後，運用測量不變性、多元潛在迴歸分析等技術以進行本研究各項議題之探討，希冀能就分析結果，提供未來研究之參考。 綜整分析後，可發現以下幾點結論： 一、在針對數學成就進行族群間之比較時，研究中在單向度假設與Rasch模式適配度檢定符合下，進而於排除顯著差異試題功能測量指標後，是運用多元潛在迴歸分析以進行本土與新移民子女數學成就之比較，分析結果顯示，在國小六年級內，並未存在顯著的族群差異，但是於國小四年級中，則是以本土子女的表現平均優於新移民子女，其差異效果為0.36，約屬Cohen(1992)認為介於中等至小的效果量，而接續於分析是否存在其它因素影響時，分析結果是顯示在先天消極的族群因素外，族群間家庭社經地位的不均衡才是真正影響之主因。 二、有關族群間之心理與背景特質比較方面，研究中在經採用測量不變性以確立工具品質，並伴隨著卡方獨立性考驗、獨立樣本t檢定之運用後，其分析結果大致顯示出新移民子女是較本土子女，在家中手足數僅有1位、位居老大或獨子女、繼親家庭與身處雙語環境等現況具有相對的多數，但是在學生認知家人、自我教育期望、親子關係、學校適應、學習策略運用、學習偏好以至課業補習、課外活動時間分派等，整體而言，則多是未具顯著的差異或屬Cohen(1992)所認為小的差異效果量範圍內。另一方面，研究中更突顯出的是族群間家庭社經地位的不平衡，確實占有極大的比重，是具備Cohen認為之中等至小的差異效果。 三、在分析心理、背景特質與數學成就關聯時，研究中在經採多元潛在迴歸分析後，其結果大致顯示：就族群與變項間之交互作用而言，國小四年級學生所認知之自我教育期望、內在動機等，相較於新移民子女，是對本土子女之數學成就有較高的影響力，但是國小六年級學生的家中手足數、家庭社經地位、記憶、控制策略運用與外控能力歸因的認知上，則是相對在新移民子女之數學成就上有較深厚的影響，而至於其它變項之分析，則多未存在族群的差異。進而，在排除族群的干擾，僅就各特質與數學成就關聯之主要效果而言，研究結果顯示除性別、家庭子女的出生序、家庭作業與課業補習分派時間等，存在不顯著或僅部份年級具備顯著效果外，其餘特質皆能符合本研究理論所預測之傾向，大致是以具備過多家中手足數或持過度的外控數學能力歸因者，是會對學生數學成就產生負面的影響，而其餘如來自完整家庭、身處主流語言環境、具備高家庭社經地位、教育期望、和諧親子關係、良好學校適應與擁有高度學習策略、偏好、動機等，則皆能正向的影響數學成就。 最後，研究中是就新移民子女定義、抽樣架構、測量指標等面向，提出對新移民子女學習成長資料庫之建立及與其它實務、研究之建議。 / The purpose of this study is to analyze neo-immigrant children’s achievement, performance in psychological traits and compare these with native children. Starting from the description of development, challenge and related researches of immigrant children in the past, we found the assessment frame of Taiwan Assessment of Student Achievement (TASA) just corresponded to the purpose we expect. Therefore, based on TASA , we decided to analyze the status and performance of neo-immigrant children in math, gender, family structure, language environment, socio-economic status, parents and self expectation, parents-children relationship, school adjustment, learning strategy, learning preference, ability attribution, academic self-concept, intrinsic motivation, time assignment of homework, school cramming, and extracurricular activity etc. Following the support of the theoretical and empirical evidences, we used the technique of measurement invariance and multiple latent regression to discover the different topics in the thesis. In sum, some conclusions are proposed. 1. In the comparison of math achievement between neo-immigrant and native children, we use the technique of multiple latent regression to test the difference after exclusion some items with significant differential item functioning. The result indicates that there is no significant difference between these two races in the sixth grade, but in the fourth grade the native children perform better than neo-immigrant children. The effect size is 0.36, and it is between medium and small degree according to Cohen(1992)’s opinion. Depended on this result, several following analyses are implemented. It shows the inequality of family socio-economic status between races is the main cause instead of the race people belong to. 2. In the comparison of psychological traits between neo-immigrant and native children, we not only use the technique of measurement invariance to ensure the qualities of assessment tools but also adopt chi-square test and independent samples t-test to examine the differences. The results indicate that the neo-immigrant children have more chances belonging to the categories of being eldest among siblings or only one child in his family, living in step-parents family, and involvement in bilingual environment. But there is almost no or just little difference between the two races in the perception of parent and self expectation, parents-children relationship, school adjustment, learning strategy application, learning preference, and the time assignment of school cramming and extracurricular activity. Besides, we found the inequality of family socio-economic status between races is the most different. The effect sizes range approximately from small to medium degree according to Cohen(1992)’s opinion. 3. In this study, we used the technique of multiple latent regression to analyze the relationship between different psychological traits and math achievement. The results indicate that as far as the interaction effects are concerned, the perception of self expectation and intrinsic motivation has greater impacts on native children’s math achievement than neo-immigrant’s in the fourth grade, but in the sixth grade the family size, family socio-economic status, the usage of memorization and control strategy, external ability attribution have greater impacts on neo-immigrant children’s math achievement than native children’s. Besides, there are no interaction effects on the remaining variables. Furthermore, as far as the main effect is concerned, the result shows that except no or just little relationship between gender, birth order, the time assignment of homework, school cramming and math achievement, the remaining variables have the similar relationships toward math achievement as we expect. That is that having too many siblings, external attribution of math ability may have negative influence on students’ achievement, but students who belong to intact family, involve in the mainstream of language environment, have higher family socio-economic status, and perceive better parent and self expectation, parents-children relationship, school adjustment etc. may have positive influence on their math achievement. Finally, some suggestions about the definition of neo-immigrant children, the way of sampling and qualities of measurement indicators are proposed. We expect they may do a greater help in the construct of the database of Prospect of Neo-Immigrant Children Learning and future usage.

The two purposes of this study are first, to provide an evaluation of an after-school basic mathematics program at the Demonstration School for the Deaf Junior Secondary School (DemoDeaf) in Mampong-Akuapim, Ghana. Second, it provides an ecological discussion exploring why DemoDeaf students do not have access to quality education. I designed and piloted the math program in 2005 and 2007 as an action researcher and volunteer with the Non-Government Organization (NGO), Signs of Hope International. The program was developed after finding six students in one JSS class could not count to one-hundred and all other students struggled with addition and/or subtraction. The program has been shown quantitatively and qualitatively to have statistically significant and positive effects on DemoDeaf students. In 2007, the number of students proficient in counting increased from thirty-four to forty-four. An analysis of the addition achievement test results indicate students advanced a total of twenty-nine levels; four students learned to add single-digit numbers together, eleven students learned how to add double-digit numbers together, and fourteen students learned how to add triple-digit numbers together. An analysis of the subtraction achievement tests indicate students advanced a total of nineteen levels; six students learned to subtract single-digit numbers, eight students learned how to subtract double-digit numbers, and five students learned how to subtract with triple-digit numbers. Sample-t-tests showed that the increase of students proficient in counting, addition, or subtraction (except for triple-digit subtraction) was statistically significant at the p-value of < .01 or < .05. The stigma and negative stereotypes embedded in the normative culture in Ghana and the majority/minority relations and power dynamics between hearing and deaf groups influence the socializing institutions of the family and deaf schools. The normative hearing culture influences the language choice parents/guardians give their deaf child and how they treat them. The perspectives and values of hearing educators and administrators influence deaf school design and create a hidden curriculum for deaf students. These separate forces meet in the classroom and not only prevent students from receiving a quality secular education, they also reinforce the low status ascription of deaf students in Ghana.