North Carolina's community colleges redesigned developmental math programs in 2011. The overall effectiveness of the redesign has not yet been evaluated. A concurrent mixed-methods study was conducted at Mid-Atlantic Community College (MACC) for a formative and summative evaluation of the redesigned program. Mezirow's transformative learning theory, along with an emphasis on designing individualized methods of instruction as outlined by Keller were the theoretical foundations of the evaluation. The extent to which the redesigned math modules affected the effectiveness of the math program at MACC was the guiding research question. Data on student outcomes and participant perceptions were collected for this concurrent mixed methods evaluation. Quantitative data from MACC institutional databases (N = 827) were used to compare the overall GPAs and mean passing grades for students in the old (2012-13) and new (2013-15) programs using an independent samples t test. There were no significant differences in students' mean passing grades or overall GPAs for the redesigned modules, compared to the semester classes. Qualitative data from 9 semi-structured interviews with 3 administrators, 3 instructors, and 3 students were analyzed inductively for thematic patterns. Qualitative results indicated that perceptions of administrators were more favorable regarding the effectiveness of the redesign than the perceptions of instructors and students and that programs implementing individualized modules need to provide professional development training to those individuals affected by the redesign. Results from this study can promote positive social change by providing information for improved teaching and learning practices among developmental math instructors.

Sixth grade students at a Mid-Atlantic, urban, PreK-8 public school have shown weak mathematical performance. In accordance with the No Child Left Behind (NCLB) Act of 2001, the local district has implemented numerous policy changes to improve performance, but no substantial improvements in test scores have been seen so far. This project study focused on the development of automaticity and fluency of math facts to address this problem. The theoretical framework of the study was based on Haring and Eaton's instructional competency hierarchy framework, which claims that students who master basic mathematics skills are better able to progress to more general and abstract skills. A modified, quasi-experimental, nonequivalent control-group design was used with 2 groups of 20 sixth grade students who were neither randomly selected nor assigned to either group. Data analysis using one-way analysis of variance revealed that computer aided instruction--specifically, Fluency and Automaticity through Systematic Teaching and Technology (FASTT) Math--was more effective than the other classroom's mathematics instruction in developing multiplication fluency. In response, a curriculum policy recommendation was drafted as a project and will be presented to the board of education to conduct additional evaluations of FASTT Math as a supplemental tool in third through eighth grades in the district. This project is expected to contribute to social change by improving mathematics achievement which will create a mathematically literate cadre of students to meet the needs of 21st century employers, thus improving the quality of life in the broader community.

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This case study examined the perceptions of administrators, teachers and parents of the implementation of an elementary school science, technology, engineering and math (STEM) academy program that featured characteristics of both magnet school programs and schoolwithin-a-school programs. I conducted interviews of key personnel, informed by classroom observations and a survey of parents to determine how stakeholders perceived equity in the access and allocation of opportunities and resources. The STEM Academy selected students from neighboring elementary schools and was housed within a larger K-5 elementary school. I found the STEM Academy teachers were widely praised for their innovations and teaching excellence, and alignment with emerging best practices. However, there were perceptions that their curriculum was neither sufficiently documented nor aligned with school division priorities, and was insufficiently communicated with school division central office leaders Academy parents, teachers, and community partners praised the Academy’s approach to curriculum, instruction, and uncommon learning experiences; but resentment and perceptions of inequity and exclusivity among most other stakeholders compromised the program implementation, leading to administrative and political pressure that challenged the Academy’s sustainability. I provide discussion and recommendations concerning elementary STEM programs, highlighting the importance of stakeholder perceptions and program evaluation. I also provide several suggestions for further research. / Ed. D.

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

本研究主要目的是以文獻分析、問卷調查、潛在成長模式等方法探討數學焦慮、數學學習動機與數學學業成就等三個變項的縱貫模式及因果結構模式。根據五百二十九位國三學生所填的五波調查問卷資料，進行兩部分研究。 研究一乃在估算數學焦慮、數學學習動機、數學學業成就的潛在改變量模式及 數學焦慮、數學學習動機、數學學業成就兩兩之間的因果結構模式。結果發現1.數學焦慮縱貫模式上，符合「焦慮遞增理論」；2.數學學習動機縱貫模式上，符合「動機先升後降理論」；3.數學學業成就縱貫模式上，符合「成就先升後降理論」； 4.數學焦慮與數學學習動機因果結構模式上，符合「動機焦慮交互激發效果理論」；5.數學焦慮與數學學業成就因果結構模式上，符合「焦慮成就交互抑制效果理論」；6.數學學習動機與數學學業成就因果結構模式上，符合「動機成就交互激發效果理論」。 研究二則依據研究一二變項因果結構統計驗證成立的三套理論，建構出三變項因果結構六模式，並驗證有無中介效果。結果顯示，1.前焦慮、中動機、後學業成就因果模式上，符合「動機未完全中介前焦慮、後學業成就理論」；2. 前動機、中焦慮、後學業成就因果模式上，符合「焦慮未完全中介前動機、後學業成就理論」；3.前焦慮、中學業成就、後動機因果模式上，符合「學業成就未完全中介前焦慮、後動機理論」；4.前學業成就、中焦慮、後動機因果模式上，符合「焦慮未完全中介前學業成就、後動機理論」；5. 前動機、中學業成就、後焦慮因果模式上，符合「學業成就未完全中介前動機、後焦慮理論」；6.前學業成就、中動機、後焦慮因果模式上，符合「動機未完全中介前學業成就、後焦慮理論」。 除了上述結果外，研究也對數學焦慮、數學學習動機與數學學業成就縱貫模式的趨勢與時間效果量，國三學生轉折點界定，數學焦慮、數學學習動機與數學學業成就適當模式產出及個別中介角色剖析有深入探討。 / This study, using literature review, questionnaire survey, and latent growth model, investigated the longitudinal model and causal model among math anxiety, learning motivation, and academic achievement. After collecting 529 students with 5 waves, I conducted two studies. The purpose of study 1 was to estimate the latent change model and the causal model of math anxiety, learning motivation, and academic achievement. Results showed that 1. The anxiety increasing theory was supported by the math anxiety longitudinal model. 2. The first increasing then decreasing theory was supported by the math learning motivation longitudinal model. 3. The first increasing then decreasing theory was supported by the math academic achievement longitudinal model. 4. The reciprocal activated effect theory was supported by the math anxiety and learning motivation causal models. 5. The reciprocal inhibitive effect theory was supported by the math anxiety and academic achievement causal models. 6. The reciprocal activated effect theory was supported by the math learning motivation and academic achievement causal models. According to the final three theories stated above and proved by study 1, I constructed the six causal models in order to verify the mediated effects of math anxiety, math learning motivation, and math academic achievement. I found that 1. Math learning motivation did not mediate fully the effects on early math anxiety and late math academic achievement. 2. Math anxiety did not mediate fully the effects on early math learning motivation and late math academic achievement. 3. Math academic achievement did not mediate fully the effects on early math anxiety and late math learning motivation. 4. Math anxiety did not mediate fully the effects on early math academic achievement and late math learning motivation. 5. Math academic achievement did not mediate fully the effects on early math learning motivation math and late math anxiety. 6. Math learning motivation did not mediate fully the effects on early math academic achievement and late math anxiety. In addition, the research also explored the longitudinal model trend and effect, the key period for 3rd year junior high school students, the proper models, and the mediated roles among math anxiety, learning motivation, and academic achievement.

Mycket forskning har ägnats åt att kartlägga skolelevers (ofta negativa) attityder till matematik. Denna studie undersöker attityder till matematik hos nio deltagare och tidigare deltagare i Matteklubben för högstadiet i Stockholm. Matteklubben är en frivillig efter skolan-aktivitet för unga som gillar problemlösning, där fler med positiv attityd kan tänkas finnas. Studien har utgått från TMA-modellen - en tredimensionell modell för attityd till matematik, med de tre dimensionerna Syn på matematik - Känslomässig inställning till matematik - Upplevd egen förmåga, där varje dimension kan ha en positiv respektive negativ pol. Datainsamling skedde genom semistrukturerade intervjuer. Därefter analyserades data med hjälp av tematisk analys. Sammantaget framträder en positiv attityd till matematik hos deltagarna. Deltagarnas syn på matematik framträder i hög grad som relationell, där de betonar matematikens strukturella och logiska uppbyggnad i sina beskrivningar av vad man uppfattar att matematik är. Alla respondenter uttrycker en positiv känslomässig inställning till matematik, även om de gör tydliga distinktioner mellan vad de gillar i matematik och vad de ogillar. Den matematiska aktivitet man tycker om handlar om ”problemlösning på riktigt”, där man vill möta utmanande problem av en passande svårighetsgrad, få tänka kreativt och gärna kunna finna lösningar med flera olika metoder. Ett undertema handlar om matematiska sammanhang och gemenskaper. Här framkommer flera erfarenheter av skolans matematik som ett mer ensamt sammanhang, där deltagarna ofta utövar matematik på egen hand, med liten lärarinteraktion och där man ger snarare än får hjälp. Vissa deltagare har dock kunnat samarbeta med klass- eller skolkamrater i sitt matematikutforskande, vilket har bidragit till en mer positiv upplevelse och inställning till ämnet. I Matteklubben beskriver deltagarna att man är mer en del av ett sammanhang, där man arbetar med samma matematiska problem och kan diskutera lösningar med andra deltagare och ledare i något högre utsträckning. Särskilt Matteklubbens tävlingar ses som sociala tillfällen, då man får diskutera problem och lösningar även med personer man inte kände innan. Vad gäller den egna upplevda förmågan så uttrycker deltagarna i stort en god tilltro till att kunna klara av skolans matematik, även om gymnasiestarten upplevts som mer utmanande. Att få yttre bekräftelse på sitt kunnande var inte oviktigt, även om flera betonade vikten av förståelse, snarare än ha många korrekt lösta uppgifter. Många deltagare har haft en stabil matematikbana, med tidigt intresse för och framgång i matematik, med uppmuntran och intresse i familjen. Några respondenter återger dock vändpunkter eller särskilda händelser, som har ändrat eller påverkat deras syn på matematik, på den egna förmågan och den känslomässiga inställningen till matematik. / A lot of research attention has been directed towards school pupils (often negative) attitudes towards mathematics. This study explores the attitude towards mathematics among nine participants and former participants in the Math club for grade 7-9 in Stockholm. The Math club is an after school activity for young people who enjoy mathematical problem solving, where possibly more positive attitudes can be found. The theoretical framework for the study is TMA - the three-dimensional model for attitude towards mathematics, with the three dimensions; Vision of mathematics – Percieved competence – Emotional disposition. Data was collected through semi structured interviews and analyzed by using thematic analysis. Overall the participants expressed positive attitudes towards mathematics. The participants express a mostly relational vision of mathematics, where they notice and appreciate the logical structure of the subject. Although all participants express their liking of mathematics, they make distinctions about what they like and dislike in mathematics, both regarding content, tasks and social context. In general there is an appreciation of creative problem solving. Many participants experienced mathematics in school as a mostly separate activity with limited help from teachers, although some have had friends with whom they shared the interest. The Math Club seemed to have offered a context in which participants worked on the same problems and could get help and discuss solutions among each other, especially during competitions. The participants were confident about their own mathematical competence, at least until the start of secondary school. Confirmation of competence were appreciated, but many participants stressed that understanding of concepts were more important than getting many right answers. Though most participants described a stable trajectory in their appreciation of math, with early interest, success and encouragement from families as common features, some incidents of turning points or special events, that led to a sudden change of vision of mathematics, the own perceived competence and liking of mathematics were described.

Doctor of Philosophy / Curriculum and Instruction Programs / Gail Shroyer / David Allen / This study was designed to gather input from early career elementary teachers with the goal of finding ways to improve elementary mathematics methods courses. Multiple areas were explored including the degree to which respondents’ elementary mathematics methods course focused on the NCTM Process Standards, the teachers’ current standards-based teaching practices, the degree to which various pedagogical strategies from mathematics methods courses prepared preservice teachers for the classroom, and early career teachers’ suggestions for improving methods courses. Both qualitative and quantitative methodologies were used in this survey study as questions were of both closed and open format. Data from closed-response questions were used to determine the frequency, central tendencies and variability in standards-based preparation and teaching practices of the early career teachers. Open-ended responses were analyzed to determine patterns and categories relating to the support of, or suggestions for improving, elementary mathematics methods courses. Though teachers did not report a wide variation in the incorporation of the NCTM Process Standards in their teaching practices, some differences were worth noting. Problem Solving appeared to be the most used with the least variability in its frequency of use. Reasoning, in general, appeared to be used the least frequently and with the most variability. Some aspects of Communication, Connections and Representation were widely used and some were used less frequently. From a choice of eight methods teaching practices, ‘Observing in actual classrooms or working with individual students’ and ‘Planning and teaching in actual classrooms’ were considered by early career teachers to be the most beneficial aspects of methods courses.