Preoperative Low Serum Bicarbonate Levels Predict Acute Kidney Injury After Cardiac Surgery

Acute kidney injury (AKI) after cardiac surgery is a common and serious complication. Although lower than normal serum bicarbonate levels are known to be associated with consecutive renal function deterioration in patients with chronic kidney injury, it is not well-known whether preoperative low serum bicarbonate levels are associated with the development of AKI in patients who undergo cardiac surgery. Therefore, the clinical implication of preoperative serum bicarbonate levels on AKI occurrence after cardiac surgery was investigated. Patients who underwent coronary artery bypass or valve surgery at Yonsei University Health System from January 2013 to December 2014 were enrolled. The patients were divided into 3 groups based on preoperative serum bicarbonate levels, which represented group 1 (below normal levels) 24 mEq/L. The primary outcome was the predicated incidence of AKI 48 hours after cardiac surgery. AKI was defined according to Acute Kidney Injury Network criteria. Among 875 patients, 228 (26.1%) developed AKI within 48 hours after cardiac surgery. The incidence of AKI was higher in group 1 (40.9%) than in group 2 (26.5%) and group 3 (19.5%) (P < 0.001). In addition, the duration of postoperative stay in a hospital intensive care unit (ICU) was longer for AKI patients and for those in the low-preoperative-serum-bicarbonate-level groups. A multivariate logistic regression analysis showed that low preoperative serum bicarbonate levels were significantly associated with AKI even after adjustment for age, sex, hypertension, diabetes mellitus, operation type, preoperative hemoglobin, and estimated glomerular filtration rate. In conclusion, low serum bicarbonate levels were associated with higher incidence of AKI and prolonged ICU stay. Further studies are needed to clarify whether strict correction of bicarbonate levels close to normal limits may have a protective role in preventing further AKI development.ope

Hepatic Sarcoidosis in a Patient with Chronic Hepatitis B Virus Infection

Sarcoidosis is a systemic inflammatory granulomatous disease affecting multiple organs, including liver, spleen, heart, eyes, and skin. Liver involvement is reported in 11.5% of cases and many studies have reported on the association between hepatitis C virus infection and sarcoidosis. However, the role of hepatitis B virus (HBV) infection as a trigger for sarcoidosis has never been reported. We describe a case of hepatic sarcoidosis in a patient with chronic hepatitis B infection, with a possible link between the two. It is the first case report of a patient with interferon-α-naïve chronic HBV infection presenting with hepatic sarcoidosis accompanied by portal hypertension and liver cirrhosis

Vitamin D deficiency is significantly associated with depression in patients with chronic kidney disease

BACKGROUND: Depression is reported to be the most common psychological problem in patients with chronic kidney disease (CKD). Several studies have reported that lower levels of serum vitamin D are significantly associated with depression. Both vitamin D deficiency and depression are prevalent in patients with CKD, yet the relationship between these two factors remains poorly understood. This study aimed to investigate the association between vitamin D levels and depression among CKD patients. METHODS: Totally, 21,257 individuals who participated in the Korean National Health and Nutrition Examination Survey (KNHANES V, VI) from 2010-2014 were screened for the study; 533 CKD patients were included. Vitamin D deficiency was defined as serum 25-hydroxyvitamin D3 [25(OH)D3] ≤10 ng/mL. Patients were divided into vitamin D deficient or sufficient groups. Depression was screened for using the Korean version of the WHO Composite International Diagnostic Interview-Short Form. The association between vitamin D deficiency and depression was evaluated by multivariate logistic regression analysis. RESULTS: The mean participant age was 70.1±9.4 years; 262 patients (49.2%) were male. The median 25(OH)D3 level was 19.1±6.9 ng/mL. The prevalence of depression was higher in CKD patients than in the general population (14.3 vs. 11.1%, P = 0.03). Additionally, the prevalence of depression was significantly higher in CKD patients with (vs. without) vitamin D deficiency (32.5% vs. 50.0%, P<0.001). Multivariate logistic regression analysis showed that vitamin D deficiency was a significant independent predictor of depression after adjusting for confounding factors (adjusted odds ratio, 6.15; 95% confidence interval, 2.02-8.75; P = 0.001). CONCLUSION: Depression was highly prevalent in CKD patients, in whom vitamin D deficiency was a significant independent predictor of depression. Therefore, management of vitamin D deficiency might help prevent depression in CKD patients.ope

Electrolyte and mineral disturbances in septic acute kidney injury patients undergoing continuous renal replacement therapy

Electrolyte and mineral disturbances remain a major concern in patients undergoing continuous renal replacement therapy (CRRT); however, it is not clear whether those imbalances are associated with adverse outcomes in patients with septic acute kidney injury (AKI) undergoing CRRT. We conducted a post-hoc analysis of data from a prospective randomized controlled trial. A total of 210 patients with a mean age of 62.2 years (136 [64.8%] males) in 2 hospitals were enrolled. Levels of sodium, potassium, calcium, and phosphate measured before (0?hour) and 24 hours after CRRT initiation. Before starting CRRT, at least 1 deficiency and excess in electrolytes or minerals were observed in 126 (60.0%) and 188 (67.6%) patients, respectively. The excess in these parameters was greatly improved, whereas hypokalemia and hypophosphatemia became more prevalent at 24 hours after CRRT. However, 1 and 2 or more deficiencies in those parameters at the 2 time points were not associated with mortality. However, during 28 days, 89 (71.2%) deaths occurred in patients with phosphate levels at 0?hour of ≥4.5?mg/dL as compared with 49 (57.6%) in patients with phosphate levels <4.5?mg/dL. The 90-day mortality was also significantly higher in patients with hyperphosphatemia. Similarly, in 184 patients who survived at 24 hours after CRRT, hyperphosphatemia conferred a 2.2-fold and 2.6-fold increased risk of 28- and 90-day mortality, respectively. The results remained unaltered when the serum phosphate level was analyzed as a continuous variable. Electrolyte and mineral disturbances are common, and hyperphosphatemia may predict poor prognosis in septic AKI patients undergoing CRRT.ope

Phosphate is a potential biomarker of disease severity and predicts adverse outcomes in acute kidney injury patients undergoing continuous renal replacement therapy

Hyperphosphatemia is associated with mortality in patients with chronic kidney disease, and is common in critically ill patients with acute kidney injury (AKI); however, its clinical implication in these patients is unknown. We conducted an observational study in 1144 patients (mean age, 63.2 years; male, 705 [61.6%]) with AKI who received continuous renal replacement therapy (CRRT) between January 2009 and September 2016. Phosphate levels were measured before (0 h) and 24 h after CRRT initiation. We assessed disease severity using various clinical parameters. Phosphate at 0 h positively correlated with the Acute Physiology and Chronic Health Evaluation II (APACHE II; P < 0.001) and Sequential Organ Failure Assessment (SOFA; P < 0.001) scores, and inversely with mean arterial pressure (MAP; P = 0.02) and urine output (UO; P = 0.01). In a fully adjusted linear regression analysis for age, sex, Charlson comorbidity index (CCI), MAP, and estimated glomerular filtration rate (eGFR), higher 0 h phosphate level was significantly associated with high APACHE II (P < 0.001) and SOFA (P = 0.04) scores, suggesting that phosphate represents disease severity. A multivariable Cox model also showed that hyperphosphatemia was significantly associated with increased 28-day (HR 1.05, 95% CI 1.02-1.08, P = 0.001) and 90-day (HR 1.05, 95% CI 1.02-1.08, P = 0.001) mortality. Furthermore, patients with increased phosphate level during 24 h were at higher risk of death than those with stable or decreased phosphate levels. Finally, c-statistics significantly increased when phosphate was added to a model that included age, sex, CCI, body mass index, eGFR, MAP, hemoglobin, serum albumin, C-reactive protein, and APACHE II score. This study shows that phosphate is a potential biomarker that can reflect disease severity and predict mortality in critically ill patients receiving CRRT.ope

Body mass index is inversely associated with mortality in patients with acute kidney injury undergoing continuous renal replacement therapy

BACKGROUND: Many epidemiologic studies have reported on the controversial concept of the obesity paradox. The presence of acute kidney injury (AKI) can accelerate energy-consuming processes, particularly in patients requiring continuous renal replacement therapy (CRRT). Thus, we aimed to investigate whether obesity can provide a survival benefit in this highly catabolic condition. METHODS: We conducted an observational study in 212 patients who had undergone CRRT owing to various causes of AKI between 2010 and 2014. The study end point was defined as death that occurred within 30 days after the initiation of CRRT. RESULTS: Patients were categorized into three groups according to tertiles of body mass index (BMI). During ≥30 days after the initiation of CRRT, 39 patients (57.4%) in the highest tertile died, as compared with 58 patients (78.4%) in the lowest tertile (P = 0.02). In a multivariable analysis adjusted for cofounding factors, the highest tertile of BMI was significantly associated with a decreased risk of death (hazard ratio [HR], 0.57; 95% confidence interval [CI], 0.37-0.87; P = 0.01). This significant association remained unaltered for 60-day (HR, 0.64; 95% CI, 0.43-0.94; P = 0.03) and 90-day mortality (HR, 0.66; 95% CI, 0.44-0.97; P = 0.03). CONCLUSION: This study showed that a higher BMI confer a survival benefit over a lower BMI in AKI patients undergoing CRRT.ope

Neck circumference predicts renal function decline in overweight women: A community-based prospective cohort study

Chronic kidney disease (CKD) is characterized by increased risks of morbidity and mortality. Upper-body subcutaneous fat, which is commonly estimated from the neck circumference (NC), was revealed to be the main reservoir of circulating nonesterified fatty acids in overweight patients. Despite a close association between NC and metabolic complications, the relationship of NC with renal function has not been fully investigated. In this study, the impact of NC on the development of incident CKD was elucidated.The data were retrieved from the Korean Genome and Epidemiology Study cohort. The subjects were followed at 2-year intervals from 2003 to 2011. Overweight was defined as a body mass index of ≥23?kg/m. A total of 4298 cohort subjects were screened. After exclusion, 2268 overweight subjects were included for the final analysis. The primary end point was incident CKD, which was defined as a composite of estimated glomerular filtration rate (eGFR)?<?60?mL/min/1.73?m or the development of proteinuria.The mean patient age was 36.3?±?3.0 years, and 1285 (56.7%) were men. They were divided into 2 groups according to the median NC in male and female subjects, separately. In both sexes, hypertension (men, P?<?0.001; women, P = 0.009) and diabetes (men, P = 0.002; women, P?<?0.001) were significantly more prevalent in the big NC group than in the small NC group. In contrast, eGFR was significantly lower only in male subjects of the big NC group (P?<?0.001), whereas it was comparable between the small and big NC groups (P = 0.167). In multivariate Cox proportional hazards regression analysis, NC values were independently associated with incident CKD development in female subjects after adjusting for multiple confounding factors (per 1?cm increase, hazard ratio [95% confidence interval] = 1.159 [1.024-1.310], P = 0.019) but not in male subjects.NC is independently associated with the development of CKD in overweight female subjects, suggesting that it could be a practical risk factor for CKD.ope

The impact of disease severity on paradoxical association between body mass index and mortality in patients with acute kidney injury undergoing continuous renal replacement therapy

BACKGROUND: Association between high body mass index (BMI) and survival benefit is confounded by comorbid conditions such as nutritional status and inflammation. Patients with acute kidney injury (AKI), particularly those receiving continuous renal replacement therapy (CRRT), are highly catabolic and more susceptible to loss of energy. Herein, we evaluated whether disease severity can modify the relationship between BMI and mortality. METHODS: We conducted an observational study in 1144 patients who had undergone CRRT owing to various causes of AKI between 2010 and 2014. Patients were categorized into four groups; underweight (/=25 kg/m(2)) according to BMI classification by the Committee of Clinical Practice Guidelines and Korean Society for the Study of Obesity. More severe disease was defined as sepsis-related organ failure assessment (SOFA) score of >/= a median value of 12. The study endpoint was death that occurred within 30 days after the initiation of CRRT. RESULTS: The mean age was 63.2 years and 439 (38.4%) were females. The median BMI was 23.6 (20.9-26.2) kg/m(2). The obese group were younger and higher SOFA score than normal BMI group. In a multivariable Cox regression analysis, we found a significant interaction between BMI and SOFA score (P < 0.001). Furthermore, obese patients were significantly associated with a lower risk of death as compared to normal BMI group after adjusting confounding factors [hazard ratio (HR), 0.81; 95% confidence interval (CI), 0.68-0.97; P = 0.03]. This association was only evident among patients with high severity (HR, 0.61; 95% CI, 0.48-0.76, P < 0.001). In contrast, in those with low severity, survival benefit of high BMI was lost, whereas underweight was associated with an increased risk of death (HR, 1.74; 95% CI, 1.16-2.60; P = 0.007). CONCLUSION: In this study, we found a survival benefit of high BMI in AKI patients undergoing CRRT, particularly in those with more disease severity; the effect was not observed in those with less disease severity.ope

생태적인 신·인간·자연 이해를 중심으로

본 논문은 오늘날 극한에 치달은 전 지구적 생태 위기의 시대에 기독교의 세계관이 보다 생태적일 수 있으며, 이에 이 위기의 시대에 대안을 제시할 수 있다는 희망에서 시작한다. 전통적 기독교 세계관은 인간중심적이고 가부장적이며 이원론적 세계관이었음을 비판받아왔다. 이러한 기독교는 지구 곳곳에서 벌어지는 심각한 생태계 파괴에 무엇보다 책임이 크며, 이 위기 상황에 응답해야 한다. 이에 본 논문은 기독교 안에서 제시될 수 있는 생태적인 신과 인간 그리고 자연 이해를 함석헌과 샐리 맥페이그의 사상을 통해 발견하고자 하는 것이다. 함석헌의 씨알사상은 서구의 기독교를 그대로 수용하지 않고 주체적으로 받아들였으며, 동양사상 그 중에서도 노장사상과의 창조적 대화를 통해서 독창적으로 정립한 것이다. 함석헌은 노장사상의 영향으로 물, 여성, 아기를 높게 평가하는 생태적인 감수성과 무위자연을 통한 스스로 하는 자유와 저항, 평화 등을 지향하게 되었다. 이러한 노장사상의 영향과 철저한 역사인식을 바탕으로 제시된 그의 씨알사상은 씨알이 지니는 생명의 원리인 스스로 함과 대듦, 조화, 전체성, 역동성 등이 내재되어 있고, 이로부터 생태적이고 유기체적인 신과 인간 그리고 자연에 대한 기독교적 이해를 발견할 수 있는 것이다. 특히 함석헌에게 씨알은 억압받고 소외된 민중을 의미하며, 그는 이러한 민중의 생명원리를 긍정하고 그들을 역사의 주체로 내세운다. 따라서 생명의 원리를 고스란히 간직한 씨알 민중은 역사의 주체이며, 나아가 이들을 통해 생명을 살릴 수 있는 가능성을 볼 수 있는 것이다. 북미 생태 여성신학자인 샐리 맥페이그 역시 전통적 기독교의 가부장적 신 이해를 비판하고 오늘날에 적합한 생태적인 기독교적 세계관으로의 패러다임 전환을 제시한다. 그는 고정화되고 특권화되기 쉬운 기독교 상징들을 경계하여 은유적 방법론을 제시하고, 어머니, 연인, 친구로의 하나님 은유를 제안한다. 또한 전통적 기독교에서 억압받았던 ‘몸’ 이미지를 회복시키고 세계를 하나님의 몸 은유로 제시하며, 전통적 기독교의 창조, 죄와 악, 구원 등을 생태적인 관점에서 이해한다. 이러한 이해 속에서 신과 인간 그리고 자연은 오늘날에 보다 적합하게 생태적으로 제시될 수 있는 것이다. 나아가 본 논문은 함석헌과 맥페이그가 삶의 자리가 다르고 시대가 다르지만, 그들의 사상이 소통할 수 있는 공통분모를 가지며, 이에 따라 두 사상의 만남을 시도한다. 두 사상은 전통적 기독교의 가부장적이고 인간중심적인 패러다임의 전환이며, 그들이 제시한 새로운 세계관은 보다 생태적일 수 있다는 공통분모를 가진다. 이 때 두 사상의 창조적 대화를 보다 효과적으로 전개하기 위해 가다머의 지평융합 개념을 사용한다. 가다머의 지평융합은 지평과 지평이 만났을 때 이루어지는 자연스러운 현상을 해석하는 방법으로 사용되는데, 본 논문에서는 지평융합이 가지는 기존 지평에 대한 존중과 더불어 두 지평이 만났을 때 나타나는 개방성, 창조성, 역동성, 포용성 등을 강조하고자 하는 것이다. 따라서 시공을 초월한 두 사상이 보다 효과적으로 만나기 위한 지평융합을 통해서 더욱 풍성해진 생태적 세계관을 제안할 수 있다. 이러한 두 사상의 대화를 통해 함석헌의 부족한 여성인식은 맥페이그의 생태여성신학으로부터 보완될 것이고, 맥페이그의 한정된 주체 인식은 함석헌의 고난 받는 ‘인식론적 특권’에 따라 민중 주체로 확대될 수 있다. 이와 같이 서로의 사상이 보완되어 더 풍성해진 세계관은 생태 위기의 오늘날 생태적이고 유기체적이며 여성적인 신관, 인간관, 자연관을 제시할 수 있을 것이다.;This thesis starts with a hope that the Christian view of the world can be more ecological in the face of the extremely serious global ecological crisis, presenting a viable alternative to the crisis. The traditional Christian view of the world has been criticized for its human-centered, patriarchal, and dualistic approach. Christianity has been responsible for the serious destruction of the ecosystem across the globe and has to respond to the crisis. In this respect, the purpose of this thesis is to identify understanding of ecological God, humans, and nature, which the Christian faith presents, through thoughts of Ham Sok-hon, and Sallie McFague. Ham&amp;apos;s &amp;apos;Ssial Thought&amp;apos; independently accepted Christianity of the West. Rather than blindly accepting it, his idea was born though the creative dialogue with oriental philosophy, especially the Lao-Chuang Thought. Influenced by the Lao-Chuang Thought, Ham sought ecological sensibility that values water, women, and babies; and self-imposed freedom, resistance, and peace through Laozi&amp;apos;s concepts of &amp;apos;it-self-so-ing&amp;apos;(Ziran自然) and &amp;apos;non-coercive action&amp;apos;(Wu Wei 無&amp;amp;#28858;). &amp;apos;Ssial Thought,&amp;apos; which was based on the Lao-Chuang Thought and Ham&amp;apos;s thorough view of history, has intrinsic values such as defiance, harmony, wholeness, dynamics, and doing by oneself, the energy of life represented by Ssial (literally means seed). An ecological and organic Christian understanding of God, humans, and nature can be found in Ham&amp;apos;s thought. As Ssial particularly means the oppressed, marginalized ordinary people to Ham, he recognized the energy of life of the grassroots or the commoners and placed them as the subject of history. Indeed, the grassroots are the subject of history as the ones who have kept spirit of life intact, opening possibilities of saving lives through the commoners. Sallie McFague, a North American Ecofeminist theologian, criticizes the patriarchal understanding of God in the traditional Christian faith and presents a paradigm shift to a Christian ecological view of world, which is fit for the world of today. McFague warns against the Christian symbols that are fixed and likely to be privileged and presents metaphorical methodology in which God could be a mother, a lover, or a friend. In addition, she restores the image of &amp;apos;the body,&amp;apos; which was repressed in the traditional Christian belief; uses a metaphor that the world is God&amp;apos;s body and understands the traditional Christian ideologies from creation, virtue and vice, to redemption in an ecological sense. Through such understanding, God, humans, and nature can be presented in an ecological way, which is more fitting for the world of today. Furthermore, this study seeks to combine Ham&amp;apos;s thought with McFague&amp;apos;s on the belief that they share a common ground for communication although they had a different place in life and lived in different times. Both have a common denominator: they represent the paradigm shift in the patriarchal and human-centered traditional Christianity; and the new world view they present can be more ecological. To effectively facilitate the creative dialogue between the two thoughts, this thesis uses Hans-Georg Gadamer&amp;apos;s philosophy, &amp;apos;Fusion of Horizon.&amp;apos; Although the Fusion of Horizon is a methodology to interpret the natural phenomenon where horizon meets another horizon, this thesis emphasizes respect for the existing horizon represented by the Fusion of Horizon and openness, creativity, dynamics, and tolerance expressed when two horizons meet. Through the Fusion of Horizon in which two thoughts can more effectively meet beyond time and space, a much more enriched ecological view of the world can be presented. Such dialogue between the two thoughts will enable Ham&amp;apos;s lack of perspective towards women to be complemented by McFague&amp;apos;s Ecofeminist Theology while McFague&amp;apos;s limited subjective consciousness to be expanded to the subject of the grassroots by Ham&amp;apos;s &amp;apos;epistemological privilege.&amp;apos; In the face of the global ecological crisis, a world view enriched by mutual complement of the two thoughts will present us with a new ecological, organic, feminine view of God, humans, and nature.Ⅰ. 서론 = 1 A. 연구의 동기와 목적 = 1 B. 선행연구 고찰 = 6 C. 연구방법 및 전개 = 12 Ⅱ. 한국 기독교의 패러다임 전환으로의 토착신학 : 함석헌의 씨□사상과 노장사상 이해를 통한 새로운 신 · 인간 · 자연 이해 = 18 A. 유영모의 노장사상 이해 = 18 1. 유영모의 노장사상과의 대화를 통한 신 · 인간 · 자연 이해 = 19 2. 유영모의 신 · 인간 · 자연 이해에 대한 비판적 고찰 = 25 B. 함석헌의 씨알사상과 노장사상 이해를 통한 유기적 · 생태적 신 · 인간 · 자연 이해 = 30 1. 씨□사상 이해 = 31 2. 신 이해 = 38 3. 인간 이해 = 46 4. 자연 이해 = 55 5. 함석헌의 신 · 인간 · 자연 이해에 대한 비판적 고찰 = 60 Ⅲ. 서구 전통 기독교 세계관의 패러다임 전환으로의 생태여성신학 : 샐리 맥페이그의 생태여성신학을 통한 새로운 신 · 인간 · 자연 이해 = 67 A. 생태여성신학의 출현과 과정 = 68 1. 생태여성신학의 출현과 배경 = 68 2. 생태여성신학의 전개 = 71 B. 샐리 맥페이그의 생태적 · 여성적 신 · 인간 · 자연 이해 = 75 1. 샐리 맥페이그의 은유 · 구성 신학적 방법론 = 75 2. 신 이해 = 79 3. 인간 이해 = 88 4. 자연 이해 = 95 5. 샐리 맥페이그의 신 · 인간 · 자연 이해에 대한 비판적 고찰 = 102 Ⅳ. 생태적이고 유기적인 신 · 인간 · 자연의 풍성한 이해를 향하여 : 함석헌의 씨□사상 · 노장사상 이해와 샐리 맥페이그의 생태여성신학의 지평융합 = 109 A. 언어 이해 = 109 B. 신 이해 = 115 C. 인간 이해 = 118 D. 자연 이해 = 125 Ⅴ. 결론 = 130 A. 종합 정리 = 130 B. 한계점과 앞으로의 연구 방향 = 133 참고문헌 = 136 ABSTRACT = 14

고등학교 학생의 대수적 사고 중 일반화의 사고에 대한 연구

고등학교 수학에서 중요하게 다루어지고 있는 대수는 대수적 사고보다는 대부분 대수적 표현을 단순화하는 것, 방정식을 푸는 것, 상징적 조작을 위한 규칙을 배우는 것으로 인식되어 왔고 다른 수학적 지식과 학생들의 실제 상황과 연결되지 못하는 절차들의 집합으로 학습되고 가르쳐 왔다. 이러한 문제점을 바탕으로, 본 연구에서는 대수학습의 목표가 되는 대수적 사고에 대한 논의를 전개하여, 대수적 사고 중 창조적이며 독립적인 학습을 가능하게 하는 일반화를 이용한 대수 학습의 지도를 위한 기초자료를 마련하고자 다음과 같은 연구문제를 설정하였다. 1. 대수영역에서 고등학교 학생들의 일반화에 영향을 주는 요인은 무엇인가? 2. 문제 해결을 통한 일반화의 경험은 대수학습에 어떤 영향을 주는가? 이러한 연구문제를 해결하기 위해 이 연구에서는 서울시 소재 B고등학교 1학년 학생 5명을 대상으로 약 2주에 걸쳐 사례연구를 실시하였다. 학생들이 제시된 일반화에 관한 문제를 어떻게 해결하는가에 대한 과정 관찰과 개별 면담을 통하여 분석한 결과 다음과 같은 결론을 얻을 수 있었다. 첫째, 대수의 선행학습과 패턴인식이 일반화에 영향을 주는 요인으로 작용을 한다. 사례를 분석한 결과 학생들은 일반화의 과정에 수치적, 기하적 패턴 인식은 하였으나, 이전의 대수학습경험의 차이가 일반화에 영향을 주고 있다. 특히, 기하적 패턴 인식을 이용한 문제에서는 모든 학생이 패턴을 인식하였음에도 불구하고, 일반화된 식을 도출할 수 있는 유용한 패턴을 발견하는 데에는 많은 차이를 보였다. 둘째, 문제 해결을 통한 일반화의 경험이 효과적인 대수 학습에 도움이 되는 것을 알 수 있다. 사례연구 결과 학생들은 일반화의 경험을 통해 문자 사용의 의미를 이해하고, 수학은 이미 완성된 것이 주어지는 것이 아니라 만들어지는 것이라는 인식을 하게 됨으로써 대수와 수학의 유용성을 인지하게 되었다. 요약하면, 고등학교 대수에서의 일반화 경험은 변수의 구성에 영향을 줄뿐만 아니라 창조적이고 독립적인 수학학습을 가능하게 한다는 것을 알 수 있다. 보다 효과적인 일반화를 이용한 대수학습을 위해서는 일반화를 통한 변수의 도입과 문제해결을 이용한 미지수의 도입을 효과적으로 연계할 수 있는 방안과 패턴인식의 차이가 일반화에 영향을 준다는 연구결과로부터 다양한 패턴인식을 볼 수 있는 유연성을 길러 줄 수 있는 방안에 대한 구체적인 연구가 지속되어야 할 것이다.;The purpose of this study was to gain fundamental frame for teaching algebra using generalization. In particular, this study investigated (a) cognitive condition that affect student&amp;apos;s construction of generalizations, (b) how students&amp;apos; experience for generalization influence on their algebra learning. The study adopted a qualitative research methodology-a case study approach-to address the research questions. Five students participated in the study. A semi-structured interview and several exercise were conducted to collect data from each student. They were generally able to recognize mathematical patterns based on their abstractions and generalizations. The exercise included consecutive numbers problems and dot rectangle problem. The focus on this research was which variables affects on construction of generalization and how these experiences influence on learning algebra. The first variable for construction of generalization is pre-algebraic learning. Misconception and error in pre-algebraic learning prevents their construction of generalization. Also, selecting more meaningful pattern algebraically is the other important variable for construction of generalization. On the other hand, these experiences for generalization helped students to understand the meaning of algebraic symbols and to the nature of mathematics made, not given.표목차 = iii 그림 목차 = iv 논문 개요 = v I. 서론 = 1 A. 연구의 필요성 및 목적 = 1 B. 연구 문제 = 4 C. 연구의 제한점 = 4 II. 이론적 배경 = 5 A. 수학적 사고 = 5 1. 정신 측정학적 관점 = 5 2. 정보처리적 관점 = 7 3. 수학적 관점 = 9 B. 대수적 사고 = 11 1. 대수의 역사적 발달 = 12 1) 산술과 관련한 대수의 발달 = 12 2) 기하와 관련한 대수의 발달 = 14 3) 산술과 기하에 관련한 대수의 합병 = 17 2. 대수의 제 관점에서의 대수적 사고 = 22 1) 일반화된 산술 = 22 2) 문제해결을 위한 절차 = 23 3) 변량 사이의 관계에 대한 연구 = 26 4) 추상적 구조에 대한 연구 = 27 3. 방법면에 관련한 대수적 사고 = 28 1) 구조화의 사고 = 28 2) 일반화의 사고 = 32 3) 추상화의 사고 = 34 4) 분석적 사고 = 36 5) 기호화의 사고 = 38 C. 일반화의 사고 = 41 III. 연구 방법 및 절차 = 43 A. 연구대상 = 43 B. 연구절차 = 46 C. 연구 도구 = 47 D. 자료수집 = 51 IV. 연구 결과 및 분석 = 52 A. 문제 해결과정의 관찰 결과 = 52 B. 연구 문제에 대한 분석 = 56 V. 요약 및 제언 = 65 참고문헌 = 68 부록 = 73 ABSTRACT = 7