4 resultados para Méso-amérique
Resumo:
The angle concept is a multifaceted concept having static and dynamic definitions. The static definition of the angle refers to “the space between two rays” or “the intersection of two rays at the same end point” (Mitchelmore & White, 1998), whereas the dynamic definition of the angle concept highlights that the size of angle is the amount of rotation in direction (Fyhn, 2006). Since both definitions represent two diverse situations and have unique limitations (Henderson & Taimina, 2005), students may hold misconceptions about the angle concept. In this regard, the aim of this research was to explore high achievers’ knowledge regarding the definition of the angle concept as well as to investigate their erroneous answers on the angle concept.
104 grade 6 students drawn from four well-established elementary schools of Yozgat, Turkey were participated in this research. All participants were selected via a purposive sampling method and their mathematics grades were 4 or 5 out of 5, and. Data were collected through four questions prepared by considering the learning competencies set out in the grade 6 curriculum in Turkey and the findings of previous studies whose purposes were to identify students’ misconceptions of the angle concept. The findings were analyzed by two researchers, and their inter-rater agreement was calculated as 0.91, or almost perfect. Thereafter, coding discrepancies were resolved, and consensus was established.
The angle concept is a multifaceted concept having static and dynamic definitions.The static definition of the angle refers to “the space between two rays” or“the intersection of two rays at the same end point” (Mitchelmore & White, 1998), whereas the dynamicdefinition of the angle concept highlights that the size of angle is the amountof rotation in direction (Fyhn, 2006). Since both definitionsrepresent two diverse situations and have unique limitations (Henderson & Taimina, 2005), students may holdmisconceptions about the angle concept. In this regard, the aim of thisresearch was to explore high achievers’ knowledge regarding the definition ofthe angle concept as well as to investigate their erroneous answers on theangle concept.
104grade 6 students drawn from four well-established elementary schools of Yozgat,Turkey were participated in this research. All participants were selected via a purposive sampling method and their mathematics grades were 4 or 5 out of 5,and. Data were collected through four questions prepared by considering the learning competencies set out in the grade 6 curriculum in Turkey and the findings of previous studies whose purposes were to identify students’ misconceptions of the angle concept. The findings were analyzed by two researchers, and their inter-rater agreement was calculated as 0.91, or almost perfect. Thereafter, coding discrepancies were resolved, and consensus was established.
In the first question, students were asked to answer a multiple choice questions consisting of two statics definitions and one dynamic definition of the angle concept. Only 38 of 104 students were able to recognize these three definitions. Likewise, Mitchelmore and White (1998) investigated that less than10% of grade 4 students knew the dynamic definition of the angle concept. Additionally,the purpose of the second question was to figure out how well students could recognize 0-degree angle. We found that 49 of 104 students were unable to recognize MXW as an angle. While 6 students indicated that the size of MXW is0, other 6 students revealed that the size of MXW is 360. Therefore, 12 of 104students correctly answered this questions. On the other hand, 28 of 104students recognized the MXW angle as 180-degree angle. This finding demonstrated that these students have difficulties in naming the angles.Moreover, the third question consisted of three concentric circles with center O and two radiuses of the outer circle, and the intersection of the radiuses with these circles were named. Then, students were asked to compare the size of AOB, GOD and EOF angles. Only 36 of 104 students answered correctly by indicating that all three angles are equal, whereas 68 of 104 students incorrectly responded this question by revealing AOB<GOD< EOF. These students erroneously thought the size of the angle is related to either the size of the arc marking the angle or the area between the arms of the angle and the arc marking angle. These two erroneous strategies for determining the size of angles have been found by a few studies (Clausen-May,2008; Devichi & Munier, 2013; Kim & Lee, 2014; Mithcelmore, 1998;Wilson & Adams, 1992). The last question, whose aim was to determine how well students can adapt theangle concept to real life, consisted of an observer and a barrier, and students were asked to color the hidden area behind the barrier. Only 2 of 104students correctly responded this question, whereas 19 of 104 students drew rays from the observer to both sides of the barrier, and colored the area covered by the rays, the observer and barrier. While 35 of 104 students just colored behind the barrier without using any strategies, 33 of 104 students constructed two perpendicular lines at the both end of the barrier, and colored behind the barrier. Similarly, Munier, Devinci and Merle (2008) found that this incorrect strategy was used by 27% of students.
Consequently, we found that although the participants in this study were high achievers, they still held several misconceptions on the angle concept and had difficulties in adapting the angle concept to real life.
Keywords: the angle concept;misconceptions; erroneous answers; high achievers
ReferencesClausen-May, T. (2008). AnotherAngle on Angles. Australian Primary Mathematics Classroom, 13(1),4–8.
Devichi, C., & Munier, V.(2013). About the concept of angle in elementary school: Misconceptions andteaching sequences. The Journal of Mathematical Behavior, 32(1),1–19. http://doi.org/10.1016/j.jmathb.2012.10.001
Fyhn, A. B. (2006). A climbinggirl’s reflections about angles. The Journal of Mathematical Behavior, 25(2),91–102. http://doi.org/10.1016/j.jmathb.2006.02.004
Henderson, D. W., & Taimina,D. (2005). Experiencing geometry: Euclidean and non-Euclidean with history(3rd ed.). New York, USA: Prentice Hall.
Kim, O.-K., & Lee, J. H.(2014). Representations of Angle and Lesson Organization in Korean and AmericanElementary Mathematics Curriculum Programs. KAERA Research Forum, 1(3),28–37.
Mitchelmore, M. C., & White,P. (1998). Development of angle concepts: A framework for research. MathematicsEducation Research Journal, 10(3), 4–27.
Mithcelmore, M. C. (1998). Youngstudents’ concepts of turning and angle. Cognition and Instruction, 16(3),265–284.
Munier, V., Devichi, C., &Merle, H. (2008). A Physical Situation as a Way to Teach Angle. TeachingChildren Mathematics, 14(7), 402–407.
Wilson, P. S., & Adams, V.M. (1992). A Dynamic Way to Teach Angle and Angle Measure. ArithmeticTeacher, 39(5), 6–13.
Resumo:
Abstract - This study investigates the effect of solid dispersions prepared from of polyethylene glycol (PEG) 3350 and 6000 Da alone or combined with the non-ionic surfactant Tween 80 on the solubility and dissolution rate of a poorly soluble drug eprosartan mesylate (ESM) in attempt to improve its bioavailability following its oral administration.
INTRODUCTION
ESM is a potent anti-hypertension [1]. It has low water solubility and is classified as a Class II drug as per the Biopharmaceutical Classification Systems (BCS) leading to low and variable oral bioavailability (approximately 13%). [2]. Thus, improving ESM solubility and/or dissolution rate would eventually improve the drug bioavailability. Solid dispersion is widely used technique to improve the water solubility of poorly water-soluble drugs employing various biocompatible polymers. In this study, we aimed to enhance the solubility and dissolution of EMS employing solid dispersion (SD) formulated from two grades of poly ethylene glycol (PEG) polymers (i.e. PEG 3350 & PEG 6000 Da) either individually or in combination with Tween 80.
MATERIALS AND METHODS
ESM SDs were prepared by solvent evaporation method using either PEG 3350 or PEG 6000 at various (drug: polymer, w/w) ratios 1:1, 1:2, 1:3, 1:4, 1:5 alone or combined with Tween 80 added at fixed percentage of 0.1 of drug by weight?. Physical mixtures (PMs) of drug and carriers were also prepared at same ratios. Drug solid dispersions and physical mixtures were characterized in terms of drug content, drug dissolution using dissolution apparatus USP II and assayed using HPLC method. Drug dissolution enhancement ratio (ER %) from SD in comparison to the plain drug was calculated. Drug-polymer interactions were evaluated using Differential Scanning Calorimetry (DSC) and FT-IR.
RESULTS AND DISCUSSION
The in vitro solubility and dissolution studies showed SDs prepared using both polymers produced a remarkable improvement (p<0.05) in comparison to the plain drug which reached around 32% (Fig. 1). The dissolution enhancement ratio was polymer type and concentration-dependent. Adding Tween 80 to the SD did not show further dissolution enhancement but reduced the required amount of the polymer to get the same dissolution enhancement. The DSC and FT-IR studies indicated that using SD resulted in transformation of drug from crystalline to amorphous form.
CONCLUSIONS
This study indicated that SDs prepared by using both polymers i.e. PEG 3350 and PEG 6000 improved the in-vitro solubility and dissolution of ESM remarkably which may result in improving the drug bioavailability in vivo.
Acknowledgments
This work is a part of MSc thesis of O.M. Ali at the Faculty of Pharmacy, Aleppo University, Syria.
REFERENCES
[1] Ruilope L, Jager B: Eprosartan for the treatment of hypertension. Expert Opin Pharmacother 2003; 4(1):107-14
[2] Tenero D, Martin D, Wilson B, Jushchyshyn J, Boike S, Lundberg, D, et al. Pharmacokinetics of intravenously and orally administered Eprosartan in healthy males: absolute bioavailability and effect of food. Biopharm Drug Dispos 1998; 19(6): 351- 6.
