3 resultados para Concept of angle
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:
The notion of sediment-transport capacity has been engrained in geomorphological and related literature for over 50 years, although its earliest roots date back explicitly to Gilbert in fluvial geomorphology in the 1870s and implicitly to eighteenth to nineteenth century developments in engineering. Despite cross fertilization between different process domains, there seem to have been independent inventions of the idea in aeolian geomorphology by Bagnold in the 1930s and in hillslope studies by Ellison in the 1940s. Here we review the invention and development of the idea of transport capacity in the fluvial, aeolian, coastal, hillslope, débris flow, and glacial process domains. As these various developments have occurred, different definitions have been used, which makes it both a difficult concept to test, and one that may lead to poor communications between those working in different domains of geomorphology. We argue that the original relation between the power of a flow and its ability to transport sediment can be challenged for three reasons. First, as sediment becomes entrained in a flow, the nature of the flow changes and so it is unreasonable to link the capacity of the water or wind only to the ability of the fluid to move sediment. Secondly, environmental sediment transport is complicated, and the range of processes involved in most movements means that simple relationships are unlikely to hold, not least because the movement of sediment often changes the substrate, which in turn affects the flow conditions. Thirdly, the inherently stochastic nature of sediment transport means that any capacity relationships do not scale either in time or in space. Consequently, new theories of sediment transport are needed to improve understanding and prediction and to guide measurement and management of all geomorphic systems.
Resumo:
Background: Women with germline BRCA1 mutations have a high lifetime risk of breast cancer, with the only available risk-reduction strategies being risk-reducing surgery or chemoprevention. These women predominantly develop triple-negative breast cancers; hence, it is unlikely that selective estrogen receptor modulators (serms) will reduce the risk of developing cancer, as these have not been shown to reduce the incidence of estrogen receptor–negative breast cancers. Preclinical data from our laboratory suggest that exposure to estrogen and its metabolites is capable of causing dna double-strand breaks (dsbs) and thus driving genomic instability, an early hallmark of BRCA1-related breast cancer. Therefore, an approach that lowers circulating estrogen levels and reduces estrogen metabolite exposure may prove a successful chemopreventive strategy.
Aims: To provide proof of concept of the hypothesis that the combination of luteinizing-hormone releasing-hormone agonists (lhrha) and aromatase inhibitors (ais) can suppress circulating levels of estrogen and its metabolites in BRCA1 mutation carriers, thus reducing estrogen metabolite levels in breast cells, reducing dna dsbs, and potentially reducing the incidence of breast cancer.
Methods: 12 Premenopausal BRCA1 mutation carriers will undergo baseline ultrasound-guided breast core biopsy and plasma and urine sampling. Half the women will be treated for 3 months with combination goserelin (lhrha) plus anastrazole (ai), and the remainder with tamoxifen (serm) before repeat tissue, plasma, and urine sampling. After a 1-month washout period, groups will cross over for a further 3 months treatment before final biologic sample collection. Tissue, plasma, and urine samples will be examined using a combination of immunohistochemistry, comet assays, and ultrahigh performance liquid chromatography tandem mass spectrometry to assess the impact of lhrha plus ai compared with serm on levels of dna damage, estrogens, and genotoxic estrogen metabolites. Quality of life will also be assessed during the study.
Results: This trial is currently ongoing.
