The Process of Selecting a Research Topic - Assignment Example

?PART A Problem: tend to be confused between all of the formulas dealing with area and perimeter Part B Why do mix up the formulas for perimeter and area? 2. Why do students confuse measuring units for perimeter and area? 3. What are the students’ common misconception regarding estimation of area and perimeter? PART C What are the students’ common misconception regarding estimation of area and perimeter? Seven key words i. Misconceptions ii. Area iii. Perimeter iv. formula v. Width vi. Length vii. Measure Two resources that I will use to find information i. Google books ii. University of Southampton: Mathematical Sciences: databases & indexes Two additional keywords i. Teaching methods ii. Curriculum Key words that yielded the most useful searches i. Misconception ii. Area and perimeter D. Annotated bibliography for five sources identified in your search. Carle, S. (1993). Student Held Misconceptions Regarding Area and Perimeter of Rectangles. Boston: University of Massachusetts. This source focuses on the misconceptions of students in relation to area and perimeter of rectangles. Carle (1993) describes that students enter classroom with personal schemas, anchored in their ideas and experiences, which impact on their interpretation, reception, and recollection of new information. The author’s essentially recommends that the teachers should understand the impacts of such schemas. The author observes that the students manipulate and apply information without difficulties in class, only to forget the content after a while. Consequently, misconceptions are entangled into schemas, hence obstructing with the reception of information. Furthermore, the author discusses a framework including Anderson's theory of memory, taxonomy of critical thinking dispositions and abilities, Ennis' definition of critical thinking and cognitive psychology. This source is directed to teachers in different levels of education and any other education professionals and bodies that are involved in teaching of mathematics. This source is very useful considering that the author is an experienced classroom teacher, who has firsthand experience on the problems that mathematics students undergo. This information is helpful in the current topic because identification of misconception is the first step towards addressing the problems that students face in mathematics. The author has explained how the process of identification starts with pre-test analysis, which has five misconceptions including spatial bias, Equality Assumptions, Conversion Conclusion, Increase/Decrease assumption, and Fallacy of multiples. Disclosure of different types of misconceptions has a direct implication on the current study, which primarily deals with the way such misconceptions affect students’ understanding of area and perimeter formulas. Also useful from this source are the several theories that the author has explained which can help teachers in establishing the process of getting rid of misconception as well as initiating education change – this information can help in formulation the solution and recommendation in the current area of study. Although this source has some very relevant information that relates to the current topic, its usefulness is somewhat limited because it was published two decades ago, and many things have since changed. Therefore, its relevance is subject to further investigations on the more recent studies, to find out if any substantial changes have occurred in connection with the author’s findings. The author concludes the thesis by noting that the multi-faceted framework is very useful in investigating ways of building lessons, while focusing on elimination of particular misconceptions. Furthermore, the author makes suggestions on the manner in which the current innovative educational methods can be improved to aid students in understanding of formulas and mathematics in general. I reacted very positively to this source, because I found its multi-faced framework of investigating students’ misconception very inspiring and a round out way of looking into the problems affecting students in relation to application of area and perimeter formulas (Carle, 1993). Sisman, G. (2009). Seventh Grade Students’ Success on the Topics of Area and Perimeter. Elementary Education Online, 8(1), 243-253. This study focuses on the reasons why 7th grade students succeed on the topics of perimeter and area. The study was conducted a with 134 seventh grade students that attended elementary schools. The study was conducted with 134 seventh grade students attending one of the public elementary schools and found that majority of the students have problems related to misconceptions as well as difficulties in using formulas for area and perimeter, hence making it difficult to understand the concepts of perimeter and area. Basically, this source is ideal for finding out the reasons why students find it difficult to understand area and perimeter, in which the recommendations made for addressing such problems, can be used in the current research area. Furthermore, this source has very useful information on the reasons why students have difficulties understanding the concepts of area and perimeter, which can lead to finding effective ways of teaching on measurement concepts and skills. What’s more, the author describes the specific areas that are confused by students, including concepts and formula of area and perimeter, and difficulties in establishing linear (length) and area units. Nonetheless, this study is limited to its subjects, educational settings and data collection instruments. The source is targeted on teachers who are teaching area and perimeter as well as educational professionals who are involved in designing of educational curriculums. The author concludes that most of the seventh grades have a superficial understanding on perimeter and area, which makes them confuse the difference between the two concepts. My reaction to this source is that students in their elementary grades have serious problems understanding basic mathematical concepts, and innovative methods need to be implemented particularly on teaching methods to address this problem. D’Amore, B., & Fandino Pinilla, M. I. (2006). Relationships between area and perimeter: Beliefs of teachers and students. Mediterranean journal for research in mathematics education, 5(2), 1-29. This paper focuses on the beliefs of teachers and students regarding the existing relationships between perimeter and area of a plane shape. In particular, the study seeks to explore the change of beliefs, the extent of incidence of examples that are provided, and the language used to express the beliefs. The author discusses a concept in relation to which the expected associations between perimeter and area exemplify a students’ behavior that compels them to verify, without disapproval, reductions and increases between entities that are positioned in relationships. This source is useful in proving that beliefs can act as obstacles as well as tools for encouraging implementation of changes in teaching fraternity, which in reality shows how the problem of misconception of areas and parameters, by students, can be addressed (D’Amore & Fandino, & Pinilla, 2006). The author concludes that the problem that presents itself to the building of a satisfactory awareness of the relationship between area and perimeter is epistemological as well as didactic in nature. For example, the author finds that didactic choices are associated with an all time use of only convex figures, which causes the misconception that hollow figures cannot be used or that using them is undesirable, among other observations. The study has used a scientific framework of reference, which is particularly limited because of its insufficient content and complexity. The audience targeted includes the teachers teaching parameter and area in any level of education, with the basic aim of bringing to their attention the impacts of beliefs on teaching area and parameters. I responded to this source with amazement because I did not know that beliefs can have such a significant influence on understanding of the relations that exists between area and parameter. Hirstein, J.J., Lamb, C.E. & Osborne, A. (1978). Student misconceptions about area measure. Arithmetic Teacher, 25(6), 10–16. This paper focuses on the understanding of area as a significant concept for students. Hirstein, Lamb and Osborne (1978) maintain that area is commonly used as a measure in everyday lives of students and that its understanding is the foundation for many models that describe number and operations with numbers. They recommend that teachers should be able to discover and diagnose misconceptions of students in this realm because this idea is both functional and useful in students’ comprehension of mathematics. More specifically, Hirstein, Lamb and Osborne (1978) were interested in identifying whether or not students understood that the area of figures remained unchanged if the figure was crumbled and reassembled together. The usefulness of using this source is founded on its identification of common misconceptions for students regarding estimation of area, and the suggestions provided for teachers to diagnose the work of students. More importantly, the study was conducted by carrying out a direct observation on the participants hence becoming very useful primary source evidence that is applied to further authenticate the subject being studied. The other important information gotten from this study includes the various misconceptions identified as relating to area, which has a direct implication to the current research question. The study was carried out by interviewing of 106 children in grades 3 to 6, who attended different schools in Texas and Ohio, hence limiting its findings to that window of grades and perhaps the place of study. The source is intended to be used by teachers who are undergoing training as well as those who are in practice, so they can get more informed regarding the problems that students undergo in understanding area and perimeter, as well as the ways these problems can be addressed. The authors conclude that teachers can diagnose students’ misconception and identify corrective measures for children (Hirstein, Lamb, & Osborne, 1978). I reacted to this source by totally agreeing with its findings as it is a very practical observation on the problems the students in the middle grades undergo while trying to understanding the concept of area. Chick, H.C., & Baker, M.K. (2005). Investigating Teachers’ Responses to Student Misconceptions. Retrieved From http://www.emis.de/proceedings This study focuses on the students’ misconceptions in relation to procedural or conceptual aspects. Chick and Baker (2005) differentiates procedural knowledge as having a focus on symbolic algorithms and representation, with conceptual knowledge as loaded with relationships. In effect, this study tackles the challenges that affect teaching of mathematics and proposes that addressing both procedural knowledge and conceptual knowledge, is difficult if teachers do not possess conceptual fluency in important topics. Studying this source is useful because it helps identifies how teachers respond to situations involving students’ errors and misconceptions, which particularly helps to better understand the current research question. Furthermore, showing how teachers are influenced to focus on procedural or conceptual aspects as a result of errors reveal an important concept that is not available in other sources that are reviewed, especially pertaining to the teachers’ pedagogical content knowledge. The study’s limitation is that a small number of teachers are used in the survey, which makes it unreasonable to quantitatively generalize about the potential responses of other teachers. Furthermore, the study is valid for only upper primary teachers. The study is targeted on academicians, researchers and students researching on related areas of pedagogy. Upper school teachers can also use the findings of the study to enrich their practice. The author concludes by suggesting that teachers can respond to misconceptions of the students in different ways, but their focus must be placed on conceptual and procedural aspects of mathematical comprehension. My response to this source was wonderful in that I found it ideal for rounding up my research area, especially because it contained essential concepts that lacked in other literature. References Carle, S. (1993). Student Held Misconceptions Regarding Area and Perimeter of Rectangles. Boston: University of Massachusetts. Chick, H.C., & Baker, M.K. (2005). Investigating Teachers’ Responses to Student Misconceptions. Retrieved From http://www.emis.de/proceedings D’Amore, B., & Fandino Pinilla, M. I. (2006). Relationships between area and perimeter: Beliefs of teachers and students. Mediterranean journal for research in mathematics education, 5(2), 1-29. Hirstein, J.J., Lamb, C.E. & Osborne, A. (1978). Student misconceptions about area measure. Arithmetic Teacher, 25(6), 10–16. Sisman, G. (2009). Seventh Grade Students’ Success on the Topics of Area and Perimeter. Elementary Education Online, 8(1), 243-253. Read More