Educational Research on Mathematics

Question: Describe about the Educational Research on Mathematics. Answer: Week 2 Theme Why Maths Matters: Illustrating importance of mathematics for people of all demographics and dispelling myths Evidence https://research.acer.edu.au/cgi/viewcontent.cgi?article=1016context=learning_processes The above article resource investigates the perceptions of school students regarding maths mathematical tasks and how mathematics teachers can play a vital role in making students dispel any misconceptions regarding the subject and instead develop considerable interest and enthusiasm. The above article was written by Professor Sarah Buckley of the Australian Council for Educational Research and primarily focuses on the anxiety experienced by students as a result of any mathematics related work. Rationale This resource points out the particular nervous sensation of anxiety which is felt by almost every school student when faced with mathematical tasks. As emotions are a vital part of the learning process, this article dwells into the various psychological disturbances felt by students, the underlying neurological phenomena that occur as a result and investigates the causes along with providing remedial action. The article also give a mention regarding the usage of advanced medical technologies like functional magnetic resonant imaging of the brain to analyse brain activities during maths anxiety that may help root out all these negative aspects. Discussions are also given about various educational and certain social myths that are associated with students mathematical ability, that are the main reasons behind feelings of maths anxiety among students. Additional myths like how girls are not expected to be good at maths and that maths are primarily important for students of technical t echnological fields are also mentioned. Application The article is quite useful in pinpointing some underlying factors that creates anxiety and terror amongst students when they face mathematical work. Private discussions can be held with those students who experience the largest levels of anxiety. They can be counselled to be strong and brave enough to face any mathematical work without hesitation. Parents can be advised to support their children regarding their nervousness towards maths, instead of rebuking them. The myths that students have regarding mathematics can be removed by showing them instances of application of maths in many non technical fields. Any and all negative school community beliefs regarding maths occurs amongst students and mainly in classrooms of the high schools, which cause decline in the academic motivation of many students. Students can thus be encouraged to hold positive discussions and encourage them to arrange unique mathematical problem solving friendly competitions amongst themselves. The exact factors that cause the formation of maths anxiety in students can be addressed/. Students mainly feel nervousness because of their lack of confidence in solving maths problems as almost all maths problems have just one correct answer. Students feel tensed and anxious because of the compulsion to find out the absolute correct answer. This particular aspect can be discussed with them, and advice can be given that it is absolutely normal to make mistakes as long as that mistake teaches something and helps in the overall learning process. (Sarah, 2013) Week 7 Theme Maths in Real World: How mathematics is interwoven in almost all everyday activities in the real world Resource https://www.sfu.ca/~rpyke/Modelling.pdf This resource illustrates several applications of mathematics that pertain to real life situations and incidences. The steps that are required to effectively and logically solve a real life problem using mathematical techniques are shown here. Several examples have been given and detailed step by step descriptions of all the mathematical solutions are shown clearly. In addition, diagrams and proper images are given that lucidly explain the associated concepts and the processes that are used to mathematically solve the real life problems. This article is aimed at facilitating the mathematical learning experience of students aged 15 to 18. Rationale This article is a clear cut presentation that clearly shows how mathematical tools and techniques are used utilized to solve day to day real life problems. Steps required to logically solve problems are properly given. The given procedures show how a word problem that describes some real world event are divide into a number of steps , that help in attaining the required solution quickly and efficiently. Linear programming and operational research techniques are described in a very simple manner using a real life example of a furniture manufacturing company. The method of explanation is very simple and clear, and it is possible for nay school student to understand it without any significant effort on their part. The article emphasizes the usage and application of simple logic on the part of the students to solve the problems and adequate help guidance regarding the steps that are require to be followed are all given in the document. Application Several unique problems are given in the above article and they have real life applications. The first problem deals with finding the profit gained by a furniture manufacturing company; how the company manufactures pieces of wood that have individual pricings and in what way they should assimilate all the various parts so as to make a considerable profit. Relations and equations are also clearly given, and if properly taught and explained to students, they can analyse and understand how mathematics and associated tools can be effectively utilized in solving day to day problems. The situation mentioned in the resource is a typical real life situation and students can gain useful insights on how mathematics is involved and interwoven in every real life situation. Formation of mathematical modelling using data, algorithm and variables is very clearly mentioned in an absolutely uncomplicated way, and this will also help students learn the process of creating effective maths modelling sys tems to obtain solutions related to any mathematical or technical problem. Selection of variables and how to appropriately modify them in order to obtain correct solutions can be shown. Furthermore, behaviour of the variables is very logically and simply shown using the basics of coordinate geometry, such a straight lines that represent linear equations in a two dimensional frame. All of these concepts are well within the scope of a high school student and hence they will find it quite easy to analyse and understand the given real life mathematical problems in the article. ("Using Mathematics to Solve Real World Problems", 2010) Week8Theme Maths and early childhood: Techniques that can be used to inspire mathematical learning in young children Resource https://www.esev.ipv.pt/mat1ciclo/DISCUSS%C3%95ES/Picture%20books.pdf The above article puts forth the technique of using picture boos to stimulate and encourage young children about mathematics and how this will in turn enhance the confidence of the children regarding the subject and any kind of mathematical or technical problem solving tasks in the present and the future. The article is written by Marja van den Heuvel-Panhuizen of the Utrecht University of The Netherlands and Humboldt University of Germany, Sylvia van den Boogard of the Utrecht University of The Netherlands and Brain Doig of Deakin University. This is an example of a planned day experience. Rationale This article effectively describes the experiences and observations of the writers regarding the usage of picture and illustrations books that help in encouraging young children of ages five to six to learn more about mathematics. Analysis done shows how these types of books can help the young children to explore in depth the various types and sections of the branch of mathematics. Through mathematical picture books students can clearly understand the basic concepts of arithmetic and mathematics along with their proper application in real life. This is possible as these books illustrate and put forth several real life situations and objects that have technical and mathematical implications .A combination of literature and pictures that lucidly describe mathematical problems along with their associated solutions, helps children learn from the angles of a particular situation or context, enhancing their overall learning experience. Application This resource clearly explains the various ways how the various real life examples and contexts given picture books with appropriate literature help in giving young children an early access and lucid understanding of several mathematical rules and their applications. Children can be taught the basic concepts of geometry through the help of these books. Their mental and cognitive development will be accelerated as a result. They can be asked to differentiate between the various shape, sizes and structures of several objects. Patterns and logical resolution of problems can be taught to them through the myriad of examples given in these types of books. Literatures given I the book can also be used to teach children about any mathematical queries that they have, which in turn help them develop their own ideas and concepts regarding the solution of mathematical problems. Pictures of various things like buildings, vehicles and landscapes are usually shown in these books along with mentione d values of distances heights and lengths etc. and children can be asked to specific or general questions regarding the various distances that are covered by any particular object or road. Other illustrations like a group or flock of animals or birds can be shown to the children and questions can be asked regarding the number of animals, how they are arranged or how many are moving or gathered together or in what direction they are moving. All these examples and contexts explained in a picture book can help in stimulating the learning nature of young children and make them more interested in mathematics. (Marja, Sylvia, Brian, 2009) Week 9 Theme Maths and Primary School: How primary schools should modify maths learning in schools Resource https://www.into.ie/ROI/Publications/MathsPrimarySchool.pdf This resource portrays certain methods through primary school children can get to love mathematics as a subject and gain a better understanding of mathematical tools and techniques that will in turn develop their logic level and problem solving levels. This article is written by the Irish National Teachers Organisation, and aims at improving the learning experience of primary school students with respect to mathematics. A survey shows the effectiveness of the methods given in the article. Rationale This article emphasizes on the importance of mathematics in the daily teaching curriculum of schools. Teachers have been asked to link mathematics to any aspect of the students environment and their own experiences. At the same time, teachers have been asked to encourage students to think logically and relate everyday experiences and activities to the mathematical world. A proper division of the mathematics curriculum structure is given in this resource, where the whole curriculum has been divided into several individual subjects such as numbers, algebra, shapes and spaces, measurements and data collection with associated analysis. Means if assessing the level or amount of a particular students mathematical learning have also been mentioned. In addition, several alternative and unconventional approaches to mathematics learning have been mentioned along with their key focuses and assessment methods. Surveys results have also been given that indicate the impacts and implications of the changes in the learning experiences on students and their learning processes. Application An effective learning experience can be achieved with the proper and perfect application of all the mentioned changes and modifications of the mathematical curriculum. Students can be taught in accordance to the various sub modules of the modified curriculum. They can be instructed to focus on their mental aptitude and ability to solve problems in a quick manner without any mistakes rather than perform lengthy written calculations with pen and paper. Recordings can be done to help students better understand the process of mental maths. They can also better learn patterns and understand certain mathematical and algebraic sequences when they are taught in these types of modulated teaching methods, which put emphasis on systematic and individualistic teaching of each branch of mathematics. Spatial awareness and real life applications of shapes, sizes and geometrics can be improved through effective integration of a geometric sub module to this teaching procedure. Data analysis by observ ing graphical representations of equations and relations is another important aspect of this particular teaching method that will help better the learning experience of students. Students will be able to better evaluate measure and interpret real life mathematical models and this will assist their ability to relate and link theories with practical applications. (John, 2006) Week 10Theme Maths and Learning Environment: How certain learning environments can help stimulate students to actively learn mathematics Resource https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/413379/Good_practice_in_primary_mathematics.pdf This article illustrates the various types of learning environments that can be created to help young children learn actively and get enthused about mathematics. This is British government article that show how practical situations can be introduced safely in eth classroom or teaching area that will help young children to learn more about numbers, mathematical and arithmetical tools and techniques. These teaching methods, if practiced, can provide young children with a very beneficial learning experience. Rationale This article shows the practical and hands on experiences are critical in helping the development of logical and deductive way of thinking and helps in all round mental development of young children. The teaching practices and procedures mentioned in this resource are collected from a wide variety of reputed schools spread all over the United Kingdom. And several useful and key findings have been summarised, that will help a teacher to understand and find out means to better the immediate learning environment of schools. The methods that can be useful to develop the mental capabilities of students and help them in developing fluency in mental calculation methods and help them one problem with several correlated problems through efficient deduction and induction. Applicatio Several methods that can be used to improve the learning environments of students are given. Practical situations and objects can be introduced in the classroom. Children can be taken out into outdoor areas. Games using numbers can be used to teach children regarding several mathematical concepts. The methods also show how students can be taken to markets and bazaars to interact with shop keepers who can teach them about the mathematical calculations that they deal with daily. New ways to solve certain mathematical problems can be taught to the students. Alternative techniques to performing addition, subtraction, multiplication and division can also be taught to the students by putting forth real life concepts and contexts in front of them, through the environment. ("Good practice in primary mathematics: evidence from 20 successful schools", 2011) Week 11 ICT in Maths: How ICT can be used to create new modalities in maths Resource https://www.voiceofresearch.org/doc/Jun-2014/Jun-2014_8.pdf The above resource portrays how information and communication techniques can be used to open up new avenues and create new innovative techniques for mathematical education. The role of ICT has been researched in this case study and focus is mainly on the role it can play in primary mathematical education. Rationale The above article shows how digital technology and communication techniques can help in expanding the scope of learning, with primary focus on mathematics. The various electronic and digital means and how they can be effectively utilized in the mathematical educational field are explained. ICT can help in accessing a wide variety of information from various sources and thus will help in broadening the viewpoint and knowledge base of a student. At the same time, digital means are very effective in providing accurate solutions and results, the key aspect of mathematics, and thus students will be able to identify and correct their mistakes if they are allowed to learn mathematics through innovative ICT. Application As evident from the rationale given, ICT can be used in classrooms with proper supervision to help students gain a broader understanding g about any subject. With regards to mathematics, students can gain access to study materials from educational institutions from any corner of the world. They can thus gain a broader understanding of any mathematical concept, relate it to any everyday situation and also witness how contemporary students from other places are solving problems. The process of transmitting and availing information is a vital component of todays educational world. Laptops, projectors, the Internet etc. all these are very useful resources in the right hands and can help teachers motivate students to understand, deduce and logically solve problems using the various data available through information and communication technologies. (Amarnath, 2014) References Amarnath, M. (2014). Ict And Its Role In Primary Mathematics Education.Voice Of Research. Good practice in primary mathematics: evidence from 20 successful schools. (2011). John, C. (2006). Maths in Primary Schoo. Marja, v., Sylvia, v., Brian, D. (2009). Picture books stimulate the learning of mathematics. Sarah, B. (2013). Deconstructing maths anxiety: Helping students to develop a positive attitude towards learning maths. Using Mathematics to Solve Real World Problems. (2010).