SOOLA

Friday, August 21, 2009

Pedagogy in Mathematics


PEDAGOGY IN MATHEMATICS


This field covers studies related to theories and practices in mathematics education for the enhancement of mathematical understanding. Amongst the approaches to be investigated, are constructivism, mastery, collaborative, contextual learning and problem-based learning. Other pedagogical perspectives include cognitively-guided instruction, zone of proximal development, expert-novice paradigm, postmodern pedagogy, critical pedagogy, development of mathematical thinking, mathematical values and beliefs, policy issues and current issues related to pedagogy of mathematics.

Teachers typically assume, according to the sources, are so prone to 'teach the same way they were taught in school.'Academic subjects such as civics, human civilisation and cultural studies require students to explore the world in search of their own knowledge. Mathematics, though base on facts and being thought in a procedural manner by teachers in school, can provide changes. For example, teachers could require students to look out for the history of how theorems are derived such as Pythagoras theorem. This not only makes the subject more interesting and more meaningful to any student as they can appreciate for themselves how such theories were derived a long time ago and still applicable today.


Technology pervades current life and has influenced our educational institutions including the manner ofinstruction and the design of curricula. Such change needs to be evaluated in terms of the impact uponboth teaching and learning. For example, the low cost, highly portable graphics calculator has become afeature of secondary school classrooms, yet are they being used mainly by teachers? How does thegraphics calculator affect the student’s comprehension and understanding of concepts? Is the use ofgraphics calculators more effective compared to the traditional chalk-and-talk methods?This paper discusses how the use of the graphics calculator changes the teaching and learning ofquadratic functions in the secondary classroom. Firstly, the paper compares teaching with the graphicscalculator to the traditional chalk-and-talk method. The second part presents and analyzes the perceptionof students to the graphics calculator in their learning of mathematical concepts. It further discusses thefindings based on data including students’ interviews that reveals how the use of graphics calculatorenhanced their learning. Finally, the paper advances several recommendations for pedagogicalstrategies when using graphics calculators.


The primary purpose for teaching mathematics is to enable students to learn and appreciatemathematics in the best way possible. With creativity, passion, and resources available to them,teachers are able to implement various techniques and strategies in the classroom to make learningmore meaningful and interesting to their students. In many classrooms, the usual way of teaching isthe chalk-and-talk method. Teachers give the input verbally or write on the board and the studentsfollow their instructions. However with the entry of technology into the classroom, the teaching ofmathematics is changed (Simonson & Dick, 1997). Technology, specifically graphics calculator,has been widely adopted by academic institutions and has influenced the pedagogy in theclassroom. For example, while graphics calculators were designed as personal tools, research byCavanagh (2005) reported that students tended to use them as a shared device. He found graphingcalculators played an important role in group activities as a kind of conversation piece for sharingmathematical ideas and making thought processes publicly available in the classroom. Thetechnology facilitated social interaction in the classroom because it acted as a common point ofreference for students as they discussed their ideas and results. Other researchers such as White(2004) have claimed that the graphics calculator has the potential to be a pedagogical Trojan Horse,subtly influencing a change in the usual teaching practices.


REF: www.google .com.my

(Abdullah & Saleh, 2005, P. 254).
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Tuesday, August 18, 2009

BLACKBOARD












Blackboard!!!Blackboard!!!Blackboard !!! What is blackboard? In sence of 21st centery (new era) all people will dont know, what is that blackboard but they are know about Electronic Blackboard or E-Blackboard.ok. Blackboard and E-blackboard is totally defferents. Blackboard is normally a large,smooth, usually dark surface of slate or other material on which to write or draw with chalk or chalk board..! BUT E-Blackboard is used computer or internet (ICT) in teaching and learning process. Its explores ways in which it can be used in teaching and learning and looks at developing effective courses such as using project in classroom teaching. We can also access Blackboard from the right hand menu on the blue Intranet screen.Further use is evolving of electronic Blackboard, accessed through the School's web site, to enhance communication with the students such as e-mail,computer conferencing, voice mail and so on. E- Blackboard also has many things we can do such as;

  • Teachers could hit a trouble maker in the middle of the forehead with a blackboard rubber without fear of missing or being sued!





  • On our latest visit we decided to choose from the blackboard menu.





  • The base should be painted matt black using blackboard paint





  • Remember that uploading a file creates a copy of the file on the Blackboard server.





  • Your personal Welcome page Your Welcome page will contain links to all of your Blackboard courses once you have enrolled in them.





  • Let me have your own recommendations; or post them to the duo board [ Our module Blackboard site ] .




Teachers and students perspective




The study deployed a survey method to collect basic data on the current practice of ICT in theteaching of Science and Mathematics at secondary schools, and to investigate teachers’ needs fortraining and support in relation to the effective use of ICT. The study focus on the Science andMathematics teachers who are currently teaching at 21 government secondary schools inKuching, Sarawak. 250 copies of questionnaires were randomly distributed to Science andMathematics teachers from 18 government schools located in Kuching, and 212 filledquestionnaires were returned. This gives a response rate of 85%.




Teachers’ perceptions on the use of ICT in classroomsRespondents’ attitudes towards the use of ICT were examined in the survey by series ofstatement reflecting positive and negative attitudes towards ICT to which respondents indicatedtheir agreement and disagreement. In general, the respondents broadly agreed that utilization ofICT makes them more effective in their teaching (75%), and more organized in their work(80%), rely less upon textbooks (37%), and better able to meet the varying needs of students(48%). While 39.2% of the respondents broadly agreed that with the uptake of ICT they needlonger blocks of time for instruction, 43.4% of them disagreed that they give up too muchinstructional responsibility with the use of technology. In general, respondents broadly agreedthat with the use of internet and technology, their lesson plans are richer (55%), and the way theyorganize classroom activities has changed (56%). A further positive sign is 85% of themindicated that they would like to integrate more ICT applications into their teaching.Table 4: Teachers’ perception on the effects of using ICT for professional tasksNR – No ResponseResponse (%) Daily Weekly Monthly Occasionally Never NRTeaching and instructional support 41.0 34.0 10.8 13.7 0.5 0.0Classroom management activities 18.9 29.7 26.9 21.7 2.8 0.0Communications 7.5 17.9 12.7 37.7 21.7 1.9Personal development 2.8 9.4 9.4 39.6 36.8 1.9Response (%) Daily Weekly Monthly 1 – 2 times a year Never NRTeaching Courseware 30.2 42.9 14.6 9.0 2.4 0.9Presentation tools 20.3 22.6 22.6 17.5 14.2 2.8Online demos 0.9 5.7 9.4 10.4 69.3 4.2Graphical visualizing tools 7.1 16.5 14.6 19.3 37.3 5.2Spreadsheets 8.0 23.6 30.7 17.0 13.2 7.5Internet browsing 17.0 35.8 26.4 12.3 7.5 0.9Hypermedia / Multimedia 7.1 14.6 23.1 19.8 29.7 5.7Simulation programmes 4.2 9.4 22.6 21.7 36.8 5.2Response (%) Strongly Agree Agree Neutral Disagree Strongly Disagree NRUsing ICT makes me more effective in teaching. 12.3 62.7 17.0 4.7 1.9 1.4ICT helps me to organize my work. 12.7 67.0 15.1 3.3 0.9 0.9Lesson plans are richer with information from internet. 5.7 49.5 33.5 8.5 0.0 2.8I have changed the way I organize classroom activities. 2.8 53.3 34.9 6.1 0.0 2.8I rely less upon textbooks. 3.3 34.0 35.4 22.6 1.9 2.8I am better able to meet the varying needs of students. 2.4 45.8 39.2 9.0 0.0 3.8I would like to integrate more ICT into my teaching. 17.0 67.5 10.8 3.8 0.0 0.9I need longer blocks of time for instruction. 5.7 33.5 33.5 22.2 1.4 3.8I give up too much instructional responsibility. 0.9 14.6 37.3 38.2 5.2 3.8




Overall, a high 87% of the respondents perceived ICT as important tool to accomplish theirprofessional tasks, and 69% of them felt that amongst the various stakeholders, teachers (asclassroom practitioners) should have a greater voice or say in how ICT is being used in schools.Table 5: Teachers’ perception on the importance of ICT to accomplish their jobVery Important Somewhat Important Neutral Somewhat Unimportant Unimportant at all NRResponse (%) 34.0 52.8 9.0 1.4 0.5 2.4Table 6: Teachers’ view - who should have a greater voice in how ICT is used in schools?Teachers Students Principals Parents District administrator NRResponse (%) 68.9 9.0 9.0 2.8 5.2 5.2Another positive development is observed when 64.2% of the respondents stated themselves tobe either confident or very confident in engaging students with technology in class.Table 7: Level of confidence in engaging students with technology in classVery Confident Confident Neutral Not very confident Not confident at all NRResponse (%) 8.5 55.7 18.4 12.3 0.9 4.2Obstacles faced and training needsRespondents were also asked to indicate their reasons for not using a broader range of ICT inclassrooms. 205 teachers responded to this question, many of them citing more than oneobstacle. The numbers of survey responses for each item are as follows:Table 8: Obstacles faced in the use of ICT in schoolsLack of technical support when things don’t work 122Lack of time in school day 118Limited knowledge on how to make full use of ICT 81Limited understanding on how to integrate ICT into teaching 69Lack of software or websites that support state standards .
















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What role can virtual manipulatives play in the classroom?


Virtual manipulatives can be used to address standards, such as those in Principles and Standards for School Mathematics (NCTM, 2000), which calls for study of both traditional basics, such as multiplication facts, and new basics, such as reasoning and problem solving. Using manipulatives in the classroom assists with those goals and is in keeping with the progressive movement of discovery and inquiry-based learning. For example, in their investigation of 113 K-8 teachers' use of virtual manipulatives in the classroom, Moyer-Packenham, Salkind, and Bolyard (2008) found that content in a majority of the 95 lessons examined focused on two NCTM standards: Number & Operations and Geometry. "Virtual geoboards, pattern blocks, base-10 blocks, and tangrams were the applets used most often by teachers. The ways teachers used the virtual manipulatives most frequently focused on investigation and skill solidification. It was common for teachers to use the virtual manipulatives alone or to use physical manipulatives first, followed by virtual manipulatives" (p. 202).
Virtual manipulatives provide that additional tool for helping students at all levels of ability "to develop their relational thinking and to generalize mathematical ideas" (Moyer-Packenham, Salkind, & Bolyard, 2008, p. 204). All students learn in different ways. For some, mathematics is just too abstract. Most learn best when teachers use multiple instructional strategies that combine "see-hear-do" activities. Most benefit from a combination of visual (i.e., pictures and 2D/3D moveable objects) and verbal representations (i.e., numbers, letters, words) of concepts, which is possible with virtual manipulatives and is in keeping with Paivio and Clark's Dual Coding Theory . The ability to combine multiple representations in a virtual environment allows students to manipulate and change the representations, thus increasing exploration possibilities to develop concepts and test hypotheses. Using tools, such as calculators, allows students to focus on strategies for problem solving, rather than the calculation itself.
According to Douglas H. Clements in 'Concrete' Manipulatives, Concrete Ideas there is pedagogical value of using computer manipulatives. He says, "Good manipulatives are those that are meaningful to the learner, provide control and flexibility to the learner, have characteristics that mirror, or are consistent with, cognitive and mathematics structures, and assist the learner in making connections between various pieces and types of knowledge—in a word, serving as a catalyst for the growth of integrated-concrete knowledge. Computer manipulatives can serve that function" (Section: The Nature of "Concrete" Manipulatives and the Issue of Computer Manipulatives, par. 2).
Christopher Matawa (1998, p. 1) suggests many Uses of Java Applets in Mathematics Education:
Applets to generate examples. Instead of a single image with a picture that gives an example of the concept being taught an applet allows us to have very many examples without the need for a lot of space.
Applets that give students simple exercises to make sure that they have understood a definition or concept.
Applets that generate data. The students can then analyze the data and try to make reasonable conjectures based on the data.
Applets that guide a student through a sequence of steps that the student performs while the applet is running.
Applets that present ''picture proofs''. With animation it is possible to present picture proofs that one could not do without a computer.
An applet can also be in the form of a mathematical puzzle. Students are then challenged to explain how the applet works and extract the mathematics from the puzzle. This also helps with developing problem solving skills.
An applet can set a theme for a whole course. Different versions of an applet can appear at different stages of a course to illustrate aspects of the problem being studied.
While the research is scarce on mathematics achievement resulting from using virtual manipulatives, Moyer-Packenham, Salkind, and Bolyard (2008) found, overall, results from classroom studies and dissertations "have indicated that students using virtual manipulatives, either alone or in combination with physical manipulatives, demonstrate gains in mathematics achievement and understanding" (p. 205). Generalizability might be a concern, however, as found in Kelly Reimer's and Patricia Moyer's action research study (2005), Third-Graders Learn About Fractions Using Virtual Manipulatives: A Classroom Study. The study provides a look into the potential benefits of using these tools for learning. Interviews with learners revealed that virtual manipulatives were helping them to learn about fractions, students liked the immediate feedback they received from the applets, the virtual manipulatives were easier and faster to use than paper-and-pencil, and they provided enjoyment for learning mathematics. Their use enabled all students, from those with lesser ability to those of greatest ability, to remain engaged with the content, thus providing for differentiated instruction. But did the manipulatives lead to achievement gains? The authors do admit to a problem with generalizability of results because the study was conducted with only one classroom, took place only during a two-week unit, and there was bias going into the study. However, results from their pretest/posttest design indicated a statistically significant improvement in students' posttest scores on a test of conceptual knowledge, and a significant relationship between students' scores on the posttests of conceptual knowledge and procedural knowledge. Applets were selected from the National Library of Virtual Manipulatives.
Boston Public Schools has a professional development initiative to provide teachers and students access to virtual manipulatives and technology equipment that directly support the district's math and technology curricula. Partially funded by a NCLB state grant, SELECT Math contains alignments for Grades 6-8, Algebra I and II, and Geometry with a Scope and Sequence calendar describing which book or chapter is being used in math classes during each month of the school year. Click on the individual book/chapter to see the related SELECT Math alignments, worksheets, and links to supporting virtual manipulatives. The project began in 2002 as a collaboration between the Boston Public Schools' Secondary Math and Instructional Technology departments, in conjunction with their partner, the Education Development Center, Inc. CT4ME believes this initiative to be valuable for middle and high school math educators throughout the country. Visit Teacher2Teacher for more on the role of manipulatives.