Everyday Mathematics is one of a number of relatively new math programs developed around the NCTM standard. Although it has been widely adopted, and praised by education innovators, it has also been criticized as one of the worst math texts introduced in recent years. A 2007 web video produced by Where's the Math singled out Everyday Mathematics for emphasizing unusual and inefficient computation methods, statements that it is a waste of time to teach traditional computation methods to proficiency, and instead spend "precious class time" on activities such as planning a trip across the country with colorful maps. However, unlike TERC, this program does cover many traditional computation methods, along with several alternatives.
1 Description of the program
2 Application in the classroom
3 Evidence of effectiveness
4 Critics and their rationale
5 Notes
6 External links
7 References
Description of the program
Scope and sequence:
According to the developers, “…[t]he developers of Everyday Mathematics believe that the groundwork for mathematical literacy should begin at a much earlier age than offered by traditional mathematics programs…”(Current Curriculum 2002).
Everyday Mathematics is based on a “spiral” curriculum, where mastery is not required before the introduction of new topics. This is contrasted to seeing an obvious progression of skill build-up occur (student masters one digit addition and moves on to two digit addition) In opposition to this view, however, “…Everyday Mathematics was designed to take advantage of the spacing effect…” (Braams 2003). It relies on the notion that regular reinforcement of important skills is necessary, emphasizing that skills should appear multiple times and throughout a course of study. The key principle in regards to spiraling and distributed practice is that mastery and fluency in basic skills are goals that should be achieved long after they are first introduced (Braams 2003).
In accordance with this belief, the Everyday Mathematics program is set up around seven mathematical strands. Those seven are as follows:
• Algebra and Uses of Variables
• Data and Chance
• Geometry and Spatial Sense
• Measures and Measurement
• Numeration and Order
• Patterns, Functions, and Sequences
• Operations
• Reference Frames (About Everything Mathematics 2003)
Features of the program:
Beyond the scope and sequence, EM has several other discerning features. The following is a listing of them, as well as an explanation for how the program incorporates them.
• Real-Life Problem Solving-
EM places a great deal of focus on real-world problems. A great deal of instruction revolves around application of mathematical concepts in everyday situations.
• Balanced Instruction-
“…Learning is conducted in whole group, small group, and individual settings. Students experience open-ended questions, hand-on explorations, supervised practice, and long term projects…” (Current Curriculum 2003).
• Multiple Methods for Basic Skills Practice-
Students practice basic skills through daily review problems, mental math activities, flash cards, games, homework, etc.
• Emphasis on Communication-
Discussion is very important to the program. Students are asked to explain their problem solving strategies. Students are also expected to listen and learn from other students.
• Enhanced Home/School Partnerships-
Information is sent home to help parents work with their children. Homework is structured so that students are meant to rework problems from previous lessons with adults in the home.
• Appropriate Use of Technology-
Technology is used within the program in a way that is meant to instruct children when and where it is appropriate to use it. This is especially true when it comes to calculators.
Application in the classroom
Below is an outline of the components of EM as they are generally seen throughout the curriculum.
Lessons:
A typical lesson outlined in one of the teacher’s manuals includes 3 parts.
1. Teaching the Lesson- This is where the new content is introduced.
2. Ongoing Learning and Practice-In this section, material is reviewed for maintenance purposes.
3. Options for Individualizing- Here is where options for extending or reteaching concepts are presented.
(Click link to view a sample of a lesson http://everydaymath.uchicago.edu/samplelessons/2nd/index.html)
Daily Routines:
Everyday, there are certain things that each EM lesson requires the student to do routinely. These components can be dispersed throughout the day or they can be part of the main math lesson.
• Math Messages- These are problems, displayed in a manner chosen by the teacher, that students complete before the lesson and then discuss as an opener to the main lesson.
• Mental Math and Reflexes- These are brief (no longer than 5 min) sessions “…designed to strengthen children's number sense and to review and advance essential basic skills…” (Program Components 2003).
• Math Boxes- These are pages intended to have students routinely practice problems independently.
• Home Links/Study Links- Everyday homework is sent home. Grades K-3 they are called Home Links and 4-6 they are Study Links. They are meant to reinforce instruction as well as connect home to the work at school.
Supplemental Aspects
Beyond the components already listed, there are supplemental resources to the program. The two most common are games and explorations.
• Games - These are counted as an essential part of the EM curriculum. “…Everyday Mathematics sees games as enjoyable ways to practice number skills, especially those that help children develop fact power…” (Program Components 2003). Therefore, authors of the series have interwoven games throughout daily lessons and activities.
• Explorations- One could, perhaps, best describe these as mini-projects completed in small groups. They are intended to extend upon concepts taught throughout the year.
Implementing all of these components is a challenge, as it requires time, and a change of attitudes from students and teachers, can also be a problem. “…Instead of fostering a competitive environment and teaching students through logical deduction, Everyday Mathematics uses a collaborative milieu and allows students to draw their own conclusions after seeing recurring math patterns. Teachers facilitate the process instead of teaching it… (Knight 2005). Teachers must also have faith in the spiral curriculum in order to implement and assess student work. Teachers who have been trained on grading for mastery, may become frustrated in application of EM.
Evidence of effectiveness
“[d]espite its critics, Everyday Mathematics has 13 years of university research behind it …” (Knight 2005).
Among positive evidence, “The research evidence about Everyday Mathematics (EM) almost all points in the same direction: Children who use EM tend to learn more mathematics and like it better than children who use other programs.” (University of Chicago 2005).
It was originally developed as a research project for the University of Chicago. “Each grade level of the Everyday Mathematics program went through a three-year development cycle that included a year of writing, a year of extensive field-testing in a cross-section of classrooms, and a year of revising…” (University of Chicago 2005).
Few other programs have been through so much testing and research, nevertheless, the program has been challenged by critics
Critics and their rationale
Criticism of EM has come from all directions. Many internet sites and web pages and even internet videos have been dedicated to countering the position of many school districts and education professionals that EM is an effective mathematics program. Many believe that EM is not just innovative, but a severely deficient and radical approach to math that should be abandoned.
One direction from which criticism comes is from parents. “..[S]uch programs as Everyday Mathematics raise the eyebrows and sometimes the ire of parents simply because they don’t use the traditional methods parents are accustomed to…” (Knight 2005). It is difficult for some to trust EM because it seems to differ so much from the math they grew up with. Many parents complain that the methods used in homework are so different from traditional methods, they are unable to assist in homework assignments. Other parents claim that their children are unable to master simple arithemetic problems. Methods such as the "lattice" multiplication method are far more tedious, and require more drawing and effort with no real advantage over traditional methods. By 2007, school districts that were considering adopting EM were encountering very negative reactions from parents when asked about the choice of EM [1]
Many professional mathematicians consider EM to be an inferior curriculum. Like many parents, they believe that overlooks or underplays basics. It does not promote the use of standard algorithms that have been tested and used for a long time by professionals who use math every day.
However, Wertheimer (2002) points out that “…[t]he mathematicians are among the few survivors of the traditional mathematics program. They are trying to apply what they know to the entire population”. He also has a great deal of reservations about the ability of these mathematicians to evaluate the complexity of educational methodology that can help everyone achieve. Mathematics education should help promote the success of everyone not just those naturally successful at math. (Wertheimer 2002). Others questioned the assumption that groups such as women and minorities cannot be expected to learn basic math facts in a traditional way, and that only "successful" groups should be learning "real math".
Beyond parents and professional mathematicians, even teachers have joined in the argument. Teachers who have encountered problems with such a radical approach have also dissented.
A common argument is that the program was not the problem, but implementation was. Critics claimed that the content was difficult for teachers to teach without a great deal of training. Much of the content in geometry and statistics goes far beyond the traditional 5th grade math most parents and elementary teachers are proficient in, because of the belief that students in early grades should be studying advanced math concepts rather than only basic facts and methods.
taken From Wikipedia.com
Sebuah blog yang kutujukan sebagai wujud cintaku kepada dia yang namanya kuabadikan, kepada dunia pendidikan, kepada negeriku serta untuk membentuk pribadiku
Selasa, 24 Juli 2007
Math Wars
Math wars is the debate over modern mathematics education, textbooks and curricula in the US that was triggered by the publication in 1989 of the Principles and Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM). The term "math wars" was coined by commentators such as John A. Van de Walle and David Klein.
Innovative curricula
Examples of innovative curricula introduced in response to the 1989 NCTM standards include:
Mathland
Investigations in Numbers, Data, and Space
Core-Plus Mathematics Project
Criticisms of reform
Critics of the "reform" textbooks say that they present concepts in a haphazard way. Procedural and traditional arithmetic skills such as long division are de-emphasized, or some say nearly totally deleted in favor of context and content which has little or nothing to do with mathematics. Some textbooks have a separate index solely for non-mathematics content called "contexts". Reform texts favor problem-solving in new contexts over template word problems with corresponding examples. Reform texts also emphasize verbal communication, writing about mathematics and their relationships with disenfranchised groups such as ethnicity, race, and gender identity, social justice, connections between concepts, and connections between representations.
One particular critical review of Investigations in Number, Data, and Space says: It has no student textbook.
It uses 100 charts and skip counting, but not multiplication tables to teach multiplication. Decimal math is "effectively not present".
Traditional textbooks
Critics of the "reform" textbooks and curricula support "traditional" textbooks such as Singapore Math and Saxon math, which emphasize algorithmic mathematics, such as arithmetic calculation, over mathematical concepts. However, even many traditional textbooks such as Saxon math usually include some projects and exercises meant to address the NCTM Standards.
Supporters of the "reform" curricula, such as Thomas O'Brien , say that supporters of traditional methods, or "parrot math", have "no tolerance for children's invented strategies or original thinking, and they leave no room for children's use of estimation or calculators."
NCTM 2006 recommendations
In 2006, the NCTM released Curriculum Focal Points, a report on the topics considered central for school mathematics. Francis Fennell, president of the NCTM, claimed that there had been no change of direction or policy in the new report, and said that he resented talk of “math wars”. Interviews of many who were committed to the standards said that, like the 2000 standards, these merely refined and focused rather than renounced the original 1989 recommendations.
Nevertheless, newspapers like the Chicago Sun Times reported that the "NCTM council has admitted, more or less, that it goofed". The new report cited "inconsistency in the grade placement of mathematics topics as well as in how they are defined and what students are expected to learn." The new recommendations are that students are to be taught the basics, including the fundamentals of geometry and algebra, and memorizing multiplication tables.
Examples of innovative curricula introduced in response to the 1989 NCTM standards include:
Mathland
Investigations in Numbers, Data, and Space
Core-Plus Mathematics Project
Criticisms of reform
Critics of the "reform" textbooks say that they present concepts in a haphazard way. Procedural and traditional arithmetic skills such as long division are de-emphasized, or some say nearly totally deleted in favor of context and content which has little or nothing to do with mathematics. Some textbooks have a separate index solely for non-mathematics content called "contexts". Reform texts favor problem-solving in new contexts over template word problems with corresponding examples. Reform texts also emphasize verbal communication, writing about mathematics and their relationships with disenfranchised groups such as ethnicity, race, and gender identity, social justice, connections between concepts, and connections between representations.
One particular critical review of Investigations in Number, Data, and Space says: It has no student textbook.
It uses 100 charts and skip counting, but not multiplication tables to teach multiplication. Decimal math is "effectively not present".
Traditional textbooks
Critics of the "reform" textbooks and curricula support "traditional" textbooks such as Singapore Math and Saxon math, which emphasize algorithmic mathematics, such as arithmetic calculation, over mathematical concepts. However, even many traditional textbooks such as Saxon math usually include some projects and exercises meant to address the NCTM Standards.
Supporters of the "reform" curricula, such as Thomas O'Brien , say that supporters of traditional methods, or "parrot math", have "no tolerance for children's invented strategies or original thinking, and they leave no room for children's use of estimation or calculators."
NCTM 2006 recommendations
In 2006, the NCTM released Curriculum Focal Points, a report on the topics considered central for school mathematics. Francis Fennell, president of the NCTM, claimed that there had been no change of direction or policy in the new report, and said that he resented talk of “math wars”. Interviews of many who were committed to the standards said that, like the 2000 standards, these merely refined and focused rather than renounced the original 1989 recommendations.
Nevertheless, newspapers like the Chicago Sun Times reported that the "NCTM council has admitted, more or less, that it goofed". The new report cited "inconsistency in the grade placement of mathematics topics as well as in how they are defined and what students are expected to learn." The new recommendations are that students are to be taught the basics, including the fundamentals of geometry and algebra, and memorizing multiplication tables.
from: wikipedia.com
Selasa, 17 Juli 2007
Learn How to Win Scholarship
To win a scholarship application you need a true strategy. The students that win the most scholarships may not have more positive qualities than you, but they use the following strategy to get noticed by the scholarship committees:
Get Prepared:
Get letters of recommendation from teachers or guidance counselor or leaders in your community. Choose these wisely (make copies).
Get a copy of your high school or college transcript (make copies).
Get involved in your community or in school activities or in your church. If your time is limited due to personal circumstances, working to help with family expenses is also an advantage.
Start writing an essay about your goals and what you have done to date to achieve them. Think about what makes you unique.
Get a picture of yourself. A school picture is perfect. Anything smaller than a wallet size head shot, will do.
Buy some clear plastic binders.
The goal here is to have numerous packages made up ahead of time, ready to submit to the various scholarship committees.The package will include:
* a clear plastic binder and within the package* the scholarship application ( you will have to insert this later when you have received each individual application)* followed by an essay that gets you noticed* followed by your transcript (some scholarships do not require this, but if it’s impressive, send it)* followed by letters of recommendation and then* place you picture in the front inside cover(on top of the application) in the lower left hand corner (this is not a requirement, but it helps to put a face to the person, for the scholarship committee deciding who receives the awards)
Get Organized:
Begin researching scholarships that match your criteria. Consider using a scholarship search service, like our service - infoBeasiswa.net
Once you have the scholarships for which you want to apply, keep track of the deadlines.
Create a chart to keep on top of all dates.
The chart should include:
* Scholarship name and phone number* Date application must be received by scholarship committee* Date you requested the application* Date you received the application* Date application with above package was mailed* Date you called the Scholarship Agency to verify they received your application package
Get Noticed:
As important as being prepared and organized, it is equally important that you have an essay that gets you noticed.
Even if you feel you master the english language, your essay should be critique by someone who has experience in essay writing.
Ask an english professor to review your essay or consider using an essay editing service.
Get Prepared, Get Organized, Get Noticed, Be Persistent and Don’t Give Up!
Get Prepared:
Get letters of recommendation from teachers or guidance counselor or leaders in your community. Choose these wisely (make copies).
Get a copy of your high school or college transcript (make copies).
Get involved in your community or in school activities or in your church. If your time is limited due to personal circumstances, working to help with family expenses is also an advantage.
Start writing an essay about your goals and what you have done to date to achieve them. Think about what makes you unique.
Get a picture of yourself. A school picture is perfect. Anything smaller than a wallet size head shot, will do.
Buy some clear plastic binders.
The goal here is to have numerous packages made up ahead of time, ready to submit to the various scholarship committees.The package will include:
* a clear plastic binder and within the package* the scholarship application ( you will have to insert this later when you have received each individual application)* followed by an essay that gets you noticed* followed by your transcript (some scholarships do not require this, but if it’s impressive, send it)* followed by letters of recommendation and then* place you picture in the front inside cover(on top of the application) in the lower left hand corner (this is not a requirement, but it helps to put a face to the person, for the scholarship committee deciding who receives the awards)
Get Organized:
Begin researching scholarships that match your criteria. Consider using a scholarship search service, like our service - infoBeasiswa.net
Once you have the scholarships for which you want to apply, keep track of the deadlines.
Create a chart to keep on top of all dates.
The chart should include:
* Scholarship name and phone number* Date application must be received by scholarship committee* Date you requested the application* Date you received the application* Date application with above package was mailed* Date you called the Scholarship Agency to verify they received your application package
Get Noticed:
As important as being prepared and organized, it is equally important that you have an essay that gets you noticed.
Even if you feel you master the english language, your essay should be critique by someone who has experience in essay writing.
Ask an english professor to review your essay or consider using an essay editing service.
Get Prepared, Get Organized, Get Noticed, Be Persistent and Don’t Give Up!
How to get a scholarship
1 Step One
Start looking for scholarships at least one year before entering college.
2 Step Two
Consider whether you are a member of an underrepresented group, in financial need, or interested in certain fields of study. Scholarships are available for those with special talents in many areas, including sports, art, science and music.
3 Step Three
Think about applying for a fellowship - a scholarship for graduate students - if you want to go to graduate school.
4 Step Four
Recognize what you can expect from a scholarship when you apply for it. Some schools offer to pay all your expenses, while others only pay for room and board.
5 Step Five
Use a No. 2 pencil to complete the application form.
6 Step Six
Be prepared to answer general questions such as name, address, social security number, date of birth, citizenship status and marital status.
7 Step Seven
Provide any necessary financial information such as total family income, number of children in your household, and number of children in college. Round dollar amounts to whole number values.
8 Step Eight
Supply information about the talent required by the scholarship for which you are applying.
9 Step Nine
Mail all the paperwork to the address listed on the application.
10 Step Ten
Endure the weeks or months of waiting to find out whether you got the scholarship and how much money you will receive from it.
Tips & Warnings
Talk to your school counselor; he or she is paid to help you make decisions about your future.
Start looking for scholarships at least one year before entering college.
2 Step Two
Consider whether you are a member of an underrepresented group, in financial need, or interested in certain fields of study. Scholarships are available for those with special talents in many areas, including sports, art, science and music.
3 Step Three
Think about applying for a fellowship - a scholarship for graduate students - if you want to go to graduate school.
4 Step Four
Recognize what you can expect from a scholarship when you apply for it. Some schools offer to pay all your expenses, while others only pay for room and board.
5 Step Five
Use a No. 2 pencil to complete the application form.
6 Step Six
Be prepared to answer general questions such as name, address, social security number, date of birth, citizenship status and marital status.
7 Step Seven
Provide any necessary financial information such as total family income, number of children in your household, and number of children in college. Round dollar amounts to whole number values.
8 Step Eight
Supply information about the talent required by the scholarship for which you are applying.
9 Step Nine
Mail all the paperwork to the address listed on the application.
10 Step Ten
Endure the weeks or months of waiting to find out whether you got the scholarship and how much money you will receive from it.
Tips & Warnings
Talk to your school counselor; he or she is paid to help you make decisions about your future.
Problem Based Learning in Mathematics
Problem-Based Learning (PBL) describes a learning environment where problems drive the learning. That is, learning begins with a problem to be solved, and the problem is posed is such a way that students need to gain new knowledge before they can solve the problem. Rather than seeking a single correct answer, students interpret the problem, gather needed information, identify possible solutions, evaluate options, and present conclusions. Proponents of mathematical problem solving insist that students become good problem solvers by learning mathematical knowledge heuristically.
Students' successful experiences in managing their own knowledge also helps them solve mathematical problems well (Shoenfeld, 1985; Boaler, 1998). Problem-based learning is a classroom strategy that organizes mathematics instruction around problem solving activities and affords students more opportunities to think critically, present their own creative ideas, and communicate with peers mathematically (Krulik & Rudnick, 1999; Lewellen & Mikusa, 1999; Erickson, 1999; Carpenter et al., 1993; Hiebert et al., 1996; Hiebert et al., 1997).
PBL AND PROBLEM SOLVING
Since PBL starts with a problem to be solved, students working in a PBL environment must become skilled in problem solving, creative thinking, and critical thinking. Unfortunately, young children's problem-solving abilities seem to have been seriously underestimated. Even kindergarten children can solve basic multiplication problems (Thomas et al., 1993) and children can solve a reasonably broad range of word problems by directly modeling the actions and relationships in the problem, just as children usually solve addition and subtraction problems through direct modeling.
Those results are in contrast to previous research assumptions that the structures of multiplication and division problems are more complex than those of addition and subtraction problems. However, this study shows that even kindergarten children may be able to figure out more complex mathematical problems than most mathematics curricula suggest. PBL in mathematics classes would provide young students more opportunities to think critically, represent their own creative ideas, and communicate with their peers mathematically.
PBL AND CONSTRUCTIVISM
The effectiveness of PBL depends on student characteristics and classroom culture as well as the problem tasks. Proponents of PBL believe that when students develop methods for constructing their own procedures, they are integrating their conceptual knowledge with their procedural skill.
Limitations of traditional ways of teaching mathematics are associated with teacher-oriented instruction and the "ready-made" mathematical knowledge presented to students who are not receptive to the ideas (Shoenfeld, 1988). In these circumstances, students are likely to imitate the procedures without deep conceptual understanding. When mathematical knowledge or procedural skills are taught before students have conceptualized their meaning, students' creative thinking skills are likely to be stifled by instruction. As an example, the standard addition algorithm has been taught without being considered detrimental to understanding arithmetic because it has been considered useful and important enough for students to ultimately enhance profound understanding of mathematics. Kamii and Dominick(1998), and Baek (1998) have shown, though, that the standard arithmetic algorithms would not benefit elementary students learning arithmetic. Rather, students who had learned the standard addition algorithm seemed to make more computational errors than students who never learned the standard addition algorithm, but instead created their own algorithm.
STUDENTS' UNDERSTANDING IN PBL ENVIRONMENT
The PBL environment appears different from the typical classroom environment that people have generally considered good, where classes that are well managed and students get high scores on standardized tests. However, this conventional sort of instruction does not enable students to develop mathematical thinking skills well.
Instead of gaining a deep understanding of mathematical knowledge and the nature of mathematics, students in conventional classroom environments tend to learn inappropriate and counterproductive conceptualizations of the nature of mathematics. Students are allowed only to follow guided instructions and to obtain right answers, but not allowed to seek mathematical understanding. Consequently, instruction becomes focused on only getting good scores on tests of performance. Ironically, studies show that students educated in the traditional content-based learning environments exhibit lower achievement both on standardized tests and on project tests dealing with realistic situations than students who learn through a project-based approach (Boaler, 1998).
In contrast to conventional classroom environments, a PBL environment provides students with opportunities to develop their abilities to adapt and change methods to fit new situations. Meanwhile, students taught in traditional mathematics education environments are preoccupied by exercises, rules, and equations that need to be learned, but are of limited use in unfamiliar situations such as project tests. Further, students in PBL environments typically have greater opportunity to learn mathematical processes associated with communication, representation, modeling, and reasoning (Smith, 1998; Erickson, 1999; Lubienski, 1999).
TEACHER ROLES IN THE PBL ENVIRONMENT
Within PBL environments, teachers' instructional abilities are more critical than in the traditional teacher-centered classrooms. Beyond presenting mathematical knowledge to students, teachers in PBL environments must engage students in marshalling information and using their knowledge in applied settings.
First, then, teachers in PBL settings should have a deep understanding of mathematics that enables them to guide students in applying knowledge in a variety of problem situations. Teachers with little mathematical knowledge may contribute to student failure in mathematical PBL environments. Without an in-depth understanding of mathematics, teachers would neither choose appropriate tasks for nurturing student problem-solving strategies, nor plan appropriate problem-based classroom activities (Prawat, 1997; Smith III, 1997).
Furthermore, it is important that teachers in PBL environments develop a broader range of pedagogical skills. Teachers pursuing problem-based instruction must not only supply mathematical knowledge to their students, but also know how to engage students in the processes of problem solving and applying knowledge to novel situations. Changing the teacher role to one of managing the problem-based classroom environment is a challenge to those unfamiliar with PBL (Lewellen & Mikusa, 1999). Clarke (1997), found that only teachers who perceived the practices associated with PBL beneficial to their own professional development appeared strongly positive in managing the classroom instruction in support of PBL.
Mathematics teachers more readily learn to manage the PBL environment when they understand the altered teacher role and consider preparing for the PBL environment as a chance to facilitate professional growth (Clarke, 1997).
CONCLUSIONS
In implementing PBL environments, teachers' instructional abilities become critically important as they take on increased responsibilities in addition to the presentation of mathematical knowledge. Beyond gaining proficiency in algorithms and mastering foundational knowledge in mathematics, students in PBL environments must learn a variety of mathematical processes and skills related communication, representation, modeling, and reasoning (Smith, 1998; Erickson, 1999; Lubienski, 1999). Preparing teachers for their roles as managers of PBL environments presents new challenges both to novices and to experienced mathematics teachers (Lewellen & Mikusa, 1999).
REFERENCES
Boaler, J. (1998). Open and closed mathematics: student experiences and understandings. "Journal for Research on Mathematics Education," 29 (1). 41-62.
Carpenter, T., Ansell, E. Franke, M, Fennema, E., & Weisbeck, L. (1993). Models of problem solving: A study of kindergarten children's problem solving processes. "Journal for Research in Mathematics Education," 24 (5). 428-441.
Clarke, D. M. (1997). The changing role of the mathematics teacher. "Journal for Research on Mathematics Education," 28 (3), 278-308.
Erickson, D. K. (1999). A problem-based approach to mathematics instruction."Mathematics Teacher," 92 (6). 516-521.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The Case of Mathematics. "Educational Researcher," 12-18.
Hiebert, J. Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1997). Making mathematics problematic: A rejoinder to Prawat and Smith. "Educational Researcher," 26 (2). 24-26.
Krulik, S., & Rudnick, J. A. (1999). Innovative tasks to improve critical- and creative-thinking skills. In I. V. Stiff (Ed.), "Developing mathematical reasoning in grades K-12." Reston. VA: National Council of Teachers of Mathematics. (pp.138-145).
Lewellen, H., & Mikusa, M. G. (February 1999). Now here is that authority on mathematics reform, Dr. Constructivist! "The Mathematics Teacher," 92 (2). 158-163.
Lubienski, S. T. (1999). Problem-centered mathematics teaching. "Mathematics Teaching in the Middle School," 5 (4). 250-255.
Prawat, R. S. (1997). Problematizing Dewey's views of problem solving: A reply to Hiebert et al. "Educational Researcher." 26 (2). 19-21.
Schoenfeld, A. H. (1985). "Mathematical problem solving." New York: Academic Press.
Smith, C. M. (1998). A Discourse on discourse: Wrestling with teaching rational equations. "The Mathematics Teacher." 91 (9). 749-753.
Smith III, J. P. (1997). Problems with problematizing mathematics: A reply to Hiebert et al. "Educational Researcher," 26 (2). 22-24.
taken from http://www.ericdigests.org/2004-3/math.html
Students' successful experiences in managing their own knowledge also helps them solve mathematical problems well (Shoenfeld, 1985; Boaler, 1998). Problem-based learning is a classroom strategy that organizes mathematics instruction around problem solving activities and affords students more opportunities to think critically, present their own creative ideas, and communicate with peers mathematically (Krulik & Rudnick, 1999; Lewellen & Mikusa, 1999; Erickson, 1999; Carpenter et al., 1993; Hiebert et al., 1996; Hiebert et al., 1997).
PBL AND PROBLEM SOLVING
Since PBL starts with a problem to be solved, students working in a PBL environment must become skilled in problem solving, creative thinking, and critical thinking. Unfortunately, young children's problem-solving abilities seem to have been seriously underestimated. Even kindergarten children can solve basic multiplication problems (Thomas et al., 1993) and children can solve a reasonably broad range of word problems by directly modeling the actions and relationships in the problem, just as children usually solve addition and subtraction problems through direct modeling.
Those results are in contrast to previous research assumptions that the structures of multiplication and division problems are more complex than those of addition and subtraction problems. However, this study shows that even kindergarten children may be able to figure out more complex mathematical problems than most mathematics curricula suggest. PBL in mathematics classes would provide young students more opportunities to think critically, represent their own creative ideas, and communicate with their peers mathematically.
PBL AND CONSTRUCTIVISM
The effectiveness of PBL depends on student characteristics and classroom culture as well as the problem tasks. Proponents of PBL believe that when students develop methods for constructing their own procedures, they are integrating their conceptual knowledge with their procedural skill.
Limitations of traditional ways of teaching mathematics are associated with teacher-oriented instruction and the "ready-made" mathematical knowledge presented to students who are not receptive to the ideas (Shoenfeld, 1988). In these circumstances, students are likely to imitate the procedures without deep conceptual understanding. When mathematical knowledge or procedural skills are taught before students have conceptualized their meaning, students' creative thinking skills are likely to be stifled by instruction. As an example, the standard addition algorithm has been taught without being considered detrimental to understanding arithmetic because it has been considered useful and important enough for students to ultimately enhance profound understanding of mathematics. Kamii and Dominick(1998), and Baek (1998) have shown, though, that the standard arithmetic algorithms would not benefit elementary students learning arithmetic. Rather, students who had learned the standard addition algorithm seemed to make more computational errors than students who never learned the standard addition algorithm, but instead created their own algorithm.
STUDENTS' UNDERSTANDING IN PBL ENVIRONMENT
The PBL environment appears different from the typical classroom environment that people have generally considered good, where classes that are well managed and students get high scores on standardized tests. However, this conventional sort of instruction does not enable students to develop mathematical thinking skills well.
Instead of gaining a deep understanding of mathematical knowledge and the nature of mathematics, students in conventional classroom environments tend to learn inappropriate and counterproductive conceptualizations of the nature of mathematics. Students are allowed only to follow guided instructions and to obtain right answers, but not allowed to seek mathematical understanding. Consequently, instruction becomes focused on only getting good scores on tests of performance. Ironically, studies show that students educated in the traditional content-based learning environments exhibit lower achievement both on standardized tests and on project tests dealing with realistic situations than students who learn through a project-based approach (Boaler, 1998).
In contrast to conventional classroom environments, a PBL environment provides students with opportunities to develop their abilities to adapt and change methods to fit new situations. Meanwhile, students taught in traditional mathematics education environments are preoccupied by exercises, rules, and equations that need to be learned, but are of limited use in unfamiliar situations such as project tests. Further, students in PBL environments typically have greater opportunity to learn mathematical processes associated with communication, representation, modeling, and reasoning (Smith, 1998; Erickson, 1999; Lubienski, 1999).
TEACHER ROLES IN THE PBL ENVIRONMENT
Within PBL environments, teachers' instructional abilities are more critical than in the traditional teacher-centered classrooms. Beyond presenting mathematical knowledge to students, teachers in PBL environments must engage students in marshalling information and using their knowledge in applied settings.
First, then, teachers in PBL settings should have a deep understanding of mathematics that enables them to guide students in applying knowledge in a variety of problem situations. Teachers with little mathematical knowledge may contribute to student failure in mathematical PBL environments. Without an in-depth understanding of mathematics, teachers would neither choose appropriate tasks for nurturing student problem-solving strategies, nor plan appropriate problem-based classroom activities (Prawat, 1997; Smith III, 1997).
Furthermore, it is important that teachers in PBL environments develop a broader range of pedagogical skills. Teachers pursuing problem-based instruction must not only supply mathematical knowledge to their students, but also know how to engage students in the processes of problem solving and applying knowledge to novel situations. Changing the teacher role to one of managing the problem-based classroom environment is a challenge to those unfamiliar with PBL (Lewellen & Mikusa, 1999). Clarke (1997), found that only teachers who perceived the practices associated with PBL beneficial to their own professional development appeared strongly positive in managing the classroom instruction in support of PBL.
Mathematics teachers more readily learn to manage the PBL environment when they understand the altered teacher role and consider preparing for the PBL environment as a chance to facilitate professional growth (Clarke, 1997).
CONCLUSIONS
In implementing PBL environments, teachers' instructional abilities become critically important as they take on increased responsibilities in addition to the presentation of mathematical knowledge. Beyond gaining proficiency in algorithms and mastering foundational knowledge in mathematics, students in PBL environments must learn a variety of mathematical processes and skills related communication, representation, modeling, and reasoning (Smith, 1998; Erickson, 1999; Lubienski, 1999). Preparing teachers for their roles as managers of PBL environments presents new challenges both to novices and to experienced mathematics teachers (Lewellen & Mikusa, 1999).
REFERENCES
Boaler, J. (1998). Open and closed mathematics: student experiences and understandings. "Journal for Research on Mathematics Education," 29 (1). 41-62.
Carpenter, T., Ansell, E. Franke, M, Fennema, E., & Weisbeck, L. (1993). Models of problem solving: A study of kindergarten children's problem solving processes. "Journal for Research in Mathematics Education," 24 (5). 428-441.
Clarke, D. M. (1997). The changing role of the mathematics teacher. "Journal for Research on Mathematics Education," 28 (3), 278-308.
Erickson, D. K. (1999). A problem-based approach to mathematics instruction."Mathematics Teacher," 92 (6). 516-521.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1996). Problem solving as a basis for reform in curriculum and instruction: The Case of Mathematics. "Educational Researcher," 12-18.
Hiebert, J. Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A., & Wearne, D. (1997). Making mathematics problematic: A rejoinder to Prawat and Smith. "Educational Researcher," 26 (2). 24-26.
Krulik, S., & Rudnick, J. A. (1999). Innovative tasks to improve critical- and creative-thinking skills. In I. V. Stiff (Ed.), "Developing mathematical reasoning in grades K-12." Reston. VA: National Council of Teachers of Mathematics. (pp.138-145).
Lewellen, H., & Mikusa, M. G. (February 1999). Now here is that authority on mathematics reform, Dr. Constructivist! "The Mathematics Teacher," 92 (2). 158-163.
Lubienski, S. T. (1999). Problem-centered mathematics teaching. "Mathematics Teaching in the Middle School," 5 (4). 250-255.
Prawat, R. S. (1997). Problematizing Dewey's views of problem solving: A reply to Hiebert et al. "Educational Researcher." 26 (2). 19-21.
Schoenfeld, A. H. (1985). "Mathematical problem solving." New York: Academic Press.
Smith, C. M. (1998). A Discourse on discourse: Wrestling with teaching rational equations. "The Mathematics Teacher." 91 (9). 749-753.
Smith III, J. P. (1997). Problems with problematizing mathematics: A reply to Hiebert et al. "Educational Researcher," 26 (2). 22-24.
taken from http://www.ericdigests.org/2004-3/math.html
Minggu, 08 Juli 2007
Oppressed Education
" Looking into the common educations in Indonesia"
Plenty of theories about education that was taught for the teaching student who was following knowledge to the tertiary institution. Theories that were studied almost all referred in the interaction between the educator and participants educated. Not only that, but, the development of participants educated also received the focus from almost the theory whole that was taught. Moreover in the aim of national education Indonesia personally according to government law no 20 year 2003 " Aim to expand competitor educated to in order to become the godly and religious human being to God, Behavior , healthy, bookish, capable, creative, self-supporting and become the democratic citizen and also hold responsible.
In existing in reality, this is very difficult to be done. It’s because of the imitating habit which grows at education culture itself. Existing teachers in this time a lot represent the old teachers. Old system and law which at a period of/to them college applied in this time have experienced of a lot of change. Unfortunately the changes received the not better response so as the development of the method of teaching them to not follow the existing path. While way of their teacher that suspected as represent of the teaching method taught in the era of Dutch colonialization. This is why education system in this time still be related/relevant with the education model applied by former colonization era. One of the causes that was complained about since beforehand was the change in the system almost each Mendiknas change. The change and the finishing of the available system it was considered deviated too far from the system that beforehand. Therefore, the teachers in the level of the executive more liked to use their teaching method personally. The method taught like this was adoption from their teacher's teaching method personally that was received when they learned to teach. Whereas their teacher's method it was warned was the method taught the colonial Dutch time. This why the education system at this time was still related to the educational model that was applied when the colonization time beforehand.
After we knew that the learning models at this time still was linked with the colonization time learning method, we see its study process. This caused the problem if still continued to be applied. At this time, we were prosecuted to have the expertise that could compete with the international market. With the available education system, we could only produce the skilled workers but was in the worker's lowered class. If it still last, forever we could only export manual laborers in order to satisfy the requirement for manpower in the market.
Indonesian must begin in realized this situation. It’s not longer the time for us to educate a multiple-skilled workers. At this time, we must begin to be focused in education specific ability oriented that could fill the international standard. So each individual must be given special provisions that will give him the creating freedom based on what skill that he/ she expert in. Eventually this capacity that will distinguish the individual from the other individual.
If beforehand a car mechanic could repair all part of the car but did not spread everywhere. At this time we must think how educated a mechanic who knew all part of the car but had the special expertise in the certain part. For example, a mechanics knew all part of the car but he had the specialization in the part engine tune up. Whereas if having the problem moreover he must hand over in other mechanics that had the specialization to the component. This must also begin to be applied in the level of basic education. Especially to the primary school. If nowadays one class was only taught by a teacher then this habit must begin to be changed. As being applied to the junior high school and the senior high school.
Some time before stood the anti corruption school. Why the anti corruption school? Because the school was our first place learned to carry out corruption. Not only the student but the teacher. Why was like this? Consciously or not, we trained ourselves for corruption with the habit to enter late and outside the class was earlier. When minor matters like that became the habit then will change to the mental attitude. As a result, this attitude will clear our life field that was other not only was trapped. When at one time we were given by the belief then we little by little processed to take what not our right. Starting from time and than into the material. The process like when we were in the classroom. This will become a habit that was regarded as natural and did not cause the problem.
We have to start to realize that the education in Indonesia were an oppressed education. The existing system only accommodates the market demand for skilled man power. On the other hand, both the expert and the process to make the skilled power personally be ignored. The expert with the expertise especially precisely not always being accommodated his opportunity to work. The higher standard of payment was became the most reason for many factory to chose the skilled power with lower education grade. Whereas the deliberate expert was brought in from other country. The process of making the skilled power personally just as banded as the skilled power expert them self. Many children of the school age that cannot finish their education because of the high educational cost. They usually end to the street child or the blue-collar worker the level was lowest. For that we need our government concern as well as any other company that needed educated and skilled manpower to develop this abandon potential recourses.
We have to start to realize that the education in Indonesia were an oppressed education. The existing system only accommodates the market demand for skilled man power. On the other hand, both the expert and the process to make the skilled power personally be ignored. The expert with the expertise especially precisely not always being accommodated his opportunity to work. The higher standard of payment was became the most reason for many factory to chose the skilled power with lower education grade. Whereas the deliberate expert was brought in from other country. The process of making the skilled power personally just as banded as the skilled power expert them self. Many children of the school age that cannot finish their education because of the high educational cost. They usually end to the street child or the blue-collar worker the level was lowest. For that we need our government concern as well as any other company that needed educated and skilled manpower to develop this abandon potential recourses.
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