File Name: teaching and learning mathematics .zip
In contemporary education , mathematics education is the practice of teaching and learning mathematics , along with the associated scholarly research.
- Mathematics education
- Teaching and Learning Mathematics
- Teaching and Learning Mathematics
- International Journal for Mathematics Teaching and Learning
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He can be reached by e-mail at Johnsonj cc. About This Document This document can be found on our Web site www. A free copy of this document can be obtained by placing an order on the website, by writing the Resource Center, Office of Superintendent of Public Instruction, PO Box , Olympia, WA , or by calling the Resource Center toll-free at If requesting more than one copy, contact the Resource Center to determine the printing and shipping charges.
This document is available in alternative format upon request. The contents of this document can be reproduced without permission. Reference to this document would be appreciated. Funding for this project was provided by the Excellence in Mathematics Initiative, a state-funded program supporting mathematics education. For questions regarding the content of this document, call Acknowledgements Various staff at the Office of Superintendent of Public Instruction helped prepare this document for publication.
Lisa Ireland and Theresa Ellsworth provided editing assistance. In as friendly and useful manner as possible, our goal is to provide a research-based overview of the potential and challenges of teaching quality mathematics K— Without this important step toward interpretation and reflection by each reader, this publication becomes yet one more resource to be piled on a shelf for reading on that rainy day that never seems to come in Washington. The mere inclusion of the word in the title of articles or workshop offerings often causes teachers and administrators to look for an escape route, whether it is physical or mental.
Yet, our intent is to counter this attitude by constructing a research-based perspective that helps both teachers and administrators further the mathematics education reform efforts in Washington at all grade levels. As Charles Kettering, an American engineer and inventor — , once said: Research is a high-hat word that scares a lot of people.
It is rather simple. Essentially, research is nothing but a state of mind—a friendly, welcoming attitude toward change … going out to look for change instead of waiting for it to come. Research … is an effort to do things better and not to be caught asleep at the switch….
It is the problem solving mind as contrasted with the let-well-enough-alone mind…. An introductory road map through this text can be useful, especially for those readersreluctant to make the trip. If we omitted mention of research results that you have found useful, we apologize for their omission and suggest that you share them with your colleagues.
Also, some of the research results mentioned may seem dated but was included because it contributes in some fashion to our current situation and concerns.
These questions range from the classroom use of calculators or manipulatives, to the role of drill and algorithmic practice, to the best models for the professional development of teachers. In most instances, the research evidence is not sufficient to answer the questions raised in a definitive manner. We suggest that even small insights or understandings are better than teaching in the dark. That is, the text should be viewed as another small step forward for Washington State teachers and administrators.
Given that road map, we ask you to now join us on this trip through the field of mathematics education research and hope that you find the journey useful. As our ultimate goal is to support teachers and administrators in their efforts to improve student learning in mathematics, we know that an increased awareness of research results is an important form of support.
Our apologies are offered if we have either misrepresented or misinterpreted the research results as reported. Also, we apologize in advance for any misleading interpretations or summaries of the research conclusions of others; these lapses were not intentional.
All of these ingredients, and their interactions, need to be investigated by careful research. Again, it is easy to be overwhelmed Begle and Gibb, Our position is that educational research cannot take into account all of these variables. The result we must live with is acceptance that educational research cannot answer definitively all of the questions we might ask about mathematics education.
At best, educational research provides information that the community of educators can use, misuse, or refuse. It is a well-established notion that research results tend not to be used by educators and at times are purposely ignored.
For example, Reys and Yeager determined that while The situation needs to change, as research results must be reflected on and integrated as an important part of the mathematics education plan and process in Washington. The entire education community—mathematics teachers, administrators, legislators, parents, and college mathematics educators—must take and share in the responsibility for this reflection process and integration of research results, whether it occurs at the individual learner level, the classroom level, the district level, the university level, or the state level.
The search for relevant research results was broad but not exhaustive. The majority of the research results have been omitted fortunately or unfortunately for the reader , with the few results selected being those that can whet your appetite and illustrate best how research can inform and educate the education community.
When it was appropriate, research results that are conflicting or complementary have been juxtaposed to prompt further reflection and discussion. Without being obtrusive, references are included for those readers who would like to pursue the ideas in more detail. Our primary constraint was to provide summaries of research results in a very concise format. In most instances, this constraint precluded any attempts to describe the actual research that was done. These omissions can be dangerous, as it may be misleading to state conclusions based on research involving a few subjects and without replication.
Furthermore, no formal effort was made to evaluate the quality of the research efforts as criteria for inclusion in this text.
As such a broad review by itself is enormous, we now leave it to you the reader to investigate further each result and evaluate its reasonableness. The reason is that the place value notions are not explicitly represented in the color of the chips or the physical sizes of the money English and Halford, The key is to build bridges between the new decimal symbols and other representational systems e.
They might not arrange the blocks in accordance with our base-ten positional notation decreasing value left-to- right or they might manipulate the blocks in any order trading whenever necessary or adding left-to-right in place values. Teachers need to be aware that both of these possibilities occur as natural events when students use base-ten blocks Hiebert, The difference is both a hindrance and an opportunity, as the designation of the unit block may shift as necessary.
For example, the base-ten block representation of the number 2. This adoption occurs despite a natural connection of decimals to whole number, both in notation and computational procedures English and Halford, The reading of decimal numbers seemingly as whole numbers e. Sowder, For example, students will mentally separate a decimal into its whole number part and its pure decimal part, such as rounding Concrete representations of both the symbols and potential actions on these symbols can help make these connections Hiebert, Furthermore, the area model allows students to encode almost any fraction whereas the set model e.
The result is an inconsistent knowledge and the adoption of rote algorithms involving these separate digits, usually incorrectly Behr et al. First, students have greater difficulty associating a proper fraction with a point of a number line than associating a proper fraction with a part-whole model where the unit was either a geometric region or a discrete set.
Second, students able to associate a proper fraction on a number line of length one often are not successful when the number line had length two i. Students who correctly compare numerators if the denominators are equal often compare denominators if the numerators are equal Behr et al. A ratio can refer to a comparison between two parts e.
Hart, c. The partition model also is more representative of the long division algorithm and some fraction division techniques English and Halford, Experiences both posing and solving a broad range of problems. Experiences using solution procedures that they conceptually understand and can explain Fuson, a. Research offers several insights relevant to this situation. First, students who recall rules experience the destructive interference of many instructional and context factors.
Second, when confronted with problems of this nature, most students tend to focus on recalling syntactic rules and rarely use semantic analysis. And third, the syntactic rules help students be successful on test items of the same type but do not transfer well to slightly different or novel problems.
However, students using semantic analysis can be successful in both situations Hiebert and Wearne, ; First, the algorithms encourage students to abandon their own operational thinking. Even less gain a reasonable understanding of either the algorithm or the answers it produces. A major reason underlying this difficulty is the fact that the standard algorithm as usually taught asks students to ignore place value understandings Silver et al.
The cognitive difficulty is compounded if the task involves division of a number by a number larger than itself. The difficulty seems to reflect a dependence on the partition model for division and a preference for using remainders M. Brown, a, b. Also, teachers should encourage students to invent their own personal procedures for the operations but expect them to explain why their inventions are legitimate Lampert, In fact, students tend to not only remember incorrect algorithms but also have more faith in them compared to their own reasoning Mack, In contrast, the common denominator approach to dividing fractions can be modeled by students using manipulatives and capitalizes on their understanding of the measurement model of whole number division using repeated subtraction Sharp, Hart, b.
Teachers must 1 recognize students who use such informal methods for a given problem, 2 recognize and value these informal methods, and 3 discuss possible limitations of the informal methods Booth,
Teaching and Learning Mathematics
Download PDF. It is essential that teachers and students have regular access to technologies that support and advance mathematical sense making, reasoning, problem solving, and communication. Effective teachers optimize the potential of technology to develop students' understanding, stimulate their interest, and increase their proficiency in mathematics. When teachers use technology strategically, they can provide greater access to mathematics for all students. Technological tools include those that are both content specific and content neutral.
Title Page. As early as second grade, girls have internalized the idea that math is not for them. Values of LEARNING Mathematics The independent variables of the study were the components of attitude in teaching mathematics in terms of confidence, anxiety, motivation and success in teaching mathematics with respect to sex, age, education, service year and salary. Teaching and learning mathematics is at the heart of education. But this statement begs the question: What is understanding? The goal is for students to be literate in mathematics so that we can prepare them for a world where the subject is rapidly growing and is extensively applied to a diverse number of fields.
Teaching and Learning Mathematics
Learning mathematics class 7 pdf. The 24 pdf files are downloaded in a ZIP file. Researchers in mathematics education are primarily concerned with the tools, methods and approaches that facilitate practice or the study of practice; however, mathematics education research The attitude towards self as a learner of mathematics and towards mathematics itself are strongly formed by the nature of experiences children have while learning Revised Edition - P activities in the class rooms.
Not a MyNAP member yet? Register for a free account to start saving and receiving special member only perks. In the previous chapter, we examined teaching for mathematical proficiency.
Metrics details. Mathematics is fundamental for many professions, especially science, technology, and engineering. Yet, mathematics is often perceived as difficult and many students leave disciplines in science, technology, engineering, and mathematics STEM as a result, closing doors to scientific, engineering, and technological careers. We propose an alternative approach to changes in mathematics education and show how the alternative also applies to STEM education.
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International Journal for Mathematics Teaching and Learning
PDF | Mathematical skills and confidence are essential for students. Given the importance of mathematical skills and confidence, this study.