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1937:, and policy evaluation—controlled, randomized experiments remain the preferred method of evaluating treatments. Educational statisticians and some mathematics educators have been working to increase the use of randomized experiments to evaluate teaching methods. On the other hand, many scholars in educational schools have argued against increasing the number of randomized experiments, often because of philosophical objections, such as the ethical difficulty of randomly assigning students to various treatments when the effects of such treatments are not yet known to be effective, or the difficulty of assuring rigid control of the independent variable in fluid, real school settings.
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concepts involves making connections between facts, procedures, and ideas. (This is often seen as one of the strong points in mathematics teaching in East Asian countries, where teachers typically devote about half of their time to making connections. At the other extreme is the US, where essentially no connections are made in school classrooms.) These connections can be made through explanation of the meaning of a procedure, questions comparing strategies and solutions of problems, noticing how one problem is a special case of another, reminding students of the main point, discussing how lessons connect, and so on.
1679:(OECD), is a global program studying the reading, science, and mathematics abilities of 15-year-old students. The first assessment was conducted in the year 2000 with 43 countries participating. PISA has repeated this assessment every three years to provide comparable data, helping to guide global education to better prepare youth for future economies. There have been many ramifications following the results of triennial PISA assessments due to implicit and explicit responses of stakeholders, which have led to education reform and policy change.
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2294:: p. 109 "Many Old Babylonian mathematical practitioners … knew that the square on the diagonal of a right triangle had the same area as the sum of the squares on the length and width: that relationship is used in the worked solutions to word problems on cut-and-paste 'algebra' on seven different tablets, from Ešnuna, Sippar, Susa, and an unknown location in southern Babylonia."
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1413:) are taught as separate courses in different years. On the other hand, in most other countries (and in a few US states), mathematics is taught as an integrated subject, with topics from all branches of mathematics studied every year; students thus undertake a pre-defined course - entailing several topics - rather than choosing courses
1654:, which recommend the most important mathematical topics for each grade level through grade 8. However, these standards were guidelines to implement as American states and Canadian provinces chose. In 2010, the National Governors Association Center for Best Practices and the Council of Chief State School Officers published the
1920:, which can eventually be tested by randomized experiments. Both qualitative and quantitative studies, therefore, are considered essential in education—just as in the other social sciences. Many studies are “mixed”, simultaneously combining aspects of both quantitative and qualitative research, as appropriate.
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assignments which lead students to practice past lessons or prepare for future lessons is more effective than those going over the current lesson. Students benefit from feedback. Students with learning disabilities or low motivation may profit from rewards. For younger children, homework helps simple
1928:
There has been some controversy over the relative strengths of different types of research. Because of an opinion that randomized trials provide clear, objective evidence on “what works”, policymakers often consider only those studies. Some scholars have pushed for more random experiments in which
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in 1543. However, there are many different writings on mathematics and mathematics methodology that date back to 1800 BCE. These were mostly located in
Mesopotamia, where the Sumerians were practicing multiplication and division. There are also artifacts demonstrating their methodology for solving
738:
in Italy in the 1300s. Spreading along trade routes, these methods were designed to be used in commerce. They contrasted with
Platonic math taught at universities, which was more philosophical and concerned numbers as concepts rather than calculating methods. They also contrasted with mathematical
1737:
Two of the most important features of teaching in the promotion of conceptual understanding times are attending explicitly to concepts and allowing students to struggle with important mathematics. Both of these features have been confirmed through a wide variety of studies. Explicit attention to
1694:
According to
Hiebert and Grouws, "Robust, useful theories of classroom teaching do not yet exist." However, there are useful theories on how children learn mathematics, and much research has been conducted in recent decades to explore how these theories can be applied to teaching. The following
1741:
Deliberate, productive struggle with mathematical ideas refers to the fact that when students exert effort with important mathematical ideas, even if this struggle initially involves confusion and errors, the result is greater learning. This is true whether the struggle is due to intentionally
1381:
Elementary mathematics in most countries is taught similarly, though there are differences. Most countries tend to cover fewer topics in greater depth than in the United States. During the primary school years, children learn about whole numbers and arithmetic, including addition, subtraction,
1092:
Games can motivate students to improve skills that are usually learned by rote. In "Number Bingo," players roll 3 dice, then perform basic mathematical operations on those numbers to get a new number, which they cover on the board trying to cover 4 squares in a row. This game was played at a
1715:
One of the strongest results in recent research is that the most important feature of effective teaching is giving students "the opportunity to learn". Teachers can set expectations, times, kinds of tasks, questions, acceptable answers, and types of discussions that will influence students'
1766:
is both the best and cheapest way to boost student achievement, student engagement, and teacher professional satisfaction. Results surpass those of reducing class size or increasing teachers' content knowledge. Effective assessment is based on clarifying what students should know, creating
1630:
Ma (2000) summarized the research of others who found, based on nationwide data, that students with higher scores on standardized mathematics tests had taken more mathematics courses in high school. This led some states to require three years of mathematics instead of two. But because this
1172:: uses class topics to solve everyday problems and relates the topic to current events. This approach focuses on the many uses of mathematics and helps students understand why they need to know it as well as helps them to apply mathematics to real-world situations outside of the classroom.
1911:, depend on small but focused samples in an attempt to understand student learning and to look at how and why a given method gives the results it does. Such studies cannot conclusively establish that one method is better than another, as randomized trials can, but unless it is understood
1667:
has the
Missouri Council of Teachers of Mathematics (MCTM) which has its pillars and standards of education listed on its website. The MCTM also offers membership opportunities to teachers and future teachers so that they can stay up to date on the changes in math educational standards.
912:'." Since the 1980s, there have been a number of efforts to reform the traditional curriculum, which focuses on continuous mathematics and relegates even some basic discrete concepts to advanced study, to better balance coverage of the continuous and discrete sides of the subject:
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gives significantly better results than the status quo. The best quantitative studies involve randomized trials where students or classes are randomly assigned different methods to test their effects. They depend on large samples to obtain statistically significant results.
555:
Although research into mathematics education is primarily concerned with the tools, methods, and approaches that facilitate practice or the study of practice, it also covers an extensive field of study encompassing a variety of different concepts, theories and methods.
1846:
Elementary school children need to spend a long time learning to express algebraic properties without symbols before learning algebraic notation. When learning symbols, many students believe letters always represent unknowns and struggle with the concept of
1615:
Throughout most of history, standards for mathematics education were set locally, by individual schools or teachers, depending on the levels of achievement that were relevant to, realistic for, and considered socially appropriate for their pupils.
743:
apprentices, which were specific to the tasks and tools at hand. For example, the division of a board into thirds can be accomplished with a piece of string, instead of measuring the length and using the arithmetic operation of division.
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for US states, which were subsequently adopted by most states. Adoption of the Common Core State
Standards in mathematics is at the discretion of each state, and is not mandated by the federal government. "States routinely review their
1915:
treatment X is better than treatment Y, application of results of quantitative studies will often lead to "lethal mutations" of the finding in actual classrooms. Exploratory qualitative research is also useful for suggesting new
1220:, and bases other than ten. Adopted in the US as a response to the challenge of early Soviet technical superiority in space, it began to be challenged in the late 1960s. One of the most influential critiques of the New Math was
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2013:
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The method or methods used in any particular context are largely determined by the objectives that the relevant educational system is trying to achieve. Methods of teaching mathematics include the following:
2181:
In other words it was known during the whole duration of
Babylonian mathematics that the sum of the squares on the lengths of the sides of a right triangle equals the square of the length of the hypotenuse.
2217:: p. 306 "Although Plimpton 322 is a unique text of its kind, there are several other known texts testifying that the Pythagorean theorem was well known to the mathematicians of the Old Babylonian period."
1234:'s most popular parody songs, with his introductory remarks to the song: "...in the new approach, as you know, the important thing is to understand what you're doing, rather than to get the right answer."
3564:"Using Statistics Effectively in Mathematics Education Research: A report from a series of workshops organized by the American Statistical Association with funding from the National Science Foundation"
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as in the United States. Even in these cases, however, several "mathematics" options may be offered, selected based on the student's intended studies post high school. (In South Africa, for example,
1374:
Different levels of mathematics are taught at different ages and in somewhat different sequences in different countries. Sometimes a class may be taught at an earlier age than typical as a special or
940:
1663:
and may choose to change or add onto the standards to best meet the needs of their students." The NCTM has state affiliates that have different education standards at the state level. For example,
2664:
1821:, and have poor short-term memory. Techniques that have been found productive for helping such students include peer-assisted learning, explicit teaching with visual aids, instruction informed by
1166:
since didactic and curriculum decisions are often dictated by the logic of the subject rather than pedagogical considerations. Other methods emerge by emphasizing some aspects of this approach.
3997:
3524:
Cook, Thomas D. (2002). "Randomized
Experiments in Educational Policy Research: A Critical Examination of the Reasons the Educational Evaluation Community has Offered for Not Doing Them".
2233:
Babylon: Focus mesopotamischer
Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne. 2. Internationales Colloquium der Deutschen Orient-Gesellschaft 24.–26. März 1998 in Berlin
702:, the academic status of mathematics declined, because it was strongly associated with trade and commerce, and considered somewhat un-Christian. Although it continued to be taught in
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appropriate activities to obtain the evidence needed, giving good feedback, encouraging students to take control of their learning and letting students be resources for one another.
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At different times and in different cultures and countries, mathematics education has attempted to achieve a variety of different objectives. These objectives have included:
1421:
Mathematics, Mathematical
Literacy and Technical Mathematics.) Thus, a science-oriented curriculum typically overlaps the first year of university mathematics, and includes
919:
From the late 1980s into the new millennium, countries like the US began to identify and standardize sets of discrete mathematics topics for primary and secondary education;
776:
has been dated back to approximately 1650 BCE, but it is thought to be a copy of an even older scroll. This papyrus was essentially an early textbook for
Egyptian students.
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This is the introductory article to an issue devoted to this debate on report of the National Mathematics Advisory Panel, particularly on its use of randomized experiments.
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tools. This type of mathematics education was implemented in various parts of Canada beginning in 2005. Discovery-based mathematics is at the forefront of the Canadian "
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Mullis, Ina V. S.; et al. (June 1997). "Mathematics Achievement in the Primary School Years. IEA's Third International Mathematics and Science Study (TIMSS)".
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maintains its own educational system. Many other countries have centralized ministries which set national standards or curricula, and sometimes even textbooks.
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During the twentieth century, mathematics education was established as an independent field of research. Main events in this development include the following:
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Nunes, Terezinha; Dorneles, Beatriz Vargas; Lin, Pi-Jen; Rathgeb-Schnierer, Elisabeth (2016), "Teaching and Learning About Whole Numbers in Primary School",
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it is therefore likely that the Pythagorean rule was discovered within the lay surveyors' environment, possibly as a spin-off from the problem treated in Db
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Losano, Leticia, and Márcia Cristina de Costa Trindade Cyrino. "Current research on prospective secondary mathematics teachers' professional identity." in
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2003:
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676:. Apprentices to trades such as masons, merchants, and moneylenders could expect to learn such practical mathematics as was relevant to their profession.
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for solving word problems. It takes time to move from arithmetic to algebraic generalizations to describe patterns. Students often have trouble with the
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requirement was often met by taking another lower-level mathematics course, the additional courses had a “diluted” effect in raising achievement levels.
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In modern times, there has been a move towards regional or national standards, usually under the umbrella of a wider standard school curriculum. In
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1983:
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1948:, such as classrooms or students. The NMAP report's preference for randomized experiments received criticism from some scholars. In 2010, the
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1330:: the teaching of mathematical results, definitions and concepts by repetition and memorisation typically without meaning or supported by
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on mathematics education in the United States had generated more than 4,000 articles after 1920, so in 1941 William L. Schaaf published a
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Chatterji, Madhabi (December 2004). "Evidence on "What Works": An Argument for Extended-Term Mixed-Method (ETMM) Evaluation Designs".
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2195:"Methods and traditions of Babylonian mathematics: Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations"
1115:: involves the use of computers to teach mathematics. Mobile applications have also been developed to help students learn mathematics.
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2230:. "Pythagorean 'Rule' and 'Theorem' – Mirror of the Relation Between Babylonian and Greek Mathematics". In Renger, Johannes (ed.).
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1306:. Problem-solving is used as a means to build new mathematical knowledge, typically by building on students' prior understandings.
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Institute of Education Sciences, ed. (2003), "Highlights From the TIMSS 1999 Video Study of Eighth-Grade Mathematics Teaching",
1242:: mathematical problems that are fun can motivate students to learn mathematics and can increase their enjoyment of mathematics.
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Similar efforts are also underway to shift more focus to mathematical modeling as well as its relationship to discrete math.
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Ma, X. (2000). "A longitudinal assessment of antecedent course work in mathematics and subsequent mathematical attainment".
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Raudenbush, Stephen (2005). "Learning from Attempts to Improve Schooling: The Contribution of Methodological Diversity".
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In the 1980s and early 1990s, there was a push to make discrete mathematics more available at the post-secondary level;
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1314:: the reinforcement of mathematical skills by completing large numbers of exercises of a similar type, such as adding
1150:: the gradual and systematic guiding through the hierarchy of mathematical notions, ideas and techniques. Starts with
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1196:) mathematics which centres around problem-based or inquiry-based learning, with the use of open-ended questions and
983:) to most students, to equip them to follow a trade or craft and to understand mathematics commonly used in news and
632:(20th–16th centuries BC) and that it was being taught in scribal schools over one thousand years before the birth of
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A renewed interest in mathematics education emerged in the 1960s, and the International Commission was revitalized.
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In 1893, a Chair in mathematics education was created at the University of Göttingen, under the administration of
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1956:) responded to ongoing controversy by extending its research base to include non-experimental studies, including
1623:, for example, standards for mathematics education are set as part of the National Curriculum for England, while
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3016:"MIT - S.B. In 1-C Civil Engineering Curriculum | Department of Civil & Environmental Engineering, MIT"
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Concurrently, academics began compiling practical advice on introducing discrete math topics into the classroom;
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2239:. Berlin: Deutsche Orient-Gesellschaft / Saarbrücken: SDV Saarbrücker Druckerei und Verlag. pp. 393–407.
1944:(NMAP) published a report in 2008 based on studies, some of which used randomized assignment of treatments to
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and the teaching of mathematics. While previous approach focused on "working with specialized 'problems' in
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populations. Basic numeracy skills, such as the ability to tell the time, count money, and carry out simple
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teaching methods are randomly assigned to classes. In other disciplines concerned with human subjects—like
1274:: an approach in which most students are expected to achieve a high level of competence before progressing.
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The Calculus of Friendship: What a Teacher and a Student Learned about Life While Corresponding about Math
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In parallel, some textbook authors began working on materials explicitly designed to provide more balance.
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Gosztonyi, Katalin. "Mathematical culture and mathematics education in Hungary in the XXth century." in
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A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form
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Anderson, John R.; Reder, Lynne M.; Simon, Herbert A.; Ericsson, K. Anders; Glaser, Robert (1998).
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1354:: a walk where experience of perceived objects and scenes is translated into mathematical language.
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Wong, Khoon Yoong. "Enriching secondary mathematics education with 21st century competencies." in
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in general), mathematics education research depends on both quantitative and qualitative studies.
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3807:"Goals for School Mathematics: The Report of the Cambridge Conference on School Mathematics 1963"
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Dreher, Anika, et al. "What kind of content knowledge do secondary mathematics teachers need?."
2657:"Passing Mathematics Just Got Easier For Students With This New Platform: Mathematica - Techzim"
2492:"Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching"
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is mathematics-intensive, often overlapping substantively with the pure or applied math degree.
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that was developed in medieval Europe. The teaching of geometry was almost universally based on
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Students with genuine difficulties (unrelated to motivation or past instruction) struggle with
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Kelly, Anthony (2008). "Reflections on the National Mathematics Advisory Panel Final Report".
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2995:
2963:
2860:
2805:
2521:
2470:
2309:
2170:
1945:
1438:
1430:
1331:
1094:
1060:
1007:
827:
577:
Elementary mathematics were a core part of education in many ancient civilisations, including
191:
125:
105:
84:
1716:
opportunities to learn. This must involve both skill efficiency and conceptual understanding.
5772:
5688:
5629:
5392:
5387:
5357:
5244:
5239:
5201:
5106:
5081:
4986:
4694:
4669:
4541:
4389:
4326:
4155:
3899:
3787:
3706:
3671:
3644:
3570:
3533:
3498:
3409:
3290:
3104:
2953:
2943:
2892:
2880:
2777:
2511:
2503:
2462:
2417:
2206:
2163:
2124:
2041:
1695:
results are examples of some of the current findings in the field of mathematics education.
1497:
1489:
1022:
925:
Researchers continued arguing the urgency of making the transition throughout the 2000s; and
856:
816:
715:
546:
272:
115:
110:
100:
1107:: an approach based on the use of mathematical software as the primary tool of computation.
848:(ICMI) was founded in 1908, and Felix Klein became the first president of the organisation.
779:
The social status of mathematical study was improving by the seventeenth century, with the
5445:
5352:
5347:
5229:
5224:
5146:
5141:
5136:
5116:
5076:
4634:
4561:
4490:
4283:
3992:
3964:
3927:
3849:
3019:
2402:
2052:
2046:
1900:
1885:
1814:
1545:
1541:
1450:
1434:
1315:
1278:
893:
761:
402:
242:
130:
3276:"International large-scale assessments, affective worlds and policy impacts in education"
3167:
1682:
1500:—and often in applied mathematics—with the requirement of specified advanced courses in
783:
creating a Mathematics Chair in 1613, followed by the Chair in Geometry being set up in
684:
30:
7531:
5572:
5465:
5285:
4712:
4639:
4346:
4115:
3355:, vol. 1, Reston VA: National Council of Teachers of Mathematics, pp. 371–404
2991:
2285:
2231:
2227:
2058:
1873:
1604:
1525:
1505:
1485:
1481:
1183:
1056:
748:
727:
586:
430:
2915:"Foundations for Success: The Final Report of the National Mathematics Advisory Panel"
1742:
challenging, well-implemented teaching, or unintentionally confusing, faulty teaching.
1041:
The teaching of advanced mathematics to those students who wish to follow a career in
904:", the emerging structural approach to knowledge had "small children meditating about
747:
The first mathematics textbooks to be written in English and French were published by
17:
7567:
6550:
5647:
5249:
5186:
5051:
4924:
4500:
4432:
4384:
3987:
3932:
3857:
Uses of technology in lower secondary mathematics education: A concise topical survey
3718:
3545:
3510:
3421:
3302:
3116:
2490:
Greefrath, Gilbert; Siller, Hans‑Stefan; Vorhölter, Katrin; Kaiser, Gabriele (2022).
2211:
2194:
2144:
1326:
1251:
1182:
within a historical, social, and cultural context. Proponents argue it provides more
905:
773:
609:
597:
578:
355:
257:
3683:
2455:"Discrete mathematics is essential mathematics in a 21st century school curriculum."
2275:
concerning the computation of the sides of a rectangle given its area and diagonal.)
5545:
5337:
4442:
4437:
4341:
2128:
1961:
1896:
1818:
1557:
1549:
1533:
1426:
1406:
1375:
1221:
1036:
972:
644:
590:
3294:
3907:
2841:
2799:
6560:
5327:
4644:
4308:
4231:
3972:
Developing 21st Century Competencies In The Mathematics Classroom: Yearbook 2016
3903:
3454:
2948:
2466:
2089:
1930:
1908:
1860:
1553:
1454:
1383:
1126:
1042:
996:
976:
838:
723:
711:
699:
621:
534:
393:
319:
252:
222:
2507:
5450:
5300:
4629:
4508:
4303:
4120:
3675:
3537:
3502:
3108:
2406:
1934:
1917:
1513:
1458:
1283:
1231:
1213:
1212:: a method of teaching mathematics which focuses on abstract concepts such as
1151:
1122:
1049:
1000:
988:
980:
960:
909:
901:
870:
820:
812:
808:
656:
652:
633:
398:
388:
3710:
3413:
2459:
Teaching and learning discrete mathematics worldwide: Curriculum and research
826:
By the twentieth century, mathematics was part of the core curriculum in all
5538:
5460:
5101:
4844:
4002:
3954:
The mathematics education of prospective secondary teachers around the world
3893:
The mathematics education of prospective secondary teachers around the world
3596:
Experimental and quasi-experimental designs for generalized causal inference
1941:
1350:
1287:
1201:
582:
526:
518:
5475:
2525:
5470:
4199:
4016:
3251:
The Experience of Middle-Income Countries Participating in PISA 2000. PISA
2115:
Dudley, Underwood (April 2002). "The World's First Mathematics Textbook".
1644:
in 2000 for the United States and Canada, which boosted the trend towards
4976:
4533:
4452:
4379:
4140:
2516:
2272:
1788:
1664:
1624:
1517:
1410:
1402:
1387:
1208:
1137:
1032:
984:
968:
953:
719:
660:
549:
542:
538:
530:
370:
360:
4022:
3369:
Trends in International Mathematics and Science Study (TIMSS) - Overview
2958:
2136:
5171:
4318:
3733:
Sparks, Sarah (October 20, 2010). "Federal Criteria For Studies Grow".
2988:
International Association for the Evaluation of Educational Achievement
2264:
2014:
International Association for the Evaluation of Educational Achievement
1620:
1580:
1398:
1162:
taught concurrently. Requires the instructor to be well informed about
740:
365:
3562:
Working Group on Statistics in Mathematics Education Research (2007).
1817:, answer impulsively, struggle with mental representations, have poor
4019:. David Klein. California State University, Northridge, United States
4006:
2994:
Center for the Study of Testing, Evaluation, and Educational Policy.
1255:
885:
668:
3353:
The Effects of Classroom Mathematics Teaching on Students' Learning
3594:
Shadish, William R.; Cook, Thomas D.; Campbell, Donald T. (2002).
3188:
3160:"Standards in Your State - Common Core State Standards Initiative"
2801:
Crossroads in the History of Mathematics and Mathematics Education
1087:
1052:
and other problem-solving strategies to solve non-routine problems
992:
939:
892:
Midway through the twentieth century, the cultural impact of the "
683:
640:
605:
3832:
Uses of Technology in Primary and Secondary Mathematics Education
2306:
Pythagoras : His Lives and the Legacy of a Rational Universe
3812:. Cambridge MA: Center for the Study of Mathematics Curriculum.
2920:. U.S. Department of Education. 2008. p. 20. Archived from
2804:. Monograph Series in Mathematics Education. Vol. 12. IAP.
2008:
1676:
1540:. Specific topics are taught within other courses: for example,
1290:
thinking by setting students open-ended, unusual, and sometimes
881:
601:
7396:
7198:
6946:
6573:
6193:
5801:
5790:
5492:
4855:
4817:
4203:
4026:
3274:
Sellar, S., & Lingard, B., Sam; Lingard, Bob (April 2018).
815:, became essential in this new urban lifestyle. Within the new
688:
Illustration at the beginning of a 14th-century translation of
4017:
A quarter century of US 'math wars' and political partisanship
2889:
For First European Congress of Mathematics, Paris, July, 1992
866:
4813:
3974:(Association Of Mathematics Educators. 2016) pp. 33–50.
3217:
1681:
1587:
is usually limited to introductory calculus and (sometimes)
1204:" debate with many criticizing it for declining math scores.
3367:
1386:
are taught, in both numeric and pictorial form, as well as
888:
in 1972, and after that, it has been held every four years.
3131:"Myths vs. Facts - Common Core State Standards Initiative"
2942:, Cham: Springer International Publishing, pp. 1–50,
1677:
Organisation for the Economic Co-operation and Development
1346:, definitions, formulas, and other aspects of mathematics.
3649:
Evidence Matters: Randomized Trials in Education Research
3283:
International Journal of Qualitative Studies in Education
1563:. Pure and applied math degrees often include modules in
27:
Teaching, learning, and scholarly research in mathematics
1884:
to answer specific questions, such as whether a certain
1250:: a vision for pre-college mathematics education in the
1043:
science, technology, engineering, and mathematics (STEM)
1035:) as an example of the intellectual achievements of the
1006:
The teaching of abstract mathematical concepts (such as
764:
works on mathematics came from Egypt in the form of the
718:. The first modern arithmetic curriculum (starting with
600:. In most cases, formal education was only available to
2859:. Toronto, Ontario: C.D. Howe Institute. pp. 4–5.
1031:
The teaching of selected areas of mathematics (such as
1017:
The teaching of selected areas of mathematics (such as
3569:. The American Statistical Association. Archived from
2885:"The Unreasonable Utility of Recreational Mathematics"
2745:"Classical Education and STEM: a Common Misconception"
2405:, Forest Hills, N.Y. : Stevinus Press, link from
1979:
American Mathematical Association of Two-Year Colleges
1492:
in mathematics substantively comprises these courses.
655:, the quadrivium included the mathematical fields of
2367:"Why We Learn Math Lessons That Date Back 500 Years"
2334:"Why We Learn Math Lessons That Date Back 500 Years"
1394:, patterns, and various topics related to geometry.
1125:, part of the classical education curriculum of the
846:
International Commission on Mathematical Instruction
7476:
7403:
7309:
7286:
7205:
7079:
6953:
6926:
6878:
6840:
6582:
6500:
6460:
6202:
6116:
6091:
5810:
5438:
5268:
5215:
5037:
4890:
4862:
4703:
4660:
4570:
4532:
4499:
4451:
4423:
4370:
4317:
4274:
4093:
4060:
663:. This structure was continued in the structure of
604:children with sufficiently high status, wealth, or
3931:
2828:Ansari, Daniel (March 2016). "No More Math Wars".
2162:
819:systems, mathematics became a central part of the
3777:"Radical Constructivism and Cognitive Psychology"
3749:"Accelerated Math: What Every Parent Should Know"
2984:Third International Mathematics and Science Study
1369:Aalto University School of Science and Technology
3449:
3447:
3445:
3346:
3344:
3342:
3340:
2716:"This Free App Will Solve Math Problems For You"
2062:, children's mathematics educational book series
1792:skills, but not broader measures of achievement.
1548:, and "math for computer science" might include
878:International Congress on Mathematical Education
3072:. UK Department of Education. 17 January 2013.
2857:What to Do About Canada's Declining Math Scores
1641:Principles and Standards for School Mathematics
1264:Principles and Standards for School Mathematics
760:. After the Sumerians, some of the most famous
608:. The oldest known mathematics textbook is the
1673:Programme for International Student Assessment
1382:multiplication, and division. Comparisons and
1230:. The New Math method was the topic of one of
4829:
4215:
4038:
3351:Hiebert, James; Grouws, Douglas (2007), "9",
2290:Mathematics in Ancient Iraq: A Social History
1282:: the cultivation of mathematical ingenuity,
706:, it was seen as subservient to the study of
552:into the transfer of mathematical knowledge.
498:
292:
8:
7502:South Georgia and the South Sandwich Islands
3557:
3555:
3329:: CS1 maint: multiple names: authors list (
2263:-146, somewhere between 2300 and 1825 BC." (
2169:. New York: Dover Publications. p. 36.
1872:As with other educational research (and the
2541:"5 Approaches to Teaching PreK-12 Numeracy"
2004:National Council of Teachers of Mathematics
1974:Advisory Committee on Mathematics Education
1636:National Council of Teachers of Mathematics
1508:. Other topics in pure mathematics include
1260:National Council of Teachers of Mathematics
859:, sorting them into their various subjects.
564:in order to improve mathematics education.
34:A child calculating with his fingers (2006)
7393:
7195:
6943:
6570:
6190:
5798:
5787:
5718:
5713:
5684:
5679:
5643:
5638:
5625:
5620:
5586:
5581:
5568:
5563:
5534:
5529:
5503:
5489:
4852:
4836:
4822:
4814:
4222:
4208:
4200:
4045:
4031:
4023:
3598:(2nd ed.). Boston: Houghton Mifflin.
3526:Educational Evaluation and Policy Analysis
2078:Mathematics education in the United States
1825:, and encouraging students to think aloud.
505:
491:
342:
310:
299:
285:
37:
3866:(Birkhäuser, Cham, 2016) pp. 71–89.
3492:
2957:
2947:
2690:Technology Solutions That Drive Education
2515:
2210:
1453:in their final year of secondary school;
1121:: the teaching of mathematics within the
3996:) is being considered for deletion. See
3805:Auslander, Maurice; et al. (2004).
2396:A Bibliography of Mathematical Education
2361:
2359:
1397:At high school level in most of the US,
1362:
558:National and international organisations
29:
3253:. France: OECD Publishing. p. 30.
2686:"5 Apps to Help All Students with Math"
2453:Hart, Eric W.; Martin, W. Gary (2018).
2327:
2325:
2123:(4). Taylor & Francis, Ltd.: 8–11.
2107:
1192:: a constructivist method of teaching (
959:The teaching of practical mathematics (
867:Shell Centre for Mathematical Education
474:
318:
214:
138:
47:
40:
3322:
2271:is an Old Babylonian clay tablet from
1984:Association of Teachers of Mathematics
1952:(essentially the research arm for the
1851:. They prefer arithmetic reasoning to
3244:
3242:
2823:
2821:
2539:Education, McGraw-Hill (2017-10-20).
2461:. ICME-13 Monographs. pp. 3–19.
2049:, primary level mathematics education
1294:. The problems can range from simple
7:
4784:
4184:
3834:(Cham, Switzerland: Springer, 2018).
3784:Brookings Papers on Education Policy
1496:study additional other areas within
1112:Computer-based mathematics education
884:in 1969. The second congress was in
803:In the 18th and 19th centuries, the
7548:
4796:
3624:National Mathematics Advisory Panel
3395:"Assessment and Classroom Learning"
2714:Mosbergen, Dominique (2014-10-22).
1942:National Mathematics Advisory Panel
1304:International Mathematical Olympiad
952:The teaching and learning of basic
944:Boy doing sums, Guinea-Bissau, 1974
3041:"Mathematics for Computer Science"
2344:from the original on 10 April 2018
1528:subject in its own right, such as
25:
4012:History of Mathematical Education
4000:to help reach a consensus. ›
3909:Theories of Mathematics Education
3895:(Springer, Cham, 2017) pp. 25-32.
3393:Black, P.; Wiliam, Dylan (1998).
2332:Gabrielle Emanuel (23 Jul 2016).
2257:To judge from this evidence alone
1464:At college and university level,
1342:, rote learning is used to teach
896:" (McLuhan) was also taken up by
7579:Mathematical science occupations
7547:
7538:
7537:
7525:
7061:Saint Vincent and the Grenadines
6555:
6546:
6545:
6103:Sahrawi Arab Democratic Republic
5873:Democratic Republic of the Congo
5767:
4795:
4783:
4772:
4771:
4759:
4183:
4174:
4173:
3372:, U.S. Department of Education,
2308:. London: Icon. pp. 78–84.
2026:Aspects of mathematics education
1958:regression discontinuity designs
475:
4680:Computational complexity theory
3952:Strutchens, Marilyn E., et al.
3839:Journal fĂĽr Mathematik-Didaktik
3819:from the original on 2010-07-15
3747:Voit, Rita (14 February 2020).
3461:from the original on 2014-10-02
3431:from the original on 2018-07-26
3376:from the original on 2012-05-08
3312:from the original on 2020-03-07
3228:from the original on 2018-03-04
3199:from the original on 2018-02-12
3141:from the original on 2017-08-02
3097:Journal of Educational Research
3076:from the original on 2 May 2012
3051:from the original on 2019-05-10
2755:from the original on 2019-02-12
2726:from the original on 2017-09-22
2696:from the original on 2021-12-26
2667:from the original on 2018-06-19
2638:from the original on 2019-04-06
2580:from the original on 2019-01-30
2551:from the original on 2021-12-26
2377:from the original on 2018-04-10
2246:from the original on 2021-02-25
2165:The exact sciences in antiquity
1298:to problems from international
1186:than the conventional approach.
1129:, which was typically based on
1055:The teaching of mathematics in
807:led to an enormous increase in
624:have confirmed that use of the
560:regularly hold conferences and
7218:Federated States of Micronesia
6513:British Indian Ocean Territory
3938:. Princeton University Press.
2429:"McLuhan: Understanding Media"
2129:10.1080/10724117.2002.11975154
2032:Cognitively Guided Instruction
1530:partial differential equations
1484:; at several US colleges, the
1063:, as well as in some selected
1:
3651:, Brookings Institution Press
3628:Scientifically based research
3295:10.1080/09518398.2018.1449982
2774:"Mathematical Current Events"
2292:. Princeton University Press.
2037:Critical mathematics pedagogy
1989:Canadian Mathematical Society
1648:. In 2006, the NCTM released
1461:are similarly often taught.
1093:"Discovery Day" organized by
789:Lucasian Chair of Mathematics
612:, dated from circa 1650 BCE.
7186:United States Virgin Islands
3786:(1): 227–278. Archived from
2212:10.1016/0315-0860(81)90069-0
6948:Education in North America
3877:. Bellevue Literary Press.
3753:Resources by HEROES Academy
3455:"Research clips and briefs"
3249:Lockheed, Marlaine (2015).
2949:10.1007/978-3-319-45113-8_1
2467:10.1007/978-3-319-70308-4_1
1863:to mean "the answer is...".
1656:Common Core State Standards
1247:Standards-based mathematics
770:Moscow Mathematical Papyrus
7595:
7398:Education in South America
4730:Films about mathematicians
2798:Sriraman, Bharath (2012).
2508:10.1007/s11858-022-01339-5
1940:In the United States, the
1880:includes studies that use
1797:Students with difficulties
1607:, and sometimes analysis.
1180:development of mathematics
766:Rhind Mathematical Papyrus
415:Relationship with sciences
7519:
7161:Saint Pierre and Miquelon
6541:
5797:
5786:
5762:
5716:
5682:
5641:
5623:
5584:
5566:
5532:
5508:Early childhood education
5501:
5488:
4851:
4753:
4299:Philosophy of mathematics
4239:
4169:
3676:10.3102/0013189x033009003
3538:10.3102/01623737024003175
3503:10.3102/0013189X034005025
3109:10.1080/00220670009598739
2496:ZDM–Mathematics Education
2394:William L. Schaaf (1941)
2084:Mathematical difficulties
1544:may be required to study
1472:will be required to take
1367:A mathematics lecture at
791:being established by the
680:Medieval and early modern
7369:Northern Mariana Islands
7181:Turks and Caicos Islands
6262:East Timor (Timor-Leste)
5858:Central African Republic
4735:Recreational mathematics
3998:templates for discussion
3956:(Springer Nature, 2017)
3859:(Springer Nature, 2016).
3711:10.3102/0013189X08329353
3632:What Works Clearinghouse
3414:10.1080/0969595980050102
3070:"Mathematics curriculum"
2304:Ferguson, Kitty (2010).
1999:Mathematical Association
1950:What Works Clearinghouse
1721:Conceptual understanding
1300:mathematics competitions
1239:Recreational mathematics
525:—known in Europe as the
7334:Cocos (Keeling) Islands
6523:Cocos (Keeling) Islands
4620:Mathematical statistics
4610:Mathematical psychology
4580:Engineering mathematics
4514:Algebraic number theory
3930:; Joffray, Don (2009).
3855:Drijvers, Paul, et al.
3402:Assessment in Education
2940:ICME-13 Topical Surveys
2193:Friberg, Jöran (1981).
1954:Department of Education
1675:(PISA), created by the
1651:Curriculum Focal Points
1569:mathematical statistics
793:University of Cambridge
268:Participant observation
263:Multivariate statistics
96:International education
7111:British Virgin Islands
6625:Bosnia and Herzegovina
4766:Mathematics portal
4615:Mathematical sociology
4595:Mathematical economics
4590:Mathematical chemistry
4519:Analytic number theory
4400:Differential equations
3928:Strogatz, Steven Henry
3873:Paul Lockhart (2009).
3699:Educational Researcher
3664:Educational Researcher
3643:Mosteller, Frederick;
3481:Educational Researcher
1882:inferential statistics
1686:
1634:In North America, the
1601:differential equations
1478:differential equations
1474:multivariable calculus
1371:
1359:Content and age levels
1332:mathematical reasoning
1164:elementary mathematics
1098:
1021:) as an example of an
956:skills to all students
945:
781:University of Aberdeen
695:
35:
18:Mathematics curriculum
7574:Mathematics education
7312:and other territories
7051:Saint Kitts and Nevis
6018:SĂŁo TomĂ© and PrĂncipe
5878:Republic of the Congo
4745:Mathematics education
4675:Theory of computation
4395:Hypercomplex analysis
4054:Mathematics education
3864:Mathematical cultures
3841:39.2 (2018): 319-341
3164:www.corestandards.org
3135:www.corestandards.org
2855:Stokke, Anna (2015).
2338:National Public Radio
2072:North American issues
1878:Quantitative research
1685:
1638:(NCTM) published the
1510:differential geometry
1447:logarithmic functions
1423:differential calculus
1366:
1344:multiplication tables
1340:traditional education
1334:. A derisory term is
1148:Conventional approach
1091:
1073:liberal arts colleges
943:
853:periodical literature
805:Industrial Revolution
704:European universities
687:
630:Old Babylonian Empire
523:mathematics education
228:Conversation analysis
33:
7200:Education in Oceania
6576:Education in Europe
6437:United Arab Emirates
5804:Education in Africa
5027:Instructional design
4725:Informal mathematics
4605:Mathematical physics
4600:Mathematical finance
4585:Mathematical biology
4524:Diophantine geometry
3830:Ball, Lynda, et al.
2883:(7 September 1993).
2830:The Education Digest
2570:"Euclidean Geometry"
2199:Historia Mathematica
2095:Mathematical anxiety
2066:Statistics education
1893:Qualitative research
1823:formative assessment
1764:Formative assessment
1747:Formative assessment
1585:Business mathematics
1573:stochastic processes
1470:engineering students
1227:Why Johnny Can't Add
785:University of Oxford
753:The Grounde of Artes
537:—is the practice of
380:Discrete mathematics
248:Factorial experiment
42:Educational research
7066:Trinidad and Tobago
6961:Antigua and Barbuda
6841:States with limited
6464:limited recognition
6093:States with limited
5792:Education by region
5518:Secondary education
5430:Teaching philosophy
5333:Pedagogical pattern
5276:21st century skills
5255:Religious education
4898:Aims and objectives
4740:Mathematics and art
4650:Operations research
4405:Functional analysis
2632:theory.stanford.edu
2599:"Axiomatic Systems"
2423:Understanding Media
1994:C.D. Howe Institute
1962:single-case studies
1909:clinical interviews
1859:and understand the
1853:algebraic equations
1830:Algebraic reasoning
1595:additionally cover
1561:mathematical proofs
1556:, probability, and
1522:Applied mathematics
1320:quadratic equations
1170:Relational approach
1154:and is followed by
1142:deductive reasoning
1119:Classical education
1104:Computer-based math
1027:deductive reasoning
880:(ICME) was held in
869:was established in
828:developed countries
823:from an early age.
756:equations like the
739:methods learned by
665:classical education
643:'s division of the
616:Pythagorean theorem
545:, and carrying out
314:Part of a series on
121:Religious education
7532:Schools portal
7001:Dominican Republic
6196:Education in Asia
5523:Tertiary education
5461:Learning resources
4952:Education sciences
4685:Numerical analysis
4294:Mathematical logic
4289:Information theory
4151:Cognitively guided
3963:2021-04-18 at the
3848:2021-04-18 at the
3045:MIT OpenCourseWare
2927:on March 17, 2015.
2895:on 7 February 2002
2401:2020-01-10 at the
1946:experimental units
1905:discourse analysis
1687:
1661:academic standards
1646:reform mathematics
1593:economics programs
1565:probability theory
1538:numerical analysis
1524:may be taken as a
1494:Mathematics majors
1372:
1262:which created the
1194:discovery learning
1160:elementary algebra
1156:Euclidean geometry
1099:
1061:actuarial sciences
1019:Euclidean geometry
967:, plane and solid
965:elementary algebra
946:
898:educational theory
772:. The more famous
758:quadratic equation
696:
628:dates back to the
562:publish literature
481:Mathematics Portal
233:Discourse analysis
139:Curricular domains
61:Education sciences
56:Curriculum studies
36:
7561:
7560:
7515:
7514:
7511:
7510:
7483:other territories
7392:
7391:
7384:Wallis and Futuna
7329:Clipperton Island
7287:Associated states
7194:
7193:
7083:other territories
6942:
6941:
6569:
6568:
6506:other territories
6189:
6188:
6120:other territories
5893:Equatorial Guinea
5782:
5781:
5757:
5756:
5753:
5752:
5748:
5747:
5744:
5743:
5739:
5738:
5676:
5675:
5671:
5670:
5667:
5666:
5662:
5661:
5617:
5616:
5612:
5611:
5608:
5607:
5603:
5602:
5560:
5559:
5555:
5554:
5513:Primary education
5484:
5483:
5373:Dialogic learning
5343:Teacher retention
5296:Critical thinking
5291:Class arrangement
5260:Special education
4935:Standardized test
4918:Course evaluation
4811:
4810:
4410:Harmonic analysis
4197:
4196:
4136:Modern elementary
4111:Three-part lesson
3945:978-0-691-13493-2
3919:978-3-642-00774-3
3900:Sriraman, Bharath
3605:978-0-395-61556-0
3260:978-92-64-24618-8
2969:978-3-319-45112-1
2881:Singmaster, David
2811:978-1-61735-704-6
2476:978-3-319-70307-7
2176:978-0-486-22332-2
1924:Randomized trials
1699:Important results
1439:analytic geometry
1431:integral calculus
1429:at age 16–17 and
1292:unsolved problems
1176:Historical method
1095:Big Brother Mouse
1014:) at an early age
851:The professional
751:, beginning with
736:reckoning schools
583:ancient Babylonia
515:
514:
470:
469:
309:
308:
126:Teacher education
106:Special education
101:School counseling
16:(Redirected from
7586:
7551:
7550:
7541:
7540:
7530:
7529:
7528:
7503:
7491:Falkland Islands
7405:Sovereign states
7394:
7374:Pitcairn Islands
7344:French Polynesia
7324:Christmas Island
7253:Papua New Guinea
7233:Marshall Islands
7206:Sovereign states
7196:
7151:Saint Barthélemy
7081:Dependencies and
6954:Sovereign states
6944:
6879:Dependencies and
6583:Sovereign states
6571:
6559:
6549:
6548:
6518:Christmas Island
6204:Sovereign states
6191:
6181:
6180:(United Kingdom)
6176:Tristan da Cunha
6172:Ascension Island
6164:
6151:
6142:
6118:Dependencies and
5811:Sovereign states
5799:
5788:
5771:
5719:
5714:
5689:Higher education
5685:
5680:
5644:
5639:
5630:Secondary school
5626:
5621:
5587:
5582:
5569:
5564:
5535:
5530:
5504:
5490:
5418:Student-centered
5403:Phenomenon-based
5393:Peer instruction
5358:Blended learning
5281:Bloom's taxonomy
5245:Gifted education
5240:Education reform
5072:Computer science
4853:
4838:
4831:
4824:
4815:
4799:
4798:
4787:
4786:
4775:
4774:
4764:
4763:
4695:Computer algebra
4670:Computer science
4390:Complex analysis
4224:
4217:
4210:
4201:
4187:
4186:
4177:
4176:
4047:
4040:
4033:
4024:
3949:
3937:
3923:
3888:
3827:
3825:
3824:
3818:
3811:
3801:
3799:
3798:
3792:
3781:
3763:
3761:
3759:
3739:
3738:
3730:
3724:
3722:
3694:
3688:
3687:
3659:
3653:
3652:
3640:
3634:
3618:See articles on
3616:
3610:
3609:
3591:
3585:
3584:
3582:
3581:
3575:
3568:
3559:
3550:
3549:
3521:
3515:
3514:
3496:
3476:
3470:
3469:
3467:
3466:
3451:
3440:
3439:
3437:
3436:
3430:
3399:
3390:
3384:
3383:
3382:
3381:
3363:
3357:
3356:
3348:
3335:
3334:
3328:
3320:
3318:
3317:
3311:
3280:
3271:
3265:
3264:
3246:
3237:
3236:
3234:
3233:
3214:
3208:
3207:
3205:
3204:
3185:
3179:
3178:
3176:
3175:
3166:. Archived from
3156:
3150:
3149:
3147:
3146:
3127:
3121:
3120:
3092:
3086:
3085:
3083:
3081:
3066:
3060:
3059:
3057:
3056:
3037:
3031:
3030:
3028:
3027:
3018:. Archived from
3012:
3006:
3005:
2979:
2973:
2972:
2961:
2951:
2935:
2929:
2928:
2926:
2919:
2911:
2905:
2904:
2902:
2900:
2891:. Archived from
2877:
2871:
2870:
2852:
2846:
2845:
2825:
2816:
2815:
2795:
2789:
2788:
2786:
2785:
2776:. Archived from
2770:
2764:
2763:
2761:
2760:
2741:
2735:
2734:
2732:
2731:
2711:
2705:
2704:
2702:
2701:
2682:
2676:
2675:
2673:
2672:
2653:
2647:
2646:
2644:
2643:
2624:
2618:
2617:
2615:
2614:
2605:. Archived from
2595:
2589:
2588:
2586:
2585:
2566:
2560:
2559:
2557:
2556:
2536:
2530:
2529:
2519:
2487:
2481:
2480:
2450:
2444:
2443:
2441:
2440:
2431:. Archived from
2418:Marshall McLuhan
2415:
2409:
2392:
2386:
2385:
2383:
2382:
2363:
2354:
2353:
2351:
2349:
2329:
2320:
2319:
2315:978-184831-231-9
2301:
2295:
2293:
2282:
2276:
2254:
2252:
2251:
2245:
2238:
2224:
2218:
2216:
2214:
2190:
2184:
2183:
2168:
2159:Neugebauer, Otto
2155:
2149:
2148:
2112:
2042:Ethnomathematics
1842:
1841:
1837:
1809:
1808:
1804:
1784:
1783:
1779:
1759:
1758:
1754:
1733:
1732:
1728:
1711:
1710:
1706:
1498:pure mathematics
1405:, and analysis (
1316:simple fractions
1048:The teaching of
1023:axiomatic system
857:classified index
817:public education
787:in 1619 and the
716:moral philosophy
626:Pythagorean rule
517:In contemporary
507:
500:
493:
479:
343:
311:
301:
294:
287:
157:Computer science
116:Female education
111:Gifted education
38:
21:
7594:
7593:
7589:
7588:
7587:
7585:
7584:
7583:
7564:
7563:
7562:
7557:
7526:
7524:
7507:
7501:
7484:
7482:
7472:
7399:
7388:
7311:
7305:
7288:
7282:
7263:Solomon Islands
7201:
7190:
7084:
7082:
7075:
6949:
6938:
6922:
6880:
6874:
6860:Northern Cyprus
6842:
6836:
6757:North Macedonia
6578:
6565:
6537:
6505:
6496:
6477:Northern Cyprus
6463:
6456:
6198:
6185:
6184:
6179:
6162:
6149:
6140:
6121:
6119:
6112:
6096:
6094:
6087:
5806:
5793:
5778:
5777:
5758:
5749:
5740:
5732:
5725:
5703:
5691:
5672:
5663:
5655:
5650:
5632:
5613:
5604:
5596:
5591:
5575:
5556:
5548:
5541:
5497:
5480:
5434:
5353:Active learning
5348:Teaching method
5323:Learning theory
5264:
5230:Autodidacticism
5225:Adult education
5211:
5152:Performing arts
5033:
4940:Teacher quality
4930:Standards-based
4886:
4858:
4847:
4842:
4812:
4807:
4758:
4749:
4699:
4656:
4635:Systems science
4566:
4562:Homotopy theory
4528:
4495:
4447:
4419:
4366:
4313:
4284:Category theory
4270:
4235:
4228:
4198:
4193:
4165:
4089:
4056:
4051:
4001:
3982:
3977:
3965:Wayback Machine
3946:
3926:
3920:
3898:
3885:
3872:
3850:Wayback Machine
3822:
3820:
3816:
3809:
3804:
3796:
3794:
3790:
3779:
3774:
3770:
3768:Further reading
3757:
3755:
3746:
3743:
3742:
3732:
3731:
3727:
3696:
3695:
3691:
3661:
3660:
3656:
3642:
3641:
3637:
3617:
3613:
3606:
3593:
3592:
3588:
3579:
3577:
3573:
3566:
3561:
3560:
3553:
3523:
3522:
3518:
3494:10.1.1.649.7042
3478:
3477:
3473:
3464:
3462:
3453:
3452:
3443:
3434:
3432:
3428:
3397:
3392:
3391:
3387:
3379:
3377:
3365:
3364:
3360:
3350:
3349:
3338:
3321:
3315:
3313:
3309:
3278:
3273:
3272:
3268:
3261:
3248:
3247:
3240:
3231:
3229:
3218:"What is PISA?"
3216:
3215:
3211:
3202:
3200:
3187:
3186:
3182:
3173:
3171:
3158:
3157:
3153:
3144:
3142:
3129:
3128:
3124:
3094:
3093:
3089:
3079:
3077:
3068:
3067:
3063:
3054:
3052:
3039:
3038:
3034:
3025:
3023:
3014:
3013:
3009:
3002:
2981:
2980:
2976:
2970:
2937:
2936:
2932:
2924:
2917:
2913:
2912:
2908:
2898:
2896:
2879:
2878:
2874:
2867:
2854:
2853:
2849:
2827:
2826:
2819:
2812:
2797:
2796:
2792:
2783:
2781:
2772:
2771:
2767:
2758:
2756:
2743:
2742:
2738:
2729:
2727:
2720:Huffington Post
2713:
2712:
2708:
2699:
2697:
2684:
2683:
2679:
2670:
2668:
2655:
2654:
2650:
2641:
2639:
2626:
2625:
2621:
2612:
2610:
2603:web.mnstate.edu
2597:
2596:
2592:
2583:
2581:
2568:
2567:
2563:
2554:
2552:
2538:
2537:
2533:
2489:
2488:
2484:
2477:
2452:
2451:
2447:
2438:
2436:
2427:
2416:
2412:
2403:Wayback Machine
2393:
2389:
2380:
2378:
2365:
2364:
2357:
2347:
2345:
2331:
2330:
2323:
2316:
2303:
2302:
2298:
2284:
2283:
2279:
2268:
2262:
2249:
2247:
2243:
2236:
2226:
2225:
2221:
2192:
2191:
2187:
2177:
2157:
2156:
2152:
2114:
2113:
2109:
2104:
2099:
2086:
2074:
2053:Pre-math skills
2047:Number sentence
2028:
2022:
1970:
1926:
1901:action research
1886:teaching method
1874:social sciences
1870:
1843:
1839:
1835:
1833:
1832:
1810:
1806:
1802:
1800:
1799:
1785:
1781:
1777:
1775:
1774:
1760:
1756:
1752:
1750:
1749:
1734:
1730:
1726:
1724:
1723:
1712:
1708:
1704:
1702:
1701:
1692:
1613:
1546:fluid mechanics
1542:civil engineers
1451:infinite series
1435:complex numbers
1419:the options are
1392:proportionality
1361:
1279:Problem solving
1178:: teaching the
1082:
1075:or universities
1057:social sciences
1025:and a model of
938:
801:
682:
618:
575:
570:
511:
466:
465:
416:
408:
407:
403:Decision theory
351:
305:
243:Factor analysis
187:Performing arts
162:Early childhood
131:Teaching method
28:
23:
22:
15:
12:
11:
5:
7592:
7590:
7582:
7581:
7576:
7566:
7565:
7559:
7558:
7556:
7555:
7545:
7535:
7520:
7517:
7516:
7513:
7512:
7509:
7508:
7506:
7505:
7498:
7493:
7487:
7485:
7477:
7474:
7473:
7471:
7470:
7465:
7460:
7455:
7450:
7445:
7440:
7435:
7430:
7425:
7420:
7415:
7409:
7407:
7401:
7400:
7397:
7390:
7389:
7387:
7386:
7381:
7376:
7371:
7366:
7364:Norfolk Island
7361:
7356:
7351:
7346:
7341:
7336:
7331:
7326:
7321:
7319:American Samoa
7315:
7313:
7307:
7306:
7304:
7303:
7298:
7292:
7290:
7289:of New Zealand
7284:
7283:
7281:
7280:
7275:
7270:
7265:
7260:
7255:
7250:
7245:
7240:
7235:
7230:
7225:
7220:
7215:
7209:
7207:
7203:
7202:
7199:
7192:
7191:
7189:
7188:
7183:
7178:
7173:
7171:Sint Eustatius
7168:
7163:
7158:
7153:
7148:
7143:
7138:
7133:
7128:
7123:
7118:
7116:Cayman Islands
7113:
7108:
7103:
7098:
7093:
7087:
7085:
7080:
7077:
7076:
7074:
7073:
7068:
7063:
7058:
7053:
7048:
7043:
7038:
7033:
7028:
7023:
7018:
7013:
7008:
7003:
6998:
6993:
6988:
6983:
6978:
6973:
6968:
6963:
6957:
6955:
6951:
6950:
6947:
6940:
6939:
6937:
6936:
6934:European Union
6930:
6928:
6927:Other entities
6924:
6923:
6921:
6920:
6915:
6910:
6905:
6900:
6895:
6890:
6884:
6882:
6881:other entities
6876:
6875:
6873:
6872:
6867:
6862:
6857:
6852:
6846:
6844:
6838:
6837:
6835:
6834:
6832:United Kingdom
6829:
6824:
6819:
6814:
6809:
6804:
6799:
6794:
6789:
6784:
6779:
6774:
6769:
6764:
6759:
6754:
6749:
6744:
6739:
6734:
6729:
6724:
6719:
6714:
6709:
6704:
6699:
6697:
6692:
6687:
6682:
6677:
6672:
6667:
6662:
6657:
6652:
6647:
6645:Czech Republic
6642:
6637:
6632:
6627:
6622:
6617:
6612:
6607:
6602:
6597:
6592:
6586:
6584:
6580:
6579:
6574:
6567:
6566:
6564:
6563:
6553:
6542:
6539:
6538:
6536:
6535:
6530:
6525:
6520:
6515:
6509:
6507:
6498:
6497:
6495:
6494:
6489:
6484:
6479:
6474:
6468:
6466:
6458:
6457:
6455:
6454:
6449:
6444:
6439:
6434:
6429:
6424:
6419:
6414:
6409:
6404:
6399:
6394:
6389:
6384:
6379:
6374:
6369:
6364:
6359:
6354:
6349:
6344:
6339:
6334:
6329:
6324:
6319:
6314:
6309:
6304:
6299:
6294:
6289:
6284:
6279:
6274:
6269:
6264:
6259:
6254:
6249:
6244:
6239:
6234:
6229:
6224:
6219:
6214:
6208:
6206:
6200:
6199:
6194:
6187:
6186:
6183:
6182:
6165:
6152:
6143:
6129:Canary Islands
6125:
6124:
6122:
6117:
6114:
6113:
6111:
6110:
6105:
6099:
6097:
6092:
6089:
6088:
6086:
6085:
6080:
6075:
6070:
6065:
6060:
6055:
6050:
6045:
6040:
6035:
6030:
6025:
6020:
6015:
6010:
6005:
6000:
5995:
5990:
5985:
5980:
5975:
5970:
5965:
5960:
5955:
5950:
5945:
5940:
5935:
5930:
5925:
5920:
5915:
5910:
5905:
5900:
5895:
5890:
5885:
5880:
5875:
5870:
5865:
5860:
5855:
5850:
5845:
5840:
5835:
5830:
5825:
5820:
5814:
5812:
5808:
5807:
5802:
5795:
5794:
5791:
5784:
5783:
5780:
5779:
5776:
5775:
5764:
5763:
5760:
5759:
5755:
5754:
5751:
5750:
5746:
5745:
5742:
5741:
5737:
5735:
5734:
5727:
5717:
5710:
5709:
5698:
5693:
5683:
5677:
5674:
5673:
5669:
5668:
5665:
5664:
5660:
5658:
5657:
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5642:
5635:
5634:
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5614:
5610:
5609:
5606:
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5601:
5599:
5598:
5593:
5585:
5578:
5577:
5573:Primary school
5567:
5561:
5558:
5557:
5553:
5551:
5550:
5543:
5533:
5526:
5525:
5520:
5515:
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5468:
5463:
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5380:
5375:
5370:
5365:
5360:
5355:
5345:
5340:
5335:
5330:
5325:
5320:
5319:
5318:
5313:
5308:
5298:
5293:
5288:
5286:Cognitive load
5283:
5278:
5272:
5270:
5266:
5265:
5263:
5262:
5257:
5252:
5247:
5242:
5237:
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5209:
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5119:
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5035:
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5032:
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5029:
5019:
5014:
5009:
5004:
4999:
4994:
4989:
4984:
4979:
4974:
4969:
4964:
4959:
4957:Evidence-based
4954:
4949:
4944:
4943:
4942:
4937:
4932:
4927:
4922:
4921:
4920:
4905:
4900:
4894:
4892:
4891:By perspective
4888:
4887:
4885:
4884:
4879:
4874:
4868:
4866:
4860:
4859:
4856:
4849:
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4727:
4722:
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4720:
4713:Mathematicians
4709:
4707:
4705:Related topics
4701:
4700:
4698:
4697:
4692:
4687:
4682:
4677:
4672:
4666:
4664:
4658:
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4655:
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4653:
4652:
4647:
4642:
4640:Control theory
4632:
4627:
4622:
4617:
4612:
4607:
4602:
4597:
4592:
4587:
4582:
4576:
4574:
4568:
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4468:
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4448:
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4429:
4427:
4421:
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4415:Measure theory
4412:
4407:
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4397:
4392:
4387:
4382:
4376:
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4368:
4367:
4365:
4364:
4359:
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4321:
4315:
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4306:
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4296:
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4280:
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4229:
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4219:
4212:
4204:
4195:
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4181:
4170:
4167:
4166:
4164:
4163:
4158:
4153:
4148:
4143:
4138:
4133:
4131:Computer-based
4128:
4123:
4118:
4113:
4108:
4103:
4097:
4095:
4091:
4090:
4088:
4087:
4082:
4080:United Kingdom
4077:
4076:
4075:
4064:
4062:
4058:
4057:
4052:
4050:
4049:
4042:
4035:
4027:
4021:
4020:
4014:
4009:
4003:Math Education
3985:
3981:
3980:External links
3978:
3976:
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3968:
3950:
3944:
3924:
3918:
3896:
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3884:978-1934137178
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3769:
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3765:
3764:
3741:
3740:
3735:Education Week
3725:
3689:
3654:
3645:Boruch, Robert
3635:
3611:
3604:
3586:
3551:
3532:(3): 175–199.
3516:
3471:
3441:
3385:
3358:
3336:
3289:(5): 367–381.
3266:
3259:
3238:
3209:
3189:"MoCTM - Home"
3180:
3151:
3122:
3087:
3061:
3032:
3007:
3000:
2992:Boston College
2974:
2968:
2930:
2906:
2872:
2865:
2847:
2817:
2810:
2790:
2765:
2751:. 2018-01-25.
2749:Clapham School
2736:
2706:
2692:. 2017-10-13.
2677:
2663:. 2018-06-16.
2648:
2619:
2590:
2561:
2545:Inspired Ideas
2531:
2502:(4): 865–879.
2482:
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2059:Sir Cumference
2055:
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2039:
2034:
2027:
2024:
2023:
2021:
2018:
2017:
2016:
2011:
2006:
2001:
1996:
1991:
1986:
1981:
1976:
1969:
1966:
1925:
1922:
1869:
1866:
1865:
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1831:
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1826:
1798:
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1722:
1719:
1718:
1717:
1700:
1697:
1691:
1688:
1612:
1609:
1605:linear algebra
1591:calculations;
1506:modern algebra
1482:linear algebra
1360:
1357:
1356:
1355:
1347:
1336:drill and kill
1323:
1307:
1275:
1267:
1243:
1235:
1205:
1190:Discovery math
1187:
1184:human interest
1173:
1167:
1145:
1116:
1108:
1081:
1078:
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1076:
1053:
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1039:
1029:
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1004:
957:
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934:
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926:
923:
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917:
894:electronic age
890:
889:
874:
863:
860:
849:
842:
800:
797:
749:Robert Recorde
728:multiplication
681:
678:
620:Historians of
617:
614:
587:ancient Greece
574:
571:
569:
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289:
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255:
250:
245:
240:
238:Evidence-based
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217:
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212:
211:
210:
209:
204:
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197:Social science
194:
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14:
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10:
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7497:
7496:French Guiana
7494:
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7359:New Caledonia
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7339:Easter Island
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7071:United States
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6893:Faroe Islands
6891:
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6877:
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6868:
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6865:South Ossetia
6863:
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6717:Liechtenstein
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6487:South Ossetia
6485:
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6338:
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6328:
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6323:
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6310:
6308:
6305:
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6300:
6298:
6295:
6293:
6290:
6288:
6285:
6283:
6280:
6278:
6275:
6273:
6270:
6268:
6265:
6263:
6260:
6258:
6255:
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6250:
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6233:
6230:
6228:
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6223:
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6210:
6209:
6207:
6205:
6201:
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6192:
6177:
6173:
6169:
6166:
6160:
6156:
6153:
6147:
6144:
6138:
6134:
6130:
6127:
6126:
6123:
6115:
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6106:
6104:
6101:
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6021:
6019:
6016:
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6011:
6009:
6006:
6004:
6001:
5999:
5996:
5994:
5991:
5989:
5986:
5984:
5981:
5979:
5976:
5974:
5971:
5969:
5966:
5964:
5961:
5959:
5956:
5954:
5951:
5949:
5946:
5944:
5941:
5939:
5936:
5934:
5933:Guinea-Bissau
5931:
5929:
5926:
5924:
5921:
5919:
5916:
5914:
5911:
5909:
5906:
5904:
5901:
5899:
5896:
5894:
5891:
5889:
5886:
5884:
5881:
5879:
5876:
5874:
5871:
5869:
5866:
5864:
5861:
5859:
5856:
5854:
5851:
5849:
5846:
5844:
5841:
5839:
5836:
5834:
5831:
5829:
5826:
5824:
5821:
5819:
5816:
5815:
5813:
5809:
5805:
5800:
5796:
5789:
5785:
5774:
5770:
5766:
5765:
5761:
5736:
5731:
5728:
5724:
5723:Undergraduate
5721:
5720:
5715:
5712:
5711:
5707:
5702:
5699:
5697:
5694:
5690:
5687:
5686:
5681:
5678:
5659:
5653:
5649:
5648:Middle school
5646:
5645:
5640:
5637:
5636:
5631:
5628:
5627:
5622:
5619:
5600:
5594:
5589:
5588:
5583:
5580:
5579:
5574:
5571:
5570:
5565:
5562:
5552:
5547:
5544:
5540:
5537:
5536:
5531:
5528:
5527:
5524:
5521:
5519:
5516:
5514:
5511:
5509:
5506:
5505:
5500:
5496:
5491:
5487:
5477:
5474:
5472:
5469:
5467:
5464:
5462:
5459:
5457:
5454:
5452:
5449:
5447:
5444:
5443:
5441:
5437:
5431:
5428:
5424:
5421:
5419:
5416:
5414:
5413:Project-based
5411:
5409:
5408:Problem-based
5406:
5404:
5401:
5399:
5396:
5394:
5391:
5389:
5386:
5384:
5381:
5379:
5376:
5374:
5371:
5369:
5368:Demonstration
5366:
5364:
5363:Contemplative
5361:
5359:
5356:
5354:
5351:
5350:
5349:
5346:
5344:
5341:
5339:
5336:
5334:
5331:
5329:
5326:
5324:
5321:
5317:
5314:
5312:
5309:
5307:
5304:
5303:
5302:
5299:
5297:
5294:
5292:
5289:
5287:
5284:
5282:
5279:
5277:
5274:
5273:
5271:
5267:
5261:
5258:
5256:
5253:
5251:
5250:Homeschooling
5248:
5246:
5243:
5241:
5238:
5236:
5233:
5231:
5228:
5226:
5223:
5222:
5220:
5218:
5214:
5208:
5205:
5203:
5200:
5198:
5195:
5193:
5190:
5188:
5185:
5183:
5180:
5178:
5175:
5173:
5170:
5168:
5165:
5163:
5160:
5158:
5155:
5153:
5150:
5148:
5145:
5143:
5140:
5138:
5135:
5133:
5130:
5128:
5125:
5123:
5120:
5118:
5115:
5113:
5110:
5108:
5105:
5103:
5100:
5098:
5097:Environmental
5095:
5093:
5090:
5088:
5085:
5083:
5080:
5078:
5075:
5073:
5070:
5068:
5065:
5063:
5060:
5058:
5055:
5053:
5050:
5048:
5045:
5044:
5042:
5040:
5036:
5028:
5025:
5024:
5023:
5022:Instructional
5020:
5018:
5015:
5013:
5010:
5008:
5005:
5003:
5000:
4998:
4995:
4993:
4990:
4988:
4985:
4983:
4980:
4978:
4975:
4973:
4970:
4968:
4965:
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4960:
4958:
4955:
4953:
4950:
4948:
4945:
4941:
4938:
4936:
4933:
4931:
4928:
4926:
4925:Psychometrics
4923:
4919:
4916:
4915:
4914:
4911:
4910:
4909:
4906:
4904:
4901:
4899:
4896:
4895:
4893:
4889:
4883:
4880:
4878:
4875:
4873:
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4861:
4854:
4850:
4846:
4839:
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4832:
4827:
4825:
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4819:
4816:
4804:
4803:
4794:
4792:
4791:
4782:
4780:
4779:
4770:
4768:
4767:
4762:
4756:
4755:
4752:
4746:
4743:
4741:
4738:
4736:
4733:
4731:
4728:
4726:
4723:
4719:
4716:
4715:
4714:
4711:
4710:
4708:
4706:
4702:
4696:
4693:
4691:
4688:
4686:
4683:
4681:
4678:
4676:
4673:
4671:
4668:
4667:
4665:
4663:
4662:Computational
4659:
4651:
4648:
4646:
4643:
4641:
4638:
4637:
4636:
4633:
4631:
4628:
4626:
4623:
4621:
4618:
4616:
4613:
4611:
4608:
4606:
4603:
4601:
4598:
4596:
4593:
4591:
4588:
4586:
4583:
4581:
4578:
4577:
4575:
4573:
4569:
4563:
4560:
4558:
4555:
4553:
4550:
4548:
4545:
4543:
4540:
4539:
4537:
4535:
4531:
4525:
4522:
4520:
4517:
4515:
4512:
4510:
4507:
4506:
4504:
4502:
4501:Number theory
4498:
4492:
4489:
4487:
4484:
4482:
4479:
4477:
4474:
4472:
4469:
4467:
4464:
4462:
4459:
4458:
4456:
4454:
4450:
4444:
4441:
4439:
4436:
4434:
4433:Combinatorics
4431:
4430:
4428:
4426:
4422:
4416:
4413:
4411:
4408:
4406:
4403:
4401:
4398:
4396:
4393:
4391:
4388:
4386:
4385:Real analysis
4383:
4381:
4378:
4377:
4375:
4373:
4369:
4363:
4360:
4358:
4355:
4353:
4350:
4348:
4345:
4343:
4340:
4338:
4335:
4333:
4330:
4328:
4325:
4324:
4322:
4320:
4316:
4310:
4307:
4305:
4302:
4300:
4297:
4295:
4292:
4290:
4287:
4285:
4282:
4281:
4279:
4277:
4273:
4267:
4264:
4262:
4259:
4255:
4252:
4250:
4247:
4246:
4245:
4242:
4241:
4238:
4233:
4225:
4220:
4218:
4213:
4211:
4206:
4205:
4202:
4190:
4182:
4180:
4172:
4171:
4168:
4162:
4159:
4157:
4154:
4152:
4149:
4147:
4144:
4142:
4139:
4137:
4134:
4132:
4129:
4127:
4124:
4122:
4119:
4117:
4114:
4112:
4109:
4107:
4104:
4102:
4099:
4098:
4096:
4092:
4086:
4083:
4081:
4078:
4074:
4071:
4070:
4069:
4068:United States
4066:
4065:
4063:
4059:
4055:
4048:
4043:
4041:
4036:
4034:
4029:
4028:
4025:
4018:
4015:
4013:
4010:
4008:
4004:
3999:
3995:
3994:
3989:
3984:
3983:
3979:
3973:
3969:
3966:
3962:
3959:
3955:
3951:
3947:
3941:
3936:
3935:
3929:
3925:
3921:
3915:
3911:
3910:
3905:
3901:
3897:
3894:
3890:
3886:
3880:
3876:
3871:
3869:
3865:
3861:
3858:
3854:
3851:
3847:
3844:
3840:
3836:
3833:
3829:
3815:
3808:
3803:
3793:on 2010-06-26
3789:
3785:
3778:
3773:
3772:
3767:
3754:
3750:
3745:
3744:
3736:
3729:
3726:
3720:
3716:
3712:
3708:
3704:
3700:
3693:
3690:
3685:
3681:
3677:
3673:
3669:
3665:
3658:
3655:
3650:
3646:
3639:
3636:
3633:
3629:
3625:
3621:
3615:
3612:
3607:
3601:
3597:
3590:
3587:
3576:on 2007-02-02
3572:
3565:
3558:
3556:
3552:
3547:
3543:
3539:
3535:
3531:
3527:
3520:
3517:
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3508:
3504:
3500:
3495:
3490:
3486:
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3475:
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3460:
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3448:
3446:
3442:
3427:
3423:
3419:
3415:
3411:
3407:
3403:
3396:
3389:
3386:
3375:
3371:
3370:
3362:
3359:
3354:
3347:
3345:
3343:
3341:
3337:
3332:
3326:
3308:
3304:
3300:
3296:
3292:
3288:
3284:
3277:
3270:
3267:
3262:
3256:
3252:
3245:
3243:
3239:
3227:
3223:
3219:
3213:
3210:
3198:
3194:
3193:www.moctm.org
3190:
3184:
3181:
3170:on 2019-06-10
3169:
3165:
3161:
3155:
3152:
3140:
3136:
3132:
3126:
3123:
3118:
3114:
3110:
3106:
3102:
3098:
3091:
3088:
3075:
3071:
3065:
3062:
3050:
3046:
3042:
3036:
3033:
3022:on 2014-07-14
3021:
3017:
3011:
3008:
3003:
3001:1-889938-04-1
2997:
2993:
2989:
2985:
2978:
2975:
2971:
2965:
2960:
2955:
2950:
2945:
2941:
2934:
2931:
2923:
2916:
2910:
2907:
2894:
2890:
2886:
2882:
2876:
2873:
2868:
2866:9780888069498
2862:
2858:
2851:
2848:
2843:
2839:
2835:
2831:
2824:
2822:
2818:
2813:
2807:
2803:
2802:
2794:
2791:
2780:on 2011-11-20
2779:
2775:
2769:
2766:
2754:
2750:
2746:
2740:
2737:
2725:
2721:
2717:
2710:
2707:
2695:
2691:
2687:
2681:
2678:
2666:
2662:
2658:
2652:
2649:
2637:
2633:
2629:
2623:
2620:
2609:on 2019-07-17
2608:
2604:
2600:
2594:
2591:
2579:
2575:
2571:
2565:
2562:
2550:
2546:
2542:
2535:
2532:
2527:
2523:
2518:
2517:11250/3054903
2513:
2509:
2505:
2501:
2497:
2493:
2486:
2483:
2478:
2472:
2468:
2464:
2460:
2456:
2449:
2446:
2435:on 2008-12-08
2434:
2430:
2425:
2424:
2419:
2414:
2411:
2408:
2404:
2400:
2397:
2391:
2388:
2376:
2372:
2368:
2362:
2360:
2356:
2343:
2339:
2335:
2328:
2326:
2322:
2317:
2311:
2307:
2300:
2297:
2291:
2287:
2281:
2278:
2274:
2270:
2258:
2242:
2235:
2234:
2229:
2223:
2220:
2213:
2208:
2204:
2200:
2196:
2189:
2186:
2182:
2178:
2172:
2167:
2166:
2160:
2154:
2151:
2146:
2142:
2138:
2134:
2130:
2126:
2122:
2118:
2117:Math Horizons
2111:
2108:
2101:
2096:
2093:
2091:
2088:
2087:
2083:
2079:
2076:
2075:
2071:
2067:
2064:
2061:
2060:
2056:
2054:
2051:
2048:
2045:
2043:
2040:
2038:
2035:
2033:
2030:
2029:
2025:
2019:
2015:
2012:
2010:
2007:
2005:
2002:
2000:
1997:
1995:
1992:
1990:
1987:
1985:
1982:
1980:
1977:
1975:
1972:
1971:
1968:Organizations
1967:
1965:
1963:
1959:
1955:
1951:
1947:
1943:
1938:
1936:
1932:
1923:
1921:
1919:
1914:
1910:
1906:
1902:
1898:
1894:
1890:
1887:
1883:
1879:
1875:
1867:
1862:
1858:
1854:
1850:
1845:
1844:
1838:
1829:
1824:
1820:
1816:
1812:
1811:
1805:
1796:
1790:
1787:
1786:
1780:
1771:
1765:
1762:
1761:
1755:
1746:
1740:
1736:
1735:
1729:
1720:
1714:
1713:
1707:
1698:
1696:
1689:
1684:
1680:
1678:
1674:
1669:
1666:
1662:
1657:
1653:
1652:
1647:
1643:
1642:
1637:
1632:
1628:
1626:
1622:
1617:
1610:
1608:
1606:
1602:
1598:
1594:
1590:
1586:
1582:
1578:
1574:
1571:, as well as
1570:
1566:
1562:
1559:
1555:
1551:
1547:
1543:
1539:
1535:
1531:
1527:
1523:
1519:
1515:
1511:
1507:
1503:
1499:
1495:
1491:
1487:
1483:
1479:
1475:
1471:
1467:
1462:
1460:
1456:
1452:
1448:
1444:
1440:
1436:
1432:
1428:
1424:
1420:
1416:
1412:
1408:
1404:
1400:
1395:
1393:
1389:
1385:
1379:
1377:
1370:
1365:
1358:
1353:
1352:
1348:
1345:
1341:
1337:
1333:
1329:
1328:
1327:Rote learning
1324:
1321:
1317:
1313:
1312:
1308:
1305:
1301:
1297:
1296:word problems
1293:
1289:
1285:
1281:
1280:
1276:
1273:
1272:
1268:
1265:
1261:
1257:
1253:
1252:United States
1249:
1248:
1244:
1241:
1240:
1236:
1233:
1229:
1228:
1224:'s 1973 book
1223:
1219:
1215:
1211:
1210:
1206:
1203:
1199:
1195:
1191:
1188:
1185:
1181:
1177:
1174:
1171:
1168:
1165:
1161:
1157:
1153:
1149:
1146:
1143:
1139:
1135:
1134:
1128:
1124:
1120:
1117:
1114:
1113:
1109:
1106:
1105:
1101:
1100:
1096:
1090:
1086:
1079:
1074:
1071:education in
1070:
1066:
1062:
1058:
1054:
1051:
1047:
1044:
1040:
1038:
1034:
1030:
1028:
1024:
1020:
1016:
1013:
1009:
1005:
1002:
998:
994:
990:
986:
982:
978:
974:
970:
966:
962:
958:
955:
951:
950:
949:
942:
935:
933:
927:
924:
921:
918:
915:
914:
913:
911:
907:
906:number theory
903:
899:
895:
887:
883:
879:
875:
872:
868:
865:In 1968, the
864:
861:
858:
854:
850:
847:
843:
840:
836:
835:
834:
831:
829:
824:
822:
818:
814:
810:
806:
798:
796:
794:
790:
786:
782:
777:
775:
774:Rhind Papyrus
771:
767:
763:
759:
754:
750:
745:
742:
737:
733:
729:
725:
721:
717:
713:
709:
705:
701:
694:
693:
686:
679:
677:
675:
674:
670:
666:
662:
658:
654:
650:
646:
642:
637:
635:
631:
627:
623:
615:
613:
611:
610:Rhind papyrus
607:
603:
599:
596:
592:
588:
584:
580:
579:ancient Egypt
572:
567:
565:
563:
559:
553:
551:
548:
544:
540:
536:
532:
528:
524:
520:
508:
503:
501:
496:
494:
489:
488:
486:
485:
482:
478:
473:
462:
459:
457:
454:
452:
449:
447:
444:
442:
439:
437:
434:
432:
429:
427:
424:
422:
419:
418:
412:
411:
404:
400:
397:
395:
392:
390:
386:
383:
381:
378:
376:
372:
369:
367:
364:
362:
359:
357:
356:Number theory
354:
353:
350:
345:
344:
341:
340:
335:
332:
330:
327:
326:
325:
324:
321:
317:
313:
312:
302:
297:
295:
290:
288:
283:
282:
280:
279:
274:
271:
269:
266:
264:
261:
259:
258:Meta-analysis
256:
254:
251:
249:
246:
244:
241:
239:
236:
234:
231:
229:
226:
224:
221:
220:
219:
218:
213:
208:
205:
203:
200:
198:
195:
193:
190:
188:
185:
183:
180:
178:
175:
173:
170:
168:
165:
163:
160:
158:
155:
153:
150:
148:
145:
144:
143:
142:
137:
132:
129:
127:
124:
122:
119:
117:
114:
112:
109:
107:
104:
102:
99:
97:
94:
92:
89:
86:
82:
79:
77:
74:
72:
69:
67:
64:
62:
59:
57:
54:
53:
52:
51:
46:
43:
39:
32:
19:
7523:
7479:Dependencies
7310:Dependencies
7296:Cook Islands
7176:Sint Maarten
7156:Saint Martin
6870:Transnistria
6502:Dependencies
6432:Turkmenistan
6397:Saudi Arabia
6168:Saint Helena
6139:
6043:South Africa
6033:Sierra Leone
5838:Burkina Faso
5730:Postgraduate
5546:Kindergarten
5398:Personalized
5378:Experiential
5338:Teacher look
5121:
5047:Agricultural
4903:Anthropology
4800:
4788:
4776:
4757:
4744:
4690:Optimization
4552:Differential
4476:Differential
4443:Order theory
4438:Graph theory
4342:Group theory
4053:
3991:
3971:
3953:
3933:
3912:. Springer.
3908:
3904:English, Lyn
3892:
3874:
3863:
3856:
3838:
3831:
3821:. Retrieved
3795:. Retrieved
3788:the original
3783:
3758:20 September
3756:. Retrieved
3752:
3737:. p. 1.
3734:
3728:
3705:(9): 561–4.
3702:
3698:
3692:
3667:
3663:
3657:
3648:
3638:
3614:
3595:
3589:
3578:. Retrieved
3571:the original
3529:
3525:
3519:
3487:(5): 25–31.
3484:
3480:
3474:
3463:. Retrieved
3433:. Retrieved
3405:
3401:
3388:
3378:, retrieved
3368:
3361:
3352:
3325:cite journal
3314:. Retrieved
3286:
3282:
3269:
3250:
3230:. Retrieved
3221:
3212:
3201:. Retrieved
3192:
3183:
3172:. Retrieved
3168:the original
3163:
3154:
3143:. Retrieved
3134:
3125:
3103:(1): 16–29.
3100:
3096:
3090:
3078:. Retrieved
3064:
3053:. Retrieved
3044:
3035:
3024:. Retrieved
3020:the original
3010:
2983:
2977:
2959:10183/164060
2939:
2933:
2922:the original
2909:
2899:17 September
2897:. Retrieved
2893:the original
2888:
2875:
2856:
2850:
2833:
2829:
2800:
2793:
2782:. Retrieved
2778:the original
2768:
2757:. Retrieved
2748:
2739:
2728:. Retrieved
2719:
2709:
2698:. Retrieved
2689:
2680:
2669:. Retrieved
2660:
2651:
2640:. Retrieved
2631:
2628:"Heuristics"
2622:
2611:. Retrieved
2607:the original
2602:
2593:
2582:. Retrieved
2574:www.pitt.edu
2573:
2564:
2553:. Retrieved
2544:
2534:
2499:
2495:
2485:
2458:
2448:
2437:. Retrieved
2433:the original
2421:
2413:
2390:
2379:. Retrieved
2370:
2346:. Retrieved
2305:
2299:
2289:
2280:
2256:
2248:. Retrieved
2232:
2228:Høyrup, Jens
2222:
2202:
2198:
2188:
2180:
2164:
2153:
2120:
2116:
2110:
2057:
1939:
1927:
1912:
1897:case studies
1891:
1871:
1819:number sense
1693:
1670:
1649:
1639:
1633:
1629:
1618:
1614:
1597:optimization
1550:graph theory
1534:optimization
1463:
1427:trigonometry
1414:
1407:pre-calculus
1396:
1380:
1376:honors class
1373:
1349:
1335:
1325:
1309:
1302:such as the
1277:
1269:
1245:
1237:
1225:
1222:Morris Kline
1207:
1198:manipulative
1189:
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1169:
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1136:taught as a
1132:
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1069:liberal arts
1037:modern world
973:trigonometry
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7553:WikiProject
7243:New Zealand
7146:Puerto Rico
7056:Saint Lucia
7006:El Salvador
6908:Isle of Man
6843:recognition
6817:Switzerland
6752:Netherlands
6561:Asia portal
6462:States with
6382:Philippines
6322:South Korea
6317:North Korea
6212:Afghanistan
6095:recognition
6048:South Sudan
5938:Ivory Coast
5654:High school
5451:Definitions
5328:Lesson plan
5217:Alternative
5122:Mathematics
5092:Engineering
4802:WikiProject
4645:Game theory
4625:Probability
4362:Homological
4352:Multilinear
4332:Commutative
4309:Type theory
4276:Foundations
4232:mathematics
4101:Traditional
3986:‹ The
3670:(9): 3–13.
3408:(1): 7–74.
2255:, p. 406, "
2205:: 277–318.
2090:Dyscalculia
1931:biomedicine
1868:Methodology
1861:equals sign
1815:basic facts
1577:Theoretical
1554:permutation
1455:Probability
1443:exponential
1384:measurement
1318:or solving
1127:Middle Ages
997:probability
989:percentages
977:probability
839:Felix Klein
734:) arose at
724:subtraction
700:Middle Ages
622:Mesopotamia
535:mathematics
446:Linguistics
436:Computation
431:Geosciences
394:Probability
320:Mathematics
253:Focus group
223:Case method
182:Mathematics
167:Engineering
48:Disciplines
7568:Categories
7141:Montserrat
7136:Martinique
7131:Guadeloupe
6986:Costa Rica
6787:San Marino
6747:Montenegro
6727:Luxembourg
6707:Kazakhstan
6610:Azerbaijan
6442:Uzbekistan
6417:Tajikistan
6332:Kyrgyzstan
6312:Kazakhstan
6232:Bangladesh
6222:Azerbaijan
6150:(Portugal)
6108:Somaliland
6028:Seychelles
5993:Mozambique
5978:Mauritania
5963:Madagascar
5918:The Gambia
5853:Cape Verde
5706:Continuing
5696:Vocational
5301:Curriculum
5235:Democratic
5207:Vocational
5197:Technology
5157:Philosophy
5039:By subject
5017:Technology
4997:Psychology
4982:Philosophy
4972:Leadership
4913:Evaluation
4908:Assessment
4630:Statistics
4509:Arithmetic
4471:Arithmetic
4337:Elementary
4304:Set theory
3823:2009-08-06
3797:2011-09-25
3580:2013-03-25
3465:2009-11-15
3435:2018-07-25
3380:2012-05-08
3316:2019-11-30
3232:2019-10-14
3203:2018-02-11
3174:2017-07-28
3145:2017-07-28
3055:2019-01-02
3026:2014-06-18
2842:1761255371
2836:(7): 4–9.
2784:2011-11-29
2759:2019-02-12
2730:2018-06-21
2700:2018-06-19
2671:2018-06-19
2642:2019-02-12
2613:2019-02-12
2584:2019-02-12
2555:2019-02-12
2439:2007-09-04
2407:HathiTrust
2381:2018-04-10
2286:Robson, E.
2250:2022-11-15
2102:References
1935:psychology
1918:hypotheses
1895:, such as
1857:minus sign
1514:set theory
1459:statistics
1415:Ă la carte
1284:creativity
1232:Tom Lehrer
1214:set theory
1152:arithmetic
1123:quadrivium
1050:heuristics
1001:statistics
981:statistics
961:arithmetic
936:Objectives
902:arithmetic
876:The first
871:Nottingham
821:curriculum
813:arithmetic
657:arithmetic
653:quadrivium
634:Pythagoras
456:Philosophy
399:Statistics
389:Set theory
207:Vocational
202:Technology
91:Technology
81:Psychology
76:Philosophy
66:Evaluation
7468:Venezuela
7413:Argentina
7213:Australia
7126:Greenland
7041:Nicaragua
7016:Guatemala
6898:Gibraltar
6722:Lithuania
6528:Hong Kong
6482:Palestine
6407:Sri Lanka
6402:Singapore
6282:Indonesia
5983:Mauritius
5539:Preschool
5439:Wikimedia
5177:Religious
5102:Euthenics
5087:Economics
5067:Chemistry
5057:Bilingual
5012:Sociology
4967:Inclusion
4947:Economics
4845:Education
4557:Geometric
4547:Algebraic
4486:Euclidean
4461:Algebraic
4357:Universal
4116:Singapore
4085:Australia
4061:Geography
3719:143471869
3546:144583638
3511:145667765
3489:CiteSeerX
3422:143347721
3303:149999527
3117:144948416
2145:126067145
1611:Standards
1388:fractions
1351:Math walk
1311:Exercises
1288:heuristic
1218:functions
1202:math wars
1131:Euclid's
987:(such as
795:in 1662.
690:Euclid's
647:into the
547:scholarly
527:didactics
519:education
461:Education
451:Economics
426:Chemistry
7543:Category
7458:Suriname
7448:Paraguay
7433:Colombia
7228:Kiribati
7091:Anguilla
7026:Honduras
6996:Dominica
6971:Barbados
6918:Svalbard
6903:Guernsey
6850:Abkhazia
6802:Slovenia
6797:Slovakia
6772:Portugal
6630:Bulgaria
6551:Category
6472:Abkhazia
6422:Thailand
6377:Pakistan
6357:Mongolia
6352:Maldives
6347:Malaysia
6247:Cambodia
6174: /
6170: /
6163:(France)
6157: /
6135: /
6131: /
6083:Zimbabwe
6058:Tanzania
5908:Ethiopia
5903:Eswatini
5883:Djibouti
5848:Cameroon
5833:Botswana
5423:Socratic
5383:Feedback
5269:Concepts
5162:Physical
5132:Military
5112:Language
5062:Business
5002:Research
4992:Politics
4977:Pedagogy
4872:Glossary
4857:Overview
4778:Category
4534:Topology
4481:Discrete
4466:Analytic
4453:Geometry
4425:Discrete
4380:Calculus
4372:Analysis
4327:Abstract
4266:Glossary
4249:Timeline
4179:Category
4161:Critical
4146:Informal
4106:Exercise
4094:Approach
4073:New York
3988:template
3961:Archived
3906:(2010).
3846:Archived
3814:Archived
3684:14742527
3647:(2002),
3459:Archived
3426:Archived
3374:archived
3307:Archived
3226:Archived
3224:. 2018.
3197:Archived
3139:Archived
3074:Archived
3049:Archived
2838:ProQuest
2753:Archived
2724:Archived
2694:Archived
2665:Archived
2636:Archived
2578:Archived
2549:Archived
2526:35291444
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2288:(2008).
2273:Eshnunna
2241:Archived
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2020:See also
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1403:geometry
1209:New Math
1138:paradigm
1133:Elements
1097:in Laos.
1033:calculus
1012:function
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969:geometry
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768:and the
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661:geometry
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6690:Iceland
6685:Hungary
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6670:Georgia
6660:Finland
6655:Estonia
6650:Denmark
6635:Croatia
6620:Belgium
6615:Belarus
6605:Austria
6600:Armenia
6595:Andorra
6590:Albania
6447:Vietnam
6362:Myanmar
6342:Lebanon
6272:Georgia
6227:Bahrain
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6133:Ceuta
6053:Sudan
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5958:Libya
5943:Kenya
5923:Ghana
5913:Gabon
5888:Egypt
5828:Benin
5476:Texts
5446:Books
5147:Peace
5137:Music
5117:Legal
5077:Death
4877:Index
4718:lists
4261:Lists
4234:areas
4156:Ethno
4121:Saxon
3817:(PDF)
3810:(PDF)
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6991:Cuba
6372:Oman
6337:Laos
6292:Iraq
6287:Iran
6063:Togo
5973:Mali
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3940:ISBN
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3879:ISBN
3760:2023
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