930:
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1926:, 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.
1727:
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.
1078:
4750:
1668:(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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2283:: 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."
1402:) 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
1643:, 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
1909:, 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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1780:
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
1917:
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
727:
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
1726:
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
1683:
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
1730:
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
1370:
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,
1081:
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
1704:
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'
1755:
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
1619:
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
1161:: 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.
1900:, 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
1656:
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.
901:'." 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:
1877:
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.
544:
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.
1835:
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
1604:
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.
732:
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.
1647:
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
7489:
1904:
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
1209:, 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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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:
2170:
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.
2206:: 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."
1223:'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."
3553:"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,
1363:
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
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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,
2653:
1810:, 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
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2976:
2002:
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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.
3612:
3513:
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".
2222:
Babylon: Focus mesopotamischer
Geschichte, Wiege früher Gelehrsamkeit, Mythos in der Moderne. 2. Internationales Colloquium der Deutschen Orient-Gesellschaft 24.–26. März 1998 in Berlin
691:, 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:
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Mathematics, Mathematical
Literacy and Technical Mathematics.) Thus, a science-oriented curriculum typically overlaps the first year of university mathematics, and includes
908:
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;
765:
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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665:. 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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1937:, 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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1319:: 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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1962:
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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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2184:"Methods and traditions of Babylonian mathematics: Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations"
1104:: involves the use of computers to teach mathematics. Mobile applications have also been developed to help students learn mathematics.
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2219:. "Pythagorean 'Rule' and 'Theorem' – Mirror of the Relation Between Babylonian and Greek Mathematics". In Renger, Johannes (ed.).
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1295:. 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",
1231:: 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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1303:: the reinforcement of mathematical skills by completing large numbers of exercises of a similar type, such as adding
1139:: the gradual and systematic guiding through the hierarchy of mathematical notions, ideas and techniques. Starts with
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1185:) mathematics which centres around problem-based or inquiry-based learning, with the use of open-ended questions and
972:) to most students, to equip them to follow a trade or craft and to understand mathematics commonly used in news and
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621:(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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1945:) responded to ongoing controversy by extending its research base to include non-experimental studies, including
1612:, for example, standards for mathematics education are set as part of the National Curriculum for England, while
3005:"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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2228:. Berlin: Deutsche Orient-Gesellschaft / Saarbrücken: SDV Saarbrücker Druckerei und Verlag. pp. 393–407.
1933:(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
1263:: 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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1247:, focused on deepening student understanding of mathematical ideas and procedures, and formalized by the
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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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1343:: 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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3796:"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?."
2646:"Passing Mathematics Just Got Easier For Students With This New Platform: Mathematica - Techzim"
2481:"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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Elementary mathematics were a core part of education in many ancient civilisations, including
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opportunities to learn. This must involve both skill efficiency and conceptual understanding.
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results are examples of some of the current findings in the field of mathematics education.
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Researchers continued arguing the urgency of making the transition throughout the 2000s; and
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1096:: an approach based on the use of mathematical software as the primary tool of computation.
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837:(ICMI) was founded in 1908, and Felix Klein became the first president of the organisation.
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The social status of mathematical study was improving by the seventeenth century, with the
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3265:"International large-scale assessments, affective worlds and policy impacts in education"
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creating a Mathematics Chair in 1613, followed by the Chair in Geometry being set up in
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1549:
1526:
1308:
1235:
1182:
1148:
1144:
1007:
953:
886:
746:
696:
583:
469:
373:
221:
165:
160:
140:
49:
44:
2904:"Foundations for Success: The Final Report of the National Mathematics Advisory Panel"
1731:
challenging, well-implemented teaching, or unintentionally confusing, faulty teaching.
1030:
The teaching of advanced mathematics to those students who wish to follow a career in
893:", the emerging structural approach to knowledge had "small children meditating about
736:
The first mathematics textbooks to be written in English and French were published by
7441:
7337:
7289:
7211:
6979:
6545:
6360:
6325:
6280:
6275:
6184:
6051:
5961:
5851:
5757:
5689:
5501:
5483:
5361:
5331:
5304:
5294:
5284:
5279:
5248:
5180:
5170:
5155:
5115:
4923:
4906:
4749:
4469:
4454:
4398:
4345:
4099:
3928:
3921:
3902:
3867:
3846:
Uses of technology in lower secondary mathematics education: A concise topical survey
3707:
3588:
3582:
3534:
3499:
3410:
3291:
3243:
3105:
2984:
2952:
2849:
2794:
2510:
2479:
Greefrath, Gilbert; Siller, Hans‑Stefan; Vorhölter, Katrin; Kaiser, Gabriele (2022).
2459:
2298:
2200:
2183:
2159:
2133:
1934:
1427:
1419:
1320:
1171:
within a historical, social, and cultural context. Proponents argue it provides more
1083:
1049:
996:
816:
465:
180:
114:
94:
73:
3672:
2444:"Discrete mathematics is essential mathematics in a 21st century school curriculum."
2264:
concerning the computation of the sides of a rectangle given its area and diagonal.)
5761:
5677:
5618:
5381:
5376:
5346:
5233:
5228:
5190:
5095:
5070:
4975:
4683:
4658:
4530:
4378:
4315:
4144:
3888:
3695:
3660:
3633:
3522:
3487:
3398:
3279:
3093:
2942:
2932:
2869:
2500:
2492:
2451:
2406:
2195:
2117:
2113:
2030:
1486:
1011:
845:
805:
704:
535:
261:
104:
99:
89:
3283:
5341:
5336:
5218:
5213:
5135:
5130:
5125:
5105:
5065:
4623:
4550:
4479:
4272:
3981:
3953:
3916:
3896:
3838:
2830:
2788:
2391:
2041:
2035:
1889:
1874:
1803:
1534:
1530:
1439:
1423:
1304:
1267:
882:
750:
391:
231:
119:
3961:
Developing 21st Century Competencies In The Mathematics Classroom: Yearbook 2016
3443:
2937:
2455:
7520:
5561:
5274:
4701:
4628:
4335:
4104:
2980:
2496:
2274:
2047:
1862:
1593:
1514:
1494:
1474:
1470:
1172:
1045:
737:
716:
575:
419:
5439:
3664:
3526:
3491:
3097:
2216:
1201:: a method of teaching mathematics which focuses on abstract concepts such as
7556:
6539:
5636:
5238:
5175:
5040:
4913:
4489:
4421:
4373:
3976:
3699:
3402:
2448:
Teaching and learning discrete mathematics worldwide: Curriculum and research
1315:
1240:
894:
815:
By the twentieth century, mathematics was part of the core curriculum in all
762:
598:
586:
567:
344:
246:
5449:
3991:
3943:
The mathematics education of prospective secondary teachers around the world
3882:
The mathematics education of prospective secondary teachers around the world
3585:
Experimental and quasi-experimental designs for generalized causal inference
5534:
5464:
5326:
4431:
4426:
4330:
2514:
1950:
1885:
1807:
1546:
1538:
1522:
1415:
1395:
1364:
1210:
1025:
961:
633:
579:
5459:
4188:
4005:
3240:
The Experience of Middle-Income Countries Participating in PISA 2000. PISA
2104:
Dudley, Underwood (April 2002). "The World's First Mathematics Textbook".
1671:
1633:
in 2000 for the United States and Canada, which boosted the trend towards
673:
19:
6549:
5316:
4633:
4297:
4220:
3892:
2505:
2078:
1919:
1897:
1849:
1542:
1443:
1372:
1115:
1031:
985:
965:
827:
712:
700:
688:
610:
523:
382:
308:
241:
211:
4011:
3358:
Trends in International Mathematics and Science Study (TIMSS) - Overview
2947:
2125:
5289:
4618:
4497:
4292:
4109:
3722:
Sparks, Sarah (October 20, 2010). "Federal Criteria For Studies Grow".
2977:
International Association for the Evaluation of Educational Achievement
2395:
2003:
International Association for the Evaluation of Educational Achievement
1923:
1906:
1502:
1447:
1272:
1220:
1202:
1151:
taught concurrently. Requires the instructor to be well informed about
1140:
1111:
1038:
989:
977:
969:
949:
898:
890:
859:
809:
801:
797:
645:
641:
622:
387:
377:
3551:
Working Group on Statistics in Mathematics Education Research (2007).
1806:, answer impulsively, struggle with mental representations, have poor
5527:
5090:
4833:
4008:. David Klein. California State University, Northridge, United States
2983:
Center for the Study of Testing, Evaluation, and Educational Policy.
1339:
1276:
1190:
571:
515:
507:
3262:
4965:
4522:
4441:
4368:
4129:
3342:
The Effects of Classroom Mathematics Teaching on Students' Learning
2261:
1777:
1653:
1613:
1506:
1399:
1391:
1376:
1197:
1126:
1021:
973:
957:
942:
708:
649:
538:
531:
527:
519:
359:
349:
3583:
Shadish, William R.; Cook, Thomas D.; Campbell, Donald T. (2002).
3177:
3149:"Standards in Your State - Common Core State Standards Initiative"
2790:
Crossroads in the History of Mathematics and Mathematics Education
1041:
and other problem-solving strategies to solve non-routine problems
881:
Midway through the twentieth century, the cultural impact of the "
5160:
4307:
3821:
Uses of Technology in Primary and Secondary Mathematics Education
2926:
2295:
Pythagoras : His Lives and the Legacy of a Rational Universe
2253:
1609:
1569:
1387:
729:
354:
3801:. Cambridge MA: Center for the Study of Mathematics Curriculum.
2909:. U.S. Department of Education. 2008. p. 20. Archived from
2793:. Monograph Series in Mathematics Education. Vol. 12. IAP.
1529:. Specific topics are taught within other courses: for example,
1279:
thinking by setting students open-ended, unusual, and sometimes
3995:
3354:
3263:
Sellar, S., & Lingard, B., Sam; Lingard, Bob (April 2018).
1244:
874:
804:, became essential in this new urban lifestyle. Within the new
677:
Illustration at the beginning of a 14th-century translation of
657:
4006:
A quarter century of US 'math wars' and political partisanship
2478:
2878:
For First European Congress of Mathematics, Paris, July, 1992
981:
855:
629:
594:
4802:
3963:(Association Of Mathematics Educators. 2016) pp. 33–50.
3206:
1576:
is usually limited to introductory calculus and (sometimes)
1193:" debate with many criticizing it for declining math scores.
3356:
1997:
1665:
1375:
are taught, in both numeric and pictorial form, as well as
877:
in 1972, and after that, it has been held every four years.
870:
590:
3763:
3120:"Myths vs. Facts - Common Core State Standards Initiative"
2931:, Cham: Springer International Publishing, pp. 1–50,
1666:
Organisation for the Economic Co-operation and Development
1335:, definitions, formulas, and other aspects of mathematics.
3638:
Evidence Matters: Randomized Trials in Education Research
3272:
International Journal of Qualitative Studies in Education
1552:. Pure and applied math degrees often include modules in
16:
Teaching, learning, and scholarly research in mathematics
1873:
to answer specific questions, such as whether a certain
1239:: a vision for pre-college mathematics education in the
1032:
science, technology, engineering, and mathematics (STEM)
1024:) as an example of the intellectual achievements of the
995:
The teaching of abstract mathematical concepts (such as
753:
works on mathematics came from Egypt in the form of the
707:. The first modern arithmetic curriculum (starting with
589:. In most cases, formal education was only available to
2848:. Toronto, Ontario: C.D. Howe Institute. pp. 4–5.
1020:
The teaching of selected areas of mathematics (such as
1006:
The teaching of selected areas of mathematics (such as
3558:. The American Statistical Association. Archived from
2874:"The Unreasonable Utility of Recreational Mathematics"
2734:"Classical Education and STEM: a Common Misconception"
2394:, Forest Hills, N.Y. : Stevinus Press, link from
1968:
American Mathematical Association of Two-Year Colleges
1481:
in mathematics substantively comprises these courses.
644:, the quadrivium included the mathematical fields of
2356:"Why We Learn Math Lessons That Date Back 500 Years"
2323:"Why We Learn Math Lessons That Date Back 500 Years"
1383:, patterns, and various topics related to geometry.
1114:, part of the classical education curriculum of the
835:
International Commission on Mathematical Instruction
2014:
652:. This structure was continued in the structure of
593:children with sufficiently high status, wealth, or
3920:
3793:
2817:Ansari, Daniel (March 2016). "No More Math Wars".
2151:
808:systems, mathematics became a central part of the
3766:"Radical Constructivism and Cognitive Psychology"
3738:"Accelerated Math: What Every Parent Should Know"
2973:Third International Mathematics and Science Study
2320:
1358:Aalto University School of Science and Technology
7554:
3438:
3436:
3434:
3335:
3333:
3331:
3329:
2705:"This Free App Will Solve Math Problems For You"
2051:, children's mathematics educational book series
1781:skills, but not broader measures of achievement.
1537:, and "math for computer science" might include
867:International Congress on Mathematical Education
3915:
3887:
3631:
3061:. UK Department of Education. 17 January 2013.
2846:What to Do About Canada's Declining Math Scores
1630:Principles and Standards for School Mathematics
1253:Principles and Standards for School Mathematics
749:. After the Sumerians, some of the most famous
597:. The oldest known mathematics textbook is the
7386:
6936:
2181:
1662:Programme for International Student Assessment
1371:multiplication, and division. Comparisons and
1219:. The New Math method was the topic of one of
4818:
4204:
4027:
3861:
3431:
3340:Hiebert, James; Grouws, Douglas (2007), "9",
3339:
3326:
2279:Mathematics in Ancient Iraq: A Social History
1785:
1271:: the cultivation of mathematical ingenuity,
695:, it was seen as subservient to the study of
541:into the transfer of mathematical knowledge.
487:
281:
7491:South Georgia and the South Sandwich Islands
3546:
3544:
3318:: CS1 maint: multiple names: authors list (
2970:
2252:-146, somewhere between 2300 and 1825 BC." (
2158:. New York: Dover Publications. p. 36.
2072:
1861:As with other educational research (and the
668:
4218:
3381:
3375:
2530:"5 Approaches to Teaching PreK-12 Numeracy"
1993:National Council of Teachers of Mathematics
1963:Advisory Committee on Mathematics Education
1709:
1625:National Council of Teachers of Mathematics
1497:. Other topics in pure mathematics include
1249:National Council of Teachers of Mathematics
848:, sorting them into their various subjects.
553:in order to improve mathematics education.
23:A child calculating with his fingers (2006)
4825:
4811:
4211:
4197:
4034:
4020:
3587:(2nd ed.). Boston: Houghton Mifflin.
3515:Educational Evaluation and Policy Analysis
3467:
2868:
2441:
2146:
2067:Mathematics education in the United States
1814:, and encouraging students to think aloud.
494:
480:
288:
274:
4041:
3855:(Birkhäuser, Cham, 2016) pp. 71–89.
3650:
3541:
3481:
2946:
2936:
2702:
2679:Technology Solutions That Drive Education
2527:
2504:
2199:
1442:in their final year of secondary school;
1347:
1110:: the teaching of mathematics within the
7188:
3985:) is being considered for deletion. See
3794:Auslander, Maurice; et al. (2004).
3237:
2786:
2385:A Bibliography of Mathematical Education
2350:
2348:
2292:
2060:
1386:At high school level in most of the US,
1351:
1076:
928:
672:
547:National and international organisations
18:
6563:
5791:
5780:
3242:. France: OECD Publishing. p. 30.
2675:"5 Apps to Help All Students with Math"
2442:Hart, Eric W.; Martin, W. Gary (2018).
2316:
2314:
2112:(4). Taylor & Francis, Ltd.: 8–11.
1735:
1181:: a constructivist method of teaching (
948:The teaching of practical mathematics (
856:Shell Centre for Mathematical Education
7555:
3721:
3083:
2843:
2816:
2273:
2260:is an Old Babylonian clay tablet from
2103:
1973:Association of Teachers of Mathematics
1941:(essentially the research arm for the
1840:. They prefer arithmetic reasoning to
1818:
604:
7385:
7187:
6935:
6562:
6183:
6182:
5790:
5779:
5481:
4844:
4806:
4192:
4015:
3685:
3233:
3231:
2812:
2810:
2528:Education, McGraw-Hill (2017-10-20).
2450:. ICME-13 Monographs. pp. 3–19.
2345:
2038:, primary level mathematics education
1283:. The problems can range from simple
4773:
4173:
3823:(Cham, Switzerland: Springer, 2018).
3773:Brookings Papers on Education Policy
3735:
3512:
3506:
2311:
1912:
1687:
1485:study additional other areas within
1101:Computer-based mathematics education
873:in 1969. The second congress was in
792:In the 18th and 19th centuries, the
7537:
4785:
3613:National Mathematics Advisory Panel
3384:"Assessment and Classroom Learning"
2703:Mosbergen, Dominique (2014-10-22).
1931:National Mathematics Advisory Panel
1293:International Mathematical Olympiad
941:The teaching and learning of basic
933:Boy doing sums, Guinea-Bissau, 1974
13:
3756:
3228:
3030:"Mathematics for Computer Science"
2807:
2333:from the original on 10 April 2018
2215:
1670:
1517:subject in its own right, such as
14:
7579:
4001:History of Mathematical Education
3989:to help reach a consensus. ›
3968:
3898:Theories of Mathematics Education
3884:(Springer, Cham, 2017) pp. 25-32.
3382:Black, P.; Wiliam, Dylan (1998).
2321:Gabrielle Emanuel (23 Jul 2016).
2246:To judge from this evidence alone
1453:At college and university level,
1331:, rote learning is used to teach
885:" (McLuhan) was also taken up by
7568:Mathematical science occupations
7536:
7527:
7526:
7514:
7050:Saint Vincent and the Grenadines
6544:
6535:
6534:
6092:Sahrawi Arab Democratic Republic
5862:Democratic Republic of the Congo
5756:
4784:
4772:
4761:
4760:
4748:
4172:
4163:
4162:
3361:, U.S. Department of Education,
2297:. London: Icon. pp. 78–84.
2015:Aspects of mathematics education
1956:
1947:regression discontinuity designs
464:
4669:Computational complexity theory
3941:Strutchens, Marilyn E., et al.
3828:Journal fĂĽr Mathematik-Didaktik
3808:from the original on 2010-07-15
3736:Voit, Rita (14 February 2020).
3715:
3679:
3644:
3625:
3601:
3576:
3461:
3450:from the original on 2014-10-02
3420:from the original on 2018-07-26
3365:from the original on 2012-05-08
3348:
3301:from the original on 2020-03-07
3256:
3217:from the original on 2018-03-04
3199:
3188:from the original on 2018-02-12
3170:
3141:
3130:from the original on 2017-08-02
3112:
3086:Journal of Educational Research
3077:
3065:from the original on 2 May 2012
3051:
3040:from the original on 2019-05-10
3022:
2997:
2964:
2920:
2896:
2862:
2837:
2780:
2755:
2744:from the original on 2019-02-12
2726:
2715:from the original on 2017-09-22
2696:
2685:from the original on 2021-12-26
2667:
2656:from the original on 2018-06-19
2638:
2627:from the original on 2019-04-06
2609:
2580:
2569:from the original on 2019-01-30
2551:
2540:from the original on 2021-12-26
2521:
2472:
2435:
2400:
2366:from the original on 2018-04-10
2235:from the original on 2021-02-25
2154:The exact sciences in antiquity
1287:to problems from international
1175:than the conventional approach.
1118:, which was typically based on
1044:The teaching of mathematics in
796:led to an enormous increase in
613:have confirmed that use of the
549:regularly hold conferences and
7207:Federated States of Micronesia
6502:British Indian Ocean Territory
3927:. Princeton University Press.
2418:"McLuhan: Understanding Media"
2377:
2286:
2267:
2209:
2175:
2140:
2118:10.1080/10724117.2002.11975154
2097:
2021:Cognitively Guided Instruction
1856:
1519:partial differential equations
1473:; at several US colleges, the
1052:, as well as in some selected
1:
4832:
3974:
3640:, Brookings Institution Press
3617:Scientifically based research
3284:10.1080/09518398.2018.1449982
2763:"Mathematical Current Events"
2281:. Princeton University Press.
2090:
2026:Critical mathematics pedagogy
1978:Canadian Mathematical Society
1637:. In 2006, the NCTM released
1450:are similarly often taught.
1082:"Discovery Day" organized by
924:
778:Lucasian Chair of Mathematics
601:, dated from circa 1650 BCE.
7175:United States Virgin Islands
4845:
3775:(1): 227–278. Archived from
2201:10.1016/0315-0860(81)90069-0
1599:
7:
6937:Education in North America
3866:. Bellevue Literary Press.
3742:Resources by HEROES Academy
3444:"Research clips and briefs"
3238:Lockheed, Marlaine (2015).
2938:10.1007/978-3-319-45113-8_1
2456:10.1007/978-3-319-70308-4_1
2008:
1852:to mean "the answer is...".
1760:
1678:
1645:Common Core State Standards
1236:Standards-based mathematics
759:Moscow Mathematical Papyrus
10:
7584:
7387:Education in South America
5482:
4719:Films about mathematicians
2787:Sriraman, Bharath (2012).
2497:10.1007/s11858-022-01339-5
1929:In the United States, the
1869:includes studies that use
1786:Students with difficulties
1596:, and sometimes analysis.
1169:development of mathematics
1068:
755:Rhind Mathematical Papyrus
561:
556:
404:Relationship with sciences
7508:
7465:
7392:
7298:
7275:
7194:
7150:Saint Pierre and Miquelon
7068:
6942:
6915:
6867:
6829:
6571:
6530:
6489:
6449:
6191:
6105:
6080:
5799:
5786:
5775:
5751:
5705:
5671:
5630:
5612:
5573:
5555:
5521:
5497:Early childhood education
5490:
5477:
5427:
5257:
5204:
5026:
4879:
4851:
4840:
4742:
4692:
4649:
4559:
4521:
4488:
4440:
4412:
4359:
4306:
4288:Philosophy of mathematics
4263:
4228:
4158:
4082:
4049:
3665:10.3102/0013189x033009003
3527:10.3102/01623737024003175
3492:10.3102/0013189X034005025
3098:10.1080/00220670009598739
2485:ZDM–Mathematics Education
2383:William L. Schaaf (1941)
2073:Mathematical difficulties
1533:may be required to study
1461:will be required to take
1356:A mathematics lecture at
787:
780:being established by the
669:Medieval and early modern
7358:Northern Mariana Islands
7170:Turks and Caicos Islands
6251:East Timor (Timor-Leste)
5847:Central African Republic
4724:Recreational mathematics
3987:templates for discussion
3945:(Springer Nature, 2017)
3848:(Springer Nature, 2016).
3700:10.3102/0013189X08329353
3621:What Works Clearinghouse
3403:10.1080/0969595980050102
3059:"Mathematics curriculum"
2293:Ferguson, Kitty (2010).
1988:Mathematical Association
1939:What Works Clearinghouse
1710:Conceptual understanding
1289:mathematics competitions
1228:Recreational mathematics
514:—known in Europe as the
7323:Cocos (Keeling) Islands
6512:Cocos (Keeling) Islands
4609:Mathematical statistics
4599:Mathematical psychology
4569:Engineering mathematics
4503:Algebraic number theory
3919:; Joffray, Don (2009).
3844:Drijvers, Paul, et al.
3391:Assessment in Education
2929:ICME-13 Topical Surveys
2182:Friberg, Jöran (1981).
1943:Department of Education
1664:(PISA), created by the
1640:Curriculum Focal Points
1558:mathematical statistics
782:University of Cambridge
257:Participant observation
252:Multivariate statistics
85:International education
7100:British Virgin Islands
6614:Bosnia and Herzegovina
4755:Mathematics portal
4604:Mathematical sociology
4584:Mathematical economics
4579:Mathematical chemistry
4508:Analytic number theory
4389:Differential equations
3917:Strogatz, Steven Henry
3862:Paul Lockhart (2009).
3688:Educational Researcher
3653:Educational Researcher
3632:Mosteller, Frederick;
3470:Educational Researcher
1871:inferential statistics
1675:
1623:In North America, the
1590:differential equations
1467:differential equations
1463:multivariable calculus
1360:
1348:Content and age levels
1321:mathematical reasoning
1153:elementary mathematics
1087:
1010:) as an example of an
945:skills to all students
934:
770:University of Aberdeen
684:
24:
7563:Mathematics education
7301:and other territories
7040:Saint Kitts and Nevis
6007:SĂŁo TomĂ© and PrĂncipe
5867:Republic of the Congo
4734:Mathematics education
4664:Theory of computation
4384:Hypercomplex analysis
4043:Mathematics education
3853:Mathematical cultures
3830:39.2 (2018): 319-341
3153:www.corestandards.org
3124:www.corestandards.org
2844:Stokke, Anna (2015).
2327:National Public Radio
2061:North American issues
1867:Quantitative research
1674:
1627:(NCTM) published the
1499:differential geometry
1436:logarithmic functions
1412:differential calculus
1355:
1333:multiplication tables
1329:traditional education
1323:. A derisory term is
1137:Conventional approach
1080:
1062:liberal arts colleges
932:
842:periodical literature
794:Industrial Revolution
693:European universities
676:
619:Old Babylonian Empire
512:mathematics education
217:Conversation analysis
22:
7189:Education in Oceania
6565:Education in Europe
6426:United Arab Emirates
5793:Education in Africa
5016:Instructional design
4714:Informal mathematics
4594:Mathematical physics
4589:Mathematical finance
4574:Mathematical biology
4513:Diophantine geometry
3819:Ball, Lynda, et al.
2872:(7 September 1993).
2819:The Education Digest
2559:"Euclidean Geometry"
2188:Historia Mathematica
2084:Mathematical anxiety
2055:Statistics education
1882:Qualitative research
1812:formative assessment
1753:Formative assessment
1736:Formative assessment
1574:Business mathematics
1562:stochastic processes
1459:engineering students
1216:Why Johnny Can't Add
774:University of Oxford
742:The Grounde of Artes
526:—is the practice of
369:Discrete mathematics
237:Factorial experiment
31:Educational research
7055:Trinidad and Tobago
6950:Antigua and Barbuda
6830:States with limited
6453:limited recognition
6082:States with limited
5781:Education by region
5507:Secondary education
5419:Teaching philosophy
5322:Pedagogical pattern
5265:21st century skills
5244:Religious education
4887:Aims and objectives
4729:Mathematics and art
4639:Operations research
4394:Functional analysis
2621:theory.stanford.edu
2588:"Axiomatic Systems"
2412:Understanding Media
1983:C.D. Howe Institute
1951:single-case studies
1898:clinical interviews
1848:and understand the
1842:algebraic equations
1819:Algebraic reasoning
1584:additionally cover
1550:mathematical proofs
1545:, probability, and
1511:Applied mathematics
1309:quadratic equations
1159:Relational approach
1143:and is followed by
1131:deductive reasoning
1108:Classical education
1093:Computer-based math
1016:deductive reasoning
869:(ICME) was held in
858:was established in
817:developed countries
812:from an early age.
745:equations like the
728:methods learned by
654:classical education
632:'s division of the
605:Pythagorean theorem
534:, and carrying out
303:Part of a series on
110:Religious education
7521:Schools portal
6990:Dominican Republic
6185:Education in Asia
5512:Tertiary education
5450:Learning resources
4941:Education sciences
4674:Numerical analysis
4283:Mathematical logic
4278:Information theory
4140:Cognitively guided
3952:2021-04-18 at the
3837:2021-04-18 at the
3034:MIT OpenCourseWare
2916:on March 17, 2015.
2884:on 7 February 2002
2390:2020-01-10 at the
1935:experimental units
1894:discourse analysis
1676:
1650:academic standards
1635:reform mathematics
1582:economics programs
1554:probability theory
1527:numerical analysis
1513:may be taken as a
1483:Mathematics majors
1361:
1251:which created the
1183:discovery learning
1149:elementary algebra
1145:Euclidean geometry
1088:
1050:actuarial sciences
1008:Euclidean geometry
956:, plane and solid
954:elementary algebra
935:
887:educational theory
761:. The more famous
747:quadratic equation
685:
617:dates back to the
551:publish literature
470:Mathematics Portal
222:Discourse analysis
128:Curricular domains
50:Education sciences
45:Curriculum studies
25:
7550:
7549:
7504:
7503:
7500:
7499:
7472:other territories
7381:
7380:
7373:Wallis and Futuna
7318:Clipperton Island
7276:Associated states
7183:
7182:
7072:other territories
6931:
6930:
6558:
6557:
6495:other territories
6178:
6177:
6109:other territories
5882:Equatorial Guinea
5771:
5770:
5746:
5745:
5742:
5741:
5737:
5736:
5733:
5732:
5728:
5727:
5665:
5664:
5660:
5659:
5656:
5655:
5651:
5650:
5606:
5605:
5601:
5600:
5597:
5596:
5592:
5591:
5549:
5548:
5544:
5543:
5502:Primary education
5473:
5472:
5362:Dialogic learning
5332:Teacher retention
5285:Critical thinking
5280:Class arrangement
5249:Special education
4924:Standardized test
4907:Course evaluation
4800:
4799:
4399:Harmonic analysis
4186:
4185:
4125:Modern elementary
4100:Three-part lesson
3934:978-0-691-13493-2
3908:978-3-642-00774-3
3889:Sriraman, Bharath
3594:978-0-395-61556-0
3249:978-92-64-24618-8
2958:978-3-319-45112-1
2870:Singmaster, David
2800:978-1-61735-704-6
2465:978-3-319-70307-7
2165:978-0-486-22332-2
1913:Randomized trials
1688:Important results
1428:analytic geometry
1420:integral calculus
1418:at age 16–17 and
1281:unsolved problems
1165:Historical method
1084:Big Brother Mouse
1003:) at an early age
840:The professional
740:, beginning with
725:reckoning schools
572:ancient Babylonia
504:
503:
459:
458:
298:
297:
115:Teacher education
95:Special education
90:School counseling
7575:
7540:
7539:
7530:
7529:
7519:
7518:
7517:
7492:
7480:Falkland Islands
7394:Sovereign states
7383:
7382:
7363:Pitcairn Islands
7333:French Polynesia
7313:Christmas Island
7242:Papua New Guinea
7222:Marshall Islands
7195:Sovereign states
7185:
7184:
7140:Saint Barthélemy
7070:Dependencies and
6943:Sovereign states
6933:
6932:
6868:Dependencies and
6572:Sovereign states
6560:
6559:
6548:
6538:
6537:
6507:Christmas Island
6193:Sovereign states
6180:
6179:
6170:
6169:(United Kingdom)
6165:Tristan da Cunha
6161:Ascension Island
6153:
6140:
6131:
6107:Dependencies and
5800:Sovereign states
5788:
5787:
5777:
5776:
5760:
5708:
5707:
5703:
5702:
5678:Higher education
5674:
5673:
5669:
5668:
5633:
5632:
5628:
5627:
5619:Secondary school
5615:
5614:
5610:
5609:
5576:
5575:
5571:
5570:
5558:
5557:
5553:
5552:
5524:
5523:
5519:
5518:
5493:
5492:
5479:
5478:
5407:Student-centered
5392:Phenomenon-based
5382:Peer instruction
5347:Blended learning
5270:Bloom's taxonomy
5234:Gifted education
5229:Education reform
5061:Computer science
4842:
4841:
4827:
4820:
4813:
4804:
4803:
4788:
4787:
4776:
4775:
4764:
4763:
4753:
4752:
4684:Computer algebra
4659:Computer science
4379:Complex analysis
4213:
4206:
4199:
4190:
4189:
4176:
4175:
4166:
4165:
4036:
4029:
4022:
4013:
4012:
3938:
3926:
3912:
3877:
3816:
3814:
3813:
3807:
3800:
3790:
3788:
3787:
3781:
3770:
3752:
3750:
3748:
3728:
3727:
3719:
3713:
3711:
3683:
3677:
3676:
3648:
3642:
3641:
3629:
3623:
3607:See articles on
3605:
3599:
3598:
3580:
3574:
3573:
3571:
3570:
3564:
3557:
3548:
3539:
3538:
3510:
3504:
3503:
3485:
3465:
3459:
3458:
3456:
3455:
3440:
3429:
3428:
3426:
3425:
3419:
3388:
3379:
3373:
3372:
3371:
3370:
3352:
3346:
3345:
3337:
3324:
3323:
3317:
3309:
3307:
3306:
3300:
3269:
3260:
3254:
3253:
3235:
3226:
3225:
3223:
3222:
3203:
3197:
3196:
3194:
3193:
3174:
3168:
3167:
3165:
3164:
3155:. Archived from
3145:
3139:
3138:
3136:
3135:
3116:
3110:
3109:
3081:
3075:
3074:
3072:
3070:
3055:
3049:
3048:
3046:
3045:
3026:
3020:
3019:
3017:
3016:
3007:. Archived from
3001:
2995:
2994:
2968:
2962:
2961:
2950:
2940:
2924:
2918:
2917:
2915:
2908:
2900:
2894:
2893:
2891:
2889:
2880:. Archived from
2866:
2860:
2859:
2841:
2835:
2834:
2814:
2805:
2804:
2784:
2778:
2777:
2775:
2774:
2765:. Archived from
2759:
2753:
2752:
2750:
2749:
2730:
2724:
2723:
2721:
2720:
2700:
2694:
2693:
2691:
2690:
2671:
2665:
2664:
2662:
2661:
2642:
2636:
2635:
2633:
2632:
2613:
2607:
2606:
2604:
2603:
2594:. Archived from
2584:
2578:
2577:
2575:
2574:
2555:
2549:
2548:
2546:
2545:
2525:
2519:
2518:
2508:
2476:
2470:
2469:
2439:
2433:
2432:
2430:
2429:
2420:. Archived from
2407:Marshall McLuhan
2404:
2398:
2381:
2375:
2374:
2372:
2371:
2352:
2343:
2342:
2340:
2338:
2318:
2309:
2308:
2304:978-184831-231-9
2290:
2284:
2282:
2271:
2265:
2243:
2241:
2240:
2234:
2227:
2213:
2207:
2205:
2203:
2179:
2173:
2172:
2157:
2148:Neugebauer, Otto
2144:
2138:
2137:
2101:
2031:Ethnomathematics
1831:
1830:
1826:
1798:
1797:
1793:
1773:
1772:
1768:
1748:
1747:
1743:
1722:
1721:
1717:
1700:
1699:
1695:
1487:pure mathematics
1394:, and analysis (
1305:simple fractions
1037:The teaching of
1012:axiomatic system
846:classified index
806:public education
776:in 1619 and the
705:moral philosophy
615:Pythagorean rule
506:In contemporary
496:
489:
482:
468:
332:
331:
300:
299:
290:
283:
276:
146:Computer science
105:Female education
100:Gifted education
27:
26:
7583:
7582:
7578:
7577:
7576:
7574:
7573:
7572:
7553:
7552:
7551:
7546:
7515:
7513:
7496:
7490:
7473:
7471:
7461:
7388:
7377:
7300:
7294:
7277:
7271:
7252:Solomon Islands
7190:
7179:
7073:
7071:
7064:
6938:
6927:
6911:
6869:
6863:
6849:Northern Cyprus
6831:
6825:
6746:North Macedonia
6567:
6554:
6526:
6494:
6485:
6466:Northern Cyprus
6452:
6445:
6187:
6174:
6173:
6168:
6151:
6138:
6129:
6110:
6108:
6101:
6085:
6083:
6076:
5795:
5782:
5767:
5766:
5747:
5738:
5729:
5721:
5714:
5692:
5680:
5661:
5652:
5644:
5639:
5621:
5602:
5593:
5585:
5580:
5564:
5545:
5537:
5530:
5486:
5469:
5423:
5342:Active learning
5337:Teaching method
5312:Learning theory
5253:
5219:Autodidacticism
5214:Adult education
5200:
5141:Performing arts
5022:
4929:Teacher quality
4919:Standards-based
4875:
4847:
4836:
4831:
4801:
4796:
4747:
4738:
4688:
4645:
4624:Systems science
4555:
4551:Homotopy theory
4517:
4484:
4436:
4408:
4355:
4302:
4273:Category theory
4259:
4224:
4217:
4187:
4182:
4154:
4078:
4045:
4040:
3990:
3971:
3966:
3954:Wayback Machine
3935:
3909:
3874:
3839:Wayback Machine
3811:
3809:
3805:
3798:
3785:
3783:
3779:
3768:
3759:
3757:Further reading
3746:
3744:
3732:
3731:
3720:
3716:
3684:
3680:
3649:
3645:
3630:
3626:
3606:
3602:
3595:
3581:
3577:
3568:
3566:
3562:
3555:
3549:
3542:
3511:
3507:
3483:10.1.1.649.7042
3466:
3462:
3453:
3451:
3442:
3441:
3432:
3423:
3421:
3417:
3386:
3380:
3376:
3368:
3366:
3353:
3349:
3338:
3327:
3311:
3310:
3304:
3302:
3298:
3267:
3261:
3257:
3250:
3236:
3229:
3220:
3218:
3207:"What is PISA?"
3205:
3204:
3200:
3191:
3189:
3176:
3175:
3171:
3162:
3160:
3147:
3146:
3142:
3133:
3131:
3118:
3117:
3113:
3082:
3078:
3068:
3066:
3057:
3056:
3052:
3043:
3041:
3028:
3027:
3023:
3014:
3012:
3003:
3002:
2998:
2991:
2969:
2965:
2959:
2925:
2921:
2913:
2906:
2902:
2901:
2897:
2887:
2885:
2867:
2863:
2856:
2842:
2838:
2815:
2808:
2801:
2785:
2781:
2772:
2770:
2761:
2760:
2756:
2747:
2745:
2732:
2731:
2727:
2718:
2716:
2709:Huffington Post
2701:
2697:
2688:
2686:
2673:
2672:
2668:
2659:
2657:
2644:
2643:
2639:
2630:
2628:
2615:
2614:
2610:
2601:
2599:
2592:web.mnstate.edu
2586:
2585:
2581:
2572:
2570:
2557:
2556:
2552:
2543:
2541:
2526:
2522:
2477:
2473:
2466:
2440:
2436:
2427:
2425:
2416:
2405:
2401:
2392:Wayback Machine
2382:
2378:
2369:
2367:
2354:
2353:
2346:
2336:
2334:
2319:
2312:
2305:
2291:
2287:
2272:
2268:
2257:
2251:
2238:
2236:
2232:
2225:
2214:
2210:
2180:
2176:
2166:
2145:
2141:
2102:
2098:
2093:
2088:
2075:
2063:
2042:Pre-math skills
2036:Number sentence
2017:
2011:
1959:
1915:
1890:action research
1875:teaching method
1863:social sciences
1859:
1832:
1828:
1824:
1822:
1821:
1799:
1795:
1791:
1789:
1788:
1774:
1770:
1766:
1764:
1763:
1749:
1745:
1741:
1739:
1738:
1723:
1719:
1715:
1713:
1712:
1701:
1697:
1693:
1691:
1690:
1681:
1602:
1535:fluid mechanics
1531:civil engineers
1440:infinite series
1424:complex numbers
1408:the options are
1381:proportionality
1350:
1268:Problem solving
1167:: teaching the
1071:
1064:or universities
1046:social sciences
1014:and a model of
927:
790:
671:
607:
564:
559:
500:
455:
454:
405:
397:
396:
392:Decision theory
340:
294:
232:Factor analysis
176:Performing arts
151:Early childhood
120:Teaching method
17:
12:
11:
5:
7581:
7571:
7570:
7565:
7548:
7547:
7545:
7544:
7534:
7524:
7509:
7506:
7505:
7502:
7501:
7498:
7497:
7495:
7494:
7487:
7482:
7476:
7474:
7466:
7463:
7462:
7460:
7459:
7454:
7449:
7444:
7439:
7434:
7429:
7424:
7419:
7414:
7409:
7404:
7398:
7396:
7390:
7389:
7379:
7378:
7376:
7375:
7370:
7365:
7360:
7355:
7353:Norfolk Island
7350:
7345:
7340:
7335:
7330:
7325:
7320:
7315:
7310:
7308:American Samoa
7304:
7302:
7296:
7295:
7293:
7292:
7287:
7281:
7279:
7278:of New Zealand
7273:
7272:
7270:
7269:
7264:
7259:
7254:
7249:
7244:
7239:
7234:
7229:
7224:
7219:
7214:
7209:
7204:
7198:
7196:
7192:
7191:
7181:
7180:
7178:
7177:
7172:
7167:
7162:
7160:Sint Eustatius
7157:
7152:
7147:
7142:
7137:
7132:
7127:
7122:
7117:
7112:
7107:
7105:Cayman Islands
7102:
7097:
7092:
7087:
7082:
7076:
7074:
7069:
7066:
7065:
7063:
7062:
7057:
7052:
7047:
7042:
7037:
7032:
7027:
7022:
7017:
7012:
7007:
7002:
6997:
6992:
6987:
6982:
6977:
6972:
6967:
6962:
6957:
6952:
6946:
6944:
6940:
6939:
6929:
6928:
6926:
6925:
6923:European Union
6919:
6917:
6916:Other entities
6913:
6912:
6910:
6909:
6904:
6899:
6894:
6889:
6884:
6879:
6873:
6871:
6870:other entities
6865:
6864:
6862:
6861:
6856:
6851:
6846:
6841:
6835:
6833:
6827:
6826:
6824:
6823:
6821:United Kingdom
6818:
6813:
6808:
6803:
6798:
6793:
6788:
6783:
6778:
6773:
6768:
6763:
6758:
6753:
6748:
6743:
6738:
6733:
6728:
6723:
6718:
6713:
6708:
6703:
6698:
6693:
6688:
6686:
6681:
6676:
6671:
6666:
6661:
6656:
6651:
6646:
6641:
6636:
6634:Czech Republic
6631:
6626:
6621:
6616:
6611:
6606:
6601:
6596:
6591:
6586:
6581:
6575:
6573:
6569:
6568:
6556:
6555:
6553:
6552:
6542:
6531:
6528:
6527:
6525:
6524:
6519:
6514:
6509:
6504:
6498:
6496:
6487:
6486:
6484:
6483:
6478:
6473:
6468:
6463:
6457:
6455:
6447:
6446:
6444:
6443:
6438:
6433:
6428:
6423:
6418:
6413:
6408:
6403:
6398:
6393:
6388:
6383:
6378:
6373:
6368:
6363:
6358:
6353:
6348:
6343:
6338:
6333:
6328:
6323:
6318:
6313:
6308:
6303:
6298:
6293:
6288:
6283:
6278:
6273:
6268:
6263:
6258:
6253:
6248:
6243:
6238:
6233:
6228:
6223:
6218:
6213:
6208:
6203:
6197:
6195:
6189:
6188:
6176:
6175:
6172:
6171:
6154:
6141:
6132:
6118:Canary Islands
6114:
6113:
6111:
6106:
6103:
6102:
6100:
6099:
6094:
6088:
6086:
6081:
6078:
6077:
6075:
6074:
6069:
6064:
6059:
6054:
6049:
6044:
6039:
6034:
6029:
6024:
6019:
6014:
6009:
6004:
5999:
5994:
5989:
5984:
5979:
5974:
5969:
5964:
5959:
5954:
5949:
5944:
5939:
5934:
5929:
5924:
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5562:Primary school
5556:
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5309:
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5302:
5297:
5287:
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5277:
5275:Cognitive load
5272:
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4946:Evidence-based
4943:
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4932:
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4926:
4921:
4916:
4911:
4910:
4909:
4894:
4889:
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4880:By perspective
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4629:Control theory
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4404:Measure theory
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4120:Computer-based
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4097:
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3992:Math Education
3970:
3969:External links
3967:
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3913:
3907:
3885:
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3873:978-1934137178
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3724:Education Week
3714:
3678:
3643:
3634:Boruch, Robert
3624:
3600:
3593:
3575:
3540:
3521:(3): 175–199.
3505:
3460:
3430:
3374:
3347:
3325:
3278:(5): 367–381.
3255:
3248:
3227:
3198:
3178:"MoCTM - Home"
3169:
3140:
3111:
3076:
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3021:
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2981:Boston College
2963:
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2895:
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2806:
2799:
2779:
2754:
2740:. 2018-01-25.
2738:Clapham School
2725:
2695:
2681:. 2017-10-13.
2666:
2652:. 2018-06-16.
2637:
2608:
2579:
2550:
2534:Inspired Ideas
2520:
2491:(4): 865–879.
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2048:Sir Cumference
2044:
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2023:
2016:
2013:
2012:
2010:
2007:
2006:
2005:
2000:
1995:
1990:
1985:
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1955:
1914:
1911:
1858:
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1820:
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1787:
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1708:
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1706:
1689:
1686:
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1677:
1601:
1598:
1594:linear algebra
1580:calculations;
1495:modern algebra
1471:linear algebra
1349:
1346:
1345:
1344:
1336:
1325:drill and kill
1312:
1296:
1264:
1256:
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1224:
1194:
1179:Discovery math
1176:
1173:human interest
1162:
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883:electronic age
879:
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863:
852:
849:
838:
831:
789:
786:
738:Robert Recorde
717:multiplication
670:
667:
609:Historians of
606:
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576:ancient Greece
563:
560:
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555:
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227:Evidence-based
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7348:New Caledonia
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6882:Faroe Islands
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6854:South Ossetia
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6706:Liechtenstein
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6476:South Ossetia
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6000:
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5990:
5988:
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5958:
5955:
5953:
5950:
5948:
5945:
5943:
5940:
5938:
5935:
5933:
5930:
5928:
5925:
5923:
5922:Guinea-Bissau
5920:
5918:
5915:
5913:
5910:
5908:
5905:
5903:
5900:
5898:
5895:
5893:
5890:
5888:
5885:
5883:
5880:
5878:
5875:
5873:
5870:
5868:
5865:
5863:
5860:
5858:
5855:
5853:
5850:
5848:
5845:
5843:
5840:
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5835:
5833:
5830:
5828:
5825:
5823:
5820:
5818:
5815:
5813:
5810:
5808:
5805:
5804:
5802:
5798:
5794:
5789:
5785:
5778:
5774:
5763:
5759:
5755:
5754:
5750:
5725:
5720:
5717:
5713:
5712:Undergraduate
5710:
5709:
5704:
5701:
5700:
5696:
5691:
5688:
5686:
5683:
5679:
5676:
5675:
5670:
5667:
5648:
5642:
5638:
5637:Middle school
5635:
5634:
5629:
5626:
5625:
5620:
5617:
5616:
5611:
5608:
5589:
5583:
5578:
5577:
5572:
5569:
5568:
5563:
5560:
5559:
5554:
5551:
5541:
5536:
5533:
5529:
5526:
5525:
5520:
5517:
5516:
5513:
5510:
5508:
5505:
5503:
5500:
5498:
5495:
5494:
5489:
5485:
5480:
5476:
5466:
5463:
5461:
5458:
5456:
5453:
5451:
5448:
5446:
5443:
5441:
5438:
5436:
5433:
5432:
5430:
5426:
5420:
5417:
5413:
5410:
5408:
5405:
5403:
5402:Project-based
5400:
5398:
5397:Problem-based
5395:
5393:
5390:
5388:
5385:
5383:
5380:
5378:
5375:
5373:
5370:
5368:
5365:
5363:
5360:
5358:
5357:Demonstration
5355:
5353:
5352:Contemplative
5350:
5348:
5345:
5343:
5340:
5339:
5338:
5335:
5333:
5330:
5328:
5325:
5323:
5320:
5318:
5315:
5313:
5310:
5306:
5303:
5301:
5298:
5296:
5293:
5292:
5291:
5288:
5286:
5283:
5281:
5278:
5276:
5273:
5271:
5268:
5266:
5263:
5262:
5260:
5256:
5250:
5247:
5245:
5242:
5240:
5239:Homeschooling
5237:
5235:
5232:
5230:
5227:
5225:
5222:
5220:
5217:
5215:
5212:
5211:
5209:
5207:
5203:
5197:
5194:
5192:
5189:
5187:
5184:
5182:
5179:
5177:
5174:
5172:
5169:
5167:
5164:
5162:
5159:
5157:
5154:
5152:
5149:
5147:
5144:
5142:
5139:
5137:
5134:
5132:
5129:
5127:
5124:
5122:
5119:
5117:
5114:
5112:
5109:
5107:
5104:
5102:
5099:
5097:
5094:
5092:
5089:
5087:
5086:Environmental
5084:
5082:
5079:
5077:
5074:
5072:
5069:
5067:
5064:
5062:
5059:
5057:
5054:
5052:
5049:
5047:
5044:
5042:
5039:
5037:
5034:
5033:
5031:
5029:
5025:
5017:
5014:
5013:
5012:
5011:Instructional
5009:
5007:
5004:
5002:
4999:
4997:
4994:
4992:
4989:
4987:
4984:
4982:
4979:
4977:
4974:
4972:
4969:
4967:
4964:
4962:
4959:
4957:
4954:
4952:
4949:
4947:
4944:
4942:
4939:
4937:
4934:
4930:
4927:
4925:
4922:
4920:
4917:
4915:
4914:Psychometrics
4912:
4908:
4905:
4904:
4903:
4900:
4899:
4898:
4895:
4893:
4890:
4888:
4885:
4884:
4882:
4878:
4872:
4869:
4867:
4864:
4862:
4859:
4858:
4856:
4854:
4850:
4843:
4839:
4835:
4828:
4823:
4821:
4816:
4814:
4809:
4808:
4805:
4793:
4792:
4783:
4781:
4780:
4771:
4769:
4768:
4759:
4757:
4756:
4751:
4745:
4744:
4741:
4735:
4732:
4730:
4727:
4725:
4722:
4720:
4717:
4715:
4712:
4708:
4705:
4704:
4703:
4700:
4699:
4697:
4695:
4691:
4685:
4682:
4680:
4677:
4675:
4672:
4670:
4667:
4665:
4662:
4660:
4657:
4656:
4654:
4652:
4651:Computational
4648:
4640:
4637:
4635:
4632:
4630:
4627:
4626:
4625:
4622:
4620:
4617:
4615:
4612:
4610:
4607:
4605:
4602:
4600:
4597:
4595:
4592:
4590:
4587:
4585:
4582:
4580:
4577:
4575:
4572:
4570:
4567:
4566:
4564:
4562:
4558:
4552:
4549:
4547:
4544:
4542:
4539:
4537:
4534:
4532:
4529:
4528:
4526:
4524:
4520:
4514:
4511:
4509:
4506:
4504:
4501:
4499:
4496:
4495:
4493:
4491:
4490:Number theory
4487:
4481:
4478:
4476:
4473:
4471:
4468:
4466:
4463:
4461:
4458:
4456:
4453:
4451:
4448:
4447:
4445:
4443:
4439:
4433:
4430:
4428:
4425:
4423:
4422:Combinatorics
4420:
4419:
4417:
4415:
4411:
4405:
4402:
4400:
4397:
4395:
4392:
4390:
4387:
4385:
4382:
4380:
4377:
4375:
4374:Real analysis
4372:
4370:
4367:
4366:
4364:
4362:
4358:
4352:
4349:
4347:
4344:
4342:
4339:
4337:
4334:
4332:
4329:
4327:
4324:
4322:
4319:
4317:
4314:
4313:
4311:
4309:
4305:
4299:
4296:
4294:
4291:
4289:
4286:
4284:
4281:
4279:
4276:
4274:
4271:
4270:
4268:
4266:
4262:
4256:
4253:
4251:
4248:
4244:
4241:
4239:
4236:
4235:
4234:
4231:
4230:
4227:
4222:
4214:
4209:
4207:
4202:
4200:
4195:
4194:
4191:
4179:
4171:
4169:
4161:
4160:
4157:
4151:
4148:
4146:
4143:
4141:
4138:
4136:
4133:
4131:
4128:
4126:
4123:
4121:
4118:
4116:
4113:
4111:
4108:
4106:
4103:
4101:
4098:
4096:
4093:
4091:
4088:
4087:
4085:
4081:
4075:
4072:
4070:
4067:
4063:
4060:
4059:
4058:
4057:United States
4055:
4054:
4052:
4048:
4044:
4037:
4032:
4030:
4025:
4023:
4018:
4017:
4014:
4007:
4004:
4002:
3999:
3997:
3993:
3988:
3984:
3983:
3978:
3973:
3972:
3962:
3958:
3955:
3951:
3948:
3944:
3940:
3936:
3930:
3925:
3924:
3918:
3914:
3910:
3904:
3900:
3899:
3894:
3890:
3886:
3883:
3879:
3875:
3869:
3865:
3860:
3858:
3854:
3850:
3847:
3843:
3840:
3836:
3833:
3829:
3825:
3822:
3818:
3804:
3797:
3792:
3782:on 2010-06-26
3778:
3774:
3767:
3762:
3761:
3743:
3739:
3734:
3733:
3725:
3718:
3709:
3705:
3701:
3697:
3693:
3689:
3682:
3674:
3670:
3666:
3662:
3658:
3654:
3647:
3639:
3635:
3628:
3622:
3618:
3614:
3610:
3604:
3596:
3590:
3586:
3579:
3565:on 2007-02-02
3561:
3554:
3547:
3545:
3536:
3532:
3528:
3524:
3520:
3516:
3509:
3501:
3497:
3493:
3489:
3484:
3479:
3475:
3471:
3464:
3449:
3445:
3439:
3437:
3435:
3416:
3412:
3408:
3404:
3400:
3396:
3392:
3385:
3378:
3364:
3360:
3359:
3351:
3343:
3336:
3334:
3332:
3330:
3321:
3315:
3297:
3293:
3289:
3285:
3281:
3277:
3273:
3266:
3259:
3251:
3245:
3241:
3234:
3232:
3216:
3212:
3208:
3202:
3187:
3183:
3182:www.moctm.org
3179:
3173:
3159:on 2019-06-10
3158:
3154:
3150:
3144:
3129:
3125:
3121:
3115:
3107:
3103:
3099:
3095:
3091:
3087:
3080:
3064:
3060:
3054:
3039:
3035:
3031:
3025:
3011:on 2014-07-14
3010:
3006:
3000:
2992:
2990:1-889938-04-1
2986:
2982:
2978:
2974:
2967:
2960:
2954:
2949:
2944:
2939:
2934:
2930:
2923:
2912:
2905:
2899:
2883:
2879:
2875:
2871:
2865:
2857:
2855:9780888069498
2851:
2847:
2840:
2832:
2828:
2824:
2820:
2813:
2811:
2802:
2796:
2792:
2791:
2783:
2769:on 2011-11-20
2768:
2764:
2758:
2743:
2739:
2735:
2729:
2714:
2710:
2706:
2699:
2684:
2680:
2676:
2670:
2655:
2651:
2647:
2641:
2626:
2622:
2618:
2612:
2598:on 2019-07-17
2597:
2593:
2589:
2583:
2568:
2564:
2560:
2554:
2539:
2535:
2531:
2524:
2516:
2512:
2507:
2506:11250/3054903
2502:
2498:
2494:
2490:
2486:
2482:
2475:
2467:
2461:
2457:
2453:
2449:
2445:
2438:
2424:on 2008-12-08
2423:
2419:
2414:
2413:
2408:
2403:
2397:
2393:
2389:
2386:
2380:
2365:
2361:
2357:
2351:
2349:
2332:
2328:
2324:
2317:
2315:
2306:
2300:
2296:
2289:
2280:
2276:
2270:
2263:
2259:
2247:
2231:
2224:
2223:
2218:
2212:
2202:
2197:
2193:
2189:
2185:
2178:
2171:
2167:
2161:
2156:
2155:
2149:
2143:
2135:
2131:
2127:
2123:
2119:
2115:
2111:
2107:
2106:Math Horizons
2100:
2096:
2085:
2082:
2080:
2077:
2076:
2068:
2065:
2064:
2056:
2053:
2050:
2049:
2045:
2043:
2040:
2037:
2034:
2032:
2029:
2027:
2024:
2022:
2019:
2018:
2004:
2001:
1999:
1996:
1994:
1991:
1989:
1986:
1984:
1981:
1979:
1976:
1974:
1971:
1969:
1966:
1964:
1961:
1960:
1957:Organizations
1954:
1952:
1948:
1944:
1940:
1936:
1932:
1927:
1925:
1921:
1910:
1908:
1903:
1899:
1895:
1891:
1887:
1883:
1879:
1876:
1872:
1868:
1864:
1851:
1847:
1843:
1839:
1834:
1833:
1827:
1813:
1809:
1805:
1801:
1800:
1794:
1779:
1776:
1775:
1769:
1754:
1751:
1750:
1744:
1729:
1725:
1724:
1718:
1703:
1702:
1696:
1685:
1673:
1669:
1667:
1663:
1658:
1655:
1651:
1646:
1642:
1641:
1636:
1632:
1631:
1626:
1621:
1617:
1615:
1611:
1606:
1597:
1595:
1591:
1587:
1583:
1579:
1575:
1571:
1567:
1563:
1560:, as well as
1559:
1555:
1551:
1548:
1544:
1540:
1536:
1532:
1528:
1524:
1520:
1516:
1512:
1508:
1504:
1500:
1496:
1492:
1488:
1484:
1480:
1476:
1472:
1468:
1464:
1460:
1456:
1451:
1449:
1445:
1441:
1437:
1433:
1429:
1425:
1421:
1417:
1413:
1409:
1405:
1401:
1397:
1393:
1389:
1384:
1382:
1378:
1374:
1368:
1366:
1359:
1354:
1342:
1341:
1337:
1334:
1330:
1326:
1322:
1318:
1317:
1316:Rote learning
1313:
1310:
1306:
1302:
1301:
1297:
1294:
1290:
1286:
1285:word problems
1282:
1278:
1274:
1270:
1269:
1265:
1262:
1261:
1257:
1254:
1250:
1246:
1242:
1241:United States
1238:
1237:
1233:
1230:
1229:
1225:
1222:
1218:
1217:
1213:'s 1973 book
1212:
1208:
1204:
1200:
1199:
1195:
1192:
1188:
1184:
1180:
1177:
1174:
1170:
1166:
1163:
1160:
1157:
1154:
1150:
1146:
1142:
1138:
1135:
1132:
1128:
1124:
1123:
1117:
1113:
1109:
1106:
1103:
1102:
1098:
1095:
1094:
1090:
1089:
1085:
1079:
1075:
1063:
1060:education in
1059:
1055:
1051:
1047:
1043:
1040:
1036:
1033:
1029:
1027:
1023:
1019:
1017:
1013:
1009:
1005:
1002:
998:
994:
991:
987:
983:
979:
975:
971:
967:
963:
959:
955:
951:
947:
944:
940:
939:
938:
931:
922:
916:
913:
910:
907:
904:
903:
902:
900:
896:
895:number theory
892:
888:
884:
876:
872:
868:
864:
861:
857:
854:In 1968, the
853:
850:
847:
843:
839:
836:
832:
829:
825:
824:
823:
820:
818:
813:
811:
807:
803:
799:
795:
785:
783:
779:
775:
771:
766:
764:
763:Rhind Papyrus
760:
756:
752:
748:
743:
739:
734:
731:
726:
722:
718:
714:
710:
706:
702:
698:
694:
690:
683:
682:
675:
666:
664:
663:
659:
655:
651:
647:
643:
639:
635:
631:
626:
624:
620:
616:
612:
602:
600:
599:Rhind papyrus
596:
592:
588:
585:
581:
577:
573:
569:
568:ancient Egypt
554:
552:
548:
542:
540:
537:
533:
529:
525:
521:
517:
513:
509:
497:
492:
490:
485:
483:
478:
477:
475:
474:
471:
467:
463:
462:
451:
448:
446:
443:
441:
438:
436:
433:
431:
428:
426:
423:
421:
418:
416:
413:
411:
408:
407:
401:
400:
393:
389:
386:
384:
381:
379:
375:
372:
370:
367:
365:
361:
358:
356:
353:
351:
348:
346:
345:Number theory
343:
342:
339:
334:
333:
330:
329:
324:
321:
319:
316:
315:
314:
313:
310:
307:
306:
302:
301:
291:
286:
284:
279:
277:
272:
271:
269:
268:
263:
260:
258:
255:
253:
250:
248:
247:Meta-analysis
245:
243:
240:
238:
235:
233:
230:
228:
225:
223:
220:
218:
215:
213:
210:
209:
208:
207:
203:
202:
197:
194:
192:
189:
187:
184:
182:
179:
177:
174:
172:
169:
167:
164:
162:
159:
157:
154:
152:
149:
147:
144:
142:
139:
137:
134:
133:
132:
131:
127:
126:
121:
118:
116:
113:
111:
108:
106:
103:
101:
98:
96:
93:
91:
88:
86:
83:
81:
78:
75:
71:
68:
66:
63:
61:
58:
56:
53:
51:
48:
46:
43:
42:
41:
40:
36:
35:
32:
29:
28:
21:
7512:
7468:Dependencies
7299:Dependencies
7285:Cook Islands
7165:Sint Maarten
7145:Saint Martin
6859:Transnistria
6491:Dependencies
6421:Turkmenistan
6386:Saudi Arabia
6157:Saint Helena
6128:
6032:South Africa
6022:Sierra Leone
5827:Burkina Faso
5719:Postgraduate
5535:Kindergarten
5387:Personalized
5367:Experiential
5327:Teacher look
5110:
5036:Agricultural
4892:Anthropology
4789:
4777:
4765:
4746:
4733:
4679:Optimization
4541:Differential
4465:Differential
4432:Order theory
4427:Graph theory
4331:Group theory
4042:
3980:
3960:
3942:
3922:
3901:. Springer.
3897:
3893:English, Lyn
3881:
3863:
3852:
3845:
3827:
3820:
3810:. Retrieved
3784:. Retrieved
3777:the original
3772:
3747:20 September
3745:. Retrieved
3741:
3726:. p. 1.
3723:
3717:
3694:(9): 561–4.
3691:
3687:
3681:
3656:
3652:
3646:
3637:
3627:
3603:
3584:
3578:
3567:. Retrieved
3560:the original
3518:
3514:
3508:
3476:(5): 25–31.
3473:
3469:
3463:
3452:. Retrieved
3422:. Retrieved
3394:
3390:
3377:
3367:, retrieved
3357:
3350:
3341:
3314:cite journal
3303:. Retrieved
3275:
3271:
3258:
3239:
3219:. Retrieved
3210:
3201:
3190:. Retrieved
3181:
3172:
3161:. Retrieved
3157:the original
3152:
3143:
3132:. Retrieved
3123:
3114:
3092:(1): 16–29.
3089:
3085:
3079:
3067:. Retrieved
3053:
3042:. Retrieved
3033:
3024:
3013:. Retrieved
3009:the original
2999:
2972:
2966:
2948:10183/164060
2928:
2922:
2911:the original
2898:
2888:17 September
2886:. Retrieved
2882:the original
2877:
2864:
2845:
2839:
2822:
2818:
2789:
2782:
2771:. Retrieved
2767:the original
2757:
2746:. Retrieved
2737:
2728:
2717:. Retrieved
2708:
2698:
2687:. Retrieved
2678:
2669:
2658:. Retrieved
2649:
2640:
2629:. Retrieved
2620:
2617:"Heuristics"
2611:
2600:. Retrieved
2596:the original
2591:
2582:
2571:. Retrieved
2563:www.pitt.edu
2562:
2553:
2542:. Retrieved
2533:
2523:
2488:
2484:
2474:
2447:
2437:
2426:. Retrieved
2422:the original
2410:
2402:
2379:
2368:. Retrieved
2359:
2335:. Retrieved
2294:
2288:
2278:
2269:
2245:
2237:. Retrieved
2221:
2217:Høyrup, Jens
2211:
2191:
2187:
2177:
2169:
2153:
2142:
2109:
2105:
2099:
2046:
1928:
1916:
1901:
1886:case studies
1880:
1860:
1808:number sense
1682:
1659:
1638:
1628:
1622:
1618:
1607:
1603:
1586:optimization
1539:graph theory
1523:optimization
1452:
1416:trigonometry
1403:
1396:pre-calculus
1385:
1369:
1365:honors class
1362:
1338:
1324:
1314:
1298:
1291:such as the
1266:
1258:
1234:
1226:
1214:
1211:Morris Kline
1196:
1187:manipulative
1178:
1164:
1158:
1136:
1125:taught as a
1121:
1107:
1099:
1091:
1072:
1058:liberal arts
1026:modern world
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4619:Statistics
4498:Arithmetic
4460:Arithmetic
4326:Elementary
4293:Set theory
3812:2009-08-06
3786:2011-09-25
3569:2013-03-25
3454:2009-11-15
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3369:2012-05-08
3305:2019-11-30
3221:2019-10-14
3192:2018-02-11
3163:2017-07-28
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2773:2011-11-29
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2428:2007-09-04
2396:HathiTrust
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2091:References
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1907:hypotheses
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1846:minus sign
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7457:Venezuela
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5972:Mauritius
5528:Preschool
5428:Wikimedia
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5076:Economics
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