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Online mathematics learning resources

4,822 bytes added, 21:44, 29 May 2014
/* Online practice and diagnostic assessment */
! Resource !! Website !! Topics covered in the video lectures !! Duration of the lectures !! Cost !! Comments on quality and links to reviews !! Computational/conceptual spectrum (scale of 1 to 5, 1 for very computational, 5 for very conceptual)
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| [[Khan AcademyCenter of Math]] (includes only math and other subjects) || [http://www.khanacademycenterofmath.org khanacademy/videos/index.orghtml Center of Math videos] || Entire school math curriculum plus large parts of the introductory college math curriculum Calculus and multivariable calculus (following textbooks published by them) || 550-15 70 minutes || Free || Functional but unremarkableThe videos are very good for in-depth learning. HoweverIn general, the ability to pause and review video lecturesteachers exhibit considerable conceptual depth. The videos are long, combined with the comprehensive curriculum coverage and integration with worked examples, may make this worthwhile. See reviews [http://blogs.edweek.org/edweek/edtechresearcher/2012/06/dont_use_khan_academy_without_watching_mmt2k_first.html here], [http://math.stackexchange.com/questions/80202/what-does-khan-academy-have-require patience to-offer-depth-rigor here], and [http://www.huffingtonpost.com/dr-keith-devlin/khan-academy-good-bad-or-_b_1345925.html here]get through || 24, but the conceptual explanations are sometimes misguided.maybe 5
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| [[PatrickJMT]] Calculus: Single Variable by Robert Ghrist (only mathUniversity of Pennsylvania) on Coursera || [httphttps://www.patrickjmtcoursera.com patrickjmtorg/course/calcsing coursera.comorg/course/calcsing] || Large parts of high school math curriculum Most relevant for people taking Advanced Placement Calculus, or who have already taken Advanced Placement Calculus and beginning college curriculum, including all of want to understand calculus somewhat better || 510-10 20 minutes || Free, but you can donate need to register and enroll to watch the author videos || Somewhat better than Khan Academy in terms of the quality of explanation, but no integration with practice exercises. The videos are very computation-oriented part of a course with quizzes and place little little emphasis course materials. However, some materials may become available only at a particular time of the year because the courses run on conceptual understanding. the academic year timetable || 4 (Write a separate review, link to it? Or find reviews) || 1, but conceptual explanations, when offered, are likely to be correct.
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| [[MIT OpenCourseWareMath Doctor Bob]] (includes only math and other subjects, math courses relevant for high schoolers include only calculus-related courses) || [http:/ocw/www.mitmathdoctorbob.edu ocw.mit.edu], most relevant subset: [http:org//ocwBasAlg.mit.edu/courses/findhtml Courses (toggle between different course types -by-topic/#cat=mathematics&subcat=calculus calculus coursesthe link goes to basic algebra)] || Most relevant for people taking Advanced Placement Calculus (or equivalent) or more advanced courses High school algebra, precalculus, calculus, and multivariable calculus, plus higher math || Since these are mostly actual lectures delivered in college classes, they are generally about 50 5-15 minutes long. || Free || Reasonably good videos. The [http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/ Highlights of Calculus] course should be the most accessible to high school students since it provides a big picture overview of calculus. (Add links to reviews?) || 3 (?)
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| [[Center of MathMIT OpenCourseWare]] (only includes mathand other subjects, math courses relevant for high schoolers include only calculus-related courses) || [http://centerofmathocw.orgmit.edu ocw.mit.edu], most relevant subset: [http:/videos/indexocw.html Center of Math videosmit.edu/courses/find-by-topic/#cat=mathematics&subcat=calculus calculus courses] || Most relevant for people taking Advanced Placement Calculus and multivariable calculus (following textbooks published by themor equivalent) or more advanced courses || Since these are mostly actual lectures delivered in college classes, they are generally about 50-70 minutes long. || Free || The videos are very Reasonably good for invideos. The [http://ocw.mit.edu/resources/res-depth learning, but their length could 18-005-highlights-of-calculus-spring-2010/ Highlights of Calculus] course should be a hindrance the most accessible to many high school studentssince it provides a big picture overview of calculus. In general, the teachers display considerable conceptual depth. (Add links to reviews?) ||4, maybe 53 (?)
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 | [[Math Doctor BobVipul's Classroom]] (only math) (COI disclosure?) || [http://www.mathdoctorbobyoutube.orgcom/BasAlg.html Courses user/vipulsclassroom YouTube channel] || Calculus and multvariable calculus (toggle between different course types -covers only selected topics) || 5- the link goes 20 minutes || Free || Similar to basic algebraCenter of Math, but shorter videos often focus on more specific topics rather than on developing an entire thread. No corresponding book, but related pages at [http://calculus.subwiki.org calculus.subwiki.org] || 4 or 5|-| [[Art of Problem Solving]] (only math)(COI disclosure?) || [http://www.artofproblemsolving.com/Videos/ homepage for videos] || High Middle school math and high school algebra, precalculus, calculus, and multivariable calculus, plus higher math precalculus. || 5-15 minutes || Free || Reasonably good Focused on computational methods, but considerable emphasis on understanding the computational processes and why they work. The videosare synced with the AoPS books and courses, so you can learn the most from the videos by also buying the books. You can also use the videos to get a sense of whether you would like to try the AoPS courses. || 3 4 or 5 ''relative to the grade level'' (?i.e., not as conceptual as the other resources, but highly conceptual relative to the grade level of the audience).
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| [[Dr. Chris Tisdell]] (only math) || [http://www.youtube.com/user/DrChrisTisdell YouTube channel] || calculus (integration onward), differential equations, and more advanced math || 10-25 minutes || Free || Reasonably good videos || 3 (?)
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| [[IntegralCALCThinkwell]] (only math) || [http://integralcalcwww.pathwrightthinkwell.com/ integralcalc.pathwrightthinkwell.com] || all of courses in high school math and calculus || ? 10-25 minutes || Paid(you can pay ~$150 for a year-long subscription to their video-based course, free trial along with many supplementary materials) || Not evaluated Lectures are accompanied by summaries appearing on the side, that help with effective learning. We would recommend this highly if it were not for the cost. || ?3, maybe 4
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| [[ThinkWellKhan Academy]] (includes math and other subjects) || [http://www.thinkwellkhanacademy.org khanacademy.org] || Entire school math curriculum plus large parts of the introductory college math curriculum || 5-15 minutes || Free || Functional but unremarkable. However, the ability to pause and review video lectures, combined with the comprehensive curriculum coverage and integration with worked examples, may make this worthwhile. See reviews [http://blogs.edweek.org/edweek/edtechresearcher/2012/06/dont_use_khan_academy_without_watching_mmt2k_first.html here], [http://math.stackexchange.com thinkwell/questions/80202/what-does-khan-academy-have-to-offer-depth-rigor here], and [http://www.huffingtonpost.com/dr-keith-devlin/khan-academy-good-bad-or-_b_1345925.html here] || courses in 2, but the conceptual explanations are sometimes misguided.|-| [[PatrickJMT]] (only math) || [http://www.patrickjmt.com patrickjmt.com] || Large parts of high school math curriculum and beginning college curriculum, including all of calculus || 105-25 10 minutes || Paid (Free, but you can pay ~$150 for a year-long subscription donate to their video-based course, along with many supplementary materials) the author || Lectures are accompanied by summaries appearing on Somewhat better than Khan Academy in terms of the sidequality of explanation, that help but no integration with effective learningpractice exercises. Highly recommended if it were not for the costThe videos are very computation-oriented and place little emphasis on conceptual understanding. (Write a separate review, link to it? Or find reviews) || 31, maybe 4but conceptual explanations, when offered, are likely to be correct.
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| [[Vipul's ClassroomIntegralCALC]] (only math) (COI disclosure?) || [http://wwwintegralcalc.youtubepathwright.orgcom/user/vipulsclassroom YouTube channelintegralcalc.pathwright.com] || Calculus and multvariable all of calculus || ? || Paid, free trial || Not evaluated || ? |} ===Our top recommendations=== We recommend the following based on the kind of learner you are: {| class="sortable" border="1"! Type of learner and stage !! Our top recommendation !! Supplementary resources|-| Middle school or early high school student (covers only selected topicsgrades 6-9) who is reasonably good at school math but has not explored math much beyond school and wants to learn algebra or precalculus. || 5-20 minutes Start with the '''Art of Problem Solving''' videos (free). If you like them, consider buying the AoPS books and enrolling in the courses (costs money, but not a lot). See our [[algebra learning recommendations]] for more. || Free Khan Academy and PatrickJMT also cover many of the topics, but less well. We would not recommend these as primary resources, but you can use them to supplement learning for topics where you are unable to find AoPS videos. ThinkWell also has videos, but these are not free.|-| Similar High school student (grades 10-12) who wants to learn calculus. || Two relatively complete course sets you can consider:<br> (a) The '''Center of Math''' videos (free) offer a strong conceptual foundation in precalculus and calculus. It may be worth buying the textbook (~$15) to supplement the videos.<br>(b) '''Coursera's "Calculus: Single Variable" course by Robert Ghrist'''. In addition to videos, but shorter you also have course materials that you can use to study.<br>See our [[calculus learning recommendations]] for more. || Three other resources to consider for videos often focus on some subtopics are: '''Vipul's Classroom''' (for a more specific topics rather than on developing an entire thread. No corresponding bookconceptual version), '''Math Doctor Bob''' (for a reasonable mix of concepts and computational techniques), and '''MIT OpenCourseWare'''.|-| High school student (grades 10-12) who has already learned Advanced Placement (AP) Calculus or equivalent but related pages wants to understand some of the trickier topics of single variable calculus at the level taught in top colleges. || The majority of the calculus playlists at '''Vipul's Classroom''' are specifically designed for people who have already studied calculus at the AP level (or slightly less) and now want to understand it at the level of a college course.<br>See our [[http://calculuslearning recommendations]] page for more.subwiki|| We also recommend watching suitable subsets of '''Robert Ghrist's Coursera course''' and the '''Center of Math''' videos.org |-| High school student (grades 10-12) who has already learned Advanced Placement (AP) Calculus or equivalent and wants to study multivariable calculus.subwiki|| Two relatively complete course sets you can consider:<br> (a) The '''Center of Math''' videos (free) offer a strong conceptual foundation in multivariable calculus. It may be worth buying the textbook (~$10) to supplement the videos.<br>(b) '''MIT OpenCourseWare''' multivariable calculus course.org] || 4'''Math Doctor Bob''' has a set of videos on multivariable calculus.<br>'''Vipul's Classroom''' has playlists dealing with partial derivatives, maybe 5gradient vectors, directional derivatives, and other select topics of multivariable calculus.
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| [[Brilliant]] || [http://www.brilliant.org brilliant.org] || Middle school and high school math and calculus, may not comprehensively cover all topics || Free || No, but they may be building it soon || Yes (?) || Yes
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| [[IXL]] || [http://www.ixl.com ixl.com] || Most of school math || about $20/month, but heavy discounts for use in classrooms, with $200/year per classroom of 30 students || ? || Yes ||
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| Varsity Tutors || [http://www.varsitytutors.com varsitytutors.com], practice tests [http://www.varsitytutors.com/practice-tests here] || Many subjects, including mathematics || practice tests are free; there are other resources on the website || || ||
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