PageSourceSearch

https://www.elementsofmathematics.com/schools

html elementsofmathematics.com collected 2026-10-08 12:51:35 UTC 71,857 bytes, 1,007 lines download raw bytes

1<!DOCTYPE html>
2<html>
3	<head>
4		<title>EMF Math</title>
5		<meta charset="UTF-8">
6		<meta name="viewport" content="width=device-width, initial-scale=1.0">
7		<meta property="og:image" content="https://www.elementsofmathematics.com/scripts/emf/css/www/images/fb-image.jpg" />
8		<meta property="og:url" content="https://www.elementsofmathematics.com/" />
9		<meta property="og:type" content="website" />
10		<meta property="og:title" content="Elements of Mathematics: Foundations" />
11		<meta property="og:description" content="Proof-based online mathematics course for motivated and talented middle and high school students." />
12		<!--/scripts/htm/mathjax.htm-->
13		
13<script src="/filedata/commonscripts/mathjax-3.2.1/imacs.mathjax.00.js"></script>
13
14		
14<script src="/filedata/commonscripts/mathjax-3.2.1/es5/tex-chtml.js" id="MathJax-script"></script>
14
15		<!--/scripts/htm/mathjax.htm-->
16		
16<script type="text/javascript" src="/filedata/commonscripts/jquery-3.4.1/jquery-3.4.1.js"></script>
16
17		
17<script type="text/javascript" src="/filedata/commonscripts/jquery-3.4.1/jquery-ui-1.12.1.custom/jquery-ui.js"></script>
17
18		<link rel="stylesheet" type="text/css" href="/filedata/commonscripts/jquery-3.4.1/jquery-ui-1.12.1.custom/jquery-ui.css" />
19		
19<script type="text/javascript" src="/filedata/commonscripts/qtip/jquery.qtip.3.0.3.min.js"></script>
19
20		<link rel="stylesheet" type="text/css" href="/filedata/commonscripts/qtip/jquery.qtip.3.0.3.min.css" />
21		
21<script type="text/javascript" src="/filedata/commonscripts/jquery/jquery.ui.touch-punch.min.js"></script>
21
22		
22<script type="text/javascript" src="/filedata/commonscripts/jquery/ui-js/jquery-ui-timepicker-addon.js"></script>
22
23		<link rel="stylesheet" type="text/css" href="/filedata/commonscripts/jquery/ui-js/jquery-ui-timepicker-addon.css" />
24		
24<script type="text/javascript" src="/filedata/commonscripts/wickedpicker.min.js"></script>
24
25		<link rel="stylesheet" type="text/css" href="/filedata/commonscripts/wickedpicker.min.css" />
26		
26<script type="text/javascript" src="/filedata/commonscripts/paper.0.12.17/dist/paper-core.no-min.js"></script>
26
27		
27<script type="text/javascript" src="/scripts/js/emf-queue.js"></script>
27
28		
28<script type="text/javascript" src="/scripts/js/geometry.js?v=1"></script>
28
29		
29<script type="text/javascript" src="/scripts/js/svg-imacs.39.js"></script>
29
30		
30<script type="text/javascript" src="/scripts/emf/03/js/stringgame.24.js"></script>
30
31		
31<script type="text/javascript" src="/scripts/emf/03/js/string.06.js"></script>
31
32		
32<script type="text/javascript" src="/scripts/emf/03/js/pascal.01.js"></script>
32
33		
33<script type="text/javascript" src="/scripts/emf/13/js/oscilloscope.01.js"></script>
33
34		
34<script type="importmap">
35		{
36			"imports":
37			{
38				"three": "https://unpkg.com/[email protected]/build/three.module.js",
39				"three/addons/": "https://unpkg.com/[email protected]/examples/jsm/"
40			}
41		}
42		</script>
42
43		
43<script type="text/javascript" src="/scripts/emf/06/js/prism.02.js"></script>
43
44		
44<script type="text/javascript" src="/scripts/emf/js/www/home.49.js?v=20260305a"></script>
44
45		<link rel="stylesheet" type="text/css" href="/scripts/emf/css/www/home.35.css?v=20260305a" />
46		<link rel="stylesheet" type="text/css" href="/scripts/emf/03/css/stringgame.01.css" />
47
48		<!-- Facebook Pixel Code -->
49		
49<script>
50			!function ( f, b, e, v, n, t, s )
51			{
52				if ( f.fbq )
53					return;
54				n = f.fbq = function () {
55					n.callMethod ?
56							n.callMethod.apply( n, arguments ) : n.queue.push( arguments );
57				};
58				if ( !f._fbq )
59					f._fbq = n;
60				n.push = n;
61				n.loaded = !0;
62				n.version = '2.0';
63				n.queue = [ ];
64				t = b.createElement( e );
65				t.async = !0;
66				t.src = v;
67				s = b.getElementsByTagName( e )[0];
68				s.parentNode.insertBefore( t, s );
69			}( window, document, 'script',
70					'https://connect.facebook.net/en_US/fbevents.js' );
71			fbq( 'init', '1131471930393388' );
72			fbq( 'track', 'PageView' );
73		</script>
73
74		<!--noscript><img height="1" width="1" src="https://www.facebook.com/tr?id=1131471930393388&ev=PageView &noscript=1"/> </noscript-->
75		<!-- End Facebook Pixel Code -->
76
77	</head>
78	<body>
79			<body class='schools'>
80		<input type='hidden' name='pid' value='45fdd436fe17e856' />
81		<input type='hidden' name='emailfrom' value='6ed1ebfa3cf04a6b16ad7d46686ca6290788e49846c11584ff4a04e2ebf8f7481758044837d5c1b8' />
82
83		<a name='home'></a>
84		<div class='content'>
85
86			<div class='schools-1'>
87				<div class='bigemf-panel'>
88					<div class='school-mainhead'>
89						<div>An Online Middle School Curriculum</div>
90						<div>for <b>Mathematically</b> Talented Minds</div>
91					</div>
92					<div class='bigemf'>
93						<div>EMF</div>
94						<div class='redbar'></div>
95					</div>
96					<div class='school-subhead'><span>Af</span>fordable. Scalable. <b>Proven</b></div>
97				</div>
98			</div>
99			<!--div style='font-family:Neucha;position:absolute;right:4px;padding:0.5em;margin:0.25em;font-size:smaller;border-color:crimson;box-shadow: 0 2px 4px rgba(0,0,0,0.5);line-height:1.2;text-align:center;' class='ui-widget ui-corner-all ui-widget-content'>
100				<div>Meet us at<br/><a href='https://www.nctm.org/Conferences-and-Professional-Development/Annual-Meeting-and-Exposition/'><b>NCTM</b> 2019</a>!</div>
101				<div>Booth<b>#636</b></div>
102			</div-->
103
104			<div class='section'>
105				<a name='about'></a>
106
107				<p style='margin:0 auto;max-width:50%;text-align:center;'>Highly talented mathematics students need nurturing, and that does <i>not</i> mean just giving them
108					the next curriculum faster! EMF is the solution.</p>
109				<br/>
110				<p style='margin:0 auto;max-width:50%;text-align:center;'>EMF News: <a target='_blank' href="https://www.imacs.org/uf-prof-knudson-visits-emf-math-students/">University professor visits EMF Math students.</a></p>
111
112				<h1>About EMF</h1>
113				<ul class='sub-menu'>
114					<li><a href='#courses'>Courses</a></li>
115					<li><a href='#technology'>Technology</a></li>
116					<li><a href='#background'>Background</a></li>
117					<li><a href='#reviews'>Reviews</a></li>
118				</ul>
119				<div class='section-content'>
120					<div>
121						<p><b>Elements of Mathematics: Foundations</b> (EMF) is an online curriculum designed for mathematically talented students that covers Pre-Algebra, Algebra, Geometry, Precalculus and beyond in grades 6&ndash;8.</p>
122						<!--p>While most programs never go beyond mathematics of the late 17th century, EMF teaches a modern approach, including thorough introductions to Abstract Algebra, Logic, Set Theory, Number Theory and Topology.</p-->
123
124						<p>EMF Offers <b>Proven Solutions</b> That Work for All Stakeholders &hellip;</p>
125
126						<!--Dan Gohl-->
127						<iframe class='youtube-video' src="https://www.youtube.com/embed/9gMc4svZ83M?rel=0" frameborder="0" allowfullscreen></iframe>
128
129						<p>&hellip; Because <b>Schools</b> and <b>Districts</b> Need to Allocate Resources Wisely</p>
130						<ul class='features'>
131							<li>Covers Pre-Algebra through Precalculus and beyond in grades 6-8.</li>
132							<li>Exceeds all national and state math standards.</li>
133							<li>Learning Management Systems integration.</li>
134							<li>Scalable for any sized district.</li>
135							<li>Affordable.</li>
136						</ul>
137
138						<!--Not your parents math-->
139						<iframe class='youtube-video' src="https://www.youtube.com/embed/mBeadfK_EnM?rel=0" frameborder="0" allowfullscreen></iframe>
140
141						<!--Olivia-->
142						<!--iframe class='youtube-video' src="https://www.youtube.com/embed/_gsFxPwu9jA?rel=0" frameborder="0" allowfullscreen></iframe-->
143
144						<p>&hellip; Because <b>Teachers</b> Want All Students to Learn and Grow</p>
145						<ul class='features'>
146							<li>Stretches the brightest students by challenging them at their ability level.</li>
147							<li>Effective in-class differentiation.</li>
148							<li>No additional teacher training required.</li>
149							<li>Automatic grading, online gradebook and weekly progress reports.</li>
150							<li>Free up time to work with non-EMF students.</li>
151						</ul>
152
153						<h2>Partner Schools, Districts and Organizations</h2>
154						<p>Join the growing ranks of school, districts and organizations providing talented students with the most advanced secondary sc
154hool mathematics curriculum available today!</p>
155						<ul class='features'>
156							<li>Broward County Public Schools, Florida</li>
157							<li>Collier County Public Schools, Florida</li>
158							<li>Denver Public Schools, Colorado</li>
159							<li>Fairbanks North Star Borough School District, Alaska</li>
160							<li>Madison School District, Arizona</li>
161							<li>Pembroke Pines Charter School, Florida</li>
162							<li>Project MEGSSS, Missouri</li>
163							<li>San Antonio Academy, Texas</li>
164							<li>Scheck Hillel Community School, Florida</li>
165							<li>Somerset Academy Pemroke Pines, Florida</li>
166							<li>St. Mark's Episcopal School, Texas</li>
167						</ul>
168
169						<!--p>Download the <a href='https://www.elementsofmathematics.com/scripts/htm/resources/emf-booklet-web.pdf'>EMF for Schools</a> brochure.</p-->
170
171					</div>
172				</div>
173
174			</div>
175
176			<div class='schools-2 bg resize-me' data-w='2048' data-h='1186'></div>
177
178			<div class='section'>
179				<a name='free-trial'></a>
180				<h1>Free Trial &amp; Licensing</h1>
181
182				<p>Licensing fees for institutions such as school districts and traditional schools vary according to the number of students enrolled in EMF. Please complete the form below to request more information or a free trial of EMF.</p>
183				<p>Homeschool? Visit <a target='_blank' href='https://www.elementsofmathematics.com/home.htm'>www.EMFmath.com</a>.</p>
184
185				<div class='aptitude-test-signup'>
186					<a name='errorscroll'></a>
187					<div class='input-outer'>
188						<div class='signuperror'></div>
189						<div class='input-div'><div>First name:</div><div><input type='text' class='wide' name='first' /> <span class='required'>&ast;</span></div></div>
190						<div class='input-div'><div>Last name:</div><div><input type='text' class='wide' name='last' /> <span class='required'>&ast;</span></div></div>
191						<div class='input-div'><div>School/district Email:</div><div><input type='text' class='wider' name='email' /> <span class='required'>&ast;</span></div></div>
192						<!--div class='input-div'><div>Phone:</div><div><input type='text' class='wide' name='phone' /></div></div-->
193						<div class='input-div'><div>School/district:</div><div><input type='text' class='wide' name='district' /> <span class='required'>&ast;</span></div></div>
194						<!--div class='input-div'>
195							<div>School type:</div>
196							<div>
197								<input type='radio' value='Public' name='schooltype' />Public
198								<input type='radio' value='Private' name='schooltype' />Private
199								<input type='radio' value='Charter' name='schooltype' />Charter
200								<input type='radio' value='Homeschool' name='schooltype' />Homeschool
201								<span class='required'>&ast;</span>
202							</div>
203						</div-->
204						<!--div>
205							<div>Approximate number of students who may be eligible:</div>
206							<div>
207								<input type='radio' value='1-5' name='studentcount' />1-5
208								<input type='radio' value='5-10' name='studentcount' />5-10
209								<input type='radio' value='10-50' name='studentcount' />10-50
210								<input type='radio' value='50+' name='studentcount' />50+
211								<span class='required'>&ast;</span>
212							</div>
213						</div-->
214						<!--div class='input-div'><div>State:</div><div><input type='text' class='wide' name='state' /> <span class='required'>&ast;</span></div></div-->
215						<div class='input-div'><div>Your position:</div><div><input type='text' class='wide' name='position' /> <span class='required'>&ast;</span></div></div>
216						<div class='input-div'><div>How did you hear about EMF?</div><div><textarea class='wider' style='height:3.5em;' name='howheard'></textarea><span class='required'>&ast;</span></div></div>
217						<div class='input-div'><div><span class='required'>&ast;</span>Required</div><div><button class='submitbutton'>Submit</button></div></div>
218					</div>
219					<div class='signuptablesuccess'>
220						<b>Thank you</b> for your inquiry. We will respond with two business days. For more information, email us at [email protected],
221						or call IMACS toll free at (888) 776-2345.
222					</div>
223
224					<div class='signuptablefailure'>
225						We're sorry, we are unable to process your registration due to a technical error. We are working to fix this
226						as quickly as possible. Please try again later.
227					</div>
228				</div>
229			</div>
230
231			<div class='schools-3 bg resize-me' data-w='2048' data-h='1384'></div>
232
233			<div class='section'>
234				<a name='faq'></a>
235				<h1>Frequently Asked Questions</h1>
236				<ul class='faq'>
237					<li>
238						<h2><a href='#'>Getting In</a></h2>
239						<div>
240							<p>
241								<i>
242									The first EMF course provides districts with a free and convenient method of selecting EMF students, and this section of the FAQ
243									deals with this process. Some districts use alternative methods of selecting suitable students, and this section will not apply.
244								</i>
245							</p>
246
247							<ul class='sub-faq'>
248								<li>
249									<div class='h'>How does a student qualify for EMF?</div>
250									<div class='answer'>
251										<p>
252											A student completes the first EMF course, <em>Operational Systems</em>, with an average of at least of 90%, during the summer preceding the start of the academic year.
253										</p>
254										<p>
255											Note that EMF is designed to be a self-study program in which students learn by closely reading the online text and carefully completing the online exercises. Prospective students should be reading at above grade level and be ready to learn new concepts through reading. Completing the <em>Operational Systems</em> course is an excellent way to gauge whether a student is ready for EMF's self-study approach.
256										</p>
257
258									</div>
259								</li>
260
261								<li>
262									<div class='h'>What is the cost to use the first EMF course to select students for the program?</div>
263									<div class='answer'>
264										<p>
265											The first EMF course is free for schools and districts that license EMF. Licensees may enroll an unlimited number of students into the first course for the purpose of using it as a screening tool for entry into the program. Please complete the licensing inquiry form on the main page for more information.
266										</p>
267									</div>
268								</li>
269
270								<li>
271									<div class='h'>What is the first EMF course about?</div>
272									<div class='answer'>
273										<p>
274											It introduces elementary group theory, modular arithmetic and non-numeric operations.
275										</p>
276									</div>
277								</li>
278
279								<li>
280									<div class='h'>When should students start the first EMF course?</div>
281									<div class='answer'>
282										<p>
283											Data show that, on average, students who study the first EMF course early in the summer obtain higher grades
284											than those who start later. Moreover, students who finish the first course with an average of 90% or
285											better may optionally begin the second EMF course in order to jump ahead of schedule.
286										</p>
287									</div>
288								</li>
289
290								<li>
291									<div class='h'>Are students allowed to get help on the first course while trying to qualify for EMF?</div>
292									<div class='answer'>
293										<p>
294											A student attempting to qualify for EMF through his or her score on <em>Operational Systems</em> is
295											limited to three Help Forum posts during that course. Experience indicates that EMF tends to be a
296											poor fit for those who need more help than this in the first course. Students who qualify to join
297											their school's EMF program and decide to continue have full access to the Help Forum beginning
298											with the second course. Note that in all courses including <em>Operational Systems</em>, students
299											are able to review prior Help Forum exchanges by clicking on the green question mark icon
300											[?] when it appears with an exercise.
301										</p>
302									</div>
303								</li>
304
305								<li>
306									<div class='h'>How long does it take to complete the first EMF course?</div>
307									<div class='answer'>
308										<p>
309											Students who have completed the first EMF course with an average of at least 90% have taken as little
310											as 10 hours, but 20&ndash;25 hours is the norm. There is no correlation between the time taken and
311											the final grade, nor between the time taken and success in EMF. However, the final grade is a very
312											strong indicator of future success in the program. Therefore, students are encouraged to take as
313											much time as they feel they need in order to completely master the covered material.
314										</p>
315									</div>
316								</li>
317							</ul>
318						</div>
319					</li>
320					<li><h2><a href='#'>Getting Help</a></h2>
321						<div>
322							<p>
323								<i>
324									To whom do EMF students, teachers and administrators turn when they need help?
325								</i>
326							</p>
327							<ul class='sub-faq'>
328								<li><div class='h'>What professional support is available to teachers and administrators? What is the cost?</div>
329									<div class='answer'>
330										<p>
331											Teachers and administrators of school and districts that license EMF receive free email and telephone support. Site visits and professional development are available for an additional fee. Please complete the licensing inquiry form on the main page for more information.
332										</p>
333									</div>
334								</li>
335
336								<li>
337									<div class='h'>Since there is no local instruction, what do students do when they need help?</div>
338									<div class='answer'>
339										<p>
340											Parents and students should note that all the information students need to understand and answer exercises is contained in the pages of the relevant section. Usually, re-reading the section several times will overcome any misunderstandings.
341										</p>
342
343										<p>
344											When students are logged into the EMF site they may access the Help Forum, in which students are
345											encouraged to post well-thought-out questions to be discussed and answered by highly-advanced students.
346											Questions that are not answered satisfactorily are filtered through to experienced instructors and
347											mathematicians who respond through the Help Forum.
348										</p>
349
350										<p>
351											<b>Note that the Help Forum is <i>not</i> designed or intended to substitute as a teacher.</b> The Help Forum is provided to answer students' specific and focused questions; however, the main responsibility for learning the material through close reading belongs to each EMF student.
352										</p>
353
354										<p>
355											For each exercise, students may read previously posted Help Forum questions and answers about
356											that exercise by clicking on the green question mark button that appears with that exercise.
357										</p>
358
359										<p>
360											To use the Help Forum, students must obey strict rules, including rules prohibiting the request
361											or provision of answers and the use of inappropriate language. Students who do not obey these rules
362											are prohibited from accessing the Help Forum and are not permitted to continue in the EMF program.
363										</p>
364
365										<p>
366											(It is worth pointing out that, historically, 85% of help requests from students taking the first
367											EMF course generate responses that encourage the student to solve the issue themselves by either
368											re-reading the section or by using the index button, and almost invariably the student overcomes
369											the issue by following this advice.)
370										</p>
371									</div>
372								</li>
373
374								<li><div class='h'>Why do you say that it's not good for parents to help their child with the EMF curriculum?
375										What if they know mathematics and want to help?</div>
376									<div class='answer'>
377										<p>
378											A rare selection of parents possess the characteristics that it takes to effectively help their
379											EMF student, namely university-level training in abstract mathematics and the ability to guide
380											young people while still allowing them to experience productive struggle. Even for such individuals,
381											refraining from helping allows their child to develop strong independent study habits that he or she
382											will certainly benefit from in high school and at university.
383										</p>
384
385										<p>
386											Parents' most important role is to provide a supportive environment in which students can study
387											without interruption or distraction, and where necessary to help with organization and time-management.
388										</p>
389									</div>
390								</li>
391
392								<li><div class='h'>Are students allowed to use calculators and graphing tools such as those available online?</div>
393									<div class='answer'>
394										<p>
395											EMF provides an integrated scientific calculator and graphing tools that students may use in completing
396											their EMF coursework. While there are sophisticated tools available online, EMF students are limited in
397											how they may use these external tools. Students are prohibited from using these tools to solve exercises
398											in EMF; however, they may use these tools to check exercise answers arrived at through their own thinking.
399											Use of external tools for any purpose on review quizzes and tests is strictly prohibited.
400										</p>
401
402										<p>
403											The use of external tools to calculate answers in earlier EMF courses is self-defeating.
404											Later courses focus on proofs for which there are no online tools. Success in the proof-based
405											courses is possible only if a student has developed strong mathematical intuition by solving problems
406											using their own brainpower. There simply is no substitute for the experience gained by
407											figuring things out for yourself.
408										</p>
409									</div>
410								</li>
411
412								<li><div class='h'>What should a student do if he or she is having technical difficulties with an EMF course?</div>
413									<div class='answer'>
414										<p>
415											Students should report the issue by clicking the &quot;Technical Support&quot; button in the Help Forum.
416										</p>
417									</div>
418								</li>
419							</ul>
420						</div>
421					</li>
422					<li><h2><a href='#'>Grades</a></h2>
423						<div>
424							<p>
425								<i>
426									The grades earned in EMF courses are used by school systems to determine the grades that appear on students' official transcripts.
427								</i>
428							</p>
429							<ul class='sub-faq'>
430								<li><div class='h'>How are EMF grades calculated?</div>
431									<div class='answer'>
432										<p>
433											Each course contains several units, each of which is either an assignment (containing exercises and review
434											problems), or a test. Raw point scores are then adjusted depending on the unit's level of difficulty.
435											A grade is then calculated as a weighted average of the assignments (60% weight) and tests (40% weight).
436											This is the <em>EMF course grade</em>. Students must maintain EMF course grades of 80% or better.
437											(Since EMF courses typically contain between eight and ten assignments, but only one or two tests,
438											it is vital that students prepare well for tests in order to obtain a high EMF course grade.)
439										</p>
440									</div>
441								</li>
442
443								<li><div class='h'>Are the EMF grades used as the basis for the students' official school grades?</div>
444									<div class='answer'>
445										<p>
446											Yes. A student's official grade for a reporting period is calculated using the EMF assignment and test grades for
447											coursework scheduled for completion during the reporting period. These grades are curved to reflect the
448											fact that EMF courses are more challenging and demanding than typical advanced math courses.
449										</p>
450									</div>
451								</li>
452
453								<li><div class='h'>What measures are taken to minimize the risk of cheating on EMF tests?</div>
454									<div class='answer'>
455										<p>
456											Before a student begins an EMF test, he or she must take two actions. First, the student must electronically sign
457											the following pledge: "I promise I will not cheat on this test. I will complete this test without help and without consulting external
458											sources, and I will not accept nor will I provide any information about this test to any entity." Secondly,
459											he or she must select a proctor who will be notified by email and is responsible for reasonably monitoring the student
460											during the test to ensure academic integrity. Typical choices for a proctor are a student's parent or math teacher.
461										</p>
462									</div>
463								</li>
464
465								<li><div class='h'>Does EMF integrate with Learning Management Systems (LMS)?</div>
466									<div class='answer'>
467										<p>
468											Yes. Students may log into EMF via their single-signin platform using EMF's Learning Tools Interoperability (LTI) interface and, depending on the LMS,
469											EMF grades may be automatically propagated to the LMS and thence to the Student Information System (SIS) system.
470										</p>
471									</div>
472								</li>
473
474								<li><div class='h'>How do parents know how their child is doing in the program?</div>
475									<div class='answer'>
476										<p>
477											A progress report is emailed to EMF parents each Monday morning showing the EMF course grade for the student's
478											current course. A real-time report card is available to parents at any time by using their child's login and
479											choosing &quot;My grades&quot; from the menu. Report cards also detail how far the student is ahead (or behind)
480											schedule, the next five upcoming weekly benchmarks, and a summary of the student's recent Help Forum activity.
481											Students are advised to try to stay at least two weeks ahead of schedule in order to allow for unforeseen
482											interruptions in progress.
483										</p>
484
485									</div>
486								</li>
487
488								<li>
489									<div class='h'>Does a student need to meet certain standards to remain in the program?</div>
490									<div class='answer'>
491										<p>
492											Yes. To remain in program, students must maintain an EMF grade of 80% or better and be no more than 14 days
493											behind schedule. If either criterion is breached, the student receives a warning that they have 14 days to raise
494											their EMF grade to 80% or better and/or catch up to the schedule. If they are not able to remedy the situation
495											in 14 days, they are transferred out of the program. Exceptions for unique situations are considered on a
496											case-by-case basis.
497										</p>
498									</div>
499								</li>
500
501
502								<li><div class='h'>Some students insist on getting everything correct. Are there do-overs in EMF?</div>
503									<div class='answer'>
504										<p>
505											Yes and No. Certain exercises in EMF allow a student one, and only one, do-over if the student's initial
506											answers would receive a score below 50%. The student is given a warning and encouraged to carefully rethink
507											his or her answers.
508										</p>
509
510										<p>
511											<em>A student learns as much, if not more, from submitting an imperfect answer and then carefully
512												reading the answer key as he or she does by submitting the correct answer.</em>
513										</p>
514									</div>
515								</li>
516							</ul>
517						</div>
518					</li>
519					<li><h2><a href='#'>Schedule and Pacing</a></h2>
520						<div>
521							<p>
522								<i>
523									EMF offers features allowing teachers to control and monitor the pace at which EMF student work.
524								</i>
525							</p>
526							<ul class='sub-faq'>
527								<li><div class='h'>Do students have to work on EMF at specific dates and times?</div>
528									<div class='answer'>
529										<p>
530											Students work on EMF during their regular mathematics lesson. However, as long as a student is
531											enrolled in an EMF course, he or she is able to work on that course whenever
532											he or she has internet access on a laptop, desktop or tablet computer.
533										</p>
534									</div>
535								</li>
536
537								<li><div class='h'>What is the appropriate pace for working through an EMF course?</div>
538									<div class='answer'>
539										<p>
540											EMF students are provided with minimum benchmarks. Students who fall two weeks behind schedule or who fail to
541											maintain an EMF course grade of 80% or better are asked to exit the program. However,
542											within this framework each student must find the pace that best suits him or her.
543										</p>
544
545										<p>
546											The appropriate pace varies considerably from student to student. It is best not to go too many days without completing
547											some EMF coursework. A student needs to keep the material fresh in his or her mind since EMF courses move along
548											steadily with little to no repetition.
549										</p>
550
551										<p>
552											In addition to his or her daily mathematics lesson, EMF students <em>need to work on EMF after school,
553												on weekends and during holidays</em>. Many EMF students work well ahead of schedule, but this should not be confused with
554											working quickly. Proceeding too quickly through EMF can be detrimental to a student's long term success in the program.
555											Students should bear in mind that there is no prize for finishing first, but significant rewards for those whose
556											meticulousness and dedication leads to a deep and lasting understanding.
557										</p>
558
559										<p>
560											Students who take the time to read and re-read EMF material and to work through the problems slowly and carefully
561											do much better. Students who are used to succeeding in regular school math despite jumping from exercise to exercise
562											and ignoring or speed-reading the intervening text quickly discover that the same approach does not work in EMF.
563											Students are also expected to take a long time puzzling through the more difficult problems, often by
564											putting pencil to paper, and without giving up too quickly. In other words, EMF rewards patience and persistence.
565										</p>
566									</div>
567								</li>
568
569								<li><div class='h'>During winter break, does a student's EMF pacing schedule &quot;freeze&quot;, or should students continue to work on EMF over the break?</div>
570									<div class='answer'>
571										<p>
572											EMF does <em>not</em> freeze the pacing schedule over winter or spring break. If a student is well
573											ahead of schedule, then he or she probably doesn't need to worry about falling behind if
574											they need to pause during a vacation. If a student is just about on schedule, then he or she should consider
575											putting in extra time after school or on weekends before the break so that there is no need to rush later on.
576											Regardless of where a student is in the schedule, it would be wise for him or her to put in
577											some regular work on EMF during vacations to keep the material fresh in the mind.
578										</p>
579									</div>
580								</li>
581
582								<li><div class='h'>Should you work on EMF if you have 15 minutes to spare?</div>
583									<div class='answer'>
584										<p>
585											Perhaps. Success with the EMF curriculum requires longer stretches of deep focus and concentration.
586											It might be better to use those 15 minutes to help free up a longer block of time later.
587										</p>
588									</div>
589								</li>
590							</ul>
591						</div>
592					</li>
593					<li><h2><a href='#'>Miscellaneous</a></h2>
594						<div>
595							<p>
596								<i>
597									Check out these miscellaneous questions we've been asked at teacher workshops and conferences.
598								</i>
599							</p>
600
601							<ul class='sub-faq'>
602								<li><div class='h'>How many students will be in the EMF program at my school?</div>
603									<div class='answer'>
604										<p>
605											This number will depend on how many students complete
606											the required summer work with a grade of 90% or better and then
607											also decide to continue with the program in the fall.
608										</p>
609									</div>
610								</li>
611
612								<li><div class='h'>How do EMF students concentrate if the classroom teacher and the rest of the class are
613										discussing different curriculum in the same room? Isn't that distracting?</div>
614									<div class='answer'>
615										<p>
616											Some schools may have enough EMF students to form a separate class. Districts work
617											with individual cases to make the best possible provision for every student, bearing in mind
618											constraints that individual schools may have. Some districts or schools may provide headsets, but parents should consider providing their child with headphones to listen to EMF videos while in class.
619										</p>
620									</div>
621								</li>
622
623								<li><div class='h'>Does a student have to take the courses in order, or can some courses be skipped or taken out of order?</div>
624									<div class='answer'>
625										<p>
626											The EMF courses must be completed in order and without skipping. These courses are
627											designed to build an intuitive foundation for mathematics through carefully planned steps.
628										</p>
629									</div>
630								</li>
631
632								<li><div class='h'>Is EMF algebra the same as the algebra taught in schools and in other online courses?</div>
633									<div class='answer'>
634										<p>
635											No. EMF teaches what mathematicians call &quot;abstract algebra&quot;. The algebra taught in high school and
636											in other online courses is a special case of abstract algebra usually referred to by mathematicians as
637											&quot;elementary algebra&quot;. Students who complete EMF earn high school credit in Algebra 1
638											and Algebra 2 (and Geometry and Precalculus). But they are also ready to take junior-level college algebra courses.
639										</p>
640									</div>
641								</li>
642
643								<li><div class='h'>Is EMF just like Khan Academy online courses?</div>
644									<div class='answer'>
645										<p>
646											No. EMF was designed from the start to be a coherent three-year course of study for mathematically talented students from 6th grade through
647											8th grade. EMF exercises use little repetition, and so it is not an appropriate tool for practicing basic math skills.
648										</p>
649									</div>
650								</li>
651
652								<li><div class='h'>Does IMACS provide any kind of documentation to show that a student has completed a course?</div>
653									<div class='answer'>
654										<p>
655											When students complete an EMF course, parents receive an email containing links to
656											a Student Transcript and Completion Certificate.
657										</p>
658									</div>
659								</li>
660
661								<li><div class='h'>Does the EMF program replace a student's middle school math program?</div>
662									<div class='answer'>
663										<p>
664											Yes. An EMF student studies the EMF program during the time allotted for his or her mathematics education.
665										</p>
666									</div>
667								</li>
668
669								<li><div class='h'>What if a student completes the program?</div>
670									<div class='answer'>
671										<p>
672											He or she will have high school credits in Algebra 1, Algebra 2, Geometry and Pre
672calculus, and will be ready to take
673											Advanced Placement classes in Calculus in 9th grade. He or she will also be ready to take junior-level college
674											courses in subjects including Discrete Mathematics, and Linear and Abstract Algebra.
675										</p>
676									</div>
677								</li>
678
679								<li><div class='h'>What technology do students need?</div>
680									<div class='answer'>
681										<p>
682											EMF is supported on the free Chrome and Firefox browsers. In addition to laptops and desktops, EMF is compatible with iPads, Android tablets, and touchscreen computers. However, some features are easier to use with a mouse or other pointing device. EMF is not compatible with smartphones. <em>Headphones are highly recommended</em>.
683										</p>
684									</div>
685								</li>
686							</ul>
687						</div>
688					</li>
689				</ul>
690			</div>
691
692			<div class='schools-5 bg resize-me' data-w='2048' data-h='1600'></div>
693
694			<div class='bottom'>
695				<div class='contact-info'>
696					<b>Questions?</b>
697					<span class='contact'>[email protected]</span>
698				</div>
699				<div><a target='_blank' href='https://www.elementsofmathematics.com/home.htm'>EMF Home Page</a></div>
700				<div class='imacs-logo'><a target='_blank' href='https://www.imacs.org'><img alt="Institute for Mathematics<br/>and Computer Science" src="/filedata/imacsweb2013/_img/logo.jpg" /></a></div>
701				<div class='copyright'>&copy; 2002 &ndash; <span class='year'>2018</span> IMACS. All rights reserved.</div>
702			</div>
703
704			<div class='popups abs'>
705				<a name='courses'></a>
706				<div class='popup courses'>
707					<h1>Courses</h1>
708					<p>EMF recognizes that certain fundamental concepts elegantly unify the various
709						branches of mathematics. EMF first teaches these concepts and then builds on that
710						foundation to explore modern mathematics while covering all of Pre-Algebra through Precalculus.</p>
711					<ol class='curriculums'>
712						<li><a href='#' class='course-name'>Operational Systems</a>
713							<div>This course covers modular arithmetic using secret codes and online games. Learn about operational systems and their properties
714								(commutativity, associativity, neutral elements, invertibility) by building interactive machines and evaluating non-numeric
715								operations. Get a solid introduction to the concepts of least common multiple and greatest common divisor, as well as
716								to the geometric notions of midpoint and reflection.</div>
717						</li>
718						<li><a href='#' class='course-name'>The Integers</a>
719							<div>This course introduces positive and negative integers with an unusual elevator and mysteriously disappearing nuts. Learn about adding, subtracting, multiplying and ordering integers by building interactive number lines and driving a balloon-popping car. Students are exposed to various theorems about integer relationships and carefully guided through the first steps of how to make a well-reasoned and logical argument in support thereof.</div>
720						</li>
721						<li><a href='#' class='course-name'>Sets, Subsets and Set Operations</a>
722							<div>This course introduces the building blocks of set theory, which provides the basic language in which most mathematical texts are written. "Set" is what mathematicians call a collection of objects; it's a tiny word but a powerful concept as you will see. Learn about set properties and relationships involving sets with whimsical videos and the increasingly challenging String Game. Through mind-stretching, interactive exercises, students cover fundamental concepts such as elements, roster names, the empty set, subsets, Venn diagrams, intersection, union, set difference and complement, and the Pascal Formula.</div>
723						</li>
724						<li><a href='#' class='course-name'>Ordered n-Tuples</a>
725							<div>This course considers what happens when order is imposed upon a collection of objects. Building on concepts introduced in <i>Operational Systems</i>, interactive features such as taxi driver navigation and the rock-paper-scissors game give context to the properties of Cartesian product sets. An intuitive study of open sentences in two variables and the graphing of their solutions plant the seeds for future courses in Algebra. Students deepen their understanding of various mathematical operations as these concepts are extended componentwise to sets of ordered n-tuples.</div>
726						</li>
727						<li><a href='#' class='course-name'>Mappings</a>
728							<div>This course examines relationships between the elements of two sets. Students explore various types of mappings, including permutations, with interactive ball sorters, slide rules and clever animations. Elementary combinatorial exercises lay the foundation for advanced concepts in Algebra, Geometry and Probability. Applying the properties of function composition, students delve into fractions and percentages in a mathematically rigorous and intuitive way.</div>
729						</li>
730						<li><a href='#' class='course-name'>The Rationals</a>
731							<div>This course builds on topics covered in previous courses in order to examine the rational numbers, commonly referred to as fractions, as a natural extension of the integers. The course uses detailed narrations and interactive number lines and coordinate planes to cover the absolute value function, the properties of operations on rational numbers, how they are ordered, and that they are densely packed, not evenly spaced as the integers are. Students learn how to solve equations of rational numbers through the foundational concept of mappings instead of with rote algebraic manipulation. Using interactive proof-builders, students also advance to the next step in learning how to construct well-reasoned and logical arguments.</div>
732						</li>
733						<li><a href='#' class='course-name'>The Decimals</a>
734							<div>This course builds upon knowledge of the rational numbers to introduce decimal numbers and their properties, arithmetic operations on decimals, and positional notation for decimals. Students learn to compute various decimal approximations of rational numbers and to evaluate errors in approximation. The course revisits percentages in relation to decimals and arithmetic operations on percentages. Students then apply what they have learned about decimals, decimal approximations, and percentages in the study of rates (that is, ratios of measured quantities), the slopes of straight lines, a case study of a fictional world in which mathematics is necessary to analyze a social and political issue, and an extended introduction to elementary descriptive statistics.</div>
735						</li>
736						<li><a href='#' class='course-name'>Probability</a>
737							<div>This course provides an introduction to elementary probability theory and covers one-stage, two-stage, and multistage random experiments, the Product Rule, counting subsets, combinatorics, and random digit generators. This is one of E
737MF's most technologically ambitious courses with over half the pages containing an interactive device, narrated animation, or virtual classroom. Using these tools students learn about, replicate, or analyze the outcomes of a wide variety of random experiments online. The course concludes with an exploration of one of the most important methods in probability &mdash; Monte Carlo simulation &mdash; and two famous questions &mdash; the birthday problem and the Monty Hall puzzle.</div>
738						</li>
739						<li><a href='#' class='course-name'>Number Theory</a>
740							<div>An exploration of numbers for their own fascinating sake is a joy that every young person should experience. This course provides that opportunity by investigating some of the most intriguing and timeless questions in Number Theory. Along the way, students learn about prime and composite numbers, prime factorization, and number bases as well as examining elegant ideas such as Euclid's Lemma, the Sieve of Eratosthenes, and the Fundamental Theorem of Arithmetic. Students expand their logical reasoning skills with an introduction to the powerful proof technique of mathematical induction. Interactive exercises help students practice their proof-writing skills with simpler conclusions, while animated narrations enhance rigorous yet accessible proofs of more significant results such as the multiplicativeness of Euler's totient function.</div>
741						</li>
742						<li><a href='#' class='course-name'>Algebra: Groups, Rings and Fields</a>
743							<div>This course focuses on the study of algebra, in particular the kind of algebra that is usually learned by mathematics majors at university. As an incidental matter, students who complete the EMF algebra series will be able to solve any high school algebra problem with ease but, more importantly, will be well-prepared to study the high-level mathematics that is at the heart of important disciplines such as public-key cryptography and particle physics. Building on a solid understanding of operational systems, this course introduces groups, rings, and fields and their mathematical properties. While typical high school algebra students are limited to applying these rules mechanically to solve numeric equations, EMF students are guided to their own intuitive &quot;discovery&quot; of these behaviors through interactive exercises involving numeric and non-numeric mathematical structures. Students continue to sharpen their logical reasoning skills by proving several of these properties using EMF's proof-building technology.</div>
744						</li>
745						<li><a href='#' class='course-name'>Algebra: Relations, Mappings, Equations</a>
746							<div>This course continues the study of abstract algebra by introducing the fundamental notion of a relation and its properties. Whereas the previous course in the EMF algebra series focused on combining elements of a set with operations, this course investigates ways of relating elements of a set, one to another. Mappings, a key mathematical construct studied earlier in EMF, are then described as special types of relations. By expanding ideas and techniques introduced in the fifth and sixth EMF courses to the general context of any field, students learn to solve linear, quadratic and rational equations with mappings by calling upon the powerful properties of relations covered in the first part of this course. As with all EMF courses, students are exposed to mathematical ideas typically not seen until college and continue to gain experience building proofs of important results.</div>
747						</li>
748						<li><a href='#' class='course-name'>Algebra: Relational and Ordered Operational Systems</a>
749							<div>This course ties together the previous two courses and completes the study of abstract algebra in EMF. Students learn how groups, rings and fields can be combined with certain kinds of relations to form new structures, specifically relational systems and ordered systems. Within such systems, techniques for solving inequalities are given a much more in-depth treatment than has been possible in earlier courses. Skeleton proofs are provided of various properties of ordered groups, rings, and fields, and students are asked to complete them and then to apply these properties to easily solve inequalities over these systems.</div>
750						</li>
751						<li><a href='#' class='course-name'>Real Functions I</a>
752							<div>This course introduces the real number system as an extension of the ordered field of rational numbers and goes on to investigate certain fundamental classes of functions on the real numbers. After learning about the real numbers and their properties, students prove that the set of real functions with function addition and multiplication form a ring. Armed with this fact, various ring properties covered in earlier EMF courses, and powerful online graphing tools, students investigate systems of first degree equations and inequalities on the real numbers. The course then turns to analyzing quadratic equations and inequalities, first graphically and then by factorization and completing the square. The analysis culminates with an in-depth derivation of the quadratic formula &mdash; typical high school algebra students are merely asked to memorize this formula &mdash; after which EMF students will be well-versed in methods for solving first and second degree equations and inequalities, as well as understanding why these methods work. Real Functions I wraps up with second look at statistics, including the normal distribution, and an introduction to trigonometry. Throughout the course, students put their understanding and skills to work on realistic, complex problems that underscore algebra's usefulness in the real world.</div>
753						</li>
754						<li><a href='#' class='course-name'>Real Functions II</a>
755							<div>This course begins with an introduction to sequences and series, including in-depth coverage of arithmetic and geometric sequences and series. Students continue to expand their knowledge of real polynomial functions such as integer and rational power functions, exponential and logarithmic functions, the absolute value function, rational functions, and asymptotes. The course builds on material from Sets, Mappings, and Probability to explore the Binomial Theorem, a fundamental result with uses as varied as the distribution of IP addresses and financial modeling. Practical applications, including two extensive case studies in statistics, continue to demonstrate algebra's usefulness in the real world. The course culminates with an introduction to the field of complex numbers as a field extension of the real field and to polynomial functions over the complex field. Throughout, EMF students will prove many of the results about real and complex functions that typical high school students are only asked to memorize and apply. With respect to developing students' proof-writing skills, Real Functions II marks the completion of the transition from outline proofs to paragraph proofs.</div>
756						</li>
757						<li><a href='#' class='course-name'>Geometry: Incidence and Transformations</a>
758							<div>This course begins the formal study of Euclidean geometry in EMF. Working in the three-dimensional context of space, the two-dimensional context of planes, and the one-dimensional context of lines, students investigate familiar geometrical figures and a variety of ways of transforming them. In the first half of the course, real-world experiences with physical objects are used to inform the mathematically rigorous construction of analogous geometric objects and the properties they should have. The second half of the course builds on concepts from Sets and Mappings in order to explore transformations &mdash; reflections, translations, rotations, and magnifications &mdash; as mappings on sets of points. Students prove numerous results that are typically taken as given in high school geometry as they ascertain which of these transformations are permutations and which permutations preserve betweenness, collinearity, angle measure, distance, and circular orientation. As this is EMF, the proofs that students complete go well beyond the basic two-column high school proof in complexity, sophistication, and consequence.</div>
759						</li>
760						<li><a href='#' class='course-name'>Geometry: Congruence and Similarity</a>
761							<div>This course continues the study of Euclidean geometry in EMF. Students begin by investigating congruent figures in order to extend their knowledge of reflections, translations, rotations, and glide-reflections, together known as isometries. They then prove that these &quot;rigid motion&quot; mappings form a group. Equipped with their understanding of group properties from EMF&#39;s abstract algebra courses, students spend the first part of this course exploring congruence and symmetry, including properties of congruent triangles and a classification of polygons in terms of their symmetry groups. The second part of the course focuses on magnifications and their properties. Students explore what happens when magnifications are composed with themselves and with isometries and discover that these compositions, known as similitudes, also form a group. The third part of the course provides an in-depth study of circle geometry incorporating multiple applications from the first two parts. Because EMF teaches mathematics as a unified body of knowledge rather than a collection of unrelated topics, students come to realize a fundamental connection between algebra and geometry that most traditional school math students will never know.</div>
762						</li>
763						<li><a href='#' class='course-name'>Geometry: Coordinates and Measurement</a>
764							<div><div>This course concludes the study of Euclidean geometry in EMF, with a focus on measurement in two and three dimensions: of area, volume, distance, taxi-distance, conic sections; introduces
765									vector spaces; and reexamines isometries in the context of coordinate systems.</div></div>
766						</li>
767						<li><a href='#' class='course-name'>Precalculus Coda</a>
768							<div>
769								This course brings together various topics covered in earlier EMF courses and expands upon that material with an extensive study of vectors in the real number plane and space, linear transformations (including orthogonal mappings), and matrices and their application in solving systems of equations. Together these topics comprise a typical Precalculus course and provide a detailed understanding of the basic principles behind The Calculus.
770							</div>
771						</li>
772					</ol>
773					<h2>Supplements</h2>
774					<p>The following supplemental short courses become available to EMF students following the completion of certain specified EMF courses.</p>
775					<ul class='supplements'>
776						<li><a href='#' class='course-name'>Pre-Algebra</a>
777							<div>
777This short course explains topics, terminology, and notation that are taught in a typical school Pre-Algebra class by relating them to the more advanced language and concepts taught in EMF. Students who successfully complete the first seven EMF courses, this supplement, and recommended practice tests will be well-prepared to take any school Pre-Algebra test and succeed in a traditional school Algebra 1 course.</div>
778						</li>
779						<li><a href='#' class='course-name'>Abstract Algebra Readiness</a>
780							<div>This short course tests a student's readiness for EMF courses 10-14, which focus on Abstract Algebra. Students who complete the first nine EMF courses should use this supplement to review the important ideas covered in those courses as these ideas provide the mathematical tools necessary to master the EMF Abstract Algebra courses.</div>
781						</li>
782						<li><a href='#' class='course-name'>Algebra 1</a>
783							<div>This short course explains topics, terminology, and notation that are taught in a typical school Algebra 1 class by relating them to the more advanced language and concepts taught in EMF. Students who successfully complete the first 13 EMF courses, this supplement, and recommended practice tests will be well-prepared to take any school Algebra 1 test and succeed in a traditional school Algebra 2 course.</div>
784						</li>
785						<li><a href='#' class='course-name'>Algebra 2</a>
786							<div>This short course explains topics, terminology, and notation that are taught in a typical school Algebra 2 class by relating them to the more advanced language and concepts taught in EMF. Students who successfully complete the first 14 EMF courses, this supplement, and recommended practice tests will be well-prepared to take any school Algebra 2 test and succeed in traditional advanced high school math courses.</div>
787						</li>
788						<li><a href='#' class='course-name'>Geometry</a>
789							<div>This short course explains topics, terminology, and notation that are taught in a typical school Geometry class by relating them to the more advanced language and concepts taught in EMF. Students who successfully complete the first 17 EMF courses, this supplement, and recommended practice tests will be well-prepared to take any school Geometry test and succeed in traditional advanced high school math courses.</div>
790						</li>
791						<li><a href='#' class='course-name'>Precalculus Readiness</a>
792							<div>
793								<div>This short course tests a students readiness for EMF's Precalculus Coda course. Students who complete
794									the first 17 EMF may use this supplement to review the important ideas covered
795									in those courses before advancing to the Precalculus Coda course.</div>
796							</div>
797						</li>
798						<li><a href='#' class='course-name'>Precalculus</a>
799							<div>This short course will explain topics, terminology, and notation that are taught in a typical school Precalculus class
800								by relating them to the more advanced language and concepts taught in EMF. Students who
801								successfully complete the entire EMF program, this supplement, and recommended practice tests will be well-prepared to take any
802								school Precalculus test and succeed in an Advanced Placement Calculus class.</div>
803						</li>
804					</ul>
805				</div>
806
807				<a name='technology'></a>
808				<div class='popup technology'>
809					<h1>Technology</h1>
810					<p>EMF is supported on the free Chrome and Firefox browsers. In addition to laptops and desktops, EMF is compatible with iPads, large Android tablets, and touchscreen computers. However, some features are easier to use with a mouse or other pointing device. EMF is not compatible with smartphones.</p>
811					<p>Examples of how EMF uses the latest technology are shown below.</p>
812
813					<ul class='technology-examples'>
814						<li><h2>Virtual Classrooms</h2>
815							<div>In EMF's Virtual Classrooms, a clever cast of professors and students discuss current course topics. Here's a simulated classroom from EMF09 (Number Theory) that introduces proof by induction:</div>
816							<iframe class='youtube-video' src="https://www.youtube.com/embed/83jq-N7_yEI?rel=0" frameborder="0" allowfullscreen></iframe>
817						</li>
818						<li><h2>Puzzles and Games</h2>
819							<div>EMF uses puzzles and games to reinforce student understanding. In this case, the <i>String Game</i> helps
820								students to understand set concepts such as union and intersection. Try your hand! Move the pieces from the right
821								onto the diagram to obtain clues about the identity of the three labels. Click on a label to make your choice.</div>
822							<div class='string-game'>
823								<div class='stringgame noauto game01 highlightonhover sg01div'>
824									<input type='hidden' name='stringcount' value='3' />
825									<input type='hidden' name='usenot' value='false' />
826									<input type='hidden' name='labels' value='' />
827									<input type='hidden' name='showlabels' value='false' />
828									<input type='hidden' name='development' value='false' />
829									<input type='hidden' name='usecurves' value='true' />
830									<input type='hidden' name='playgame' value='true' />
831									<input type='hidden' name='placed' value='' />
832								</div>
833							</div>
834						</li>
835						<li><h2>Experiments</h2>
836							<div>EMF uses modern technology to generate experiments such the <i>Galton Box</i> shown below, as well as many interesting Markov chain simulations.</div>
837							<div class='pascal pascal02 noauto'>
838								<input type='hidden' name='pathwidth' value='20' />
839								<input type='hidden' name='labelfontsize' value='15px' />
840							</div>
841							<div class='buttondiv'>
842								<button class='beanbutton'>Bean!</button>
843								<button class='manybutton'>Many beans!</button>
844							</div>
845						</li>
846						<li><h2>Animations</h2>
847							<div>Hundreds of animations and interactive tools help students understand difficult concepts
848								with relative ease. In this animation, the sun's rays make the ball's shadow appear as the wheel turns at a steady pace, resulting in a distance-time graph of a sine curve:
849							</div>
850							<div class='oscilloscope2'>
851								<input type='hidden' name='type' value='auto' />
852							</div>
853							<div class='oscilloscope2-startbutton' style='text-align:center;'><button>Start</button></div>
854						</li>
855						<li class='explorations'><h2>Explorations</h2>
856							<div>
857								Today, computers and even many mobile devices have capabilities that teachers could only dream of a few years ago.
858								EMF uses the very latest technology to allow students to explore mathematics in ways that are only now becoming possible.
859								Consider, for example, the <i>extrusion</i> illustrated below. Press the buttons to extrude the plane object to a solid,
860								then zoom, rotate and drag this 3D object to explore it.
861							</div>
862							<div class='extruder www'></div>
863						</li>
864					</ul>
865				</div>
866
867				<a name='reviews'></a>
868				<div class='popup reviews'>
869					<h1>Reviews</h1>
870
871					<h2>Broward County EMF Survey</h2>
872
873					<p style='margin-top:0;'>The following is a sampling of findings from an anonymous survey given to EMF families in Broward County Public Schools, Florida in spring of 2016.</p>
874
875					<ul>
876						<li>100% of parents reported that their child's ability to analyze complex problems, self-study skills, and ability to focus for extended periods of time had improved since beginning EMF.</li>
877						<li>92% of parents report that their child enjoys doing EMF and finds EMF challenging.</li>
878						<li>92% of parents think that EMF has made their child more ready for high school and college mathematics than they would have been without it.</li>
879					</ul>
880					<p>Read the <a target='_blank' href='https://www.elementsofmathematics.com/scripts/htm/resources/bcps-emf-survey-2016.pdf'>full summary</a> of the 2016 Broward County Public Schools EMF Survey.</p>
881
882					<h3 style='margin-top:10px;'>Student Quotes</h3>
883
884					<ul>
885						<li>"EMF is a tough program, but it pays off. I learned how to prove concepts, and I learned to work harder and on a schedule." &mdash; Andrei Chekmasov, EMF Student</li>
886						<li>"EMF allows students to avoid the trap of believing that math is nothing but problems to solve with rules and a calculator." &mdash; Corbin Diaz, EMF Student</li>
887						<li>"EMF is definitely the course for students with a thirst for mathematical knowledge." &mdash; Luke Freed, EMF Student</li>
888						<li>"After doing EMF, I not only understand how to use formulas but I can actually prove them. This program changed me from a girl who loved math into a real mathematician." &mdash; Skylar Gamberg, EMF Student</li>
889						<li>"EMF is a way of looking at everything that you took for granted in earlier years, and proving them to make them more detailed and complete." &mdash;
889 Ian Gonzalez, EMF Student</li>
890						<li>"EMF is challenging in a good way &mdash; like a puzzle. You're working hard, improving your mind, and still having fun!" &mdash; Grace Hancock, EMF Student</li>
891						<li>"EMF is way more exciting than other math programs and keeps you on your toes. I enjoy it even when it takes a really long time to solve the hardest problems." &mdash; Imaan Nanji, EMF Student</li>
892						<li>"I cannot even imagine what my life would have been like without having seen the beauty of mathematics through EMF." &mdash; Vievie Romanelli, EMF Student</li>
893						<li>"EMF has increased my ability to write proofs and my mathematical skill overall. It has some of the most interesting mathematical concepts I have ever seen." &mdash; Albert Wang, EMF Student</li>
894						<li>"Now that I have completed EMF, I can attest to their claim that their students will be ready to take calculus. I am currently about half way through AP Calculus BC and am having no problem at all with the material. &mdash; Alexander Yue, EMF Student</li>
895						<li>"If you're good at math but could sleep through math class because you find it boring, EMF is awesome and will actually keep you awake. &mdash; Isabella Yeung, EMF Student</li>
896					</ul>
897
898					<!--
899										<ul style="padding-left:20px">
900											<li>&quot;[EMF] allows you to use your intelligent brain more than you ever have before.  In the normal classes I would be bored when the teacher would go over the lesson over and over and over.&quot;</li>
901											<li>&quot;You're working hard, improving your mind, and still having fun!&quot;</li>
902											<li>&quot;Don't give up when it gets hard, ask questions, take your time, possibly work at home, and you will be rewarded in the long run.&quot;</li>
903										</ul>
904					-->
905				</div>
906
907				<a name='background'></a>
908				<div class='popup background'>
909					<h2>A Brief History</h2>
910					<p>In the mid 1960s, facing a shortage of home-grown mathematicians and scientists, the US Office of Education (later to
911						become the US Department of Education) made a huge investment in mathematics curriculum development projects.
912						So-called New Math was designed to replace the traditional mathematics curriculum for students
913						across the board. The effort is generally regarded as having failed, not least because insufficient
914						funds were allocated to support the necessary and substantial teacher retraining.</p>
915
916					<p>At the same time the more focused <em>Elements of Mathematics</em> (EM) project set itself the task of
917						replacing the standard program for mathematically talented students. EM would take precocious
918						ten-year-olds and prepare them to learn undergraduate-level mathematics by seventh grade and
919						upper division mathematics as college freshmen. The middle school portion of this curriculum
920						became known as <em>Elements of Mathematics: Foundations</em> (EMF).
921					</p>
922
923					<p>Unfortunately, not only did EM require that teachers be retrained &hellip; they also needed to have mathematics
924						degrees, greatly exacerbating implementation issues. Nevertheless, EM was taught and survived for
925						many years at a handful of centers in the US to the benefit of mathematically talented children
926						lucky enough to live in those locations.</p>
927
928					<p>In 2011, a mathematics educator and EM alumna was clearing out an attic when she came across
929						her old Foundations textbooks. In light of the many recent technological advances, she wondered whether there
930						might now be a way to teach it <em>without</em> the need to employ highly skilled mathematicians and to
931						make it accessible to talented students <em>anywhere</em>. A successful pilot study ensued, and
932						the following year, EMF was launched as
933						an online, self-study, self-contained mathematics program for talented middle school students.</p>
934
935					<h2>Recommended Reading</h2>
936					<p><a target='_blank' rel = 'nofollow' href='http://devlinsangle.blogspot.com/2018/05/calculation-was-price-we-used-to-have.html'>Calculation was the price we used to have to pay to do mathematics</a>. Prof. Keith Devlin, <em>Devlin's Angle,</em> 2 May 2018.</p>
937
938					<p><a target='_blank' href='https://www.maa.org/external_archive/devlin/LockhartsLament.pdf'>A Mathematician&#39;s Lament</a>. Paul Lockhart, 2002.</p>
939
940					<h2>Additional Information</h2>
941					<p><a target='_blank' href='https://www.imacs.org/emf-reveals-the-beautiful-and-creative-side-of-math/'>EMF Reveals the Beautiful and Creative Side of Math</a>. <em>The IMACS Blog,</em> 11 Oct. 2019.</p>
942
943					<p><a target='_blank' href='https://www.imacs.org/developing-math-talent-beyond-competitions/'>Beyond Math Competitions: Developing Math Talent to Its Fullest Potential</
943a>. <em>The IMACS Blog,</em> 28 Jun. 2019.</p>
944
945					<p><a target='_blank' href='https://www.imacs.org/uf-prof-knudson-visits-emf-math-students/'>University of Florida Professor Delivers Math Lectures to BCPS Top Middle and High School Students</a>. <em>Broward County Public Schools,</em> 10 Jun. 2019.</p>
946
947					<p><a target='_blank' href='https://www.imacs.org/talented-middle-school-math-students-forge-early-path-to-university-coursework/'>Talented Middle School Math Students Forge Early Path to University Coursework</a>. <em>The IMACS Blog,</em> 6 Mar. 2019.</p>
948
949					<p><a target='_blank' href='https://www.imacs.org/emf-vs-traditional-approach-to-math/'>EMF Math vs. The Traditional Approach to Learning Mathematics</a>. <em>The IMACS Blog,</em> 20 Feb. 2019.</p>
950
951					<p><a target='_blank' rel = 'nofollow' href='http://districtadministration.com/press-release/online-gifted-math-program-allows-middle-school-students-in-illinois-district-to-study-advanced-math/'>Online Gifted Math Program Allows Middle School Students in Illinois District to Study Advanced Math</a>. <em>District Administration,</em> 12 Oct. 2018.</p>
952
953					<p><a target='_blank' href='https://www.imacs.org/emf-reflections-isabella-yeung/'>Gifted EMF Alumna Shares Advice for Current & Future Students</a>. <em>The IMACS Blog,</em> 27 Aug. 2018.</p>
954
955					<p><a target='_blank' href='https://www.imacs.org/emf-math-for-talented-middle-school-students/'>EMF Math For Talented Middle School Students is Complete!</a> <em>The IMACS Blog,</em> 23 Jul. 2018.</p>
956
957					<p><a target='_blank' rel = 'nofollow' href='http://districtadministration.com/challenging-mathematically-talented-middle-school-students/'>Challenging mathematically talented middle school students</a>. <em>District Administration,</em> 8 May 2018.</p>
958
959					<!--p><a target='_blank' rel = 'nofollow' href='https://www.districtadministration.com/content/online-math-program-talented-students-doubles-enrollment-florida-s-broward-county-public'>Online Math Program for Talented Students Doubles Enrollment in Florida's Broward County Public Schools</a>. <em>District Administration,</em> 23 Oct. 2017.</p-->
960
961					<a target='_blank' rel = 'nofollow' href='https://www.imacs.org/home/about-us/news/emf-bcps-doubles-enrollment/'>Online Math Program for Talented Students Doubles Enrollment in Florida's Broward County Public Schools</a>. <em>District Administration,</em> 23 Oct. 2017.
962
963					<p><a target='_blank' href='https://www.imacs.org/gifted-math-a-better-alternative-to-acceleration/'>Gifted Math: A Better Alternative to Acceleration</a>. <em>The IMACS Blog,</em> 17 Nov. 2016.</p>
964
965					<p><a target='_blank' rel = 'nofollow' href='https://thejournal.com/articles/2016/08/02/broward-county-schools-to-expand-online-math-program-for-gifted-students.aspx'>Broward County Schools to Expand Online Math Program for Gifted Students</a>. <em>THE Journal,</em> 2 Aug. 2016.</p>
966
967					<p><a target='_blank' rel = 'nofollow' href='http://www.prnewswire.com/news-releases/online-gifted-math-program-to-grow-to-several-hundred-students-in-broward-county-public-schools-300307665.html'>Online Gifted Math Program to Grow to Several Hundred Students in Broward County Public Schools</a>. <em>PR Newswire,</em> 2 Aug. 2016.</p>
968
969					<p><a target='_blank' href='https://www.eimacs.com/blog/2015/02/not-your-fathers-algebra-a-new-online-course-for-talented-students/'>Not Your Father's Algebra: A New Online Course for Talented Students</a>. <em>The IMACS Blog,</em> 12 Feb. 2015.</p>
970
971					<p><a target='_blank' href='https://www.eimacs.com/blog/2012/10/imacs-introduces-elements-of-mathematics-foundations/'>IMACS Introduces Elements of Mathematics: Foundations</a>. <em>The IMACS Blog,</em> 25 Oct. 2012.</p>
972
973					<h2>IMACS</h2>
974					<p>EMF is developed by the Institute for Mathematics and Computer Science (<a target='_blank' href='https://www.imacs.org'>IMACS</a>), an independent teaching
975						and educational research institute with 25 years' experience developing original curriculum for talented K-12 students.
976						IMACS' curriculum has been used in prestigious programs such as Duke's Talent Identification Program and
977						Johns Hopkins University's Center for Talented Youth. Over 4,500 students from across the US and around the
978						world attend local IMACS classes or study its online courses.</p>
979
980				</div>
981			</div>
982
983			<ul class='menu'>
984				<li>Home</li>
985				<li>About</li>
986				<li class='freeat'>Free Trial</li>
987				<li>FAQ</li>
988			</ul>
989		</div>
990		<div class='menu-bars'>
991			<div class='bar'></div>
992			<div class='bar'></div>
993			<div class='bar'></div>
994		</div>
995		<div class='mobile-menu abs'>
996			<div class='emf-small'><img src='/scripts/emf/css/www/images/emf-256.png' alt='EMF' /></div>
997			<div class='closebutton'>
998				<div class='bar'></div>
999				<div class='bar'></div>
1000			</div>
1001			<ul class='resize-font' data-r='0.1'></ul>
1002		</div>
1003	</body>
1004
1005
1006	</body>
1007</html>

Line numbers count LF bytes from the start of the resource, as the search results do. Vendor segments are library code the classifier recognised; they are stored but not indexed. Bytes are shown as Latin1 characters, one per byte.