This video describes the EMF approach to teaching modern mathematics, and describes the individual EMF courses:

More information on EMF may be found on the Elements of Mathematics: Foundations website. EMF is provided by District 220 for qualifying Extended Math students.

Why Extended Math-EMF?

• Why should my middle school student learn such advanced mathematics? What about the basics?

  Mathematically talented students typically master the basics with little effort. As a result, they often become bored with and disengaged from math. They also fail to develop the mental resiliency and study skills that come with having to work hard at math problems designed for their ability level.

  It is useful to separate out the two ways in which EMF is college-level: (1) the sophisticated use of logic and reasoning via proofs, and (2) the introduction of modern topics such as Topology. That certain topics and analytical tools are modern does not equate to them being difficult.

  EMF incorporates all the concepts from a traditional curriculum but uses a logic and proof-based approach not usually entrusted to students until college. Talented middle school students who are intellectually mature and motivated can benefit from this more sophisticated approach; it develops creative thinking skills that are not easily replaced by computer processing power as algebraic manipulation skills already have. In short, EMF prepares students with skills for the future, not skills of the past. (Additional reading)

  EMF's incorporation of exciting topics in modern mathematics—topics not typically covered by traditional school math and hence usually met only at college—makes it far more interesting and intellectually engaging. These topics represent areas of active research as opposed to traditional school math subjects that were understood completely by the late 17th century. The idea of cutting off a child's education in literature, history or science at the 17th century is ludicrous. The same applies to mathematics.

• What does a "blended approach" mean?

  District 220's implementation of the EMF curriculum embraces a blended approach that puts the students and the teachers at its center. Classes are taught through teacher and student modeling and interaction, in addition to students completing the online EMF courses. Teachers lead in-class discussions to introduce new material, model problem-solving strategies, and answer questions about previously covered material. At home and in class, students are expected to reinforce their understanding through close reading of the online EMF text and careful completion of the assigned exercises.

  Parents and students should note that, in addition to paying attention to teacher-led discussions in class, close reading of the online course material is critical to success in EMF. Students who are used to skimming or skipping the reading in traditional math classes will quickly find that following the same approach in EMF causes their understanding, and consequently their grades, to suffer greatly.

Getting In

• How does a student qualify for Extended Math-EMF?

  District 220 students qualify for Extended Math-EMF based on the district's identification process. Generally, students are performing at or above the local 90th percentile in achievement and cognitive data. Please reference the District 220 webpage for Extended Services identification details.

  Note that Extended Math-EMF students are expected to learn the material through both teacher-led classroom discussions and close reading of the online text. Prospective students should be reading at above grade level and be ready to reinforce new concepts through careful reading.

• What is the first EMF course about?

  It introduces elementary group theory, modular arithmetic and non-numeric operations.

• I elected to take Extended Math-EMF as my full-time math program — can I change my mind?

  Yes, students can exit the Extended Math-EMF curriculum and move into Accelerated Math, however, some topics may be revisited using a traditional math approach. To change a math pathway, please contact the District 220 teacher and the Director of Extended Services.

Getting Help

• What should a student do if they need help understanding the material when their teacher is not available?

  Parents and students should note that all the information students need to understand and answer exercises is contained in the online text of the relevant section. Usually, rereading the section, revisiting previous exercise problems and using the model answers given will overcome any understandings.

  When students are logged into the EMF site they may access the Help Forum, in which students are encouraged to post well-thought-out questions to be discussed with highly-advanced students who provide guidance on thinking. Questions that are not answered satisfactorily are filtered through to experienced instructors and mathematicians who respond through the Help Forum.

  Note that the Help Forum is not designed or intended to substitute as a teacher. The Help Forum is provided as an additional resource outside of the classroom to answer students' specific and focused questions.

  For each exercise, students may read previously posted Help Forum questions and answers about that exercise by clicking on the green question mark button that appears with that exercise.

  To use the Help Forum, students must obey strict rules, including rules prohibiting the request or provision of answers. Students who do not obey these rules will be prohibited from accessing the Help Forum and will not be permitted to continue in the EMF program.

  (It is worth pointing out that, historically, 85% of help requests from students taking the early EMF courses generate responses that encourage the student to solve the issue themselves by either re-reading the section or by using the index button, and almost invariably the student overcomes the issue by following this advice.)

• Why do you say that it's not good to help your child with the EMF curriculum? What if you know mathematics and you want to help?

  A rare selection of parents possess the characteristics that it takes to effectively help their Extended Math-EMF student, namely university-level training in abstract mathematics and the ability to guide young people while still allowing them to experience productive struggle. Even for such individuals, refraining from helping allows your child to develop strong independent study habits that he or she will certainly benefit from at university.

  Parents' most important role is to provide a supportive environment in which students can study without interruption or distraction, and where necessary to help with organization and time-management. Please also encourage your child to advocate for him or herself with the Extended Math teacher.

• Are students allowed to use calculators and graphing tools such as those available online?

  EMF provides an integrated scientific calculator and graphing tools that students may use in completing their EMF coursework. While there are sophisticated tools available online, Extended Math-EMF students are limited in how they may use these external tools. Students may use the external sites' tools as investigative and research tools, and to check answers arrived at through their own thinking, but are prohibited from using these tools to generate answers directly. Use of external tools for any purpose on EMF tests is strictly prohibited.

  The use of external tools to calculate answers in earlier EMF courses is self-defeating. Later courses focus on proofs for which there are no online tools. Success in the proof-based courses is possible only if a student has developed strong mathematical intuition by solving problems using their own brainpower. There simply is no substitute for the experience gained by figuring things out for yourself.

• What should my child do if he or she is having technical difficulties with an EMF course?

  Students should report the issue by clicking the "Technical Support" button in the Help Forum.

Grades

• How are EMF grades calculated?

  Each course contains several units, each of which is either an assignment (containing exercises and review problems), or a test. Raw point scores are then adjusted depending on the unit's level of difficulty. A grade is then calculated as a weighted average of the assignments (60% weight) and tests (40% weight). This is the EMF course grade. District 220 students should strive to maintain EMF course grades of 80% or better. (Since EMF courses typically contain between eight and ten assignments, but only one or two tests, it is vital that students prepare well for tests in order to obtain a high EMF course grade.)

• Are the EMF grades used as the basis for the students' report card grades?

  Yes. A student's official report card grade reflects the EMF assignment and test grades on coursework scheduled for completion during the grading period, in-class assessments given by the student's teacher and the student's Math Journal. Extended Math course grades are aligned to the middle school grading policy at Station and Prairie Campus: EMF summative assessments and in-class summative assessments account for 90% of the course grade, while EMF exercises account for 10% of the course grade.

• How will I know how my child is doing in the program?

  Parents may access the District 220's Infinite Campus electronic gradebook to monitor student's progress. *Note: The EMF gradebook is supplemental and does not reflect all assignments comprising of the Extended Math course grade.

• Does my child need to meet certain standards to remain in the program?

  Students who earn a grade of 'C' or below for work done in the Extended Math-EMF class will be monitored closely. Extended Math teachers will communicate with parents to develop a plan of action to support the student for the following quarter or trimester. If the student continues to struggle within the Extended Math-EMF class, a recommendation may be made to exit the student from the program.

• My child insists on getting everything correct. Are there do-overs in EMF?

  Yes and No. Certain exercises in EMF allow a student one, and only one, do-over if the student's initial answers would receive a score below 50%. The student is given a warning and encouraged to carefully rethink his or her answers.

  As a reminder, the District 220 middle school grading policy will count EMF exercises as 10% of the course grade.

Schedule and Pacing

• When are the 18 EMF courses scheduled for completion?
  • 6th grade: EMF01-EMF08 (Pre-Algebra)
  • 7th grade: EMF09-EMF12 (Algebra 1)
  • 8th grade: EMF13-EMF14 (Algebra 2 and Precalculus)
  • 9th grade: EMF15-EMF18 (Geometry and Precalculus)
• What is the appropriate pace for working through an EMF course?

  Extended Math teachers provide students with a benchmark schedule that they should follow. Students should work diligently to stay on schedule, but this should not be confused with working faster. Proceeding too quickly through EMF can be detrimental to a student's long term success in the program. Students should bear in mind that there is no prize for finishing first, but significant rewards for those whose meticulousness and dedication leads to a deep and lasting understanding.

  Students who take the time to read and re-read EMF material and to work through the problems slowly and carefully do much better. Students who are used to succeeding in regular school math despite jumping from exercise to exercise and ignoring or speed-reading the intervening text will quickly discover that the same approach will not work in EMF. Students are also expected to take a long time puzzling through the more difficult problems, often by putting pencil to paper, and without giving up too quickly. In other words, EMF rewards patience and persistence.

• Should a student work on EMF if they have 15 minutes to spare?

  Probably not. Success with the EMF curriculum requires longer stretches of deep focus and concentration. It would be better to use those 15 minutes to help free up a longer block of time later.

Miscellaneous

• Does a student have to take the courses in order, or can some courses be skipped or taken out of order?

  The EMF courses must be completed in order and without skipping. These courses are designed to build an intuitive foundation for mathematics through carefully planned steps.

• Does the Extended Math-EMF program replace my child's middle school math program?

  Yes. Your child will study the EMF program during the time allotted for his or her mathematics education. Your child's report card grades in mathematics are calculated from the grades obtained in the EMF courses, in addition to in-class assessments given by your child's teacher.

• Is EMF algebra the same as the algebra taught in schools and in other online courses?

  No. EMF teaches what mathematicians call "abstract algebra." The algebra taught in high school and other online courses is a special case of abstract algebra usually referred to by mathematicians as "elementary algebra." The first nine EMF courses teach the foundational concepts and tools needed in order to learn abstract algebra.

  Students who complete 8th grade Extended Math-EMF will earn a high school credit for Algebra 2.

• What technology do students need?

  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. Headphones are highly recommended.