# Subject Catalog

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# TPS Math Courses

#### Why choose TPS Math classes?

TPS has been teaching math worldwide since 1997. Our courses and outcomes are displayed and compared worldwide, where we have a consistent reputation for providing excellent math preparation with top scores on U.S. and global testing. We know what constitutes an excellent math program and an effective math course.

- Full scope math classes grades 4 through 12
- Top scores worldwide on AP Calculus BC, AP Calculus AB and AP Statistics exams
- Dual college credit in College Math, Precalculus, and Calculus (AB and BC)
- Solid foundation in Algebra, Geometry and Algebra 2 for SAT, ACT and higher math and science
- Two levels of Math (Standard and Honors) in every grade

U.S. high school students rank in the bottom 1/4 to 1/2 (exact ranking depends on the study) in math achievement compared to other developed countries. This data is reflected in current studies by the International Organization for Economic Cooperation and Development, the U.S. National Assessment of Educational Progress, and PEW Research. It is also reflected consistently in these and similar studies going back at least two decades. This is not just a “public education” problem — U.S. private schools, Christian schools, and home education fare no better as statistical groups.

TPS has been teaching math worldwide since 1997. Our students live all around the world, including the top countries in the studies. Our courses and outcomes are displayed and compared worldwide, where we have a consistent reputation for providing excellent math preparation with top scores on U.S. and global testing. We know what constitutes an excellent math program and an effective math course.

We also know from experience why most math courses are not as effective for preparation and most math programs cannot show reliable outcomes. In choosing math textbooks and curricula over the past 20+ years, TPS has considered or reviewed every major high school math curriculum (that we know of) written in English. We have also done readiness testing with students from public schools, private schools, and a wide array of online math course providers. **Based on all of our experience and testing, the elements that are essential to an effective math program (and lacking in less effective programs) are:**

**Full scope curriculum.** The topics that must be covered and skills that must be mastered in Algebra, Geometry, Functions, and Trigonometry (which is Algebra 1, Geometry, Algebra 2, and Precalculus) are ultimately determined by the study of Calculus. However, the average parent (and many high school math teachers) does not have enough knowledge or experience to identify whether their student’s math course is full scope or has omitted important material. Math curricula targeted at the homeschool market are particularly susceptible in this issue because they are intentionally reduced in scope to make them easier to self-study, but the problem also exists in the growing number of online offerings that claim to provide a full HS math course in a semester or a summer, or some other shortened period or relaxed pace. A full scope HS math course is 36 weeks of teaching and testing — it can be compressed a little, but not into a semester or summer without significant loss of content and evaluation. We have administered final exams to students who have recently completed shortened courses from reputable providers, and the results are never been comparable to students completing the full course.

**Inductive problem-solving.** One of the greatest benefits of learning math — even for the student with no interest in math or science — is that it teaches inductive problem solving where you start with a general situation and an objective, and you must first inductively determine a series of problem steps to reach the objective and then deductively step through the necessary formulas and equations to solve each problem and achieve a correct final solution. One of the quickest ways to make HS math easier is to eliminate the inductive setup and skip to the formulas and deductive applications. This again is a common aspect of homeschool math programs and shortened math courses.

**Frequent and cumulative testing.** More than in any other subject, math builds on itself relentlessly topic by topic from Algebra through Calculus and beyond. More than any other subject, study of math is “unforgiving” of any unlearned or misunderstood concepts. Students in higher math with significant gaps in prior math must either fill in the prior gaps or fail to learn the higher concepts (which is why many students never know their potential or why some fields seem unattainable for them later despite their interest). While it may seem encouraging and enlightened to teach math with minimal formal evaluation and without cumulative testing, this also virtually ensures that the student will not learn and retain enough math to keep moving upward in full scope courses. When a student applies to a TPS math course from a prior math course that was reduced in scope and testing, we sometimes administer a cumulative final exam to the student in the course he just completed. Even when the student has just finished the prior course and is presumably at peak retention, he or she is almost never able to pass a cumulative final exam. There is no substitute for frequent and cumulative math testing with teacher evaluation of the problem solving process to ensure a student learns and retains the math needed to move upward through the series of topics that build their way to higher math and science.

**Why does this matter to your student?** TPS teaches one of the most effective Precalculus and Calculus programs available anywhere (check our AP scores). We get many applications for our Precalculus course from students who did not take our Algebra 2 or prior courses. We are forced to disapprove many of these (sending them to repeat Algebra 2 and/or Geometry) because there are too many holes in the prior math background.

**But how does this matter if your student is going to be a non-math/science major and may never take Precalculus?** You would be surprised where Algebra, Geometry and even much of Algebra 2 show up in other fields and careers, including design careers, social studies research, field work, and medical support and health careers — just to name a few. This is why most colleges require that the student have taken math through Algebra 2, and SAT/ACT tests include math through Algebra 2.

Whether you have a strong enthusiastic math student or a reluctant one, do him or her a favor (even if it’s not fun) and **make sure he gets a solid math education through Algebra 2 that doesn’t cut out important math concepts or reduce them to formulas**. After that, he or she can decide where to go with (or without) math, but at least the options won’t have been limited back in early high school.

TPS offers a solid standard (non-honors) math track suitable for all students, including the student who may never take Precalculus. We also offer an honors math track for students who are “good at math” or who like math or who probably will take Precalculus. You can even start on one track and switch to the other, but either way you will learn the math you need for whatever comes after.

**What Others Are Saying**

Read what other students and parents have to say about TPS math classes.

**TPS Math Classes**

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#### Elementary Math (before Pre-Algebra)

TPS offers Elementary Math (i.e, Math prior to Pre-Algebra) in two tracks: *Accelerated* and *Fundamentals*. Both tracks are thorough preparation for Pre-Algebra, the transitional course that bridges a student from concrete to abstract in preparation for Algebra and beyond.

TPS *Math Accelerated* is based on the *Singapore Math* curriculum, which introduces more advanced topics a little sooner. Our testing has shown that students who do well in TPS *Math Accelerated 6* are prepared to go straight to Algebra, effectively skipping a year of Math.

TPS *Math Fundamentals* is based on the *Math Mammoth* curriculum, highly regarded for its rigor and accessibility. It thoroughly prepares a student for the crucial transition of Pre-Algebra, which also uses the *Math Mammoth* curriculum.

**Accelerated:** More advanced topics in greater depth

Grade 4: Math Accelerated 4

Grade 5: Math Accelerated 5

Grade 6: Math Accelerated 6

Note: Strong Math Accelerated 6 students may skip Pre-Algebra and go straight to Algebra.

**Fundamentals:** Solid foundation for Pre-Algebra or Pre-Algebra (Honors)

Grade 5-6: Math Fundamentals 5

Grade 6-7: Math Fundamentals 6

#### Pre-Algebra through college-level Math

Pre-Algebra is the transitional course that bridges a student from concrete to abstract in preparation for Algebra and beyond. TPS offers math from Pre-Algebra through Algebra 2 in two tracks: *Honors* and *Standard*.

TPS *Honors* and *Standard* tracks are both thorough preparation for college and career. Honors courses go deeper into some topics, assign some harder problems in homework and tests, and add a few more topics — all designed to better prepare a student for Calculus. Honors class lectures and discussions move a little faster and spend a little less time on review. Though Honors courses are ideal for preparing for Calculus, students who do well in the Standard courses will also be prepared to do well in Precalculus and Calculus. Students who start in one track can switch tracks later if needed, based on grades or changing academic goals.

TPS offers a wide range of options after *Algebra 2*, including *Precalculus (Honors)* followed by *Calculus BC* or *Calculus AB*; Statistics; or *College Math (Quantitative Reasoning)*. TPS Precalculus and Calculus BC and AB are eligible for college dual credit.

**Honors:** Prospective Math/Science majors or other students preparing for Calculus

Grade 6-7 (Summer before Pre-Algebra): Pre-Algebra Prep Camp (Math 6 Review)

Grade 6-7: Pre-Algebra (Honors)

Grade 7-8 (Summer before Algebra): Algebra Prep Camp (Pre-Algebra Review)

Grade 7-8: Algebra (Honors)

Grade 8-9 (Summer before Geometry): Summer Algebra Review

Grade 8-9: Geometry (Honors)

Grade 9-10 (Summer before Algebra 2): Algebra Review, Geometry Review (will be made available if there are sufficient requests)

Grade 9-10: Algebra 2 (Honors)

Grade 10-11 (Summer before Precalculus): Algebra 2 Review

Grade 10-11: Precalculus (Honors)

Grade 11-12: AB Calculus, BC Calculus

**Standard:** Prospective Social Science or liberal Arts majors, or students preparing for AP Statistics or college-level Quantitative Reasoning or Trigonometry (Precalculus)

Grade 7-8 (Summer before Pre-Algebra): Pre-Algebra Prep Camp (Math 6 Review)

Grade 7-8: Pre-Algebra

Grade 8-9 (Summer before Algebra): Algebra Prep Camp (Pre-Algebra Review)

Grade 8-9: Algebra

Grade 9-10 (Summer before Geometry): Summer Algebra Review

Grade 9-10: Geometry

Grade 10-11 (Summer before Algebra 2): Algebra Review, Geometry Review (will be made available if there are sufficient requests)

Grade 10-11: Algebra 2

Grade 11-12 (Summer): Algebra 2 Review

Grade 11-12: Precalculus (Honors), College Math (Quantitative Reasoning), AP Statistics

Grade 12: AB Calculus

To find more details on these and related courses, please select the “Math” category in our Course Catalog.