On what basis do you claim the classes offered are “honors” level?

There are no specific guidelines to define honors level courses.  In general, an honors level course either covers more topics than a general course, or covers the same topics but in more depth.  I seek to do both. I have specifically chosen texts that push the students and do not shy away from assigning the harder problems.  I also supplement the texts with additional assignments as needed. Harold Jacobs, who authored the Geometry text that I use, created a list of suggested homework assignments for both general and honors level courses, and I follow the one for honors level.  Forester, the author of the texts I use for Algebra I, Algebra II, and Advanced Math, incorporates math modeling problems that set his texts apart from others.  These and other challenging problems he includes qualify the texts to be used in honors level courses.

My child has been using a curriculum that integrates geometric concepts into the other high school math courses rather than having Geometry as a separate course. Could he enter your program in Algebra II or Advanced Math without having had Geometry?

The study of geometry incorporates two aspects: proof and practical application. A curriculum that incorporates geometry into other math courses usually only covers practical application. I am a firm believer in learning proof-based geometry because it teaches logic. Learning to construct a proof helps in just about any other subject. I incorporate Jacobs’ Geometry in the sequence of classes I teach because it has not minimized proofs as have many other Geometry texts. I recommend students take Geometry after Algebra I and before Algebra II, but it can be taken in conjunction with Algebra II if an ambitious, hard-working student needs to do so in order to take Calculus in high school.  I require students to have had a geometry class that includes proofs before taking Advanced Math.

What is the difference between Jacobs’ Geometry: Seeing, Doing, Understanding and Euclid’s Elements?

Jacobs’ Geometry is a modern high school textbook with both instruction and assignments for the student. Students with no background in proofs can pick up this book, learn the different types of proofs as well as the logic behind each, and eventually write original proofs. The book also teaches practical applications of geometry, including calculations, Cartesian geometry, and trigonometric ratios. Euclid’s Elements is an ancient book that is simply a compilation of geometric proofs. Students usually study these proofs until they understand them and can demonstrate them on their own. Though the text is excellent for the study of logic, it does not assign proofs for students to draft themselves, nor does it include problems of application like those students may encounter on the SAT or ACT. Students who have no background in logic or geometry may find the text daunting. It is generally considered a college-level text.

What is the best way to prepare my child for Algebra I in elementary school?

Singapore Math is at the top of my list for elementary students as well as middle school students who have not yet mastered arithmetic. The textbooks are inexpensive and excellent. A solid grasp on fractions, decimals, percents, ratios and word problems is necessary for a person entering Algebra I, and Singapore Math covers all of these topics very well.

If your child is switching to Singapore Math from a different curriculum, you may want to have him take the placement test offered on the Singapore Math website (singaporemath.com).

You can purchase books at singaporemath.com. I recommend using the Primary Mathematics US Edition. For the level you choose, I recommend buying the following books:

1) Primary Math Textbook U.S. edition (essential)

2) Primary Math Workbook U.S. edition (essential)

3) Home Instructor Guide (optional)

4) Answer Key 1A-3B or 4A-6B (essential)

An interesting article concerning Singapore Math can be found at:


What Pre-Algebra textbook do you recommend to prepare my child for Algebra I?

The students who have had the best success in my Algebra I class have used a variety of Pre-Algebra books, and none in particular stands out.  What does stand out is that these students are disciplined and are able to think abstractly.  To make the most of any Pre-Algebra course, I recommend you do the following:

1)  Make math a regular part of your daily school routine.  Discipline in this subject is key.  Those who do math sporadically are at a severe disadvantage coming into Algebra I.

2)  Make sure your child fully understands a concept and works the problems successfully before going on.  If a student is getting test scores in the 80% range, you may think he is doing well, because a B is a pretty good grade; however, he may be consistently missing the same type of problem (such as thinking that a negative number times a negative number is a negative number) and that mistake is getting further and further engrained in his mind.  Such mistakes are hard to “undo” in the future.

3)  Make sure your child “shows his work,” and does so neatly.  This is the time to encourage your child to do more and more work on paper and discourage solving whole problems in his head.  The student who is not as gifted in math, but works problems on paper in a neat and orderly way, usually out-performs the student who is naturally gifted in the subject and solves problems mentally.  Eventually all math students will have to work problems out on paper, and this is the best time to transition to that if your child is used to solving problems mentally.

4)  Wait until your child is old enough to think abstractly (I recommend 8th or 9th grade) before pushing him into Algebra I.

My child has always done well in math, but struggled through Pre-Algebra. Should he repeat it or begin Algebra I?

There are three main reasons that a student struggles in higher level math classes:

1) Lack of the ability to think abstractly.

2) Lack of understanding.

3) Lack of discipline.

If the student is entering ninth grade and has a solid grasp of arithmetic, I would recommend that he proceed to Algebra I. Most students have developed abstract thinking skills by that age.

If the student is younger, I would recommend that he repeat Pre-Algebra.

For a student to succeed, he needs to have a schedule that includes doing math every school day. Math is not a subject that should be done sporadically. He should also have a knowledgeable person to turn to when he does not understand a concept.

My child struggled through Algebra I. Should he repeat it or proceed to the next math class?

If a student does not have a solid grasp of Algebra I (for example, he got a C or lower in the class), I would recommend he repeat the subject. Algebra II does include a review of key Algebra I concepts because most students take Geometry between Algebra I and Algebra II and need a refresher. Algebra II does not reteach those concepts, though. A student who did not understand them in Algebra I will almost certainly struggle to keep up in Algebra II.

If you do not want to spend a whole year repeating Algebra I, at a minimum I would suggest that your student spend a summer with a personal tutor going back through the Algebra I book and mastering the key concepts.

Do you recommend students taking Geometry or Algebra II after Algebra I?

I recommend that students take Geometry and then Algebra II, not because one is dependent upon the other, but because most students do not stop taking math after getting three math credits in high school. Taking Advanced Math through Liberty Tutorials, College Algebra in college, or any other higher math class is definitely easier when the Algebra II material is fresh rather than on the heels of Geometry. People who recommend taking Algebra II first usually do so with the idea that it is easier to do so when the Algebra I material is fresh. That is not so important, though, because Algebra II texts always begin with a review of Algebra I; the assumption in the industry is that Algebra II students have not seen Algebra I for a whole year. On the other hand, the Advanced Math text that I use begins with no review of Algebra II because it is a continuation of the material in that course, and the assumption is that students have just finished Algebra II and can proceed with no review.

Who should consider taking Advanced Math?

1) Anyone interested in pursuing math, science, computer science, or medical related major in college. Advanced math will help you prepare for required math courses in college and may be a prerequisite for declaring your major.

2) Anyone planning on applying to a highly competitive college. Taking optional higher level math classes will not only look good on your transcript, they will also help boost standardized test scores such as the ACT, SAT, or SAT subject tests.

3) Anyone hoping to earn leadership or academic scholarships. Colleges look for students who challenge themselves when awarding certain scholarships. High test scores factor into many scholarships as well.

4) Anyone who enjoys math. If you take pleasure in solving difficult problems and have done well in Algebra II, I encourage you to take Advanced Math. The work the course requires will be good exercise for your brain and give you a sense of accomplishment as well.

Why do you use Paul Foerster’s textbooks?

Foerster’s Algebra and Trigonometry textbook is unique in the textbook industry.  Foerster, who worked as an engineer before becoming a high school math teacher in Texas, writes from the perspective of one who knows how the concepts covered in the text will be used in real-life situations.  Each chapter culminates with a math modeling lesson that applies the material to problems that engineers, scientists, or others in math related fields may actually face.  These are not typical word problems, but rather lengthy situations that students learn to model with mathematical equations, from which they can draw conclusions and extrapolate data.  Foerster does not trade the teaching of pure mathematics for the teaching of practical mathematics, however.  Mathematicians rate his texts very highly for their clear, logical, and thorough handling of mathematical concepts, including proofs, which are often neglected entirely in today’s high school texts.

Foerster’s Algebra I text fully prepares students for the Algebra and Trigonometry text.  It not only presents the material clearly, but also draws students to the subject with thought provoking problems.  Foerster does not rely on repetition, but instead presents increasingly challenging problems in each problem set.  Students find this approach more interesting and engaging than an approach which has them do the same type of problem over and over in order to gain mastery.

A student considering a career in a math related field should find Foerster’s texts not only engaging, but also superb preparation for what lies ahead.  All students will be stretched to think more logically and analytically, skills that are valuable in all walks of life.

Why do you not use Saxon textbooks?

I no longer use Saxon textbooks because my experience using Saxon materials revealed these issues:

1) The cycling of topics can cause a disruption in the logical flow of mathematical thought. When up to two weeks might separate lessons that are usually found back-to-back in other algebra books, it is a bit of a challenge for students to see how a subsequent lesson builds on the prior lesson. Students continually need to shift gears, so to speak, when jumping from topic to topic.

2) Since the homework is primarily composed of review problems, students do not have a chance to truly delve into the new concept being taught. They do not fully master the new concept by solving a wide variety of problems that incorporate the concept in various ways before moving onto a new lesson. Even though the student will encounter more of these problems in future lessons, mastery of one lesson should occur before the student builds upon it in a future lesson.

3) As a particular type of problem is reviewed from lesson to lesson, the new problems are usually very similar to the initial few problems presented on the topic. There doesn’t seem to be a building in the complexity of the problems. In traditional algebra textbooks, the thirty or so problems at the end of each lesson begin with easy problems just like those presented in the lesson and build to more complex problems or problems that involve more analytical thought to solve. The Saxon problems do not seem to do that.

4) The Saxon books tend to over emphasize drill and “following the steps.” Even word problems follow a given pattern so the students can follow given steps to work through them. There is a void of problems that develop abstract thought or force students to think creatively.

5) Saxon books do not always adequately prepare students studying a math related field in college. The complete lack of proof in Saxon textbooks is one significant problem. The lack of more challenging problems is another.

Please Note:  I have had a number of students come to Liberty Tutorials who had used Saxon materials previously.  Usually these students are well-prepared in terms of their mathematical competency and abilities.  Most of them would say that they disliked math when using the Saxon books, but they did acquire proficiency, nonetheless.   The Saxon program seems to succeed in producing students who can compute, but is weak in terms of encouraging creativity in problem solving as well as developing analytical reasoning.