Saxon Math addresses this very well in the meeting book portion of grades K-3. It is the pattern recognition part of Saxon that I consider to be one its strengths as a curriculum.

I will list the cons first. Singapore does not have enough drill, nor enough explanation to help those who are unfamiliar with teaching math. The HIG are helpful, but may not always address the variety of problems. The drill can be supplemented with an outside program or drill sheets. Fortunately, there is a Singapore Math Forum to help with problem questions. Now for the pros: Singapore is wonderful at presenting concepts. You see what happens when you borrow in a subtraction problem or why you carry the one in an addition problem. You see what is going on in a division problem. You see different ways to think of a multiplication problem. Visualizing the concepts helps the child understand what is actually happening when writing math symbols. It does this in a fun way :thumbup:. My favorite part of their curriculum though is the intensive practice and challenging word problems. These books teach the child to creatively solve problems and learn how to deal with frustration, because the answers are not always so obvious. In the process of being frustrated the mind has been stretched and soon the child learns how to think 'outside of the box' [as long as the teacher goes over the correct way to get the solution if the child doesn't understand a problem]. It demands more creative thinking from the child. HTH :)

One course that I used I already had the text for. The problem sets were similar to the Analysis course I took in graduate school. It was not hard to follow along, and it provided detailed solutions in an easy to read typed up pdf file. I have not checked out the Physics courses, so I don't know if it provides solutions or not. It would be worth it to check and see.

I have used some briefly for my own self study in mathematical analysis. This is from their website: MIT OpenCourseWare (OCW) is a web-based publication of virtually all MIT course content. OCW is open and available to the world and is a permanent MIT activity. What is MIT OpenCourseWare? MIT OpenCourseWare is a free publication of MIT course materials that reflects almost all the undergraduate and graduate subjects taught at MIT. OCW is not an MIT education. OCW does not grant degrees or certificates. OCW does not provide access to MIT faculty. Materials may not reflect entire content of the course. I downloaded and printed off the course material for self study. Some of the courses have lectures that you can watch as well which come with transcripts in case you cannot understand the speaker. It is free, but they encourage and accept donations. Good Luck :)

Have you ever actually used Saxon?

We like it to. None of my kids hate math, either. ;)

It sounds to me like you are asking how to choose a math curriculum. You would want a math program that teaches both the why and the how of mathematics as clearly as possible. Look for a program that has been around for awhile with a proven record or find research that supports the program you are considering. Research the author's background, and check that the author has a demonstrated background in mathematics - something that convinces you that this person knows the material and knows it well enough to teach it to your child. Consider your own background and children's abilties in math and work within those parameters to make a choice that is the best for you and your family situation. Finally, remember there is no royal road to geometry (to quote Euclid). Math is hard work, and if someone tells you that it should always be easy and fun, they are not telling you everything. Good Luck :)

I would recommend the teaching manuals. I have a background in mathematics, and the TM helps me to not go too fast. Things that I may think are easy, the child may struggle with; so the TM helps me to slow down a bit. Good Luck:)

If you do decide to switch him to Singapore, I would also recommend the Intensive Practice workbooks (in addition to the CWP). These IP books are more challenging than the workbook and are quite good at making the child 'think outside the box.' Good Luck :)

I have not used Horizons, but I can compare Saxon and Singapore. Saxon is broader in that it covers more topics than Singapore. Singapore takes on fewer topics but goes much more in depth. Singapore has excellent word problems. Saxon has excellent drill. HTH! :)

The reason that we want to redefine subtraction in terms of addition is that we want to use the algebraic field properties of the real number system: such as commutative, associative, and distributive laws. All order relationships in the real number system - all algebraic inequalities rest on two simple axioms regarding the set of positive numbers: Axiom I: If a is a real number, then one and only one of the following statements is true: a is 0, a is a positive number, or a is a negative number (ETA: which means -a is positive when a is a negative number) Axiom II: If a and b are members of the positive numbers, then the sum a+b and the product a*b are members of the positive numbers. When subtraction is redefined in terms of addition then we can work with it much easier since addition is commutative and associative, but subtraction is neither commutative nor associative. In other words, addition is much easier to work with than subtraction, so we don't want to mess with subtraction.

The why has to do with fundamentals of the real number system. Be careful of the distinction: Looking at the set of real numbers we have: negative numbers, zero, and the positive numbers. The negative of a number a is defined to be the number -a such that a + -a = 0. A negative number is defined to be the negative of a positive number. Now: If a and b are arbitrary real numbers, then their difference, a-b is a real number. So either a-b is an element of 0 (that is a=b), a-b is an element of the positive numbers (that is a<b), or -(a-b)= (b-a) is an element of the positive numbers (that is b>a). This is a reformulation of the Axiom which states: If a is a real number, then one and only one of the following statements is true: a is the unique member 0 of the set O; a is a positive number of the set P of positive numbers; -a is a member of the set P. Here is a proof: To show: (-a) + (-b) = -(a + b). (1) (-a) + a = 0 (2) (-b) + b = 0 (3) 0 + (-b) + b = 0 (4) (-a) + a + (-b) + b = 0 (5) ((-a) + (-b)) + (a + b) = 0 (6) (-a) + (-b) = 0 - (a + b) (7) (-a) + (-b) = -(a + b) We can always think of subtraction as an addition problem (adding the opposite). This distributive property of multiplication over addition to real numbers can be extended to polynomials as well. In other words, it has to do with the order relationships of the real number scale and how we define them.

I agree with the advice of the two previous posters...math, math, math. I turned down a job offer as a software engineer to pursue my doctorate in math. My degree at that time was a B.S. in Math with a computer science minor along with several others. It is also important that he develop good communication (including writing) skills. Good Luck. :)

This is a great idea...I plan to do this when my children are a bit older. Science is on the top of my list along with Reading and Math.

I have worked through Intoduction to Inequalities. This book -with its more elementary level proofs - gives the reader a taste of what graduate level math is like, yet it is written in way to be understood by a high school math student. It sets the stage for real analysis which is generally taken the senior year of an undergraduate math major or the first year of a graduate school math. Prerequisites would be at a minimum one who has mastered Algebra II and some Geometry. I think having taken the first semester of Calculus would also be helpful, but not necessary. Even with Calculus, parts of this book may still be hard to understand. So it is helpful to be patient. It has answers (or intermediate steps) in the back of the book; but you will still have to think through the logic for the answers to make sense. It introduces mathematical induction in Chapter 2. The book's focus is on inequalities which are very important in mathematics. The first three chapters are on axioms or "tools of the trade", chapter four - derives some of the most used inequalities used in analysis, chapter five - inequalities are used to treat maximization and minimization problems, and finally chapter six focuses on properties of distance. The author clearly enjoys math, and reading this book was delightful. A book like this should not be rushed through, and it would be a good way for your son to see if pure math is really for him. Do all the exercises for the best results. Good luck. :)

With the exception of religious texts, mine is Principles of Mathematical Anaylsis by Walter Rudin. It had a huge impact on my life, although it is probably not the sort of book one would think of as being inspirational...

I tutored math for awhile as an undergraduate. I was asked by a computer science professor who doubled as a high school calculus teacher to tutor some of her students. I met my students in a public library. I did not have a teaching certificate, but my students seemed to do pretty well - making the honor roll as I recall. You could try posting an ad in the paper, and perhaps meeting in a public library.

My husband reads all the time, and he has an amazing book collection. He has accepted my eccentricity of reading mostly math books, and no longer teases me about it. :001_smile:

You have some wise comments here which :iagree:with. I would also stress the understanding of math above and beyond science because those who are weak in the sciences tend to struggle with the math within the science.

I have yet to meet anyone who enjoys memorizing math facts. ;) Memorization of math theorems and the like is normal if your student ever moves into graduate and even some college level math. Memorization of math should not be the enemy so to speak. Math is a very detail oriented and precise subject. It helps immensely if one can see the big picture as well, but there is a place for careful consideration and memorization at the college and graduate level...should your child go that route.

I think that a balance between traditional and conceptual math would be the best choice. One should have a mastery of the basic math facts (without a calculator) in addition to a conceptual understanding of what is going on in the problem. I think it very important to have drill (without killing fun). I am left-handed (right-brained??). I learned math a more traditional way, but I usually drew pictures of what I was studying to help me picture the concept or problem. Look for a balance. Good Luck! :)

I would like to read one book per month. I mostly read math books and work through the exercises, so if I can get through one per month I'll be happy. ;) I am a fan of Jan Austen novels as well!

The more math, the better. ;)

:grouphug:

I give grades to most things, but my children do not usually see them unless they look back through their workbooks. It is more for my informational purposes. In addition I grade my daughter's exams, and we discuss them afterwards. I encourage her to show her work. If she chooses not to, and gets the question wrong she knows that I will count it wrong. We agree to the rules at the start of the exam. I use an Excel spreadsheet. I have a back-up hard drive to save them on. Grading gives me a detailed description to help me see their progress and also helps me monitor which sections they need to work on.