One big reason for the new schedule is that the newer textbooks are not as rigorous as the older books. One algebra 1 book I saw a few years back did not even get to quadratic equations (or perhaps mentioned them in the last chapter, I can't remember for sure -- but many classes never get to the last chapter of their books). If that is what the school is doing for "algebra 1", then of course they need to start earlier in order to cover all the standard high school math sequence. I think it may be something similar to grade inflation, but it's the title of the course that has been inflated.

For those of you lurking on this thread, perhaps this will help answer the question. I was reading today the intro to level 3 of KISS Grammar (psyching myself up to get back to schoolwork after an extended holiday), which is approximately middle school at my pace. It could be the third year of grammar, if you started in 3rd-4th grade and worked steadily. We started in 2nd grade and worked sporadically, so we entered level 3 around the end of 6th grade. Anyway, reading this introduction reminded me of what I hate about traditional grammars: that they give you a huge pile of jargon to memorize, with only the simplest of sentences to analyze -- sentences that are made just for the exercise and that therefore fit the rules they have decided to teach. KISS Grammar is different because it teaches students to analyze real sentences. So, for instance, a middle school student like my daughter may never have heard terms like "definite pronoun" or "past perfect progressive tense", but she can identify all the nested subordinate clauses in a sentence like the following and explain exactly what role each clause is playing in the sentence. [Quoting from the introduction to Level 3 of KISS Grammar. The red lines are part of the marking that the student does in analyzing the sentence: vertical lines mark the end of a main clause, while square brackets surround the subordinate clauses.] ... But consider the following sentence from the children's book Mrs. Piggle-Wiggle's Magic, by Betty MacDonald:Mrs. Jones looked at him suspiciously | but he widened his large blue eyes | and -- [as he was only eight years old, a little small for his age and seemed even smaller in ten-year-old Jan's pajamas, [which he had swiped the night before [because he had forgotten [that he had stuffed his own in the window seat [when he was cleaning up his half of the room]]]]] -- Mrs. Jones convinced herself [that he wasn't fooling] and let him go out to play. | That sentence contains three main clauses and six subordinate clauses. And note the five closing brackets after "room." Those subordinate clauses are stacked five deep. And by the time they have mastered KISS Level 3.1.3, students should be able to identify every one of them! ...

Well, that depends on what you mean by "need to know them." You definitely need to be able to see how the word is working in the sentence, to be able to recognize whether it is a subject or the object of a preposition or a direct object or whatever. But my big complaint about the grammar programs I've tried is that they give you a huge pile of jargon to memorize, with only the simplest of sentences to analyze -- sentences that are made just for the exercise and that therefore fit the rules they have decided to teach. KISS Grammar is different because it teaches students to analyze real sentences. So, for instance, a middle school student like my daughter may never have heard the terms "definite pronoun" or "indefinite pronoun", but she can identify all the nested subordinate clauses in a sentence like this and explain exactly what role each clause is playing in the sentence. [Quoting from the introduction to Level 3 of KISS Grammar, which is approximately the 3rd year of study. The red lines are part of the marking that the student does in analyzing the sentence: vertical lines mark the end of a main clause, while square brackets surround the subordinate clauses.] ... But consider the following sentence from the children's book Mrs. Piggle-Wiggle's Magic , by Betty MacDonald: Mrs. Jones looked at him suspiciously | but he widened his large blue eyes | and -- [ as he was only eight years old, a little small for his age and seemed even smaller in ten-year-old Jan's pajamas, [ which he had swiped the night before [ because he had forgotten [ that he had stuffed his own in the window seat [ when he was cleaning up his half of the room ]]]]] -- Mrs. Jones convinced herself [ that he wasn't fooling ] and let him go out to play. | That sentence contains three main clauses and six subordinate clauses. And note the five closing brackets after "room." Those subordinate clauses are stacked five deep. And by the time they have mastered KISS Level 3.1.3, students should be able to identify every one of them! ...

High school trig is not a full year course -- there isn't that much material to cover. It is always combined with other pre-calculus topics. What the textbook writers and schools choose to call the course varies from one place to another, but I'd be willing to bet that those who had a full year course called just plain "Trig" covered about the same material as those who had a course called "Analytic Geometry and Trig" or "Precalculus with Trig" or whatever.

Why do you need to know terminology like "indefinite pronouns", especially if it's only unit 2? I'd rather focus on how sentences are put together to make sense than learn a lot of jargon. Have you considered KISS Grammar?

Can he do the problems if you read them to him, perhaps rewording any unusual language? Word problems sometimes have funky language that we adults don't notice, but that throws young students into confusion. For instance, when a word problem says, "If Joe gave George 23 stickers, how many would he have left?" students tend to start thinking, "Well, what if he didn't? Or what if he gave him 25 of them, or 19?..." I suppose they think the "if" part is the question, when all that "if" means in a math problem is "for this problem, we are going to say that the following is true...." If he cannot solve the problems when you do them orally, then I'd say his rote-learning skills have outstripped his understanding of math. In that case, I recommend a diet of all story problems, orally, in a give-and-take conversational game. You make up a problem for him to solve, and then he makes up one for you, and then you trade again. If he can't figure out how to solve a problem, act it out. Notice whether sets of things are being put together, or split apart, or separated into same-size groups, or whatever. Use the problems in the book as idea-starters, but translate them into familiar objects and activities to make them easier to imagine. I think this sort of story problem game is the most important thing you can do for a student your son's age. It provides a wonderful foundation for understanding math. If you let him go on with abstract, textbooky math calculations when he cannot do word problems, then all he is doing is learning trained-monkey tricks. He needs to understand what is behind the numbers, how they relate to real situations, how they express and represent things in the real world.

KISS Grammar is wonderful, but it does require face time (but only about 10 mins per day, 3-4 days per week), and it takes longer than one year to get through the system -- but your child is not "behind" because everyone starts KISS at the beginning. If you are really interested in it, I would start by searching the forum here. We've had several threads in the last few months. For instance, here is a general introduction, and here is a question about how KISS compares to other programs.

If you add 66 band students + 150 in sports = 216 students in both, then you have counted some of the students twice, right? 36 of the students are counted in both, so we have to subtract the double-counting: 216-36=180 students in both activities. BUT if you are drawing the Venn diagram, then you write 36 in the middle, as you describe. Then in the sports circle, where it doesn't overlap, you will fill in the number for everyone who takes sports but not band: 150-36=114. And in the other part of the band circle, you will fill in the rest of the band members, the ones that don't take sports: 66-36=30. And then, when you add all those students together, everyone will be counted just once, and we had better get the same answer we did at first: 36+114+30=180 students. So, it depends on what you are trying to find. If you are just calculating the total (which is what the problem asked for), you don't have to subtract the 36 from each group. That is, you don't need to find out how many students are NOT taking both activities. We only subtract 36 once, to cancel out the fact that these students were double-counted. BUT if you want to fill out every part of the Venn diagram, then you have to put the 36 students in their own compartment AND you have to find out how many of each group is left who are not taking the other activity -- so in that case you subtract from each group.

Grade on a curve = Adjusting the grades to fit your class, so that whether the students bomb the test or do really well, you will get the same average grade. A teacher would do this because he/she assumes that performance on the test reflects as much on the teacher as on the student -- perhaps he/she wrote a test that's unreasonably difficult or unreasonably easy -- but that there should be a certain proportion of A, B, C, etc. students in any classroom. Weighted grades = Counting some grades more heavily than others when computing an average grade. For instance, a teacher might weight the final exam as 50% of the class grade, four tests at 10% each, and then homework as the final 10% of the grade. Teachers usually have at least a little discretion on how they weight the grades. Percentages vs. decimals = These can be written either way, at the teacher's discretion. For example, 80% is the same as 0.80. Usually, these grades are for recordkeeping during a class, and then are translated into a final A, B, C, etc. for the transcript, based on whatever weighting system the teacher prefers. Grade point average = What gets more confusing is that most schools use a 4-point or 6-point scale when averaging grades between classes -- that is, to get an overall idea of how well the student has done. For example, an A is worth 4 points, B 3 points, etc. The point value of the grade is multiplied by the number of credits for that class, then those numbers are added together for all classes, and finally you divide by the total number of credits earned. In high school, a full year course usually counts as one credit (or 1/2 credit for a one semester class), but in college the credits are usually determined by how many lecture hours the class meets each week and range from 1-6 credits for a one semester class. The grade point average is usually rounded to two or three decimal places and is reported in a prominent place on the transcript, normally at the top. Weighted grades = Coming back to this topic again, some schools weight certain classes more heavily when calculating the grade point average, perhaps by assigning additional credits to an AP class or something. I've never been at a school that did this, so I'm not sure how it works. But if you do it, you may want to mention it on the transcript.

For elementary and middle school, I don't bother with grades of any sort. When it comes to their official high school, what Kiana described is almost exactly my method -- usually the student and I sit down together and discuss their level of understanding/accomplishment in each class we list on the transcript. My kids go to the community college for dual credit their last year of high school, so they do have some grades other than Mommy-grades. (And they've all discovered that Mommy-grades are tougher!) I've graduated four students so far, and the community college and the University of Illinois have both accepted our transcripts without question.

:iagree: This is exactly how I remember it being taught when I was doing Primary Math 2B with my son. It's nice, because it turns the subtraction into addition, which most students prefer. Instead of "539-70" you calculate "439+30" -- easy peasy! BUT with mental maths there is always more than one way to do a calculation. Another easy way is to "take away in parts" -- so, first take away the 30 tens you have, leaving 509 with 40 more to take away. Then, if the student knows his number bonds for 10, it's fairly easy to see that you will end up with a something-60-something (ignoring the other digits momentarily to focus on the tens, taking away 4 tens will leave 6 remaining), so the answer must be 469. The one thing I would NOT do is try to practice "borrowing" in my head. Way too much trouble! I know some people do it that way, but it's too many numbers for me to keep in mind at once.

Well, there is a big difference between "letting him go ahead and memorize them" and pushing memorization, IMO. But really, there is a world of "living math" books, games, and other resources that one can bring in at any age to "go sideways" for awhile. For instance, these activities make advanced concepts like functions and fractals understandable to early-elementary (and even preschool) students. For a student who detests memorization, like the original poster's son, I recommend an approach that minimizes memory work.

I agree! a bottom piece has much less frosting :(

It sounds like the textbook is just introducing this idea for exposure -- for a peek ahead at what will come in 6th grade and above. If it bothers your daughter, I would ignore it. But if she's intrigued by the idea of doing "big kid" math (my children always loved doing algebra in elementary school), here is a way to explain it that may make more sense: Word Algebra. That is, write the equation with words instead of just initials: length = width + 2 Translate the equal sign as "is the same as", and you have a normal sentence written in mathese. Blog posts about word algebra: Elementary Problem Solving: The Tools Penguin Math: Elementary Problem Solving 2nd Grade Ben Franklin Math: Elementary Problem Solving 3rd Grade Algebra: A Problem in Translation

All students should start with the introductory fractions lesson, according to the website. That should take about a month or two, and it should give you a pretty good idea whether your daughter will like the program. The fractions lesson is all free on the website, so you can make up your mind before putting any money on the line.

Sounds like a readiness thing to me. She's only 5yo, according to your signature. She probably needs to do some mental maturing. I would hold off on Singapore math and other formal lessons until things like "break 8+6 into 8+2+4" seem easy to her, before going on. Meantime, check out some of the wonderful activities at Moebius Noodles.

At 7yo, I wouldn't even try to push memorization, but I guess I'm more laid-back than most. I think it's more important to talk about strategies for figuring things out. I don't have my kids work on memorization (other than playing math games) until 3rd-4th grade. I wrote a series of posts about the times table on my blog, if you're interested.

Yes, KISS is teaching something different from traditional grammar for now. KISS builds gradually, and the helping verb lessons (and least the ones I remember) are early in Level 1 -- basically the first year of study -- when the student is learning to recognize subjects and verbs. Finding subjects and verbs can be plenty hard enough for a beginner, so we don't want to discourage the student with complications. Infinitive phrases and other verbals are mentioned late in Level 2 (but only enough for the students to begin recognizing that they aren't part of the verb), and then become the focus of study in Level 4 -- roughly the 4th year of study, though my daughter and I have been stretching our lessons out longer than that. At that level, the KISS explanation will be exactly the same as what Analytical Grammar says. Or at least, one of the KISS explanations will be that. KISS Grammar always allows for alternative explanations, if they make sense, and in this case I think it would depend on how you read the sentence whether you consider "to swim" as part of the action (the finite verb) or as the direct object. My guess is that some people will see it one way and some the other, and I don't think Ed would consider it wrong either way. Also, KISS won't bother to separate "helping" and "main" verbs, after those early lessons. The only reason there are lessons about helping verbs is so children will realize the finite verb might include more than one word -- that they can't just find one verb and assume they are finished. But at any stage, the important idea is for the student to mark the sentence as it makes sense to him. So if your son marks "will begin to swim" as the verb, that's fine. If he marks "will begin" as the verb and recognizes that "to swim" is something else, but doesn't know how to mark it (or marks it as the complement), that's fine, too. But if he did something like just mark "swim" as the verb, that would be wrong, because a sentence like "he swim" does not make sense -- that would be a signal to go back and reconsider the marking, to find the extra parts of the verb and make it sensible. This sort of multiple-right-answers approach is, in my experience, unique to KISS Grammar and is one of the reasons I love it. It matches the way we come to understand language, bit by bit. And it allows students to analyze real sentences from real literature, even though they haven't yet learned all the constructions. In most of the levels, the KISS Analysis Key contains all the markings for all levels (for the teacher's information), but the students are only expected to do what they've learned. And they are expected to get confused and make mistakes, because these are not pretend sentences made up for the lesson. They are real sentences from real books, and they often have complications. In our experience, my daughter and I average 1-2 sentences per lesson where we say, "I don't know. Here's my best guess, now what does the AK say?" Sometimes we read the AK, and it makes sense, and we can see what Ed means. But on occasion, we like our explanation better than what is written there. Then we write a note to the Yahoo group to make sure we're allowed to explain it our way, and so far he's always said it's fine. (And at least once, he changed the AK to add our idea as an alternate explanation, which I thought was cool!)

Khan Academy is free and designed for self-directed learning. If you think you remember everything from elementary school (that is, you'd be working at least at a prealgebra level) then you could try Alcumus (also free). It will definitely challenge you, in a good way. My favorite thing from the last few years has been learning to count -- that is, to solve the types of permutation, combination, and probability puzzles you will meet in Alcumus.

You could have her try out the Alcumus program. It's free, and it will probably give you a good idea whether the AoPS style fits her.

My favorite math for little ones is not to use a schooly math program, but to play around with numbers, shapes, and other math ideas. Best resource by far: Moebius Noodles Other ideas from my blog: Elementary Problem Solving: The Early Years

Sometimes students struggle with math because there are so many steps to each problem. Often we teachers (and even most math programs) don't recognize how very many little steps we take for granted. For example, I went through a fairly "simple" mixed number problem on my blog and counted 7 major steps required to solve it, most of which consisted of many smaller steps: Subtracting Mixed Numbers: A Cry for Help A wonderful math program that breaks everything down to the basic steps is JUMP Math. It doesn't cost you anything to try it, except the cost of some printer ink and about one month's worth of lesson time. It's a different approach to teaching, and to make it succeed will probably take a bit of mental revamping -- but if it succeeds, it could make a world of difference for your son. Background to help you understand the program External Research that Supports JUMP Math's Approach The barriers that keep students from learning math, and how JUMP Math is designed to answer each problem. Teachers, students, parents, tutors and other educators describe their experiences using JUMP Math Videos about the program. The most helpful to me in understanding the program were the videos featuring John Mighton and . The latter includes encouraging comments from several students, too. Review of JUMP Math at the NY Times What you need to start the program You have to create a free account on the website to download the books. Everyone starts with the Introductory Unit on Fractions, then after your student finishes that unit (which should take about a month), you proceed to whichever grade-level book is appropriate for your son: Teacher's Manual for Getting Ready for JUMP Math: Introductory Unit Using Fractions (read and follow it carefully) Student workbook Answer key for practice test and final test

To really enjoy this, your students need to know a little bit about exponents and factorials, but those are easy to learn... "Exponents" at Math is Fun "Factorial !" at Math is Fun And then try this challenge together: 2012 Mathematics Game I suggest working together to make a list of some basic powers and factorials and then figuring out the numbers 1-10 together. After that, students should be ready to continue on their own. Print and cut out these cards to help you think about various combinations: 2012 Year Game Manipulatives High school students should be able to get most of the numbers 1-27, and several of the higher ones. You might post this worksheet on the 'fridge and have students initial or sign by the numbers they figure out: 2012 Year Game Worksheet I find it helpful to know if someone has found a number I'm missing, so I can focus my thinking on the numbers that are possible (because there will almost certainly be several that are impossible).

To really enjoy this, your students need to know a little bit about exponents and factorials, but those are easy to learn... "Exponents" at Math is Fun "Factorial !" at Math is Fun And then try this challenge together: 2012 Mathematics Game I suggest working together to make a list of some basic powers and factorials and then figuring out the numbers 1-10 together. After that, students should be ready to continue on their own. Print and cut out these cards to help you think about various combinations: 2012 Year Game Manipulatives Logic Stage students should be able to get most of the numbers 1-25, and a few of the higher ones. You might post this worksheet on the 'fridge and have students initial or sign by the numbers they figure out: 2012 Year Game Worksheet I find it helpful to know if someone has found a number I'm missing, so I can focus my thinking on the numbers that are possible (because there will almost certainly be several that are impossible).

I think of AoPS more as "math for puzzle's sake." The idea that a challenging math puzzle can be fun on its own, without needing any "real world" application, seems to be one of the driving forces behind the site.