<p>At my HS (at least, a long time ago), the order went: Alg 1, Geometry, Alg2&Trig, then right to either Calculus AB or Calc BC - no precalculus course offered. If you finished up the sequence, you could choose to take Statistics (also offered for other students who didn’t want to go the Calc route), or choose to take Calc 3. </p>
<p>Regarding kids not being ready for Algebra before high school: Algebra can begin to be taught quite early (after all when you ask grade school students 8+?=15 or ?*9=72; you are at the beginnings of using algebra.) The biggest obstacle, in my opinion, is the lack of arithmetic skills, expecially in dealing with fractions/decimals and how to add,subtract, multiply and divide with them. (It sure does make algebra easier if you can work with fractions/decimals easily.) I’ve taught a little math summer camp in my neighborhood for nearly 10 years , always taking 5-7th grade kids who were struggling in math, and had them working on the basics of algebra 1 by the end of the summer. They understood the basics of the concepts, how to work with +/- integers, powers, and balancing equations. I homeschool my own thru 8th grade (after having taught for 15 years) and my son, who’s in College, and daughter, who’s still in middle school, will both have finished Alg 2 when they complete 8th grade. They are not “math geniuses” - it’s more that they’ve just been taught all along how to play/manipulate numbers, and they have a firm grasp of working with +/- integers, rational and radical numbers. Math can be a very fun, exciting topic, but it is most often not presented that way. Not to mention, many grade school teachers (like my colleagues) had not had good experiences in their own “math past” and therefore could not instill a real enjoyment for math that I think is missing. </p>
<p>One day, maybe in my next life when I have more free time, I’ll get involved with overhauling math curriculum/textbooks!</p>
<p>hsmom2dncrs–our kids were doing “basic” algebra in kindergarten, doesn’t mean they really understood it, but they could memorize the patterns for solving the problems. Sure, SOME kids are ready for algebra earlier than others, those kids should be allowed to move ahead, but forcing those not ready for a full slate of algebra in 8th grade should not be forced to take it. People wonder why students don’t like math???</p>
<p>“Of the 320 high schools in the state, 94 require students to take four years of math, while the majority call for three years of the subject. Some of the Western Massachusetts high schools that require four years of math are Granby Senior, Franklin County Technical, Palmer, Sabis International Charter, Gateway Regional and West Springfield, officials said.”</p>
<p>It looks like MA graduations vary and some high-schools require three years and some four but, given these requirements, it doesn’t appear that any students are required to take Algebra I in middle-school as you have four years to complete diploma requirements in high-school.</p>
<p>I’m not suggesting that kids be “forced” to go anywhere they’re not ready. I think an overhaul is needed in the WAY math is taught (especially in regards to the attitude/perception that goes with it) - and then I think we would find that a lot more students could actually be ready to tackle algebra in 7th or 8th grade. Besides the perception of math as “difficult”, and the way the curriculum is organized, the other roadblocks IMHO, are that math is better taught in smaller groups (10-15 students), and we need to let kids still manipulate objects/representations for a lot longer time.</p>
<p>Kids pick up language skills, language and behavior from their observations in the home and in other environments. If kids are in a math-rich environment, then they can pick learn arithmetic, algebra or calculus when they are young. Arithmetic doesn’t have to be taught before algebra - it can be taught concurrently - though some of the operations may have to be simplified or omitted. Arithmetic is actually quite complicated - we have the concept of place value which we take for granted but there are a bunch of rules in there which aren’t intuitive so we learn by memorization and use. The arithmetic operations are actually quite simple in concept but the numbering system is more complicated and teaching about the numbering system may make learning the other stuff easier.</p>
<p>I am a bit lost on why kids can’t be ready. I understand a lack of skills but what has maturity got to do with Algebra? </p>
<p>American children start an year later compared to the rest of the world (people in India, China, European countries finish 12th by age 17 as a norm). Most of their curriculums complete upto trigonometry in 10th which means they start algebra around 6-7th or by age 11 or 12.</p>
<p>California is adopting Common Core Standards along with 44 other states. Algebra readiness preparation starts in Kindergarten. The expectation is that when Algebra 1 is taught, students will be successful. As it stands now the majority of 8th graders struggle then repeat low level algebra through high school. Of course Algebra 1 will continue to be offered in 7th grade but it won’t be forced on to 8th graders who aren’t ready.</p>
<p>I agree with SteveMA on this one, from personal experience. I was told by a tutor that children achieve “math maturity” at different rates. This was true for us. I have two children who breezed through Alg 1 in 8th grade, continuing to AP Calc in 12th. Our third child struggled with Alg 1 in 8th grade (good private school, 15 students in the class, so no deficits to blame). He repeated Alg 1 in 9th, with A’s both semesters. I don’t see the point in forcing Alg 1 on students who are not ready. It really becomes a negative experience when you do that.</p>
<p>Some believe that younger students don’t have the brain maturity to handle abstract concepts so that they are better off with learning math that’s related to things that they can see, hear and feel.</p>
<p>Others feel that we’d be better off teaching abstractions first and then the details later on. That would be akin to an object-oriented approach in software parlance.</p>
<p>While my husband was in graduate school, I taught math at a small private K-3 school in New Jersey where the headmaster had written a math program for primary students. I earned my teaching credential in California and had taught for a few years there before coming to this quaint little school house, but I had never seen anything like this dynamite math curriculum </p>
<p>It was all about number theory. Kindergarten students learned addition and subtraction by standing on a big plastic number line on the floor of the classroom, and they would move backwards and forwards- although the words “addition” and “subtraction” were not introduced until first grade, when the first graders would use the number line as well introduced to negative numbers. In my first grade class, the concepts of more than and less than were introduced, along with the mathematical signs >,=,<, and we would orally go through equations every day, never even lifting a pencil. By mid year, the first graders were not only adding and subtracting, but “borrowing” as well, and they understood what they were doing. Students would practice their equations with a box of cut-out numbers and signs and a jar of stones which they would count out one-by-one, creating their equations by laying out the number squares and stones on the paper. Several times a week, we’d open the day with the class making up a word problem that they would then illustrate. Before long, the students were independently creating wonderful word problems of their own using the concepts we were working with. </p>
<pre><code>I agree that students need to be developmentally ready for abstract mathematics, such as algebra, but I’m convinced that the problem is that we don’t teach math in the right way early enough for them to develop their abstract thinking in our public schools.
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<p>What I was doing in my small private in N.J. would never be considered where I had taught in CA. Who would think first graders could learn what a negative number means?
These kids really did understand what they were doing, although some grasped the concepts faster than others. But it was a wonderful basis for learning more advanced math. I incorporated some of this math curriculum when my own kids were little to supplement their primary curriculum, and I know it helped them later.</p>
<p>Sounds like something out of the “New Math” movement.</p>
<p>This movement failed and generally received scorn and derision over the decades but I think that the approach is solid. The problems were in the implementation in textbooks, teacher training and parents being unfamiliar with the approach. I think that a lot of teachers weren’t familiar with the concepts and ideas and teaching without understanding can be a problem.</p>
<p>The Sets and Numbers curricular materials by Suppes and Hill (I looked it up on Amazon and was surprised to see used textbooks for sale from the 1960s) are an example of this approach and I think that they were the materials used in the early grades of EPGY at Stanford. We used these materials with our kids when they were young along with a more traditional curriculum from back in the late 80s, early 90s.</p>