<p>“I know. More correctly, tax policy is PART of fiscal policy. But they are not identical, there is more to fiscal policy than just taxes. I didn’t know I was going to be proofread”</p>
<p>okay. Its a hot button for me, cause there are pols and pundits out there who say “Fiscal stimulus can have no impact”, usually citing some nonkeynsian economist to that effect, but who then go on and say “Well a recession is a terrible time to raise taxes”, implicitly for reasons of demand, and ignoring the contradiction.</p>
<p>IE Keynsianism is nonsense when spending is discussed, but is perfectly reasonable when taxes are discussed. The higher up the income scale the taxes are aimed at, the more reasonable Keynsianism seems.</p>
<p>The real basic problems are that nobody at ground level is very optimistic about the future. Consumers won’t spend, companies won’t hire, banks won’t lend. None of these are easily impacted by government policy short of massive direct aid for buyers of things–auto and housing credist, etc. Giving much of the aid to governments to spend on projects was particularly ineffective at achieving fast stimulus.</p>
This may very well be true, but lets not forget how we got here. Back in the good 'ol days, when teachers were free to teach and kids were free to learn and so on, when they gave tests to see whether the kids actually <em>could</em> answer basic test questions in various subjects they could not. </p>
<p>I’ve yet to hear anyone claim that because kids were doing so well on the tests the teaching methodology was changed to “teach to the tests”. Far from it. Its only in response to the poor performance when kids were asked to actually demonstrate basic skills in reading comprehension, math, etc. that the teaching approach changed. One could argue that the current approach hasn’t done better, but to argue that because the current approach isn’t producing wondrous results we should go back to the old methods seems somewhat facetious.</p>
<p>There is more than learning than being able to answer test questions, I’ll readily agree. Yet without even reaching the basic level of achievement in reading, math, and the sciences the tests are used to assess then you have to question whether anything of consequence is being learned. And that’s where we were when the testing movement began.</p>
<p>Similar situation with junior d, but with precalculus, except unlike the OPs kid who has gotten a B on a test, my student is doing quite poorly. Oh, and she had the watered-down version of Geometry and Algebra 2… In which she got acceptable to very good grades. We now have a private tutor and are trying to figure out how to recoup. Teacher will not allow anyone to look at the test; same story there, since the tests could be given to someone else. All tests and quizzes are multiple choice. The teacher never looks at their calculations, not even for homework, which – though collected-- is only noted for completion. They do not go over the homework in class, though the teacher does go over a couple of the more difficult problems. This teacher has a reputation among the students at this school as an extremely poor teacher. School has a policy of NEVER switching students’ classes based on the teacher. Oh, and when students struggle, the school’s response is that clearly they are not going over their notes or studying or doing homework (oh, wait, homework has been turned in and student has been going to the student-run tutoring group (in addition to now private tutoring). Must not be trying. Good for OP for being on this with 8th grader. I have not taken math since college and was not looking over the coursework the last two years, except to be surprised over the “no proofs.” This was a “Geometry in 9th” student. This is the third year in a row that d has gotten a teacher reputed to be poor; other d had gotten quite solid math instruction at this school. Best of luck to the OP.</p>
<p>Isn’t math precise and determinable such that conjectures are generally unnecessary? Why not just learn to calculate something properly, rather than guess and hope you’re right? The new philosophy is that kids should “discover math for themselves.” Why reinvent the wheel? Plenty of brilliant people over the age of 12 have spend years forming the field of mathematics. Surely my middle school daughter’s contributions to the subject are not required*******</p>
<p>Beautiful, TheGFG!!!</p>
<p>I spent my D’s middle school years battling our school district over the touchy-feely math program that had D “learning” fractions in 6th grade (!!!) by filling different sized cans and pouring water into a larger vessel. I was mortified by the lack of actual MATH in the math program. For three years, I researched, spoke with administrators, lobbied the school district, etc … in the end, I put my kids in private school. D had to work extra-hard in 9th grade to make up lost ground; S spent his middle school years learning actual algebra.</p>
<p>My friend is a community college professor. This year, she is teaching college algebra to high schoolers in a dual-enrollment program. She goes to 2 different high schools to teach. At one school, the kids are challenged but are working hard to rise to the challenge. At the other school, there are kids in her class that haven’t even had Algebra 2 yet. She has tried her best to help these kids, but they won’t even do the homework. A couple weeks ago, the school guidance counselor sent her an email stating that a math teacher in the school complained that she is “too hard,” basing this on comments from her former students; the GC requested a meeting with her, the principal, and a district administrator. Friend took an administrator for the CC along to the meeting. Turns out the school refuses to accept responsibility for placing students in the class who are not actually ready for college algebra, they feel that there shouldn’t be so much homework, they want her to make her tests easier, and they want extra credit opportunities. In other words, the school wants the kids to get a good grade in a college math class without actually earning that grade.</p>
<p>Part of the problem is that more and more of our teachers are not well-educated themselves. The current generation of educators came out of modern schools and were poorly taught too. How many times have we had to correct “answers” given by the teacher or contradict their instructions for how to solve a problem? It happens often enough to be scary, especially when we aren’t allowed to see the test papers. The brightest kids sometimes do know more than their teachers, and quite possibly have the answer right that was marked wrong.</p>
<p>Today my D was typing up a final draft of an essay, from the first draft that had been edited by her teacher. The teacher had “corrected” the essay to make it grammatically incorrect! When the objective case was needed, the woman felt that “I” sounded better than “me” and changed it. I had D change it right back and told her that if this means she gets points taken off, then so be it. This teacher brags she attended the same middle school as D. Well, that it explains it I guess. Similar scenarios have been common in our household over the years.</p>
<p>On a more upbeat note, I am informed by my D and my neighbor’s D that geometry proofs are alive and well in our school district. It’s been a few years since my D was taking accelerated Geometry Hons., so I thought that maybe things had changed since then. But my neighbor’s daughter took Hons. (not accelerated) Geometry last year and she said that their tests and homework were almost all proofs. So my second D who will be in Geometry(hopefully hons) next year, will be proving theorems and corollaries as well.</p>
<p>On the subject of “conjectures” in mathematics, many famous mathematicians past and present have put forth conjectures, based on their intuition. Some of these conjectures are long standing problems awaiting proof. Any time one of these conjectures is proved, it is very big news in the mathematical world. Perhaps middle school teachers are trying to encourage students to think beyond, and develop mathematical intuition. That being said, however, I am no proponent of touchy-feely math. The pendulum has swung way too far in that direction. We need to give students some hard skill building training as part of their education. A shocking number of students have no algebra skills at all.</p>
I hate to beat this to death, but there is no such thing as “college algebra” as you are using the term. Any basic algebra course taught at the college level is remediation for people coming in with poor or rusty algebra/trig/pre-calculus skills they should have learned in high school.</p>
<p>I have a lot of math books in my home library.</p>
<p>College Algebra and Trigonometry, F. Lane Hardy, Dekalb College
Charles E. Merrill Publishing Company
A Bell & Howell Company</p>
<p>PREFACE</p>
<p>The material contained in this text consists of the standard topics
which one usually associates with the title College Algebra and
Trigonometry. A short chapter on simple logic has been included in an
appendix for those who wish to cover this material</p>
<p>The exercise sets usually begin with simple programmed questions and
those are followed by routine computational type problems. Students
should be urged to cover the answers to the programmed exercises until
they have obtained their own answers.</p>
<p>…</p>
<p>Here’s Example 1-3 from the book:</p>
<p>Let P(x) express: “x is a triangle of Euclidean geometry and the sum
of the interior angles of x is 180 degrees,” and let Q(y) express: “y
is a triangle of Euclidean geometry.” Then if A = {x | P(x)} and B =
{y | Q(y)}, we have A = B. This is easily established by using (1-1)
above, and observing that A is a subset of B and B is a subset of
A. It is clear that every member of A is a member of B so that A is a
subset of B; and also, since in Euclidean geometry every triangle has
an angle sum of 180 degrees, B is a subset of A.</p>
<p>(I substituted words in place of symbols)</p>
<p>Would the typical high-school student that passed Algebra 2 understand
the above paragraph?</p>
<p>Geometry for Enjoyment & Challenge was a great book. It was part of the old McDougal Littell mathematics series from the early 90s. The new incarnation is less rigorous.</p>
<p>The quality of a textbook is inversely proportional to the number of irrelevant or off-topic graphics included.</p>
<p>I personally love the historical notes in math and science books. I think that most students ignore this stuff because it doesn’t contribute to their grades and I think that this is a shame. I went through the first five video lectures of the Yale Open Course Organic Chemistry site and I think that about half of the lectures talked directly about history. I was a bit surprised to see that there were students in the class that could answer the seemingly random history questions on chemistry that the professor tossed out to the class. I assume that the Professor could spend so much time on history because the students could study a lot of the course material on their own.</p>
<p>I think that you’re referring to the color graphics that contribute to the costs of modern textbooks. Harold Jacobs often has cartoon drawings to open a chapter, provide puzzlers or make a funny point. These are simple hand-drawn non-color items and I do think that they add to his textbooks.</p>
<p>I recall using Leslie Lamport’s book on LaTeX, a computer-based typesetting program that I used in the 1980s. His book was a follow-on to Don Knuth’s TexBook. Lamport’s book had the hand-drawn cartoons in his book that added to the material in the chapters. I always appreciated that additional artwork in technical books. Even moreso than the current trend of turning textbooks into strength-training equipment.</p>
<p>graphics: the drawings and photographs in the layout of a book</p>
<p>There’s nothing wrong with images that relate to the subject material or examples from other subjects. But including graphics just for the sake of having graphics is not good. A picture of two people watching TV just because there happens to be an example involving television doesn’t help (you can find this near the beginning of the new McDougal Littell book).</p>
<p>You are trying to prove what using a logic example from a 1973 textbook? This isn’t typically taught in today’s “college algebra” course. I’ve taught college algebra, college algebra and trig, and finite mathematics numerous times. I also took college algebra and pre-calculus as an undergrad. They were basically remediation courses and didn’t involve logic or texts from 1973. One of the courses involved some fairly obscure factoring theorems, but that’s about the extent of the novelty.</p>
<p>ETA: DS has had Geometry, Algebra 2, and Pre-calc, and is now in AP calc, and he says he understands your example just fine.</p>
<p>The expectations of the college algebra class in my friend’s case are not remedial (based on the state standards for high school algebra 2). Whether or not our state standards are as high as those in your state, sylvan, I could not say. What I do know is that this CC’s algebra class picks up where the high school curriculum standards leave off.</p>
<p>to OP–yes the books have been dummied down. “back in the day” only the college track kids took Geometry. Now everyone takes it to be college eligible (notice I didn’t say college ready). For the most part this is not a result of their teacher not understanding the math, but politicians deciding what will be taught. Teachers are forced to do the best they can. My son also had “conjecture geometry” in the 8th grade–I didn’t worry about it. As he got into higher honors and AP classes, the teachers were able to introduce formal proof–although at a higher level. He did fine and his SAT II’s did not suffer.</p>
<p>If a child struggles with proof at the higher level (which the average person does) having proofs in a geometry class would not have helped. They’re just plain hard. They do teach a good work ethic, but kids these days have so much more on their plates than students in the past that I am sure they are picking it up elsewhere.</p>
<p>Don’t get me wrong–I am not defending it. A geometry class based on formal proof is great for students that are math-minded (what a fun class to teach with the right kids!) but is just not a reality for the majority. Too bad the honor’s class is not more challenging. Before you blame the school, see how much experience the teacher has – most likely it is less than 5 years (the amount of time before 50% of the teachers quit). The more experienced teachers are also able to stand up to administration (who have likely been there less than 5 years also) and teach what they know the kids need. Complaining in these situations will go on deaf ears.</p>
Nonetheless, it is basically considered remedial at the college level. They may take up with what is often designated as “pre-calculus”, but pretty much everything prior to calculus itself is not considered “college level” when it comes to mathematics. That they may not actually teach the material at your high school (and how do your students take AP Calc then?) is irrelevant.</p>
<p>I would expect someone that has passed precalc to be able to understand
that paragraph. But I wouldn’t expect most that passed Algebra 2 but
have not yet taken precal to understand it.</p>