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Trig seems to be taking forever...any insights?

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Now that ds is in his second ch of the trig section (in the Alg II/Trig Dolciani '65 book), we've hit a major slowdown....


It can take an hour to do 2 problems...Ds says they just take him a long time...


Here I was thinking he would be finished with the book by the middle of April.


Any insights?




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I have the 1968 Dolciani, Wooton, Beckenbach and Sharron version. I'm not sure how different our books might be. Chapter 11 is "Trig and Circular Functions"; chapter 12 is "Trig Identities and Formulas". Is it the trig identities that are taking so long? Some can take awhile due to lots of algebraic manipulation steps or because an idea on how solve it led to a dead end. On the other hand, some verifications of identities go very quickly. They take practice. Do you think there are enough examples in the Dolciani book? There are a lot of web resources for identities as well as other trig topics.


If you can be more specific about what kinds of problems or give an example I will try to be helpful.


Full disclosure: I am self-teaching myself trig with a variety of precalc books; I have gotten through identities, inverses, law of sines, law of cosines. Still left to do are vectors, polar equations.

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Do you have the teacher's edition? It says that Ch.1-10 is a basic algebra II course. Then you can either do the trig chapters or skip over to the "Enhanced Algebra" chapters, which are, as I recall, elements of pre-calc. The book was not designed to be finished all the way through in a year. I'm going from memory, but if you don't have the teacher's manual, let me know and I'll pull mine and get more detail.

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If I had to do it over again,and I will with dd's, I'd take lots of time with the trig and make sure he memorized the basic trig identities. Ds did Foerster's Alg II/Trig, which had three chapters of trig. He saw it again in the first year of Calc (not calc 3) and didn't remember it.


We didn't do pre-calc; Foerster has a pre-calc book now but didn't in the 1980's set we were using. If you're planning on doing a year of pre-calc, it should also be covered there.

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I concur....you really need to look the text over. We encountered a number of trig texts that covered far, far more than just trig-precalc. Dh went through, separated the algebra 2 review out because DD didn't need it, and took out the calc 1 and above topics. Many times the books "expose" the student to the concepts though they aren't trig-precalc topics.


Once he reduced the assignments down to true trigonometry and pre-calc only topics, she completed the credit in 7 months. DD is an excellent mathematician so it might take other students longer.


We have not used Dolciani so I can't speak to your specific issue but I do agree with the above posters that there may be chapters or portions of chapters in your text that do not need to be fully covered in order to legitimately give full credit for trig/pre-calc.



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Trig is a system that makes perfect sense once the pieces are assembled, but, before that epiphany occurs, it often appears as disjointed in a student's mind. I say this as a math major who spent a Christmas vacation a long, long time ago teaching herself trig--despite having aced it in previous course work.


I would begin with a review. Make sure that your student is comfortable with conversions between radians and degrees. Master the unit circle. Have your student write in the standard values and be able to verbalize the values of standard angles (degree and radian) without a calculator. The question that I ask in many trig situations is "Where am I?" Know which quadrant an angle is in and the signs of the trig values for that quadrant.


Know the definition of the trig functions as triangular measure relations and how the functions relate to each other. Students do not need to memorize 101 trig identities that they will forget anyway. They do need to know basic identities (Pythagorean, sum/difference) but most identities are simply derived from others. When I am not using say half angle identities regularly, I may not remember which is plus and which is minus, but I can derive a half angle formula and figure it out. Teach how to derive things.


When I was in high school, the course was called Algebra II/Trig and used the text you are using or some slightly newer version of it. We did trig in that course as I did trig with my son as part of Algebra II. He struggled. When we revisited trig in precalc (using Dolciani's Analysis book), he immediately caught on. I was stunned after the difficulties of the previous year. Repeated exposure helps here. Now my son is preparing for an AP Calc exam and trig does not bother him--although he does continue to confuse things on occasion.


Keep plugging away is all I can say.


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I am so grateful for all your advice! All of you!


I was starting to think that maybe he couldn't go any farther in math - that he had reached his limit (not that he couldn't do anything, just that he should not be going for Calculus)


So your collective advice is giving me my breath back. He/We can still keep at it for awhile and see if he "gets the trig picture" in the next 6 months.


Just this morning I was rechecking how long these lessons are taking and realized that actually the first trig chapter (Trig functions and Complex Numbers) took 26 days! The second chapter (Trig Identities and Formulas) has taken 11 and he's on 5/11 lessons. So that could easily be another 26...he says it's not hard, just time-consuming.


In response to certain questions -

Jane - a review is a good idea - I'm sure that he has some of those concepts down, but it would be good to pinpoint weaknesses..I like the teaching to derive suggestion.... the proofs did take him a long time...


Faith - I appreciate the suggestion - I'll look ahead to the Pre-calc book and see what is covered again - maybe in a different way (Jane you said your son found it easier in the Modern Intro book - was it presented differently?)


Susan - I'm intrigued that there is MUS for identities - do you have a link? I thought they just did basic math.


ITGWNorth - we will be doing pre-calc, I just thought that it would be building on this info and that he needed to do this too...


Dee - What you wrote is quite interesting. I have the TE for '77 but only glanced briefly and just presumed that the "well-trained mind" would do the whole book. :001_smile: In '77, those 'extended' chapters (progressions, expansions, matrices, permutations, etc) come before the trig part, so he did them first, even though in the '65 they are second. I figured they got some insight about which was better to do first. Though now I'm not quite sure. He certainly moved through them faster though.


Susan you help me not feel so bad.


Janice - Funny, in the '65, the "circular functions" are in a separate chapter with their "inverses". But the middle chapter seems to be the same. The proofs of the identities was one thing that took ages. I'll get back to you if I need more problems.


Two more questions...



In this second chapter there was only one set of "oral questions" so far...generally I find those helpful in gaining facility. Is it naive to think that should be doable for deriving identities (if I could find that kind of problem..)? Anyone know where to find that kind of oral exercise?



In Alg II, he was only doing 1 hr/day and occasionally homework. When you do trig or pre-calc, how many hours/day - is it up to 2hr/day, 5d/wk? Maybe he's just not putting in enough time as well?


(It's good to hear different opinions to see the range of possibilities)...


Thanks so much!


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