Jump to content

Menu

Ray's Upper Level Math


Recommended Posts

There are some things I like and some things I don't. I'm going off this book: http://books.google.com/books?id=cj8YAAAAYAAJ&pg=PA7&source=gbs_toc_r&cad=3#v=onepage&q&f=false

 

Pro:

He starts off with word problems designed to get students to have an intuitive understanding of variables in linear equations. I feel that a student who had begun with this might be much less likely to, for example, take x + x and write "= x squared".

 

Con: I find the subsequent presentation of the definitions and notation (in lesson I - definitions and notation) absolutely terrible. There are about 50 definitions dumped on the hapless student, with few computational examples and no computational practice to enable them to work on them. Very few students would acquire more than rote learning from this section, and would be very confused as to which definition goes where. I am not really sure how this is supposed to be taught -- if perhaps the definitions were to be interspersed as needed, but I tend to doubt it given the date of the book.

 

Con: The terminology is somewhat antiquated, including the English explanations. For example, when he is explaining how to add similar quantities with like signs, he has written "Add together the coefficients of the several quantities, and to their sum annex the common letter, or letters, prefixing the common sign." Similarly, for adding similar quantities with unlike signs, he has written "Find the sum of the coefficients of the similar positive quantities; also, the sum of the coefficients of the similar negative quantities. Subtract the less sum from the greater; then, to the difference prefix the sign of the greater, and annex the common literal part." Now, these explanations are not WRONG or BAD. But they are written in English which is likely to be unfamiliar to many students, so you will spend a fair amount of time translating.

 

Summary: I think this would make an excellent teacher's resource book for someone who is both good at algebra and slightly outmoded English. It is free, and the explanations are nonstandard, so it would be a good source of further explanations. Furthermore, I believe that going through the introductory section *before* doing a standard algebra class would help a student develop a more intuitive understanding of variables. (Of course, so would doing something like Hands on Equations or Zaccaro's Real World Algebra, and in modern terminology). But the archaic terminology (including not only the English, but also the mathematical) is likely to be a hindrance to a student. I would only recommend this as a supplement.

Link to comment
Share on other sites

There are some things I like and some things I don't. I'm going off this book: http://books.google.com/books?id=cj8YAAAAYAAJ&pg=PA7&source=gbs_toc_r&cad=3#v=onepage&q&f=false

 

Pro:

He starts off with word problems designed to get students to have an intuitive understanding of variables in linear equations. I feel that a student who had begun with this might be much less likely to, for example, take x + x and write "= x squared".

 

Con: I find the subsequent presentation of the definitions and notation (in lesson I - definitions and notation) absolutely terrible. There are about 50 definitions dumped on the hapless student, with few computational examples and no computational practice to enable them to work on them. Very few students would acquire more than rote learning from this section, and would be very confused as to which definition goes where. I am not really sure how this is supposed to be taught -- if perhaps the definitions were to be interspersed as needed, but I tend to doubt it given the date of the book.

 

Con: The terminology is somewhat antiquated, including the English explanations. For example, when he is explaining how to add similar quantities with like signs, he has written "Add together the coefficients of the several quantities, and to their sum annex the common letter, or letters, prefixing the common sign." Similarly, for adding similar quantities with unlike signs, he has written "Find the sum of the coefficients of the similar positive quantities; also, the sum of the coefficients of the similar negative quantities. Subtract the less sum from the greater; then, to the difference prefix the sign of the greater, and annex the common literal part." Now, these explanations are not WRONG or BAD. But they are written in English which is likely to be unfamiliar to many students, so you will spend a fair amount of time translating.

 

Summary: I think this would make an excellent teacher's resource book for someone who is both good at algebra and slightly outmoded English. It is free, and the explanations are nonstandard, so it would be a good source of further explanations. Furthermore, I believe that going through the introductory section *before* doing a standard algebra class would help a student develop a more intuitive understanding of variables. (Of course, so would doing something like Hands on Equations or Zaccaro's Real World Algebra, and in modern terminology). But the archaic terminology (including not only the English, but also the mathematical) is likely to be a hindrance to a student. I would only recommend this as a supplement.

 

Wow. Thank you so much. I feel that the arithmetic series is amazing, but I don't have much comparison for the Algebra and such. I've been wanting to go through upper level math myself, to be ahead of the game, so I've been looking around. You stated some things I probably would not have realized. Thanks.

Link to comment
Share on other sites

Wow. Thank you so much. I feel that the arithmetic series is amazing, but I don't have much comparison for the Algebra and such. I've been wanting to go through upper level math myself, to be ahead of the game, so I've been looking around. You stated some things I probably would not have realized. Thanks.

 

Ah, you want it for yourself -- I will admit I was a little confused with your signature :D

 

Allow me to make a recommendation then.

 

If you want to go through math yourself, I think you can choose any college developmental series and just work your way through it. If you choose older editions, you can find them extremely cheaply (+shipping, but still it should be less than 5 bucks per book).

 

For example, Lial's introductory and intermediate algebra -- http://www.amazon.com/Introductory-Intermediate-Algebra-4th-Edition/dp/0321575695 -- has 127 used copies from $0.65. (note that the combined books are not what I'd recommend for a first exposure -- they are a little more condensed -- so if you were the type of student who worked very very hard to get a C in high school algebra you might want to get the single-course editions).

 

With these college textbooks, you can buy a "student solutions manual" (make sure to match editions). This will give you completely worked-out solutions to all of the odd-numbered exercises in the textbook. Now these books have a bajillion exercises, so doing all the odds will be more than enough. Here's the manual that matches the textbook I posted starting at $0.56 -- http://www.amazon.com/Student-Solutions-Introductory-Intermediate-Algebra/dp/0321576128/ref=sr_1_2?ie=UTF8&qid=1401661240&sr=8-2&keywords=lial+introductory+and+intermediate+algebra+student+solutions+manual (this is another advantage they have over a book like Ray's).

 

The Lial's are not the only texts out there -- Bittinger, Martin-Gay, Gustafson, and many others are equally good. I've used all of these authors for various levels of mathematics. Any of them should be suitable for a conscientious student.

 

As a suggestion, though -- don't allow yourself to get into the habit of looking at the solutions manual as soon as you get a little bit frustrated. If you get frustrated, work on a different problem and then return to the one that has frustrated you, but do return. If you still can't get it with a second try, then take a sheet of paper, find the solution you want, and cover all but the first line. Then see if you can figure it out with that line for a hint. If you're still stuck, move the sheet of paper down one and look at the second line. And so on.

 

If you have a little more to spend and want more of a challenge, you can also investigate the excellent Art of Problem Solving series. Many adults have reported that they achieved a far greater understanding after working through those. However, some others found them too challenging and/or did not care for the discovery learning aspect. I noted the low-cost resources first because I suspected that one reason you were interested in Ray's was because it was free.

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

 Share

×
×
  • Create New...