rob Posted August 5, 2016 Share Posted August 5, 2016 (edited) I'm posting this request here because of the title of her book: Pre-Algebra: An "Accelerated" Course 😀 Edited August 5, 2016 by rob Quote Link to comment Share on other sites More sharing options...
disposed to learn Posted August 5, 2016 Share Posted August 5, 2016 I was disappointed to find out that The Well Trained Mind Academy is using Saxon as their only textbook. Quote Link to comment Share on other sites More sharing options...
Dmmetler Posted August 5, 2016 Share Posted August 5, 2016 They also have an AOPS/Singapore based class, IIRC. Quote Link to comment Share on other sites More sharing options...
disposed to learn Posted August 5, 2016 Share Posted August 5, 2016 Sure they'll learn/memorize the methods of algebra from the AoPS/Singapore based class, but presenting the motivation for those methods within the structure of algebra is one of the strong points of Dolciani's Algebra Structure and Method textbooks. 1 Quote Link to comment Share on other sites More sharing options...
disposed to learn Posted August 6, 2016 Share Posted August 6, 2016 For example, the FOIL method of multiplying binomials mentally is usually presented, as such, and rote memorized. If instead, it is introduced in the context of finding the area of rectangles of side lengths (ax+b) and (cx+d), and then generalized to finding the area of any rectangle; this will undoubtedly provide a more meaningful experience than just memorizing patterns for writing squares of binomials as trinomials. 1 Quote Link to comment Share on other sites More sharing options...
raptor_dad Posted August 6, 2016 Share Posted August 6, 2016 For example, the FOIL method of multiplying binomials mentally is usually presented, as such, and rote memorized. If instead, it is introduced in the context of finding the area of rectangles of side lengths (ax+b) and (cx+d), and then generalized to finding the area of any rectangle; this will undoubtedly provide a more meaningful experience than just memorizing patterns for writing squares of binomials as trinomials. Dolciani is certainly more geometric/visual in its presentation but I think your claim is unfair to AoPS Algebra. They have a sidecar on geometric factoring on p115 in Chapter 4(Factoring) and revisit that in a geometric sidebar in Chapter 10(Getting Started with Quadratics) which is immediately after the introduction of the FOIL method and the next part of the text says Using these gimmicks to understand how to multiply binomials is fine, but don't rely on them to memorize how to multiply binomials. For example, how is FOIL going to get you through expanding the product of (x^2 - x +4) (x^2 - 2x +3)? If you understand how to multiply binomials, extending that understanding to more complicated expressions is easy. Dolciani certainly has a more extensive geometric approach in my 1965 Structure Method Algebra. Chapter 7 is great.The visual proofs in the problem sets for section 7-5 are real gems. Problem 3 showing that (a+b)^2 - (a-b)^2 = 4ab and the others remind me of the visual proofs of the Pythagorean theorem. Dolciani is more visual but I think AoPS does a fine job developing understanding well beyond the algorithmic. Also, I think both groups miss the boat by just not introducing grid multiplication of numbers first and then expanding that to algebra. Quote Link to comment Share on other sites More sharing options...
rob Posted August 6, 2016 Author Share Posted August 6, 2016 (edited) So, is anyone interested in joining a "Dolciani" social group? http://forums.welltrainedmind.com/groups/268-dolciani/ Edited August 6, 2016 by rob Quote Link to comment Share on other sites More sharing options...
MarkT Posted August 6, 2016 Share Posted August 6, 2016 Also, I think both groups miss the boat by just not introducing grid multiplication of numbers first and then expanding that to algebra. like this ? https://en.wikipedia.org/wiki/Grid_method_multiplication Quote Link to comment Share on other sites More sharing options...
raptor_dad Posted August 7, 2016 Share Posted August 7, 2016 (edited) like this ? https://en.wikipedia.org/wiki/Grid_method_multiplication Exactly. Same thing FOIL but easily extended to multiplying trinomials with a 3x3 grid or a trinomial times a binomial with a 3x2 grid. Just like in arithmetic multiplication, I think beginners in algebra have two related problems 1) Rememberring the algorithm 2) A simple working memory issue of tracking where they are in the process and not missing pairs. The grid helps with 1 and completely removes the working memory issue. Once the process is internalized you drop the grid and go on your way. Edited August 7, 2016 by raptor_dad 2 Quote Link to comment Share on other sites More sharing options...
Lucy the Valiant Posted August 7, 2016 Share Posted August 7, 2016 Hey, I'll join! Just finished Pre-Algebra last year, and we've started Algebra this year - I'm a former English teacher, highly skeptical of my mathematical abilities, but determined to self-educate as long as this is working for all of us. Predicting I can get at least through Alg / Geometry / Alg II. 2 Quote Link to comment Share on other sites More sharing options...
disposed to learn Posted August 24, 2019 Share Posted August 24, 2019 (edited) whelp i'm back, after 3 years, anyone interested in chatting about dolciani? perhaps, we can catalogue the various dolciani threads on this site? Edited August 24, 2019 by disposed to learn Quote Link to comment Share on other sites More sharing options...
disposed to learn Posted August 24, 2019 Share Posted August 24, 2019 (edited) for example creating a "master thread" of all the various questions tagged "Dolciani"? Edited September 28, 2019 by disposed to learn Quote Link to comment Share on other sites More sharing options...
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