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Topic: [math-learn] Other Comments On High School Algebra 2
Replies: 44   Last Post: May 12, 2011 8:18 AM

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John Anderson

Posts: 5
Registered: 5/5/11
Re: [math-learn] Other Comments On High School Algebra 2
Posted: May 5, 2011 7:40 AM
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att1.html (18.9 K)

The Saxon texts strategically distribute the content typically found in chapters and units within more traditional texts.  This allows more time and practice for skills and concepts to be mastered before the next increment of rigor is added.  The daily, cumulative practice is the glue that holds the approach together.  Doug Rohrer from the University of South Florida has done some interesting research regarding the advantages of mixed and spaced practice, the method used in the Saxon approach.


John Anderson



________________________________
From: "starcap50@aol.com" <starcap50@aol.com>
To: math-learn@yahoogroups.com
Sent: Thursday, May 5, 2011 4:40 AM
Subject: Re: [math-learn] Other Comments On High School Algebra 2


 
Hello,

I took my own high school Algebra 2 course back in 1966, and I can think of
several differences between the course I had that year and the Algebra 2
courses I see today.

First and foremost in my mind, the subject of matrices was not covered in
the Algebra 2 course I took in 1966. I'm curious. Does anybody here know
roughly when matrices began to be taught in our high school Algebra 2
textbooks and curriculums?

Next, if my memory is correct, the subject of conics was not covered in as
much depth in 1966 as they are today. To cite one example, I do not
remember having to graph hyperbolas, whose centers are not at the origiin, and
then having to calculate the equations of their asymptotes.

In regard to the subject of imaginary and complex numbers, I do not
remember this topic being taught in my own Algebra 2 course in 1966. Perhaps, my
memory is failing me. However, I have a copy of a 1990 Algebra 2 textbook,
in which this topic is presented in considerable depth.

One thing I find to be rather curious is that the Algebra 1 textbooks I see
today make no mention of imaginary and complex numbers. When a problem
such as finding the square root of negative 4 is presented, the Algebra 1
textbooks quickly explain that there are no real solutions and leave it at
that.

Then fast forward to Algebra 2, during which students learn that there
really is an "answer" to finding the square root of negative 4, which is 2i.

Another difference is that the topic of Probability was not taught in any
of the junior high or high school math courses of the 1960s.

Another thing I see are inconsistencies in the manner in which various
topics are taught and presented in the Algebra 2 textbooks and their teachers.

For example, some teachers completely ignore the topic of solving systems
of 3 equations in 3 variables. Others go into it at great depth.

The Glencoe Algebra 2 textbook teaches both the diagonal method and the
expansion of minors method for finding the determinant of a 3 X 3 matrix.
In contrast, the expansion of minors method is completely ignored by the
Algebra 2 textbook from McDougal-Littel. In addition, McDougal-Littel does
not present the proportion method for solving problems with direct, inverse,
and joint variation.

One of my students at a different private school uses the brand new Saxon
Algebra 2 textbook (the one with the blue cover). I find the manner in
which it jumps from one lesson topic to another, with little or no continuity
or connection between successive lessons, to be very confusing. I found
the same type of problem with the new Saxon Geometry textbook with a
student I tutored last year.

In addition, this private school teaches Algebra 2 only as a one-semester
half-year course. Personally, I do not think justice can be served for the
majority of high school students, in order to achieve an adequate and
thorough instruction of Algebra 2 course during only one semester.

As a result, their Algebra 2 teacher "cherry picks" the Algebra 2 lessons
of her choice and skips over many of the textbook lessons. So far, she has
skipped each and every single lesson on the topic of matrices.

At least, in our local public schools, taking Algebra 2 as a one-semester
course is an option for the more accelerated students, with its instruction
during an entire school year being the "norm" for the vast majority of
students.

Okay, I'll stop now. I just wanted to share these additional comments and
observations.

Best Wishes,

Dennis

In a message dated 5/4/2011 1:01:52 P.M. Eastern Daylight Time,
rfermat@yahoo.com writes:




Given all the posts about Algebra 2, it seems that the situation is roughly
the same as when I took the sequence of courses Algebra 1, Geometry,
Algebra 2, more than a few decades ago.

Given that, and this is what I was really getting at, I think having
complex numbers in Algebra 2 is inappropriate. That is too sophisticated a topic
for a third mathematics course. Very few such students would have the
maturity to understand complex numbers.

Lacking such depth, the subject would degenerate into mindless formalism
and button pushing. That is the antithesis of education.

Robert H. Lewis
Fordham University
_http://www.fordham.edu/academics/programs_at_fordham_/mathematics_departme/
what_math/index.asp_
(http://www.fordham.edu/academics/programs_at_fordham_/mathematics_departme/what_math/index.asp)

--- On Wed, 5/4/11, _starcap50@aol.com_ (mailto:starcap50@aol.com)
<_starcap50@aol.com_ (mailto:starcap50@aol.com) > wrote:

> From: _starcap50@aol.com_ (mailto:starcap50@aol.com) <_starca
p50@aol.com_ (mailto:starcap50@aol.com) >
> Subject: Re: [math-learn] RE: "Algebra 2" problem
> To: _math-learn@yahoogroups.com_ (mailto:math-learn@yahoogroups.com)
> Date: Wednesday, May 4, 2011, 8:10 AM
> Hello,
>
> This was no misprint.
>
> The first equation in this system was written exactly as
> below, with the
> negative 1 on the right hand side.
>
> The teacher did say that there would be one problem which
> would involve an
> imaginary number solution to be written in ordered pair
> form.
> Apparently, this was that problem.
>
> Dennis
>
> In a message dated 5/4/2011 7:43:23 A.M. Eastern Daylight
> Time,
> _jmmvy62@verizon.net_ (mailto:jmmvy62@verizon.net)
> writes:
>
>
>
>
> math-learnHello all,
>
> I assumed there was a misprint in that x^2 + y^2 = -1
> equation, and
> that the "-1" was "supposed" to be 1.
>
> In my eight years of teaching/tutelage etc I've never
> come across an
> equation of an imaginary circle / having negative
> radius.
>
> Meanwhile, I am curious about how students would
> react to the
> equation sin^2 x + cos^2 x > 1. Hmmm.....
>
> -John Morse
>
> hang glider pilot near Albany NY
>
> [Non-text portions of this message have been
> removed]
>
>
>
>
>
>
> [Non-text portions of this message have been removed]
>
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
> _math-learn-fullfeatured@yahoogroups.com_

(mailto:math-learn-fullfeatured@yahoogroups.com)
>
>
>


[Non-text portions of this message have been removed]




[Non-text portions of this message have been removed]



Date Subject Author
5/5/11
Read [math-learn] Other Comments On High School Algebra 2
Dennis
5/5/11
Read Re: [math-learn] Other Comments On High School Algebra 2
John Anderson
5/5/11
Read RE: [math-learn] Other Comments On High School Algebra 2
John Clement
5/5/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/5/11
Read RE: [math-learn] Other Comments On High School Algebra 2
John Clement
5/5/11
Read Re: [math-learn] Other Comments On High School Algebra 2
John Anderson
5/5/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/5/11
Read RE: [math-learn] Other Comments On High School Algebra 2
John Clement
5/5/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/5/11
Read RE: [math-learn] Other Comments On High School Algebra 2
John Clement
5/5/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/5/11
Read RE: [math-learn] Other Comments On High School Algebra 2
John Clement
5/5/11
Read Re: [math-learn] Other Comments On High School Algebra 2
John Anderson
5/5/11
Read RE: [math-learn] Other Comments On High School Algebra 2
John Clement
5/5/11
Read Re: [math-learn] Other Comments On High School Algebra 2
John Anderson
5/7/11
Read RE: [math-learn] Other Comments On High School Algebra 2
Robert Lewis
5/7/11
Read [math-learn] Other Comments On High School Algebra 2
Scott Anderson
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Lewis
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Dennis
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Ralph A. Raimi
5/7/11
Read RE: [math-learn] Other Comments On High School Algebra 2
John Clement
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Scott Anderson
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/7/11
Read RE: [math-learn] Other Comments On High School Algebra 2
John Clement
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Dennis
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/8/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Lewis
5/8/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Dennis
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/8/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/12/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Dennis
5/5/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Dennis
5/5/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/5/11
Read RE: [math-learn] Other Comments On High School Algebra 2
John Clement
5/5/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Hansen
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Lewis
5/7/11
Read RE: [math-learn] Other Comments On High School Algebra 2
John Clement
5/7/11
Read RE: [math-learn] Other Comments On High School Algebra 2
Robert Lewis
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Lewis
5/7/11
Read Re: [math-learn] Other Comments On High School Algebra 2
Robert Lewis

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