tag:blogger.com,1999:blog-8231784566931768362.post7274057555470966424..comments2023-09-09T08:21:55.454-04:00Comments on MathNotations: How Much Factoring In 1st Year Algebra?Dave Marainhttp://www.blogger.com/profile/13321770881353644307noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-8231784566931768362.post-54878391691291231922010-01-10T07:18:37.504-05:002010-01-10T07:18:37.504-05:00Mathmom,
There are many outstanding math teachers ...Mathmom,<br />There are many outstanding math teachers I've had the pleasure to work with who understand the importance of connecting procedures to understanding and who try to make sense of the WHY in math. <br /><br />But, textbooks have forever compartmentalized mathematics which leads to <b>teaching skills in isolation</b>. It takes knowledge, experience, and the utmost dedication to develop lesson plans which help students understand the motivation for and the reasoning behind procedures. <br /><br />This is why preservice education for prospective math teachers is so critical and one of the reasons I started this blog. I'm hoping in some small way to influence young teachers.Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-5041141922403733812010-01-09T23:33:57.264-05:002010-01-09T23:33:57.264-05:00Many textbooks omit the fact that after you obtain...<i>Many textbooks omit the fact that after you obtain the solutions of a quadratic equation with the quadratic formula, you can then relate those solutions to the factoring of the corresponding quadratic expression. Opportunity is lost for emphasizing the connection between zeros and factors.</i><br /><br />Wait, really? Why else would students be factoring if not to find zeros? Students are just taught to factor for the sake of factoring, without knowing why one would want to do such a thing? That's abusrd. :( The understanding of what it's for is much more important than the acutal skill, IMO (especially since calculators/computers can do this for us now).mathmomhttps://www.blogger.com/profile/05869925405540832241noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-35308050117641738612010-01-09T05:50:24.761-05:002010-01-09T05:50:24.761-05:00Reva,
Thank you for your profound and very importa...Reva,<br />Thank you for your profound and very important reply.<br /><br />"Factoring should be emphasized as a skill, but should also be accompanied by its deep connections to solutions of equations and zeros and x-intercepts."<br /><br />This quote from your comment should appear in every teacher's guide for Alg I or II!<br /><br />Several thoughts come to mind here:<br /><br />(1)If I were hiring a new secondary math teacher, I would check to see if you were the professor! How lucky these students are. <br /><br />(2) Let me know if there's an opening in your school! I'd love to co-teach with you. If not, then let's collaborate on a guide for prospective high school math teachers. Email me!!<br /><br />(3) Your theme of helping preservice teachers to recognize the interrelationships among math concepts is the most crtical piece and one I've been attemipting to share on this blog from its inception. We can't expect our teachers to do this unless they are shown how!Dave Marainhttps://www.blogger.com/profile/13321770881353644307noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-37279919371597017622010-01-08T08:47:46.034-05:002010-01-08T08:47:46.034-05:00I think factoring is a useful skill that should re...I think factoring is a useful skill that should remain in the Algebra 1 curriculum. However, it is usually taught independently of other concepts, such as connections to graphs of polynomials and solutions of polynomial equations. Many textbooks omit the fact that after you obtain the solutions of a quadratic equation with the quadratic formula, you can then relate those solutions to the factoring of the corresponding quadratic expression. Opportunity is lost for emphasizing the connection between zeros and factors.<br /><br />Last semester, my junior math majors thought that all factoring happened over the integers since this is all that they have practiced. Since most of these students were future hs math teachers, driving home the Fundamental Theorem of Algebra and connecting it to the factoring techniques they already know was a big emphasis in my Intro to Proofs course.<br />(See my Geogebra applet:<br />http://www.mymathspace.net/geogebra/poly5.html)<br /> <br />Factoring should be emphasized as a skill, but should also be accompanied by its deep connections to solutions of equations and zeros and x-intercepts. If these connections appear later in the year, that's okay. But its should be tied up all together at some point in Algebra 1 or 2.Reva Narasimhanhttps://www.blogger.com/profile/10937073963777248872noreply@blogger.comtag:blogger.com,1999:blog-8231784566931768362.post-4494489854875792542010-01-06T23:25:28.621-05:002010-01-06T23:25:28.621-05:00Hey Dave!
I find that the "proof" at the...Hey Dave!<br />I find that the "proof" at the last part of this blog entry pretty interesting and useful for me and my students (I'm a tuition teacher in Malaysia anyways). <br /><br />Your blog has been useful for my students especially those who are taking the Additional Mathematics. I frequent your blog to get some inspiration to teach the subject. (:<br /><br />By the way, since you're a blogger, maybe we can have a deal here. I saw that you have advertisements on your blog. <br /><br />I'm helping a friend (on a part time basis) to find bloggers who are interested in putting paid text links on published articles. Bloggers get paid an amount of money for putting these links. <br /><br />If you're interested in this idea, do feel free to contact me via e-mail. My e-mail address is kevlinefm1910@hotmail.com<br /><br />Keep up the good work, Dave!kevlinefmhttps://www.blogger.com/profile/11373896104767973248noreply@blogger.com