Mr. Howe

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Please note: You may continue to use this page type if you desire. <P class=MsoNormal style="MARGIN: 0in 0in 0pt; TEXT-ALIGN: center" align=center><U>Parent and Student AlgebraII/Trig Information Sheet<o:p></o:p></U></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt">AlgebraII/Trig is a very important course in terms of concepts that students must learn and retain for Calculus.<SPAN style="mso-spacerun: yes"> </SPAN>Sometimes Algebra II/Trig has the reputation of being difficult.<SPAN style="mso-spacerun: yes"> </SPAN>One factor that causes this perception is that it is the first math course that requires a large amount of previously acquired knowledge be transferred across space and time.<SPAN style="mso-spacerun: yes"> </SPAN>Included in this package is the cover sheet for the Algebra Transfer Package, which discusses how we try to give the students the tools to recall previously learned material and help them distinguish between previously learned material and new material.</P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt">This document contains some important information that may help you understand the nature of this course, the expectations, and things that you may want to consider as the year progresses.<SPAN style="mso-spacerun: yes"> </SPAN>First, I have often run across articles that discuss the nature of learning mathematics in terms of “struggle.”<SPAN style="mso-spacerun: yes"> </SPAN>Below are some quotes from an article from the “Bulletin of the National Association of Secondary School Principals” called “Finding the Glory in the Struggle:<SPAN style="mso-spacerun: yes"> </SPAN>Helping Our Students Thrive When Math Gets Tough.”</P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0.5in 0pt; TEXT-INDENT: 27pt">“<U>Ultimately, math comes easily to no one, and therein lies its glory</U>.<SPAN style="mso-spacerun: yes"> </SPAN>It is precisely in this struggle that math offers the most to our young people.<SPAN style="mso-spacerun: yes"> </SPAN>Mathematics offers them an opportunity to learn how to work through the struggle, how to bring to it what they have, how to find and use the things they need.<SPAN style="mso-spacerun: yes"> </SPAN>But this struggle is too often misinterpreted, and agony results.</P> <P class=MsoNormal style="MARGIN: 0in 0.5in 0pt; TEXT-INDENT: 27pt"><U>Struggling in mathematics is not the enemy, any more than sweating is the enemy in basketball, it is part of the process and a clear sign of being in the game.<SPAN style="mso-spacerun: yes"> </SPAN>Math asks our students to think in ways they are not used to thinking; they will be asked to look at the obvious in ways they’re not accustomed to, and then we’ll ask them to explore the not-so-obvious in similar ways.<SPAN style="mso-spacerun: yes"> </SPAN>A rigor of thinking and a clarity of expression is demanded that will stretch them beyond familiar styles.<SPAN style="mso-spacerun: yes"> </SPAN>Much of this will require abstracting and reasoning beyond what they know.<SPAN style="mso-spacerun: yes"> </SPAN>It will also require an honest pursuit, there really are no shortcuts.<o:p></o:p></U></P> <P class=MsoNormal style="MARGIN: 0in 0.5in 0pt; TEXT-INDENT: 27pt"><U>But for this effort, it provides so many rewards</U>.<SPAN style="mso-spacerun: yes"> </SPAN>Math does not hide its mysteries; they are there for anyone who seeks them.<SPAN style="mso-spacerun: yes"> </SPAN>Because math is tough, because it is honest, and because it is principled, the rewards math offers to those who persist in the struggle go far beyond the concept that is mastered.<SPAN style="mso-spacerun: yes"> </SPAN><U>Watch a youngster who has stuck with the struggle and come to a real understanding of a mathematical concept on his own efforts.<SPAN style="mso-spacerun: yes"> </SPAN>He can conquer the world, and if you tell him otherwise, he simply won’t believe you.<SPAN style="mso-spacerun: yes"> </SPAN>He knows what he has done, and he knows that if he can do that, he can do anything.</U></P> <P class=MsoNormal style="MARGIN: 0in 0.5in 0pt; TEXT-INDENT: 27pt">If the parent accepts the struggle, then the student can.<SPAN style="mso-spacerun: yes"> </SPAN>And even more important, if the parent values the struggle, and sees math as more than just a series of right answers, the young person can approach mathematical learning in a way that will not only make success in mathematics more likely, but carry over to pursuits far beyond the mathematics classroom.”</P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt">Fortunately, learning mathematics is not a continuous struggle in a well designed course like ours.<SPAN style="mso-spacerun: yes"> </SPAN>In fact, we try to present to the students that the learning of mathematics is very manageable.<SPAN style="mso-spacerun: yes"> </SPAN>But, there will usually be times that the abstractness demanded will cause a temporary struggle.<SPAN style="mso-spacerun: yes"> </SPAN>As the article says, it is important that the student work through this struggle and that he/she take the credit for working through the struggle.<SPAN style="mso-spacerun: yes"> </SPAN>I would add that the student must not give anyone else the credit for working through the struggle, such as a tutor, a parent, or even the teacher.</P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt">Learning math has two components, learning concepts and doing problems associated with those concepts.<SPAN style="mso-spacerun: yes"> </SPAN>In a student’s elementary school and early middle school arithmetic courses the student would typically do a lot of problems (drill sheets) until they have some concepts in their head to do problems.<SPAN style="mso-spacerun: yes"> </SPAN>That is, the student did problems to figure out what the concepts were.<SPAN style="mso-spacerun: yes"> </SPAN>To learn material in math courses (Algebra and higher), the student must learn in the opposite direction.<SPAN style="mso-spacerun: yes"> </SPAN>The student must learn concepts first (concepts are single sentences), and then do problems to “test” their understanding of the already learned concepts.<SPAN style="mso-spacerun: yes"> </SPAN>This reverse in the direction they study and learn material is the major struggle for some students, especially the accelerated students.</P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; TEXT-INDENT: -0.25in; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt">We may give students an “Algebra Comprehensive Exam (ACE)” at the end of the year.<SPAN style="mso-spacerun: yes"> </SPAN>This will be an exam over all major concepts learned for the full course, not just second semester.<SPAN style="mso-spacerun: yes"> </SPAN>Students must change their view of learning from simply preparing for unit tests to permanently learning material.</P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt">Enclosed with this document are the following handouts.</P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt"><U>Some additional thoughts:<o:p></o:p></U></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; TEXT-INDENT: -0.25in; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt">1.<SPAN style="mso-spacerun: yes"> </SPAN>In this course we have both accelerated and non-accelerated students. I want to remind you that students do not have to accelerate to take Advanced Placement Calculus at Cascia, like they would at other schools.<SPAN style="mso-spacerun: yes"> </SPAN>At other schools the typical sequence of courses used to be able to take AP Calculus is as follows:</P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; TEXT-INDENT: -0.25in; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt 27pt; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt">9<SUP>th</SUP> – Geometry, 10<SUP>th</SUP> – Algebra II or Algebra II/Trig, 11<SUP>th</SUP> - Pre-Calc, 12<SUP>th</SUP> – AP Calc</P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt">Our normal non-accelerated curriculum is as follows:</P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt 27pt; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt">9<SUP>th</SUP> – Algebra I, 10<SUP>th</SUP> – Geometry, 11<SUP>th</SUP> - Algebra II/Trig, 12<SUP>th</SUP> – AP Calc</P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; TEXT-INDENT: -0.25in; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt">As you can tell, we do not have the pre-calculus course in this sequence.<SPAN style="mso-spacerun: yes"> </SPAN>A typical pre-calculus course is mostly review of the same material as previous courses.<SPAN style="mso-spacerun: yes"> </SPAN>Pre-calculus courses are normally taught by the same teachers that teach the AP Calculus courses.<SPAN style="mso-spacerun: yes"> </SPAN>The assumption is that the previous courses were not taught at an abstract level, and the “higher level” teacher must go back to help students understand mathematics and what was behind the math they have been doing.<SPAN style="mso-spacerun: yes"> </SPAN>At Cascia, we have designed Algebra I, Geometry, and Algebra II/Trig to develop the student abstractly, and we do not have the attitude that only calculus teachers have the skill to draw the student to an abstract level of thinking.</P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; TEXT-INDENT: -0.25in; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt"><o:p> </o:p></P> <P class=MsoNormal style="MARGIN: 0in 0in 0pt 0.25in; TEXT-INDENT: -0.25in; mso-pagination: none; tab-stops: 289.0pt 325.0pt 361.0pt 397.0pt 505.0pt 541.0pt 577.0pt 613.0pt 649.0pt 685.0pt 721.0pt 757.0pt 793.0pt 829.0pt 865.0pt 901.0pt 937.0pt">2.<SPAN style="mso-spacerun: yes"> </SPAN>The fact that most of our math courses are developed using collaboration is mentioned in the “Negative Effects of Tutoring Handout”.<SPAN style="mso-spacerun: yes"> </SPAN>In developing lesson plans and “end of course” tests we ran across information concerning the purpose of the “No Child Left Behind Act” and the high stakes tests associated with this program.<SPAN style="mso-spacerun: yes"> </SPAN>The purpose is to force schools and teachers to collaborate and use research and data.<SPAN style="mso-spacerun: yes"> </SPAN>That is, if a teacher’s students do not do well on these tests then they are forced to talk to other teachers and use research and data.<SPAN style="mso-spacerun: yes"> </SPAN>We have used collaboration and research on department courses for over thirty years.<SPAN style="mso-spacerun: yes"> </SPAN>This causes our courses to be very well designed and strong.<SPAN style="mso-spacerun: yes"> </SPAN>With reasonable academic maturity and academic aggressiveness, the student will make great strides this year. </P> Or, would you like to view and optionally restore one of these previous versions? 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Mr. Howe

AlgII/Trig Student-Parent Information

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