Why Do I, As a Middle Grades Math Teacher, Need to Know About Calculus and Analytic Geometry

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Why Do I, As a Middle Grades Math Teacher, Need
to Know About Calculus and AnalyticGeometry?

• Carol S. Alton
• Summer, 2008
• CUI 688

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Why do I need to know about Calculus and Analytic
Geometry?

• 1 Increased Professional Content Knowledge
• 2 Important Mathematical Connections
• 3 More Focused Direction in Planning and
  Instruction

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Reason 1 Increased Professional Content
Knowledge

• Teachers are poorly prepared by education
  schools to teach math.
• Education students should be taking courses that
  give them a deeper understanding ..and explain
  how math concepts build upon each other and why
  certain ideas need to be emphasized in the
  classroom.
• Article Title Schools for Teachers Flunk at Math
• http//msnbc.nsn.com/id/25378336

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Reason 1 Increased Professional Content
Knowledge

• This course has already (yes, in the short time
  we've been in class) shown me that I need to
  understand the higher level math concepts which
  will in turn help me teach my sixth graders their
  concepts in a more productive and meaningful way
  
• Jennifer Apple, 7-4-08 

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Reason 1 Increased Professional Content
Knowledge

• Reflection on quote from Jennifer Apple
• Jennifer feels that with an increased
  professional content knowledge she can better
  prepare her students for the more advanced math
  courses they will take in the future. I
  completely agree that this is true of all math
  teachers.

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Reason 2 Important Mathematical Connections

• In reference to the PK Model, Quinn wrote,
• It is a theory of the growth of mathematical
  understanding as a whole, dynamic, leveled but
  non-linear, transcendently recursive process. 
  
• - Quinn, 2003

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Reason 2 Important Mathematical Connections

• As discussed in our class students need to be
  mathematically savvy in the following middle
  grades concepts in order to have a solid
  foundation for the calculus topics. - Julie
  Rao, 7-1-08

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Reason 2 Important Mathematical Connections

• Reflection on Quote from Julie Rao
• The table Julie posted in her blog really helped
  me make some essential connections among middle
  grades math and Calculus. Throughout the course,
  I referred back to this table to confirm my
  understandings.
• I now understand that
• - Integrals are the area bound under a curve.
• - The derivative is the slope of the line that is
  tangent to the curve. The derivative is also how
  much a quantity is changing (rate of change) at
  some given point.
• - The unit circle links many middle school
  concepts and high school concepts angles, right
  triangles, coordinate graphing, fractions,
  cosine, sine, and tangent, ratios.

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Middle School Math Connects to Calculus
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Reason 3 More Focused Direction in Planning and
Instruction

• Quote from an article posted on the Calculus
  Concept Wiki 
• Teachers should develop activities for
  students that are aimed at providing students
  with firm conceptual underpinnings of calculus.
  The conceptions that students bring from their
  previous mathematical experiences strongly
  influence how they make sense of the calculus
  concepts they encounter.
• Article Title Exponential Growth and The Rule
  of 70
• http//www.ecofuture.org/pop/facts/exponential70.
  html
• Reflection I strongly feel the better
  teachers know where the students are headed in
  their future math courses, the better they can
  focus their lessons to help them in this
  transition.

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The Unit Circle Activity

• We used the unit circle to find measures of
  triangles in radians (an angles position with
  respect to the circumference in terms of Pi).
• This activity helped me connect several concepts.
  Knowledge of two sides in special right triangle
  gives knowledge of the third by means of
  Pythagorean Theorem, and of the values of the
  trig functions for the angles in the triangle.
  The slope of the tangent line is the derivative.
• This helped me see where my students were headed
  with these concepts in the future.

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Concept of Calculus (on Wiki)The information
below really helped me initially grasp the
concept of Calculus.

• Calculus takes the ordinary rules of algebra and
  geometry and tweaks them so they can be used on
  more complicated problems.
• Calculus takes a problem that cant be done with
  regular math because things are constantly
  changing (curves on a graph) and zooms in on the
  curve until it becomes straight and then uses
  regular math to finish the problem.

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Definition of Calculus from Wiki Supports
Calculus takes the ordinary rules of algebra and
geometry and tweaks them so they can be used on
more complicated problems.