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Your Students… Where Are They Headed? What Do They Need? (with your help)
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Transcript of Your Students… Where Are They Headed? What Do They Need? (with your help)
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Your Students…Where Are They Headed?
What Do They Need?(with your help)
Jeff Morgan Chair, Department of Mathematics
Director, Center for Academic Support and Assessment
University of Houston
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Shameless Advertising
• High School Mathematics Contesthttp://mathcontest.uh.edu
• Houston Area Calculus Teachers Association AP Calculus Workshopshttp://www.HoustonACT.org
• EatMath Algebra I Teacher Workshopshttp://www.EatMath.org
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(continued)
• Online Practice AP Testing in Calculus and Statistics (info at http://www.HoustonACT.org)
• Online Practice AP Chemistry Testing(Beginning Spring 2009)
• Online Materials (see http://online.math.uh.edu)
• UTeach Replication (teachHOUSTON)
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Technology Tool Tips
• PDF Annotator
• Mimio Notebook
• WinPlot
• Bamboo Tablet
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Back to Business…
Interesting Trends and Observations
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Fall Freshmen Math
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F96 F97 F98 F99 F00 F01 F02 F03 F04 F05 F06 F07
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Fall Calculus I, II and III
Math 2433 enrollment: Summer 06 = 62, Summer 07 = 106.
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F96 F97 F98 F99 F00 F01 F02 F03 F04 F05 F06 F07
M1431
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Fall Math Below Calculus
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F96 F97 F98 F99 F00 F01 F02 F03 F04 F05 F06 F07
1300 Fundamentals ofMathematics
1310 College Algebra
1311 Elementary Math.Modeling
1312 Intro. To Math.Reasoning
1313 Finite Math
1314 Elements of Calculus
1330 Precalculus
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Concerns
• Prerequisite Knowledge
– Arithmetic
– Graphing Knowledge
– Algebraic Skills
• Student Performance
– Independence
– Responsibility
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Previous Attitude
They are adults. Let them find their own way.
Current Attitude
Force them to work hard.
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2003 - Actions In MathematicsBelow Calculus I
• Improved Placement Testing - Fall 2007• No Adjunct or Graduate Student Instruction• Mandatory Attendance• Daily Class Grades• Daily Written Homework• Weekly Online Quizzes• Online Course Materials• Increased Tutoring Availability• Common Exams and Common Grading• Improved Instruction and Course Coordination
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2007 - Actions In Calculus I
• Improved Placement Testing – Fall 2007• Mandatory Attendance (40%)• Daily Class Grades (40%)• Weekly Written Homework (75%)• Weekly Online Quizzes (100% 2005)• Online Course Materials (100% 2005)• Increased Tutoring Availability (2003)• Common Exams and Common Grading (2005)• Improved Course Coordination (2005)• Peer Pressure
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Performance Data - College Algebra
1310 Fall 06 A B C D F W
Number 662 409 313 212 247 242
Cumulative 662 1071 1384 1596 1843 2085
% 32 20 15 10 12 12
Cum. % 32 51 66 77 88 100
Improved performance with increased standards.
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Performance DataPreCalculus
1330 Fall 06 A B C D F W
Number 206 156 127 101 111 146
Cumulative 206 362 489 590 701 847
% 24 18 15 12 13 17
Cum. % 24 42 57 69 82 100
Maintained performance with increased standards.
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Performance DataCalculus I
1431 Fall 06 A B C D F W
Number 215 290 229 181 258 248
Cumulative 215 505 734 915 1173 1421
% 15 20 16 13 18 18
Cum. % 15 35 51 64 82 100
.
Time will tell…
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The Bottom Line
Students will only work as hard as you require them to work.
If you want more from your students, then demand more.
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Which Missing Skills Are Crippling Students in College?
(…the same ones that cripple them in your classroom…)
• Simple Arithmetic
• Simple Algebraic Manipulation
• Graphing and Understanding Basic Shapes
• Simple Geometry
• Critical Thinking
• A Sense of Responsibility
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Simple Arithmetic
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Example – Basic Fractions
87
2
3
1
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Example – Integer Manipulation
14138
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Solutions
• Restrict calculator usage.
• Encourage drill and kill arithmetic for 5 minutes each day.
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Simple Algebraic Manipulation
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Example – Facts Through Experimentation
11
false?or True
2
22
xx
baba
baba
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Example – Facts Through Experimentation
cos2cos2cos
sinsin
coscos
false?or True
(if they are proceeding to calculus)
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Comments
• Not everything has to be memorized.
• Encourage students to experiment.
• We expose students to so much of the forest, that they don’t know the difference between an oak and a pine.
• Students need to be able to organize their work.
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Example – Lines 1
A line with slope 3 / 2 passes through the
point 2, 3 . Give the equation of the
line in slope-intercept form.
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Example – Lines 2
form.intercept -slopein line
theofequation theGive .14,2point
he through tpasses 3 slope with lineA
aa
a
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Example – Lines and Quadratics
?9,1
throughpass alsoit Can .14,2point
he through tpasses 3 slope with lineA
aa
a
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Graphing and Understanding Basic Shapes
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Please…
2
3
Make sure students can graph
2 6
2 3
1
y x
y x x
y x
yx
y x
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More…
Make sure students can graph
sin
cos
tan
y x
y x
y x
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You Can’t Keep Yourself From Reading “Stop”
2
Give the Basic Shape of
3 2
2 3 1
1
cos
y x
y x x
yx
y x
y x
(this is a different drill)
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Example – Why Shape Is Important?
A line with slope 3 passes through the
point 2 ,4 1 . Are there any points that
this line can not contain? Explain.
a
a a
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Example - Growth
xy
xxy
xxy
xxy
xxy
x
2
20100
10
252
310
? of valueslargefor larger isWhich
5
3
2
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Notes
• Your students will be required to create simple graphs without a calculator, and also think about the shapes of simple graphs.
• Your students should know everything about lines and parabolas (except foci), square root, 1/x, sine and cosine.
• Your students should have seen an asymptote.
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Simple Geometry
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What Geometric Concepts are Important?
• Pythagorean Theorem
• Areas of triangles, rectangles and circles.
• Circumference of rectangles and circles.
• The sum of the angles in a triangle.
• The facts associated with isosceles and equilateral triangles.
• Triangle trigonometry (if they are proceeding to calculus).
Honestly, that’s it!
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Combining Arithmetic, Algebra and Geometry
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In General, We Are Happy If Students
• Can do simple arithmetic and basic algebra.• Know everything about lines.• Know everything about parabolas (except foci).• Can solve linear and quadratic equations.• Can factor simple quadratics, complete the square and
use the quadratic formula.• Have seen an asymptote.• Know the shapes of basic functions (nothing tricky).• Know the area formulas for circles, rectangles and
triangles, and know the perimeter of a circle and a rectangle.
• *Know the trig functions at the special angles.• Can organize their work.
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Critical Thinking
Can your students find the error in an argument?
Can your students combine ideas without seeing a previous example?
Do your student know the difference between a definition and an example?
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Example – Simple Critical Thinking
Determine what lead from the initial equation
to the subsequent equations, and find the error.
3 2 1 0
3 2 1
3 2 1
2 2
1
x
x
x
x
x
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A Sense of Responsibility
This Is The #1 Employer Requirement!