Your Students…Where Are They Headed?

What Do They Need?(with your help) Jeff Morgan

Chair, Department of MathematicsDirector, Center for Academic Support and

AssessmentUniversity of Houston

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

(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)

Technology Tool Tips

• PDF Annotator• Mimio Notebook• WinPlot• Bamboo Tablet

Back to Business…

Interesting Trends and Observations

Fall Freshmen Math

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

F96 F97 F98 F99 F00 F01 F02 F03 F04 F05 F06 F07

Fall Calculus I, II and III

Math 2433 enrollment: Summer 06 = 62, Summer 07 = 106.

0

200

400

600

800

1000

1200

1400

F96 F97 F98 F99 F00 F01 F02 F03 F04 F05 F06 F07

M1431M1432M2433

Fall Math Below Calculus

0

500

1000

1500

2000

2500

3000

F96 F97 F98 F99 F00 F01 F02 F03 F04 F05 F06 F07

1300 Fundamentals ofMathematics1310 College Algebra

1311 Elementary Math.Modeling1312 Intro. To Math.Reasoning1313 Finite Math

1314 Elements of Calculus

1330 Precalculus

Concerns• Prerequisite Knowledge

– Arithmetic

– Graphing Knowledge

– Algebraic Skills

• Student Performance

– Independence

– Responsibility

Previous Attitude

They are adults. Let them find their own way.

Current Attitude

Force them to work hard.

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

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

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.

Performance DataPreCalculus

1330 Fall 06 A B C D F WNumber 206 156 127 101 111 146Cumulative 206 362 489 590 701 847% 24 18 15 12 13 17Cum. % 24 42 57 69 82 100

Maintained performance with increased standards.

Performance DataCalculus I

1431 Fall 06 A B C D F WNumber 215 290 229 181 258 248Cumulative 215 505 734 915 1173 1421% 15 20 16 13 18 18Cum. % 15 35 51 64 82 100

.

Time will tell…

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.

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

Simple Arithmetic

Example – Basic Fractions

872

31

Example – Integer Manipulation

14138

Solutions

• Restrict calculator usage.• Encourage drill and kill arithmetic for 5

minutes each day.

Simple Algebraic Manipulation

Example – Facts Through Experimentation

11

false?or True

2

22

xx

baba

baba

Example – Facts Through Experimentation

cos2cos2cossinsincoscos

false?or True

(if they are proceeding to calculus)

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.

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.

Example – Lines 2

form.intercept -slopein line

theofequation theGive .14,2point he through tpasses 3 slope with lineA

aaa

Example – Lines and Quadratics

?9,1

throughpass alsoit Can .14,2point he through tpasses 3 slope with lineA

aaa

Graphing and Understanding Basic Shapes

Please…

2

3

Make sure students can graph

2 6

2 3

1

y x

y x x

y x

yx

y x

More…

Make sure students can graph

sin

cos

tan

y x

y x

y x

You Can’t Keep Yourself From Reading “Stop”

2

Give the Basic Shape of

3 2

2 3 11

cos

y x

y x x

yx

y xy x

(this is a different drill)

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.

aa a

Example - Growth

xy

xxy

xxy

xxy

xxy

x

2

20100

10

252

310

? of valueslargefor larger isWhich

5

3

2

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.

Simple Geometry

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!

Combining Arithmetic, Algebra and Geometry

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.

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?

Example – Simple Critical Thinking

Determine what lead from the initial equationto the subsequent equations, and find the error.

3 2 1 0

3 2 13 2 1

2 21

x

xxxx

A Sense of Responsibility

This Is The #1 Employer Requirement!