1 ged and beyond sabes west tom mechem, ged state chief examiner january 29, 2009

1

GED and Beyond

SABES WestTom Mechem, GED State Chief Examiner

January 29, 2009

2

The Handwriting Is On The Wall

• $27.53/hour

• 8 out of 10 of the fastest-growing jobs in MA require an Associate’s Degree or higher

(24 out of 30 nationwide)

• “Two years of post-secondary education are needed…to emerge out of poverty.” – John Comings

3

There can be no “Post-Secondary”

without the “Secondary.”

4

The GED Diploma Has Tangible Value

• You cannot support a family without some post-secondary education.

• You cannot access post-secondary education without a high-school credential.

• If you do not have a high school diploma, the GED diploma is far and away the most viable alternative.

5

Viability of the GED Diploma

• It is the same test in all 50 states

• 97% of the colleges and universities in the country accept the GED diploma as exactly equivalent to a high school diploma

• 95% of the employers in the country accept the GED diploma as exactly equivalent to a high school diploma

6

GED…

How can we get more of our students to pass the GED tests?

7

…Beyond• How can we help more of our GED

graduates avoid developmental courses in college?

• How can we help more of our GED graduates succeed in college courses?

• How can we start preparing our GED students right now for the 2012 GED tests?

8

You have to pass the GED tests and earn the diploma;butYou must also be prepared to succeed in college

9

For both the GED and Beyond:

Math Is The Major Impediment

10

GED Reasons for Failure(“Almost Theres” & “Sure Things”

only)

Failed Math only

Failed WRI only

Other

51%

35%

14%

51%

14%

35%

11

Roxbury man, distraught over the thought of failing his GED exam, found himself under

arrest Monday afternoon for taking his anger out on his dishes, police report

• The suspect told police he became so frustrated about possibly failing his GED exam that he allegedly smashed a glass bowl and cups as he was washing dishes, according to a police report. Cops said they saw broken glass all over the floor leading to the kitchen of the suspect’s Dudley Street apartment.

• Charles E. Figueroa was charged with willful and malicious destruction of property.

12

College

• 7% of ABE students earn a GED diploma• 66% of GED Examinees say they are

taking the tests to get into college• 27% of GED grads ever enroll in college• Of those:

– Less than 1 in 5 completes two years of college

– 4% ever complete four years of college

13

Predictors of Postsecondary Attrition

• Delayed enrollment• Part-time enrollment• Full-time employment• Dependent children• Single-parent status• Lack of financial support• Lack of Academic Readiness

14

One Culprit: Developmental Courses

• 85% of GED grads entering CC require at least one developmental course

• If a CC entrant requires two or more developmental courses, the chances are almost nil that this person will earn an Associate’s degree

15

Unindicted Co-Conspirator: The ACCUPLACER Test

GED entrants vs. total incoming CC cohort

• Reading: GED entrants do better

• Writing: GED entrants do as well in avoiding developmental courses; not as well in being placed in advanced writing classes

• Math: GED entrants do much, much worse

16

You have to pass the GED Math Test;but

You also have to pass the ACCUPLACER Algebra Test

17

Understand Better the Specific Skill Sets Necessary to Pass

the GED Tests

• Most-Missed Questions From GEDTS• Item-Writing Manuals from GEDTS• Inside Info from GEDTS• Information From the USDOE Math

Symposium (August 2006)• My Own and Other Teachers’ Experiences• Techniques Borrowed from Teaching

Reading

18

“Resonance”

19

Pythagorean Theorem(1 or 2 Problems per test)

Reasons For A Wrong Answer

• Don’t recognize it as a Pythagorean Theorem problem

• Can’t handle the formula• Aren’t fluent with exponents• Can’t solve for the length of one

of the legs

20

Tom Mechem’s “Hit List”(Items That Resonate)

•Notation•Order of Operations•Triangles & Angles•Ratio and Proportion•“Reverse” Algebra•Charts, Graphs, and Tables

21

Ratio and Proportion

• Relationship Between Fractions, Decimals, and Percents

• Three Types of “Fractions”---a part of a whole---an expression of probability---a ratio

• “Per” Problems• Similar Triangles• Functions (Graphs)

22

Carla’s Frame Shop determines the cost of framing a painting with the following formula:

C = 15 + x2/10

C is the cost (in dollars) for framing, and x is the largest dimension (in inches) of the painting to be framed.

If Simon has a painting that is 20 inches by 30 inches, what is the total amount he would pay Carla’s shop to frame it?

23

Correct Response:

C = 15 + x2/10

C = 15 + (30)2/10

C = 15 + 900/10

C = 15 + 90 = 105

24

Typical Errors C = 15 + x2/10

C = 15 + (30/10)2 = 24(Division before Exponents)

C = 15 + 60/10 = 21(faulty understanding of Exponents)

C = (15 + 900)/10 =91.50(Addition before Division or

Left-To-Right)

25

Of all the items produced at a manufacturing plant on Tuesday, 5/6 passed inspection. If 360 items passed inspection on Tuesday, how many

were PRODUCED that day?

(1) 300 (2) 432 (3) 492 (4) 504 (5) 3000

Overwhelming favorite as the most-popular WRONG answer?

300!

26

Fluency

“Automatic Information Processing”

“…stuff you do without thinking so your brain can think about

other stuff…”

27

GED Math Fluency

•Specific Math Knowledge (Resonance)

•The Math on the GED Test Is Embedded In Word Problems

28

Comprehension Strategies

• Vocabulary• Important Phrases and Sentences• Who Is the Narrator and What Is Her

Purpose?• Metacognition

– Identify where the difficulty is– Identify what the difficulty is– Restate the difficult phrase or sentence– Look back in the text for clues

29

The ACCUPLACER Test

Areas of Emphasis (Elementary Algebra)

• Operations with Signed Numbers• Absolute Value• Operations with Polynomials• Quadratic Equations

30

Survival on the ACCUPLACER

Students must be able to:

• Add radicals and algebraic fractions• Evaluate algebraic expressions• Factor polynomials• Factor the difference of squares• Square binomials• Solve linear equations

31

Philosophies: GED vs. ACCUPLACER

• GED: “GED examinees represent a very diverse population with respect to age, educational background, and future goals. The item contexts should reflect that.”

• ACCUPLACER: determine ability level for college placement.

32

Two Math Problems

GED“Big Papi Ortiz has a beautiful, grassy,

rectangular back yard that measures 120 feet by 90 feet. He intends to build a square stone patio in his yard. The patio will measure 60 feet on a side. Once the patio is built, how many square feet of grass will he have in his yard?”

7200 square feet

33

Two Math Problems (cont.)

ACCUPLACER

“A rectangle has a length of 2a + 4 and a width of a – 3. If the formula for the area of a rectangle is area = length x width, what is the area of this rectangle?”

2a2 -2a -12

34

Two More Math Problems

GED

A survey asked 300 people which of the three primary colors, red, yellow, or blue was their favorite. Blue was selected by 1/4 of the people, red by 1/3 of the people, and the remainder selected yellow. How many of the 300 people selected YELLOW?

(1) 75 (2) 100 (3) 125 (4) 200

(5) 175

35

Two Math Problems (cont.)

ACCUPLACER

1 + 1 = y+3 y

The fraction x2 + 8x +16 x2 – 16

can be written as which of the following?

36

8. If 2x – 3(x + 4) = - 5, then x = A. 7B. - 7C. 17D. – 17

9. – 3(5 – 6) – 4(2 – 3) =

A. - 7B. 7C. - 1D. 1

Sample ACCUPLACER Signed Number Problems

37

Another ACCUPLACER Sample Problem

6. If x > 2, then x2 – x – 6x2 – 4 =

A. x – 32 B. x – 3x – 2

C. x – 3x + 2 D. 3/2

38

Another ACCUPLACER Sample Problem

Find the product of the binomials:   (2a - 3b)(a + 2b)

a. 2a² + ab - 6b²

b. -12a²b² c. 2a² - 6b²

d. 2a² + 7ab - 6b²        

39

Philosophies: GED vs. ACCUPLACER

• GED: “If it doesn’t resonate, you can get it wrong and survive.”

• ACCUPLACER: “If you get it wrong, you are doomed.”

40

41

2012 GED Tests: Math

• Number Operations/ Sense: 10-16% • Geometry/Measurement: 24-30% • Data Analysis, Prob. & Stats: 24-30% • Algebra, Functions, Patterns: 24-30% • Calculator: Casio fx-300ES (complicated!)• Trig? No. Right Triangle Applications? Yes.

42

Toward a Unified GED/Accuplacer Curriculum

A Problem

Arithmetic skills are not a reliable predictor of nor a necessary prerequisite for Algebra skills

(In fact, they may get in the way)

43

Arithmetic May Be the Problem With Algebra

This runs counter to intuition • if you’re good at one aspect of math, you’ll

be good at another

And to traditional teaching practice • Master arithmetic before being introduced

to Algebra• Keep “spiraling” back

44

• Math students (maybe all students) are “change-resistant”

• Calls into question the emphasis on the ACCUPLACER Arithmetic Test.

45

Two Reasons Arithmetic Is a Problem

• Limited concept of the “equals” sign(“total” rather than “mathematical

equivalence”)(a “do something” sign rather than a

relational symbol)

• Limited concept of the “minus” sign(only “subtract” rather than also “negative

something” [-3] and “the opposite of” [-x]

46

A “Problem” Problem

3 + 4 + 5 = + 2

47

Another “Problem” Problem(word problems leading to an algebraic

solution)

Some money is shared between Maria and Ted so that Maria gets $5 more than Ted gets. Ted gets “x” dollars. Use algebra to write Maria’s amount. The money to be shared is $47. Use algebra to work out how much Maria and Ted would each get.

48

Another “Problem” Problem(numerical or geometric patterns leading to an

algebraic expression)

BANQUET TABLES

Arrangement 1 Arrangement 2 Arrangement 3

Arrangement 1 seats four people. How many people can be seated at Arrangement 10?

49

“Algebrafy the Arithmetic”or

“Algebrafy Before Arithmetic”

• Notation• Order of Operations• Triangles & Angles• Ratio and Proportion• “Reverse” Algebra• Charts, Graphs, and Tables

50

Using what they already know: students can generalize from

arithmetic knowledge

• Use of a Number Line

51

Using what they already know: students can generalize from

arithmetic knowledge

• Use of a Number Line• Algebrafy Word Problems

52

Set-Up Problems

Juan is a computer salesman. He earns $400 per week, plus a commission of $200 for each computer he sells. Which expression below represents his earnings for a week in which he sold 3 computers?

1.(400)(200) + 3 2.3(200) - 400 3.3(200) + 400 4.3 x 400 5.(200 ÷ 3) + 400

53

Using what they already know: students can generalize from

arithmetic knowledge

• Use of a Number Line• Algebrafy Word Problems• Commutative, Associative, & Distributive

Properties

54

Commutativea+b = b+a

ab = ba

Associativea+(b+c) = (a+b)+c

a(bc)=(ab)c

Distributivea(b+c)=ab+ac

55

Toward a Unified GED/Accuplacer Curriculum

• Using what they already know: students can generalize from arithmetic knowledge

• Use of a Number Line• Algebrafy Word Problems• Commutative, Associative, & Distributive

Properties• Algebrafy Ratio and Proportion

56

Toward a Unified GED/Accuplacer Curriculum

• Using what they already know: students can generalize from arithmetic knowledge

• Use of a Number Line• Algebrafy Word Problems• Commutative, Associative, & Distributive

Properties• Algebrafy Ratio and Proportion• Graphing Linear Equations

57

Do We Need a Different Class Design?

• More Intensity

• Greater Frequency

• Managed Enrollment

• College Prep Track

58

Tom Mechemtmechem@doe.mass.edu781-338-6621

www.wtamu.edu/academic/anns/mps/math/mathlab

www.purplemath.com