1 ged and beyond sabes west tom mechem, ged state chief examiner january 29, 2009
TRANSCRIPT
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GED and Beyond
SABES WestTom Mechem, GED State Chief Examiner
January 29, 2009
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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
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There can be no “Post-Secondary”
without the “Secondary.”
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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.
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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
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GED…
How can we get more of our students to pass the GED tests?
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…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?
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You have to pass the GED tests and earn the diploma;butYou must also be prepared to succeed in college
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For both the GED and Beyond:
Math Is The Major Impediment
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GED Reasons for Failure(“Almost Theres” & “Sure Things”
only)
Failed Math only
Failed WRI only
Other
51%
35%
14%
51%
14%
35%
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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.
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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
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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
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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
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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
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You have to pass the GED Math Test;but
You also have to pass the ACCUPLACER Algebra Test
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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
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“Resonance”
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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
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Tom Mechem’s “Hit List”(Items That Resonate)
•Notation•Order of Operations•Triangles & Angles•Ratio and Proportion•“Reverse” Algebra•Charts, Graphs, and Tables
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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)
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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?
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Correct Response:
C = 15 + x2/10
C = 15 + (30)2/10
C = 15 + 900/10
C = 15 + 90 = 105
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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)
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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!
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Fluency
“Automatic Information Processing”
“…stuff you do without thinking so your brain can think about
other stuff…”
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GED Math Fluency
•Specific Math Knowledge (Resonance)
•The Math on the GED Test Is Embedded In Word Problems
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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
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The ACCUPLACER Test
Areas of Emphasis (Elementary Algebra)
• Operations with Signed Numbers• Absolute Value• Operations with Polynomials• Quadratic Equations
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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
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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.
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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
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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
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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
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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?
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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
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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
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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
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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.”
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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.
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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)
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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
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• Math students (maybe all students) are “change-resistant”
• Calls into question the emphasis on the ACCUPLACER Arithmetic Test.
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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]
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A “Problem” Problem
3 + 4 + 5 = + 2
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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.
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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?
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“Algebrafy the Arithmetic”or
“Algebrafy Before Arithmetic”
• Notation• Order of Operations• Triangles & Angles• Ratio and Proportion• “Reverse” Algebra• Charts, Graphs, and Tables
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Using what they already know: students can generalize from
arithmetic knowledge
• Use of a Number Line
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Using what they already know: students can generalize from
arithmetic knowledge
• Use of a Number Line• Algebrafy Word Problems
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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
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Using what they already know: students can generalize from
arithmetic knowledge
• Use of a Number Line• Algebrafy Word Problems• Commutative, Associative, & Distributive
Properties
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Commutativea+b = b+a
ab = ba
Associativea+(b+c) = (a+b)+c
a(bc)=(ab)c
Distributivea(b+c)=ab+ac
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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
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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
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Do We Need a Different Class Design?
• More Intensity
• Greater Frequency
• Managed Enrollment
• College Prep Track
