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Retooling the GED Math Classroom for College Success

The Handwriting Is On The Wall. $27.53/hour9 out of 10 of the fastest-growing jobs in MA require Associate's Degree or higherTwo years of post-secondary education are neededto emerge out of poverty." John Comings. There can be no Post-Secondary" without the Secondary.". You have to p

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Retooling the GED Math Classroom for College Success

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    1. Retooling the GED Math Classroom for College Success Network 2009 Tom Mechem, GED State Chief Examiner October 22, 2009

    2. The Handwriting Is On The Wall $27.53/hour 9 out of 10 of the fastest-growing jobs in MA require Associate’s Degree or higher “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. You have to pass the GED tests and earn the diploma; but You must also earn a post-secondary degree or official credential.

    5. For both “Secondary” (GED) and “Post-Secondary”: Math Is The Major Impediment

    6. College 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

    7. 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

    8. 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

    9. “Algebra is the Gatekeeper”

    10. You have to pass the GED Math Test; but You also have to pass the ACCUPLACER Algebra Test

    11. 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

    12. 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.

    13. 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

    14. 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

    15. 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?

    16. Sample ACCUPLACER Signed Number Problems

    17. 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.”

    19. So What Are We Gonna Do?

    20. First, What Are We NOT Going To Do?

    21. Common Knowledge, Called Into Question, v.1 “The higher you score on the GED tests, the better chance you have of passing the ACCUPLACER.” Not True!!

    22. Common Knowledge, Called Into Question, v.2 “Get your arithmetic skills up to par; then you can move to algebra and have a better chance of mastering algebraic skills.” Not True!!

    23. 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

    24. 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]

    25. A “Problem” Problem (basic arithmetic) 3 + 4 + 5 = + 2

    26. Common Knowledge, Called Into Question, v.3 “If you fail the ACCUPLACER Algebra test, go into an arithmetic remedial course. Success there will prepare you to re-take and pass the Algebra test.” Not True!!

    27. “Algebra Skills Are the Single Most Accurate Predictor of College Success.” (Even if you’re an English major!)

    28. “Incorporate GED Subject Matter into an Algebra Course Designed to Develop Algebraic Habits of Mind.”

    29. Two Key Components Sound Pedagogical Principles (I know we have these) A Coherent and Integrated Curriculum (We have a ways to go)

    30. Pedagogical Principles (plagiarized from Steve Hinds) Math learning that is meaningful and not “rote-ful” Lecture is almost non-existent Rules can be the endpoint, not the starting point Use what they already know: Functions in context and number relationships can illuminate more abstract algebra ideas Ask students to think like scientists Student talk is more important than teacher talk – questioning, alternate solutions, collaboration, student errors.

    31. A Coherent Curriculum Depth, Rather Than Breadth Move Forward, Spiral Back Open, Rather Than Closed

    32. Tom Mechem tmechem@doe.mass.edu 781-338-6621

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