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etadd_47(3) - Division on Autism and Developmental Disabilities

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TABLE 2<br />

C<strong>on</strong>tent St<strong>and</strong>ards, Alternate Achievement, <strong>and</strong> Task Analyses Used in Math<br />

Nati<strong>on</strong>al St<strong>and</strong>ard<br />

(NCTM) based <strong>on</strong> 6-8 th<br />

grade b<strong>and</strong>s<br />

Algebra: Represent <strong>and</strong><br />

analyze mathematical<br />

situati<strong>on</strong>s <strong>and</strong><br />

structures using<br />

algebraic symbols.<br />

Geometry: Specify<br />

locati<strong>on</strong>s <strong>and</strong> describe<br />

spatial relati<strong>on</strong>ships<br />

using coordinate<br />

geometry <strong>and</strong> other<br />

representati<strong>on</strong>al<br />

systems. Use<br />

visualizati<strong>on</strong>, spatial<br />

reas<strong>on</strong>ing, <strong>and</strong><br />

geometric modeling to<br />

solve problems.<br />

Measurement: Apply<br />

appropriate techniques,<br />

tools, <strong>and</strong> formulas to<br />

determine<br />

measurements.<br />

Data Analysis <strong>and</strong><br />

Probability: Formulate<br />

questi<strong>on</strong>s that can be<br />

addressed with data<br />

<strong>and</strong> collect, organize,<br />

<strong>and</strong> display relevant<br />

data to answer them.<br />

Competency Goal(s) from<br />

state st<strong>and</strong>ard course of<br />

study st<strong>and</strong>ards<br />

Use <strong>and</strong> evaluate algebraic<br />

expressi<strong>on</strong>s. Solve simple<br />

(<strong>on</strong>e- <strong>and</strong> two-step)<br />

equati<strong>on</strong>s or inequalities.<br />

Represent problem<br />

situati<strong>on</strong>s with geometric<br />

models. Identify, predict,<br />

<strong>and</strong> describe dilati<strong>on</strong>s in<br />

the coordinate plane.<br />

Develop flexibility in solving<br />

problems by selecting<br />

strategies <strong>and</strong> using<br />

mental computati<strong>on</strong>,<br />

estimati<strong>on</strong>, calculators or<br />

computers, <strong>and</strong> paper <strong>and</strong><br />

pencil.<br />

Collect, organize, analyze,<br />

<strong>and</strong> display data<br />

(including box plots <strong>and</strong><br />

histograms) to solve<br />

problems.<br />

followed the same guidelines described under<br />

the descripti<strong>on</strong> of the dependent variable. No<br />

feedback was given to students during baseline<br />

probes. Data was graphed <strong>and</strong> visually<br />

inspected after each sessi<strong>on</strong>. After baseline,<br />

the same procedures were followed to c<strong>on</strong>tinue<br />

to probe whatever unit was receiving<br />

instructi<strong>on</strong>. That is, <strong>on</strong>e or two times a week<br />

prior to the less<strong>on</strong>, the graduate student c<strong>on</strong>-<br />

Alternate Achievement<br />

st<strong>and</strong>ards addressed in<br />

this study Task Analysis<br />

Solve simple <strong>on</strong>e-step<br />

equati<strong>on</strong>s that relate<br />

to stories about daily<br />

events.<br />

Identify <strong>and</strong> describe<br />

the intersecti<strong>on</strong> of<br />

figures in a plane.<br />

Draw line segments<br />

<strong>and</strong> a coordinate<br />

plane to dem<strong>on</strong>strate<br />

spatial sense for<br />

familiar c<strong>on</strong>texts like<br />

grocery store.<br />

Develop numbers sense<br />

for real numbers.<br />

Develop flexibility in<br />

solving mathematical<br />

problems by selecting<br />

strategies <strong>and</strong> using<br />

appropriate<br />

technology. Use next<br />

dollar strategy to<br />

solve problems<br />

related to everyday<br />

transacti<strong>on</strong>s.<br />

Collect, organize <strong>and</strong><br />

display data to solve<br />

problems from<br />

familiar events.<br />

ducted the task analytic assessment for that<br />

unit. At the end of a unit, all units were reprobed<br />

before the next was introduced.<br />

Interventi<strong>on</strong><br />

Identify problem statement. Identify<br />

first, sec<strong>on</strong>d, <strong>and</strong> last fact in story.<br />

Name unknown quantity “x”. Place<br />

facts in correct sequence <strong>on</strong><br />

Equati<strong>on</strong> Prompt. Identify<br />

operati<strong>on</strong> needed to solve problem.<br />

State soluti<strong>on</strong> to problem. State<br />

soluti<strong>on</strong> in story c<strong>on</strong>text.<br />

Identify problem statement. Identify<br />

points <strong>on</strong> map using facts from<br />

story. Draw line segments formed<br />

from identified points. Identify<br />

plane formed from line segments.<br />

State soluti<strong>on</strong> to problem. State<br />

soluti<strong>on</strong> in story c<strong>on</strong>text.<br />

Identify problem statement. Identify<br />

dollar amount from fact in story.<br />

Count number of <strong>on</strong>e dollar bills<br />

equal to given dollar amount.<br />

Count out <strong>on</strong>e more dollar, (if<br />

verbal, may say “<strong>and</strong> <strong>on</strong>e more”<br />

while counting <strong>on</strong>e more). State<br />

soluti<strong>on</strong> to problem. State soluti<strong>on</strong><br />

in story c<strong>on</strong>text.<br />

Identify problem statement. Record<br />

data from story <strong>on</strong> graph. Identify<br />

choice with “more”. State soluti<strong>on</strong><br />

to problem. State soluti<strong>on</strong> in story<br />

c<strong>on</strong>text.<br />

The mathematics interventi<strong>on</strong> included (a)<br />

mathematics word problem stories based <strong>on</strong><br />

familiar activities, (b) a graphic organizer <strong>and</strong><br />

Grade-Aligned Sec<strong>on</strong>dary Math / 379

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