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Are you confused by terms that educators use? The ASCD Lexicon of Learning might be what you need.

 

 

 

Standardized Test Preparation and
Tips for Success

 

 

NCLB, Common Core, and Solid Test Preparation Advice

 

No Child Left Behind legislation required states to measure students' progress in reading and mathematics annually in Grades 3-8 and at least once in Grades 10-12 by 2005-2006.  It also required administration of the National Assessment of Educational Progress (NAEP) every two years in reading and mathematics.  Beginning in 2014-2015 school year, learners face an additional testing challenge in that their assessments of learning will be via computer-based online testing of the Common Core standards.  Assessments are being developed by PARCC and SBAC and may take from 8-10 hours to complete (Gewertz, 2013).

As a result, there is concern among educators about the nature of these tests and what appears to be an excessive focus on test preparation.  Online testing poses additional concerns about required technology, sufficient bandwidth, learners' technology skills, and new forms of test anxiety. 

In A Case Study of Key Effective Practices in Ohio's Improved School Districts, Research Associates Aaron Kercheval and Sharon Newbill (2002) reported the key effective test preparation strategies included:

• Direct instruction in test-taking skills
• Extensive use of practice tests
• Instructional practice altered to mirror form and content of the proficiency tests
• Intervention strategies to identify students needing help to pass proficiency tests
• Variety of intervention/remediation programs offered at variety of times during school day, and before/after school
• Intervention specialists hired or teachers reassigned or paid to conduct remediation programs
• Students recognized and rewarded for success (p. 37).

According to Douglas Reeves (2004), "Even if the state test is dominated by lower-level thinking skills and questions are posed in a multiple-choice format, the best preparation for such tests is not mindless testing drills, but extensive student writing, accompanied by thinking, analysis, and reasoning" (p. 92).  Silver, Strong, and Perini (2007) found that student success on standardized tests, regardless of grade level or content area, hinges on 12 core skills relating to those ideas.  They grouped those skills into four categories in what they call "Hidden Skills of Academic Literacy."  They said, "If we expect students to perform well on state tests, we must teach them how to apply these skills without cutting into content." Unfortunately, the skills that follow have been "radically undertaught and rarely benchmarked" (Part One: Introduction section):

1. Reading and study skills: collect and organize ideas through note making; make sense of abstract academic vocabulary; read and interpret visual displays of information;
2. Reflective skills: construct plans to address questions and tasks; use criteria and guidelines to evaluate work in progress; control or alter mood and impulsivity;
3. Thinking skills: draw conclusions, make and test inferences, hypotheses, and conjectures; conduct comparisons using specific criteria; analyze the demands of a variety of higher-order thinking questions;
4. Communication skills: write clear, well-informed, coherent explanations in all content areas; write comfortably in the following non-fiction genres: problem/solution, decision making, argument, comparative; read and write about two or more documents. (Part One: Introduction section, Figure E).

Emphasis on  literacy was one key effective practice in Ohio's improved school districts (Kercheval & Newbill, 2002). In other words, good instruction is the best test preparation!

What has changed for Common Core assessments, however, in relation to that good instruction is that teachers need to ensure that their learners also have the technology skills to perform well on tests administered online.  Learners need practice with the new testing formats, and new types of questions.  They need practice with the same and must be able to enter test responses via a keyboard, sometimes placing those in boxes on the screen.  They also need good "mousing" or "touchscreen" skills to enter responses via click and drag into particular places on a screen.  And they need to build endurance for working long periods of time at the computer via gradual focused exposure to the new testing scenario.

 

 

Teaching to the Test

We would hope that teachers use a broad range of curricular materials and activities that address standards--what we have identified as important for students to know and be able to do.  Teaching to the test is not a new practice brought about by NCLB, nor will it be any different for preparing learners for testing of the Common Core standards.  Teachers have been doing it for as long as standardized tests have been used to make important educational decisions. 

Years ago, William Mehrens (1989) stated, "Although teaching to the test is not a new concern, today's greater emphasis on teacher accountability can make this practice more likely to occur. Depending on how it is done, teaching to the test can be either productive or counterproductive" (para. 2, 3).  Those words are still true.  He and his colleague Kaminski (1989, cited in Mehrens, 1989) suggested the following seven points on the continuum along which practices range from ethical to unethical, or legitimate to illegitimate.

Ethical:

1. giving general instruction on district objectives without referring to the objectives that the standardized tests measure;

Typically Ethical:

2. teaching test-taking skills;

Cross-over point depends on inferences you wish to draw from the test and lies between:

3. providing instruction on objectives where objectives may have been determined by looking at the objectives that a variety of standardized tests measure (The objectives taught may or may not contain objectives on teaching test-taking skills.);
4. providing instruction based on objectives (skills and subskills) that specifically match those on the standardized test to be administered;
5. providing instruction on specifically matched objectives (skills and subskills) where the practice or instruction follows the same format as the test questions;

Mehrens (1989) indicated, "The inferences you typically wish to draw from test scores are general in nature and will be inaccurate if you limit instruction to the actual objectives sampled in the test or, worse yet, to the actual questions on the test" (Summary section).

Unethical:

6. providing practice or instruction on a published parallel form of the same test;
7. providing practice or instruction on the test itself. (Seven Points on the Continuum section).

Educators will observe, however, that current test prep efforts do include using questions from old tests, which state departments of education release.  Technically, these are not parallel forms of the same test.

Good Instruction

So how does one plan for good instruction?  For many teachers, instruction has come to mean addressing as many standards as possible.  But, state exams do not test every benchmark annually.  To assist teachers with providing good instruction leading to improved student outcomes, O'Shea (2005) suggested that teachers have copies of standards and frameworks for each subject they teach, and use them along with related state documents to plan lessons in regularly scheduled grade-level or subject matter team meetings.   Instruction should not include  "unchallenging student desk work, including word searches, sentence completion exercises, puzzles, and other forms of response sheets not linked to standards" (p. 13).  In addition to identifying a topic and rationale, a truly standards based lesson would include:

• statements of specific content standards to be addressed in the lesson.
• objectives that translate the standards into outcomes-based language.  This means that objectives include descriptions of student behaviors or products that should result from the instruction. 
• curriculum materials and instructional activities sequenced to elicit the performances stated in the objectives. 
• assessments of student work based on performances and behaviors identified in the objectives. Teachers might save examples of student work meeting standards.  Bloom's Taxonomy, which lists behavioral verbs, is often used as a resource when writing performance descriptions in objectives and assessments.

Further, O'Shea (2005) indicated that districts should:

• identify critical standards to be achieved in each subject for each grade level.
• develop a curriculum pacing guide that informs teachers when their students should achieve critical standards throughout the school year.
• use benchmark tests to measure the achievement of important standards at quarterly intervals throughout the school year.
• use the benchmark assessment system to inform teachers of the progress that each of their students is making toward the achievement of crucial standards likely to be assessed on annual standards-based tests. (p. 14)

Joan Herman and Eva Baker (2005) said that there should be a strong predictive relationship between students' performance on benchmark tests and their performance on state assessments.  They cautioned, however, that aligning benchmark tests too closely with a state's tests may accelerate curriculum narrowing.  Tests should "focus on the big ideas of a content area" and be designed to "allow students to apply their knowledge and skills in a variety of contexts and formats" (p. 49).  For mathematics test items, this might include giving short answers, using multiple choice with extended explanations for why an option was selected, and drawing pictures to demonstrate a concept.  They provided the following six criteria to help educators make benchmark testing effective:

• Standards and benchmark assessments should be aligned from the beginning of test development.
• Enhance the diagnostic value of assessment results through initial item and test structure design.  Distracters should be built into multiple choice items to reveal common student misunderstandings.  Likewise, extended response items should reveal students' potential misconceptions.
• To ensure fairness for all students, including English language learners and students with disabilities, language used should not be unnecessarily complex.  Contexts used should be familiar to student subgroups and not hinder them from demonstrating what they know.
• Data should reveal test quality and include psychometric indices that reveal the reliability of the assessments.
• Reports should be user-friendly so that educators can easily interpret results.  Schools might need to provide additional guidance and support for teachers to use the results (e.g., pedagogical knowledge, alternative materials, teams to analyze results).
• Benchmark testing should meets its purposes and requires systematic design and continual evaluation.

Many are concerned that standards-based instruction neglects the diverse learning needs of students.  However, Carol Ann Tomlinson (2000) indicated, "There is no contradiction between effective standards-based instruction and differentiation" (i.e., attending to the diverse needs of learners). "Curriculum tells us what to teach: Differentiation tells us how."  For any standard, "Differentiation suggests that you can challenge all learners by providing materials and tasks on the standard at varied levels of difficulty, with varying degrees of scaffolding, through multiple instructional groups, and with time variations. Further, differentiation suggests that teachers can craft lessons in ways that tap into multiple student interests to promote heightened learner interest in the standard. Teachers can encourage student success by varying ways in which students work: alone or collaboratively, in auditory or visual modes, or through practical or creative means" (p. 9).

The Big Picture

A major survey study conducted by Williams, Kirst, Haertel, et al. (2010) in the 2008-2009 school year in 303 California middle schools echoes many of the recommendations noted above.  The study illustrates a culture change that must take place within districts to focus on student outcomes and illustrates that test preparation and standards-based instruction is not solely the role of individual teachers. Student responsibility and parent involvement are key, as are the roles of district, state, and federal leadership.  Although the study yielded practices that have a potential to positively affect achievement on standardized tests in math and English language arts (ELA) at the middle school level, the major findings are worthy of consideration for implementation at all K-12 levels for ELA and math.  Readers are cautioned that this was correlational research, not experimental research.  Hence, cause and effect conclusions between practices and outcomes can not be drawn.  Illustrative major findings in the Narrative Summary of Gaining Ground in the Middle Grades: Why Some Schools Do Better include:

• An intense schoolwide focus on improving academic outcomes most distinguishes higher- from lower-performing middle grades schools.
• In higher-performing schools, curricula and instruction are closely aligned with state academic standards.
• Higher-performing schools use assessment and other student data extensively to improve student learning and teacher practice.  Data are used throughout the year in higher-performing schools, rather than just a few times a year as seen in lower-performing schools.
• Higher-performing middle grades schools emphasize early identification and proactive intervention for student academic needs.
• Every role in a professional community of educators is important to making gains in middle grades student outcomes.  This includes practices by teachers, principals, and superintendents.

You can read a more complete review of this study at our Research Corner for Standards, Raising Achievement, Assessment, and How People Learn.

 

 

Buy additional test prep materials via CT4ME.

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Testing Preparation in Your State and Practice Questions

 

Become a Smart Learner--Raise your Skills! According to Education Week's 2010 Quality Counts report, many states provide educators with benchmark assessments or item banks linked to their state standards (p. 41). Learn more about standardized tests in your state, and the National Assessment of Educational Progress (NAEP) using resources in this section.

 

All States:

Brainchild Online Assessment: Subscription based by schools or individuals.  But demo questions are available online for your state. Lessons include multimedia instruction, study mode with immediate feedback, test mode with review of mistakes, self-directed student learning plan.

National Assessment of Educational Progress has released numerous questions from past NAEP assessments, along with data about student performance on specific questions.  An overview of NAEP and major findings from past assessments are included. NAEP reports, the tools featured in Explore NAEP Questions "can be used to supplement classroom instruction, provide additional insight into the content of the assessment, and show what students nationally or in your state or district know and can do."  Readers should consider, however, that the NAEP is not considered a high stakes test.  Gerald Bracey (2009) reports on characteristics that make it a poor accountability tool.  For example, no student ever takes the entire test, nor do districts, schools, or individual students find out how they performed.  Thus, students might not take NAEP as seriously as they would the ACT or SAT or their state high stakes tests (p. 33).

Programme for International Student Assessment (PISA) from the Organisation for Economic Co-Operation and Development surveys "15-year-olds in the principal industrialised countries. Every three years, it assesses how far students near the end of compulsory education have acquired some of the knowledge and skills essential for full participation in society."  The U.S. is among participating countries.  Sample questions are available.  Gerald Bracey (2009) notes that PISA is not a high stakes test and points out flaws in using results as a measure of the quality of U.S. schools.  Chief among those is comparing results of a nation with a diverse population of over 300-million people to results of small "homogeneous city-states like Hong Kong and Singapore."  Formal schooling differs among nations as to when students start school, policies differ in relation to repeating grades, and schools might not be serving the entire population, particularly those from low-income families.  The design of test items also fall into question when one considers difficulty in translating questions into several languages, and keeping those questions free of culture bias (p. 34).

Alabama: Alabama Department of Education Assessment and Accountability lists information about its state tests and sample questions under its publications section.

Alaska: Item samplers/practice tests for math, science, reading, and writing are available for grades 3-10 and the high school exam.

Arkansas: Arkansas Department of Education Testing and Student Assessment (ArkansasEd.org) contains booklets with released test items.

Arizona: AIMS Sample Tests for grades 3-8 and high school.  Math includes questions and answer keys.  Exams contains formula and reference sheets of value for anyone.  As additional help for the high school math test, each math strand is accompanied by notes and practice problems from web resources.

California:

• California Department of Education High School Exit Examination (CAHSEE) program resources: released test questions are grouped by strands. 
• HSTutorials.net has animated and step-by-step audio-visual tutorials in pre-algebra, algebra, and geometry and tutorials and resources related to test prep for California's High School Exit Exam for math.

Colorado: Colorado Student Assessment Program (CSAP) Released Items.

Connecticut: Connecticut State Department of Education: Assessment.  Among resources are released test questions for the Connecticut Academic Performance Test, and a set of skills checklists.

Delaware: Delaware Student Testing Program

Florida: Florida Comprehensive Assessment Test (FCAT) at the Florida Department of Education.  Get released test questions.  Note: the Florida Department of Education, the National Science Foundation, and FOR-STEM have provided funding for the CPALMS (Collaborate, Plan, Align, Learn, Motivate, Share) initiative whose mission is to provide instructional resources vetted by peers and experts and professional development for implementation of the Common Core Standards.  You find curriculum, activity, and general resources and an extensive collection of lesson plans, and more.

Georgia: Practice questions for the state tests at the end of the year from the Georgia Department of Education is via the Georgia Online Assessment System. Note that anyone can use the generic passwords and log-in IDs to access questions.  Both are the same, as Grade1, Grade2, ...Grade8, and Gradehs.

Idaho: Idaho Standards Achievement Tests (ISAT) sample test items.  Math items are listed for grades 3-10.

Illinois: Illinois State Board of Education sample interactive online tests for the Illinois Standards Achievement Tests (ISAT).  Math tests for grades 3-8 are posted.

Indiana: Indiana Department of Education has resources and sample test items under its section for Student Testing: ISTEP+grades 3-10; high school end of course exams (e.g., algebra 1 and algebra 2) and college entrance exams.  Of value for math educators everywhere are the resources associated with teaching each standard, which include classroom activities and assessments.    "For grades K-8, the classroom assessments include short standards-based quizzes for each standard or cluster of related standard indicators. At the high school level, the assessments are designed to measure student progress at the end of the course."  To help prioritize standards, core standards are marked as such.

Iowa: Iowa Department of Education: Student Assessment.  "Iowa uses the Iowa Tests of Basic Skills (ITBS), for grades 1-8 and Iowa Tests of Educational Development (ITED) for high schoolers as [their] annual statewide assessment."

Kansas: Kansas Department of Education Career, Standards, and Assessment Services also has an Assessment Literacy Project available online with 21 modules appropriate for all educators.  W. James Popham provides the introductions to these modules.

Kentucky: Kentucky Department of Education released test items for end of course and K-PREP.

Louisiana: The Louisiana Department of Education provides the Louisiana state content standards, lesson plans, web resources, and sample assessment items aligned to Louisiana content standards.  See sections for testing and curriculum/standards.

Maine: Maine participates in the New England Common Assessment Program (NECAP) and there are released test items to view.

Maryland: Maryland State Department of Education releases a form of the high school assessment each year to provide students, teachers, and the public an example of how students are being assessed.  Mathematics includes the forms for algebra/data analysis and geometry.  View items, take the tests online, and get scoring information.  Caveats for items selected for public viewing are presented.  Test items for grades 3-8 for math are also provided.

Massachusetts:

• Massachusetts State Department of Education released test and re-test items from its comprehensive assessment system, MCAS.
• Socrato.com is a web-based test prep and assessment site, which features tests in multiple grades to prepare for MCAS.  Teachers can also upload their own questions and track student progress.

Minnesota: Minnesota Department of Education has testing resources and item samplers.

Mississippi: Mississippi Department of Education Office of Student Assessment includes practice test items for grades 3-8 and high school (e.g., algebra 1).

Missouri: Grade Level Assessments with released items for grades 3-8 in math and End-of-Course Assessments with released items and practice tests.  Released items include Algebra I, Algebra II, and Geometry; practice tests are in Algebra I.

Montana: Montana Office of Public Instruction: Curriculum and Assessment includes released math test items for its state testing program.

Nebraska: Nebraska Statewide Assessment (NeSA) practice tests for math include paper/pencil forms for grades 3-8, 11.

New Hampshire: New Hampshire Department of Education Math Curriculum, practice test questions and information, and NECAP released test questions for math.  Note: New Hampshire Department of Education, Rhode Island Department of Education, and Vermont Department of Education have developed a common set of Grade-Level Expectations, known as the New England Common Assessment Program Grade-Level Expectations (NECAP GLEs).

New Jersey: New Jersey Department of Education: Assessment. Released questions from the testing program are found under elementary, middle, and high school.

New Mexico: New Mexico Standards Based Assessments includes released items with student work, which are representative of the kinds of questions learners in grades 3-8 will encounter.

New York:

• High School Regents exams
• Oswego City School District (NY) offers three levels of test prep: Elementary Test Prep for grades K-4, Intermediate Test Prep for grades 5-8, and a Regents Exam Prep Center for high school algebra, geometry, algebra 2/trig.

North Carolina: North Carolina Public Schools released test forms for grades 3-8 and high school.

Ohio:

• Ohio Department of Education Testing.  Information about legally mandated testing of Ohio students including diagnostic tests, achievement tests, Ohio Graduation Tests and proficiency tests. See also the Practice tests, which include Ohio Graduation Test prep and also Grades 3-8 Achievement Practice Test Materials and standards.  These are located at the portal for Ohio Statewide Testing.  Also see the Mathematics Crosswalk and the new Model Curriculum documents for K-8 and highschool.  The Mathematics Crosswalk details the relationship between the 2001 Ohio Academic Content Standards in Mathematics and the 2010 Common Core State Standards for Mathematics.  The new Model Curriculum for K-8 and high school, adopted by the State Board of Education on March 15, 2011, is posted by grade level and course.

For this School Year! Target your test prep with CT4ME resources.  CT4ME developed Preparing Your Students for the Ohio Graduation Test in Mathematics.  Help your students to review concepts and practice questions correlated to grades 8-10 mathematics benchmarks.  These materials are also relevant for students in other states.

• Go Figure? --According to the introduction, "The purpose of the Go Figure? Interactive Multimedia Project is to help students review for the mathematics section of the Grades 5-7 Ohio Academic Achievement Tests.  It contains a DVD with eight, 20-minute dramatic videos, a CD-ROM edu-game, print materials, and the Web Site," all brought to you from the WOUB Center for Public Media."
• What's the Problem? --Reality Math for the Ohio Graduation Test is an intervention resource project funded by eTech|Ohio and produced by Ohio University students at the WOUB Center for Public Media.  This free series of eight 10-12 minute videos focuses on the uses of mathematics in the real world through parodies of different television reality shows.  The episodes are linked to grades 8-10 benchmarks in the Ohio Content Standards for Math (critical thinking/problem solving across the curriculum).  CT4ME is featured among the Teacher's Resources for these episodes.
• OGT Mentor, a division of MCAS Mentor in Massachusetts,  contains resources for teachers and students preparing for the Ohio Graduation Tests.  Resources are also available for grades 3-5, and 6-8.

NOTE: Ohio educators should be aware of http://www.conversationoneducation.org/ where you will find updates on Reforming Ohio's Education System for the 21st Century (2009), which is Governor Ted Strickland's Education Reform and Funding Plan.  The Governor's plan will:

• Replace the OGT with the ACT Plus. All students will now have a four part composite assessment including the ACT end of course exams, a service learning project and a senior thesis project

• Provide the ACT exam to all students without charge

• Revise the assessments for grades 3-8 to align with the information and skills taught in core subjects and the updated 21st Century curriculum. (p. 5)

Oklahoma: Oklahoma School Testing Program for grades 3-8 and "end of instruction" secondary tests include a set of representative released items.  High school math includes algebra l, algebra II, and geometry items.

Pennsylvania: Math item and scoring samplers for grades 3-8, 11 are among resource materials for assessment.  Reading, writing, science resources are also included.

Rhode Island: Rhode Island Department of Elementary and Secondary Education: New England Common Assessments Program (NECAP) with released test items, practice tests, and support resources.  Note: Vermont and New Hampshire also participate in the NECAP.

South Carolina: South Carolina State Department of Education PASS test information and sample items for grades 3-8.

South Dakota: South Dakota Department of Education: Assessment has information on its state testing program.

Tennessee: Tennessee Comprehensive Assessment Program (TCAP) sampler items and practice tests for grades 3-8.

Texas:

• Mathematics TEKS Toolkit from the University of Texas at Austin contains resources for implementing the mathematics Texas Essential Knowledge and Skills (TEKS) and for improving math programs in Texas.  However, mathematics educators throughout the country will appreciate the clarifying activities and assessments for K-8 and high school courses (algebra 1, geometry, algebra II, pre-calculus; and mathematical models and applications).  These are linked to specific standards by grade level, strand, and content area.
• Texas Education Agency: Released Tests, Answer Keys, and Scoring Guides.  The Student Assessment Division developed online versions of the released TAKS™ and exit-level TAAS™ tests, and the end-of-course examinations.  Interactive online versions of recent TAKS mathematics tests (and other subjects tested) are available for grades 3-11, with some in Spanish for grades 3-6.

Utah: Utah Test Item Pool Service for K-6 elementary and 7-12 secondary levels (math 7, applied math I and II, pre-algebra, elementary algebra, geometry)  Tests arranged by standard and objective.  Also available are sample test items with answers for the Utah Basic Skills Competency Test.

Vermont: Vermont Department of Education: New England Common Assessments Program (NECAP) with released test items, practice tests, and support resources.  Note: Rhode Island and New Hampshire also participate in the NECAP.

Virginia:

• Virginia State Standards Practice tests in mathematics, science, and technology.  Mathematics tests are available for grades 3, 5, 8 and algebra I, algebra II, and geometry.  Practice concepts in multiple choice form with answers.  Exams can also be customized by number of problems presented and by strand.
• Henrico County Public Schools (VA) has developed a web site for its mathematics courses in middle and high school.  As a work in progress, their "goal is to create interactive, engaging, web pages that students will want to investigate and explore. Theses pages are different from a printed textbook in that they use java-based scripts, other web sites, software program files and browser plug-ins."  Middle school has courses 1, 2, and 3.  High school has integrated math 1, algebra 1 and 2, geometry, advanced algebra/trig, math analysis/trig, and statistics.  Within each course, multimedia use is extensive.  Do look at this site, as material is also appropriate for self-paced review and practice with concepts addressed on state testing.

Washington:

• State of Washington Test Questions and Practice/Sample Tests
• Port Angeles School District Math Practice Problems for Washington's Measurements of Student Progress (MSP) and the High School Proficiency Exam (HSPE).  Problems by grade level (K-8 and High School) presented in the web site are recommended for student use to communicate (in written form) understanding of math content.  The series of problems are grouped by number sense, measurement, geometry, algebraic sense, probability and statistics, logic, and problem solving strategies.  Note: The problems at the Port Angeles School District for the former WASL are still useful, even though the Washington Assessment of Student Learning (WASL) was replaced in spring 2010 by the MSP and HSPE.  See the Port Angeles School District, Washington, Sample Math Questions for the former WASL assessments.

West Virginia: Teach 21 and Learn 21, the latter of which is an interactive website with educational games, online video instruction, virtual field trips and other internet resources for preK-2, 3-5, 6-8, and 9-12.  Math is a focus area, and there are other subjects.

Wisconsin: Wisconsin Department of Public Instruction released items from the Wisconsin Knowledge and Concepts Examinations (WKCE). Educators in all states might also appreciate ide@s from the University of Wisconsin.  PK-16 educators have gathered internet resources in a searchable database by subject and grade with standards-aligned lessons, interactive tools, videos, digital images, and so on for use in curriculum development and classroom instruction.  In mathematics, for example, there are over 1500 resources.

 

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Other Tips and Test Prep Materials

 

 

HOT! Quick tips for standardized test preparation: Read Duke and Ritchhart's article No Pain, High Gain at Scholastic.  They discuss strategies for reading comprehension, mathematics, reducing test-taking stress, and teaching format fundamentals.  In mathematics, for example:

• Make word problems a priority;
• Stress number sense;
• Focus on estimation; and
• Emphasize mental math.

HOT! Formative assessments for standardized test preparation: ASSISTments is a free web-based tutoring program for 4th to 10th grade mathematics. The program was developed by Professor Neil Heffernan at Worcester Polytechnic Institute (WPI) in Massachusetts and numerous colleagues (e.g., at Carnegie Mellon and WPI students, faculty and staff as well as many cooperating teachers) with funding and support from a variety of sources, including grants from the US Department of Education and the National Science Foundation.  "The word “ASSISTments” blends tutoring “assistance” with “assessment” reporting to teachers. This gives teachers fine grained reporting on roughly 120 skills that the system tracks per grade level." The developers identified skills using standards from many states, and their observations of many state assessments.  As a formative assessment tool, "Math teachers assign problem sets to their students to do on the computer, and students are tutored on the items they get wrong. Teachers log on to the System and study detailed reports about their students’ difficulties and strengths. Teachers can use content developed at WPI or write their own content"  (Teacherwiki.assistment.org, section: About ASSISTments).  Those who access the teacher wiki for ASSISTments will also find links to several Massachusetts MCAS tests (Grades 3, 5, 6, 7, 8, & 10) from prior years.  Numerous schools in the US are taking advantage of ASSISTments for their students.  CT4ME highly recommends this program.

HOT! Free math software for standardized test preparation that responds to emotions: Wayang Outpost is "an intelligent electronic tutoring system that uses multimedia and animated adventures to help prepare middle and high-school students for standardized math tests, such as the SAT, MCAS and CA-Star."  Learners get help from "animated study partners who offer advice and encouragement while reflecting the range of the student's own emotions," thus potentially reducing math anxiety and frustration. The program is funded by several research programs at the National Science Foundation, and the U.S. Department of Education. "As the student progresses though the math problem presented, Wayang Outpost adjusts instruction, using individualized strategies that are effective for each student. It is available free to teachers, schools, after-school programs, and for use from home." (About section).

CollegeAtlas.org: Study Skills Guides for College Students. While meant for college, this site has tips beneficial for all students, regardless of level.  You'll find sections devoted to general study skills, reading and writing, test taking and preparation for a variety of test types, time management, memory techniques, and subject specific study skills that also include for math.

College Board offers test preparation materials, tips for success, and other information related to its tests: SAT, PSAT/NMSQT, the Advanced Placement program (AP Central), and College Level Examination Program (CLEP).

College Entrance Exam Math Prep: "EduCAD Learning Solutions has taken 50 of the most complex type of math problems that a student would see when taking the SAT or ACT and put them into a free application that can be used by anyone preparing for these college entrance exams. ... This is not a drill system ... the system presents problems in a way that allows you to work through them with help offered when you need it."  Steps in solutions are provided.

Cuesta College: Math Study Skills includes multiple pages of academic support devoted to math study skills and test taking skills, referenced from Winning at Math, a 1997 work by Paul D. Nolting, Ph.D.  Of particular value are the 10 steps to better test-taking.

DOME SAT Review is a free comprehensive SAT Test Prep program online with a catalog of material including over 100 study guides, a database of 5,000+ SAT vocabulary building flashcards, practice quizzes, and simulated practice tests.

Education Atlas: Study Skills Guide for Students is a resource for "developing effective study skills, improving reading comprehension, discovering your own personal study style, learning to manage your time more efficiently and learning the best way to prepare for exams." This section of the site contains general study skills guides, test taking guides, and study skills resources by subject.

Educational Testing Service Formative Assessment Item Bank includes complete assessment coverage for K-12 Math and Language Arts.  This web-based resource is available for a small fee per student.  "State test standards are identified, so you can create customized assessments that help target instruction on the most critical standards that students need to master."  The Instructional Data Management System "[g]ives you the ability to add components such as scoring, reporting and curriculum management, as your district needs them."

eHow features how to's on just about any topic, including articles and videos.  Standardized test prep is featured in the section for Education.

Family Education Network: Standardized Tests: Preparation and Advice. See some sample questions by grade level (elementary, middle, high school), and get more tips for success.  A section for SAT and ACT test advice and practice questions is included.

Glencoe Mathematics Online Study Tools contains self-check quizzes, chapter tests, standardized test prep questions, and vocabulary questions.  Multiple-choice is included.  Select your state, then textbook.

HSTutorials.net has animated and step-by-step audio-visual tutorials in pre-algebra, algebra, and geometry and tutorials and resources related to test prep for California's High School Exit Exam for math.

HOT for CCSS: Illustrative Mathematics Project is a work in progress to produce illustrative tasks that students would be expected to do related to each of the Common Core State Standards for Mathematics.  Sections address illustrations for the K-8 and High School standards.  The project is an initiative of the Institute for Mathematics & Education and the Bill & Melinda Gates Foundation.

Internet4Classrooms: Access activities on specific concepts within mathematics strands for grades 1-8 and an extensive list of standardized testing practice sites.

Intervention Central provides intervention ideas in the areas of general academic strategies, reading, writing, math, behavior modification, studying and organization, classroom management, and making rewards work.  This site is brought to you by J. Wright, a school psychologist in Syracuse, New York.

IXL Math from IXL Learning is a math practice site, which has problem sets for preK-8 and algebra and geometry.  The site provides a colorful, engaging environment for mastering skills.  Guests can access "20 problems per day" for free with feedback on answers to help with understanding; however, the service is subscription based.  Full benefits (e.g., student progress tracking and reports; and an awards system for learners who reach their goals) are gained with membership.

Jefferson Lab (VA), although primarily for science education, has some good puzzles and games suitable for use with elementary students to help them master basic math facts using addition, subtraction, multiplication, and division; also practice use of < = >, place value, and coordinates.  Speed to complete exercises in noted as a motivation element.

Kidtest.com helps students from kindergarten through college to do better on achievement tests.  The site contains several practice U.S. state and Canadian province achievement tests online and features near immediate grading and feedback reports.  An online educational supplies store and online flashcards are offered.

Kids Place Mathematics from Houghton Mifflin Company contains online quizzes and tests and brainteasers correlated to their mathematics textbooks for grades 1-6, and additional test taking skills.

Math Counts Problem Solving Strategies lists eight strategies with an example of each.  Math Counts is a well-recognized organization that provides contests for middle school students nationwide.  Also see their problem of the week archive, extended activities, and read about algebraic thinking.

MathDrills by Elias Saab of the University of Missouri will help students to prepare for Mathcounts, SAT and ACT math problems.  In addition, the basic skills sections can be used by students in upper elementary through high school settings.  Answers and hints are provided.  Sections include problems on distance, speed, and time; problems on job completion, roots of polynomials, factoring polynomials, percentage word problems, arithmetic and fraction attack (+, -, x, /), bases, linear equation drills, prime factorization, and LCM and GCD.  Elias Saab also maintains the Online Test Page.

HOT for CCSS: Mathematics Common Core Toolbox has sample task items for elementary, middle, and high school from the PARCC Prototyping Project, posted by The Charles A. Dana Center at the University of Texas at Austin.

Mathematics Tutorials from San Antonio College is the online version of what a student might get from a tutor in a lab setting.  It is a first-rate series of modules starting with basic mathematics through pre-calculus and calculus for business with slide shows, pdf files for printing content, and online exercises in multiple choice format with feedback to help students in courses taught at the college.  However, the exercises in the basic mathematics courses through algebra are very good for helping students prepare for state standardized testing in math, as well.  Highly recommended.

Math 10 Pure: Lance Burns at the Argyll Center in Edmonton, Canada, has developed materials for this course.  He includes notes, video explanations, online interactive quizzes with explanations for answers to problems, and unit exams for the following topics: polynomials, rational expressions, relations and functions, real numbers, numbers patterns, coordinate geometry, measurement, and statistics.  This site provides great reinforcement and review on many of the topics included on U.S. high school assessment exams.

Number2.com has free online test prep for the SAT, ACT, and GRE exams.

HOT! Open-Ended Math Problems posted at the Franklin Institute web site is specifically designed for middle school students to prepare for solving open-ended math problems on standardized tests.  Although these are geared to Philadelphia (PA) standards, all middle school learners and even some high school learners will benefit.  There are problem sets for each month September through April with three levels of difficulty.  Problems are included for each major math strand: number theory, measurement, geometry; patterns, functions, algebra; and data, statistics, and probability.  Possible answers and rubrics for assessment are also provided.

Saxon Publisher's Online Activities include over 125 practice activities to help students master content presented in their K-12 math texts.  As activities are clearly titled, these will benefit learners regardless of text used.

Shmoop offers SAT prep at a small fee per student.  This learning and teaching resource was made by experts and educators from Stanford, Harvard, Berkeley, and other top universities.

SparkNotes: Math Study Guides include review explanations and problem sets for pre-algebra, algebra 1 and 2; geometry 1,2, and 3; trigonometry, pre-calculus, and advanced placement calculus levels AB, BC 1, and BC2.  There's also test prep for SAT, ACT, GRE, and AP courses.  Other subjects are also included at this site.

Study Guides and Strategies contains several sections: study skills, preparing for tests, taking tests; improving research, project management, reading, writing, science, and math skills.

Study Island is a commercial product for standardized test prep in your state for elementary and high school grade levels and exit exams or end of course exams--whatever your state requires.  The developers link their multiple choice questions to specific state standards.  The program is web-based offering diagnostics and instruction and will generate various reports to help monitor mastery.  Study Island also has a Common Core Benchmarking Program to help identify areas of student proficiency in relation to the Common Core State Standards.

Test Preparation Study Center has a blog with tips and information for students preparing for exams.  You'll also find help for specific exams, including state high school tests and college entrance and teacher certification.  Among popular category pages are:

• Multiple Choice
• How to Take a Test

That Quiz is a real find.  K-12 students can select practice tests (customized for their needs) with varying degrees of difficulty using integers, fractions, concepts (time, money, measurement, place value, graphs), geometry, algebra, calculus, probability,  and more.  Some are interactive and offer manipulatives (e.g., ruler, protractor).  Select to view in Spanish, if needed.

Trends in International Mathematics and Science Study Test your mathematics and science knowledge by completing TIMSS items in the Dare to Compare challenge! TIMSS provides reliable and timely data on the mathematics and science achievement of U.S. students compared to that of students in other countries.  See how well your students stack up.  Answers are provided as feedback.

USATestprep is a subscription based online product "to help high school and middle school students understand their state's required standards and prepare them for high-stakes, standardized tests."  Materials include practice exams, automatic grading and tracking for individual students, an ability to create custom benchmark tests, arcade-style games, interactive skill work, and printable puzzles, worksheets, activities, and more.  Free trials are available to qualified educators.

 

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NCLB Supplemental Education Services and Tutoring

 

NCLB requires schools that fail to meet Annual Yearly Progress goals for a third consecutive year to offer parents of low-income (Title I) students a choice of tutoring from among a state-approved list of Supplemental Education Service (SES) providers.  Your state is required to identify SES tutoring providers for the geographic region in which your district is located.  The U.S. Department of Education provides a list of state contacts and state information to find state policies and progress, lists of approved providers, and other state SES information among its SES resources.  Studies and reports on SES are also among resources. Districts, likewise, are required to notify parents about the availability of services, at least annually.

Get more information about state and local education association responsibilities, monitoring requirements and services, arranging for such services, the role of parents, provider responsibilities and funding in NCLB Supplemental Educational Services Non-Regulatory Guidance (June 13, 2005) at http://www.ed.gov/policy/elsec/guid/suppsvcsguid.doc.  This 55-page document is from the U.S. Department of Education.  Answers to frequently asked questions on school choice and SES are at http://www.ed.gov/parents/schools/choice/choice.html.

Tutoring Guidelines

Just as in the classroom, tutors need to be qualified.  They need subject-matter expertise.  Certification and prior teaching experience is a plus.  A tutor needs to know if the student has a learning disability, and if so, the tutor should have skills in working with the specific disability.  If not, then the tutor and/or program might not be appropriate for that student.  Edward Gordon (2006) provided the following suggestions on what to look for in a good tutoring program.

• Check if the student has learning disabilities.  "Past research reveals that tutoring is most effective when it helps students literally 'learn how to learn.' ...students often fail to master important basic skills because of subtle undiagnosed learning disabilities, dyslexia, underachievement and other learning issues that may limit study skills"  (para. 4).
• Ensure that tutoring is individualized and that tutors are recording progress.  "Good tutoring -- particularly diagnostic/developmental tutoring -- closely observes and records student learning strengths and weaknesses on a class-by-class basis...This precise remedial approach is ongoing throughout the student's tutoring sessions" (para. 5).
• "Tutors need to follow a written curriculum that helps individualize their instruction" (para. 7).
• Ensure parental support.  "Tutors need to coach parents on how to better encourage good study habits and motivate their child's daily learning at home" (para. 8).

Gordon and his colleagues Ronald Morgan, Judith Ponticell, and Charles O'Malley (2004) provided the same and additional advice in Tutoring Solutions for No Child Left Behind: Research, Practice, and Policy Implications.

Note:  A teacher (shorelineschools.org) recommended TeachingTextbooks.com as a source for texts (grades 5-7, pre-algebra, algebra 1 and 2, geometry, and pre-calculus) that have the potential to minimize a need for personal tutors (personal communication, July 31, 2008).  According to the developers, "Using a Teaching Textbook is like having a friendly tutor available at the push of a button, but for only a fraction of the cost."  Texts are designed to be used by independent learners and home-schooled students.  They provide maximum explanation and are accompanied by CDs with "audiovisual step-by-step explanations for every single one of the almost 3,500 problems in the book" (FAQ section).

 

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References

 

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Go to Preparing Your Students for the Ohio Graduation Test in Mathematics

 

See related topics: Math Resources and Math Manipulatives.