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 begins with a short essay, No Child Left Behind and Solid Test Preparation Advice. Resources follow, which include:
Don't miss CT4ME's Test Prep Help this School Year!
Educators will appreciate our Six Steps to Success and resources to help your students to review concepts and practice questions correlated to grades 8-10 mathematics benchmarks. Each set of strand resources for the state high school exam is accompanied by a downloadable test prep booklet. Students, regardless of the state in which you live, can benefit.
Hot news of January 2012! CT4ME.net was named in the Schools.com list of 20 indispensible online test prep resources.
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. As a result, there remains concern among educators about the nature of these tests and what appears to be an excessive focus on test preparation. For example, 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:
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):
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!
Teaching to the Test?--An Answer to Consider
Jeff Weinstock (2008) of T.H.E. Journal provided food for thought for critics of standardized testing. "When the system works the way it should, teaching to the test is a misnomer. It's not the test that teachers are teaching to, but the state learning standards embedded in the test. Has the student learned this, that, and the other?...Count me among those who think introducing some accountability into math instruction is an idea whose time has come. I can't suffer another generation of supermarket cashiers who become disoriented when I hand over $8.07 for a $7.82 bill" (p. 8).
Read Dr. Patricia Deubel's full commentary, Accountability, Yes. Teaching to the Test, No featured April 10, 2008, in T.H.E. Journal.
Read Dr. Patricia Deubel's full commentary on the rise of online testing and concerns for educators who will be preparing students for new Common Core State Standards assessments, featured September 15, 2010, in T.H.E. Journal.
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. 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.
Cross-over point depends on inferences you wish to draw from the test and lies between:
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).
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.
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:
Further, O'Shea (2005) indicated that districts should:
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:
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:
You can read a more complete review of this study at our Research Corner for Standards, Raising Achievement, Assessment, and How People Learn.
Test Prep and Math Realities
Read Dr. Patricia Deubel's commentary, "Test Prep and Math Realities," featured September 27, 2007, in T.H.E. Journal SmartClassroom.
Buy additional test prep materials via CT4ME.
The Amazon widget below shows books using the search phrase: test prep math. You can also use the widget to search with other key words. Suggestions include:
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.
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.
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.
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.
North Carolina: North Carolina Public Schools released test forms for grades 3-8 and high school.
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.
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.
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.
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.
According to the National Mathematics Advisory Panel (2008) in its Foundations for Success:
Anxiety about mathematics performance is related to low mathematics grades, failure to enroll in advanced mathematics courses, and poor scores on standardized tests of mathematics achievement. It also may be related to failure to graduate from high school. At present, however, little is known about its onset or the factors responsible for it. Potential risk factors for mathematics anxiety include low mathematics aptitude, low working memory capacity, vulnerability to public embarrassment, and negative teacher and parent attitudes. (p. 31)
Most likely, everyone has experienced math anxiety at one time or another. It is an emotional response that often comes from negative experiences working with teachers, tutors, classmates, or family members. Symptoms include panic (feeling helpless about an ability to do better and putting pressure on yourself, which affects your ability to concentrate), paranoia (feeling that everyone but you knows the answer), passivity (feeling that regardless of what action you might take, you were just not born with math ability; hence you do nothing to overcome the problem), no confidence (you continually question yourself and approach math by memorizing rules and procedures, rather than through understanding concepts). Identifying the source of your problem may be a first step in overcoming it.
In addition to outward behavior manifestations of math anxiety, there is biological evidence of its existence. According to Dr. Venod Menon of the Stanford University School of Medicine, "Math anxiety is an under-studied phenomenon, which still lacks formally established diagnostic criteria ... it is possible for someone to be good at math, but still suffer from math anxiety" (Digitale, 2012, para. 5). Menon and his team of researchers used brain scans in their study of 46 second- and third-grade students with low and high math anxiety, and found that "Children with high math anxiety were less accurate and significantly slower at solving math problems than children with low math anxiety. The results suggest[ed] that, in math anxiety, math-specific fear interferes with the brain’s information-processing capacity and its ability to reason through a math problem" (para. 12-13). "His team’s observations show[ed] that math anxiety is neurobiologically similar to other kinds of anxiety or phobias" (para. 7). Results may lead to new strategies for treatment of it, as in ways suggested for treatment of other anxieties and phobias.
Hence, educators must take math anxiety seriously. Learn more about what math anxiety is, how to take possession of your math anxiety, and get some strategies for how to study math and take tests.
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:
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."
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:
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.
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.
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.
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).
Know the Purpose of the Test You Take!
There are two kinds of state tests describing student achievement and each has a different purpose. Mark O'Shea (2005) provides the following important difference between the two:
Understand Test Accommodations for Students with Special Needs
Students with special needs such as those with disabilities, limited English language and English language learners also are subject to taking large-scale assessments, including standardized tests. CTB/McGraw-Hill (2005) developed Guidelines for Inclusive Test Administration to help educators use appropriate test accommodations and then make valid and useful interpretations for both criterion- and norm-referenced test scores. Guidelines fall within three categories:
Category 1. "Category 1 accommodations are not expected to influence student performance in a way that alters the standard interpretation of either criterion- or norm-referenced test scores. Individual student scores obtained using Category 1 accommodations should be interpreted in the same way as the scores of other students who take the test under default conditions. These students’ scores should be included in summaries of results without notation of accommodation(s)" (p. 8). Examples: Students take the test alone or in a study carrel, or have directions read aloud or recorded. ELL might need bilingual directions. Some students might need to give responses to a scribe or use sign language.
Category 2. "Category 2 accommodations may have an effect on student performance that should be considered when interpreting individual criterion- and norm-referenced test scores" (p. 9). Examples: Students are given extra time to complete a timed test. ELL are given audiotaped test items provided in native language version or a side-by-side bilingual test or translated version provided for content other than Reading and Writing.
Category 3. "Category 3 accommodations are likely to change what is being measured and have an effect that alters the interpretation of individual criterion- and norm-referenced scores. This occurs when the accommodation is strongly related to the knowledge, skill, or ability being measured (e.g., the use of a Braille test where not all items in the non-Braille version are administered in Braille)" (p. 9). Example: Students are permitted to use calculators or tables on a math computation test when the intention is to measure computation skills without calculator use.
Consider math applications for test prep using your mobile devices.
Adapster SAT Math is an iPhone or iPod app available for a small price at iTunes. After taking a diagnostic test, it differentiates and individualizes learning via a customized study plan based on the results. It has over 1000 questions and 150 lessons covering major math strands. See a review of this product.
Bracey, G. (2009, November). The big tests: What ends do they serve? Educational Leadership, 67(3), 32-37.
CTB/McGraw-Hill. (2005). Guidelines for inclusive test administration. Monterey, CA: Author. Retrieved from http://www.ctb.com/ctb.com/control/researchArticleMainAction?articleId=475&p=ctbResearch
Digitale, E. (2012, March 21). Imaging study reveals differences in brain function for children with math anxiety. Stanford, CA: Stanford University School of Medicine. Retrieved from http://med.stanford.edu/ism/2012/march/math.html
Education Week. (2010). Standards, Assessments, Accountability, pp. 39-41. In Quality Counts 2010. Retrieved from http://www.edweek.org/media/ew/qc/2010/17sos.h29.saa.pdf
Gordon, E. (2006, November 29). America needs to wise up about need for quality tutoring. Chicago Sun Times.
Gordon, E., Morgan, R., Ponticell, J., & O'Malley, C. (2004, March). Tutoring solutions for No Child Left Behind: research, practice, and policy implications. NASSP Bulletin, 88(638), 59-68.
Herman, J. L., & Baker, E. L. (2005, November). Making benchmark testing work. Educational Leadership, 63(3), 48-54.
Kercheval, A., & Newbill, S. (2002). A case study of key effective practices in Ohio's improved school districts. Bloomington, IN: Indiana Center for Evaluation and Education Policy. Retrieved from http://ceep.indiana.edu/projects/PDF/200202_Key_Effec_Prac_Final_Report.pdf
Mehrens, W. A. (1989). Preparing students to take standardized achievement tests. Practical Assessment, Research & Evaluation, 1(11). Retrieved from http://pareonline.net/getvn.asp?v=1&n=11
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education. Retrieved from http://www.ed.gov/about/bdscomm/list/mathpanel/index.html
O'Shea, M. (2005). From standards to success. Alexandria, VA: ASCD.
Reeves, D. B. (2004). Accountability for learning: How teachers and school leaders can take charge. Alexandria, VA: ASCD. ISBN: 0-87120-833-4.
Reforming Ohio's Education System for the 21st Century. (2009). Retrieved from http://www.conversationoneducation.org/dotAsset/6277.pdf
Silver, H., Strong, R., & Perini, M. (2007). The strategic teacher: Selecting the right research-based strategy for every lesson. Alexandria, VA: ASCD. Retrieved from http://www.ascd.org
Tomlinson, C. A. (2000, September). Reconcilable differences? Standards-based teaching and differentiation. Educational Leadership, 58(1), 6-11. Available in ASCD archived issues: http://www.ascd.org/portal/site/ascd/menuitem.a4dbd0f2c4f9b94cdeb3ffdb62108a0c/
U.S. Department of Education. (2003, August). NCLB Supplemental Educational Services Non-Regulatory Guidance. Retrieved from http://www.ed.gov/policy/elsec/guid/suppsvcsguid.doc
Weinstock, J. (2008, February). Make it a test worth teaching to. T.H.E. Journal, 35(2), 8.
Williams, T., Kirst, M., Haertel, E., et al. (2010). Gaining ground in the middle grades: Why some schools do better. Mountain View, CA: EdSource. Retrieved from http://www.edsource.org/middle-grades-study.html