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Standardized Test Preparation and
Tips for Success

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In Standardized Test Preparation and Tips for Success, you'll find:


Don't miss CT4ME's Test Prep Help this School Year!

See CT4ME's Common Core Resources for high school learners.  Use these all year long to address each of the domains within the Common Core math standards.

Visit our extensive collection of resources for Preparing Your Students for the Ohio Graduation Test in MathematicsSunshine gif with smiling mask and pencil marking correct test answerEducators 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.


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Test Preparation Advice


US Map 50 states GifNo 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.

The Every Student Succeeds Act (ESSA) maintains the requirement that each state implement "a set of high quality student academic assessments in mathematics, reading or language arts, and science" (114th Congress, 2015, p. S.1177-24) among its provisions.  Further, mathematics and reading or language arts assessments will be administered in each of grades 3 through 8, and at least once in grades 9 through 12 (p. S.1177-25).

Beginning in 2014-2015 school year, learners faced a new testing challenge in that their assessments of learning would be via online testing of the Common Core standards.  Organizations such as PARCC and SBAC began developing assessments.  Tests were predicted to take learners from 8-10 hours to complete (Doorey, 2014; Gewertz, 2013).  As a result, educators became concerned about the nature of these tests and what appeared to be an excessive focus on test preparation.  Online testing posed additional concerns about required technology, sufficient bandwidth, computerized test security, learners' technology skills, and new forms of test anxiety.

Become Familiar with Updated Policies for Computerized Testing

Computerized testing raises new issues that require updating of test security laws and policies, as policies written for standardized testing administered via paper-and-pencil are no-longer sufficient.  ACT has a highly relevant report in this regard: The End of Erasures: Updating Test Security Laws and Policies for Computerized Testing by Michelle Croft (2014).

Croft (2014) outlined many concerns, noting that computerized testing does not eliminate cheating and test piracy.  Such practices just take on different forms.  Unique risks include such things as "educators logging in to tests to view questions or change student responses, computer hacking; keystroke logging; printing, emailing, or storing test information in a computer outside the test delivery system. ... there is a greater risk of students accessing the Internet and other programs during testing" (p. 1).  There's concern about students using their own devices for testing and who has administrative privileges.  How should workstations be positioned and secured so that students can't see what's on the monitors of others.

Croft (2014) recommended that states update their state statutes and regulations to reflect the shift to computer-administered assessments, concentrate efforts on controlling test access, and ensure that there is a single test security section within the updated manual that contains answers for any question that a test administrator has about test security.  For example, policies should consider how student login information is secured.  There should be rules on how tests are reactivated if disrupted:

The rules should emphasize having more than one proctor aid in the reactivation, and most importantly, proctors should maintain a log of all reactivations to provide documentation in the event of an investigation. Likewise, the technology should be secure and the testing window should be as short as possible to reduce the likelihood that items are compromised.  Finally, states should actively monitor test access issues through data reports to determine if there have been excessive logins or logins at times when testing should not occur (e.g., on the weekends), and have clear policies in place detailing how violations will be handled. (p. 4)

The test security section should also include an itemized list of what materials are secure (e.g., work folders, student authorization tickets with IDs and passwords, session rosters, scratch paper, reference sheets).  "Information about who can access the test should be clearly articulated. In addition, there should be information on how to report test security concerns and possible violations, which can be applicable regardless of the testing format" (Croft, 2014, p. 4).

Thus, educators should become familiar with any new policies regarding computerized test administration, including what they, test proctors, and students may and may-not do.

Use Effective Test Prep Strategies with Learners

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):

  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!

Ensure Learners Acquire Technology Skills

Kid on a computer imageWhat has changed for Common Core assessments, however, in relation to that good instruction is that teachers need to ensure their learners also have the technology skills to perform well on tests administered online.  Per Kristine Gullen (2014), "If we want an online assessment to capture a student's level of learning, rather than that student's ability to navigate technology, teachers must integrate these skills into their instruction, giving students practice before administering high-stakes exams on a computer" (p. 69).  Hence, among the best ways to prepare learners for new assessments is to integrate test preparation into every day lessons using CCSS-type questions linked to the curriculum and to use technology for assessments and as a content learning tool.  It's more effective than a two-week or more crash effort for test prep prior to the actual high-stakes exam (Miller, 2014).

Learners need practice with the new testing formats, and new types of questions.  For example, multiple choice questions might have more than one answer.  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.  Fluid keyboarding skills will help minimize frustration when answering constructed-response questions.  They also need good "mousing" or "touchscreen" skills to enter or remove responses via click or drag and drop 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.

Gullen (2014) noted that learners also need skills highlighting text, drawing lines and creating graphs on a screen, operating an online calculator, and using a scroll bar.  The need to use a scroll bar might be increased if learners also need to increase font size, an accommodation feature.  Above all learners need "opportunities to build a level of comfort with the actual keyboards, screens, eternal mouse or touch pads, and so on that they'll use during the assessment" (p. 71).  Piloting online assessments from PARCC or SBAC or your state will help in this endeavor, as will debriefing learners following those about their difficulties and recommendations for additional skills they need to develop.

Teachers also need to be aware of online testing accommodations that might be needed for special needs learners.  Such learners should not be expected to take a standardized test online without having adequate experience with identified accommodations they will need.  For example, visually impaired learners might need text-to-speech readers, particularly if they have typically had human readers.  Some might need a zoom feature to enlarge text.  This feature to magnify might be embedded in the test for all learners.  Those with motor impairments might need a scribe, or an assistive technology or special equipment such as a recording device to enter responses.  English language learners might need a translation for certain words; however, teachers should check the testing rules regarding the use of electronic word-for-word dictionaries (e.g., computer-based, web-based, or hand-held) for online standardized testing.

Teach to the Standards, Not to the Test

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 commentary, Accountability, Yes. Teaching to the Test, No featured April 10, 2008, in T.H.E. Journal.

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.


Taming the Test iconWe 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 or ESSA, 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.


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

Typically Ethical:

  1. teaching test-taking skills;

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

  1. 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.);
  2. providing instruction based on objectives (skills and subskills) that specifically match those on the standardized test to be administered;
  3. 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).


  1. providing practice or instruction on a published parallel form of the same test;
  2. 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.

Plan for 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:

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).

Consider the Big Picture--Everyone Counts

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 include:

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


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Math Anxiety and How to Minimize It


Boy with glasses having difficulty taking a test GifAccording 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.

Do you have math anxiety?  Take a self-test from Dr. Ellen Freeman of also has a short assessment to determine whether you have test anxiety and what to do about it.

Anxiety's Role in Math Performance

Does math anxiety lead to poor performance or does poor math performance lead to math anxiety?  Research is mixed as to which comes first, the emotion or poor performance.  Carey, Hill, Devine, and Szücs (2016) discussed theories:

Student performance on math exams can to be affected by the strategies they use to prepare for exams and the time they spend on those.  In their study of math exam preparation and math anxiety, Jenifer, Rosek, Levine, and Beilock (2022) included the following test prep strategies: "reading textbook section(s) for the first time, rereading textbook section(s), reviewing homework solutions, solving practice problems, reading examples of solved problems, and reviewing notes" (p. 3).  They found that problem-solving was the most effortful study strategy and that "math anxiety was associated with less planned engagement with effortful problem-solving during studying. Moreover, the avoidance of effortful problem-solving engagement partially mediated the association between math anxiety and exam performance, marking it as a potential target for intervention" (p. 1).

Jenifer, Rosek, Levine, and Beilock (2022) found that "math-anxious students avoid engaging with effortful study strategies, specifically solving practice problems, when preparing for a math exam" (p. 4).  When solving problems, "math-anxious students were less likely to prioritize harder practice problems compared to their less anxious peers" (p. 4).  Further, "math anxiety was related to how effortful students perceived particular study strategies to be, with greater anxiety being associated with ranking solving practice problems as more effortful and with ranking rereading the textbook as less effortful. These findings seem to suggest that math-anxious students’ avoidance of effortful study strategies may be caused by biased perceptions of the amount of effort required for certain study behaviors" (p. 6).

Biological Evidence

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.

What teaching strategies help minimize math anxiety?

Findings from research are particularly relevant for pedagogical methods that have been successful with learners, particularly in terms of reducing math anxiety.  However, the potential for a bidirectional relationship between math anxiety and math performance per Carey et al. (2016, Reciprocal Theory section) would suggest that any interventions should address both math anxiety and math performance.

Blazer (2011) reviewed strategies that teachers can use to help reduce students' anxiety, thus leading to better achievement for all:

Researchers at Stanford University School of Medicine (2015) found that one-on-one tutoring can be used to relieve math anxiety.  Grade 3 learners with high math anxiety participated in the study.  The tutoring "fixed abnormal responses in the brain's fear circuits," as noted by functional MRI brain scans.

Can learners reduce negative affects of anxiety?

Write about your anxiety.

Educators must take math anxiety seriously.  One way to potentially help learners reduce the negative affects of their math anxiety is writing about it prior to taking a math test, as suggested in Neuroscience and Education:  A Review of Educational Interventions and Approaches by Neuroscience (Howard-Jones, 2014) commissioned by the Education Endowment Foundation in London.  Howard-Jones noted:

"An intervention focused on controlling negative emotional response has reported improved achievement. Writing about anxieties may be one way to rehearse such control. Following on from laboratory-based studies, a school-based intervention was carried out among students aged 14-15 years (N=106).  These students first rated their own anxiety and were then randomly allocated into two groups. For 10 minutes, immediately before a maths test, one group wrote about mathematics-related anxieties and the other about a topic not in the test. Amongst students who had had rated themselves as more anxious, those who wrote about their anxieties significantly outperformed maths anxious students in the other group, performing similarly to less maths anxious students." (p. 16)

This aforementioned study was conducted by Gerardo Ramirez and Sian L. Beilock in 2011.  Read the details in Writing About Testing Worries Boosts Exam Performance in the Classroom.

Learn How to Learn Math.

How to Learn Math: StudentsAnother potential strategy to minimize anxiety is for students to learn how to learn math.  Dr. Jo Boaler of Stanford University has a short, free course at called "How to Learn Math" for any student in all levels of mathematics.  There are six short lessons about 10 to 20 minutes each.  You'll get some key information on the brain and learning, and effective strategies for learning math.  Concepts include overcoming myths about math, math and mindset, mistakes and speed; number flexibility, math reasoning, and connections; number patterns and representations; and math in life, nature, and work.  The course also features videos of math in action.

Additional Resources

Paper on fire for hot newsLearn 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.


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Test Preparation in Your State and Practice Questions

Smart Learner -- Weight Lifter Gif

Become a Smart Learner--Raise your Skills!  Many states provide educators with benchmark assessments or item banks linked to their state standards. Learn more about standardized tests in your state, and the National Assessment of Educational Progress (NAEP) using resources in this section.


Question markAre your students ready for the Common Core math exams?  You can find out by using Benchmark Now! from Naiku for Grades 2-High School.  It "combines the assessment delivery, auto-scoring, and intuitive standards-based reporting features of Naiku with professionally developed end-of-year summative assessments that include a variety of question item types – including technology enhanced – tied to the Common Core State Standards in ELA and Math."

Learn more about the Common Core Standards and Standards in Your State, as provided by the Common Core State Standards Initiative.

Do benchmark assessments really affect achievement? Per Robert Slavin (2019), "Benchmark assessments are only useful if they improve scores on state accountability tests."  However, the bad news is that "Research finds that benchmark assessments do not make any difference in achievement."  This perspective is supported by studies that included benchmark assessments.  A summary of findings for 6 elementary reading studies and 4 elementary math studies indicated mean effect sizes on achievement as essentially zero.

Slavin (2019) suggested possible reasons as to why benchmark assessments do not make a difference:

  1. "First, perhaps the most likely, is that teachers and schools do not do much with the information from benchmark assessments. ... Results of benchmark assessments are different for each student."
  2. A second reason is that "it takes time to score and return benchmark assessments, so by the time a team of teachers decides how to respond to benchmark information, the situation has moved on."
  3. "Third, benchmark assessments may add little because teachers and principals already know a lot more about their students than any test can tell them."

For those reasons, Slavin (2019) suggested schools can save a lot of time and money by eliminating benchmark assessments.  "Yes, teachers need to know what students are learning and what is needed to improve it, but they have available many more tools that are far more sensitive, useful, timely, and tied to actions teachers can take."


Concerned about CCSS Math Tests?

Read Dr. Patricia Deubel's commentary, Are We Ready for Testing under Common Core State Standards?, featured September 15, 2010, in T.H.E. Journal.  Learn about the rise of online testing and concerns for educators who will be preparing students for new Common Core State Standards assessments.

Readers might be interested in CCSSI Mathematics, a blog that "takes an independent look at the Common Core State Standards Initiative."  Among concerns are those on question designs and learner potential problems in using technology to answer them.

State and Consortia Assessments

Most states release summative test items and CT4ME has links to those from this site.

In 2017 New Meridian took over management of PARCC's testing business and has a special site with resources.  Of interest are its Released Items and Math Test Design.  In the latter New Meridian includes test specifications, performance-level descriptors, evidence statements including calculator designations, and a Mathematics High Level Blueprint that "defines the total number of tasks and/or items for any given grade/course assessment, the item types, and the point values for each.  These are intended to help the "general public better understand the design of the state summative assessments."

SBAC Practice and Training Tests include sets of assessment questions for grades 3–8 and high school in both English language arts/literacy and mathematics.

SBAC Tools for Teachers is an online collection of classroom resources with "Educator-created lessons, activities, strategies, and professional development to help tailor instruction and boost learning."

Consortia Developing Alternative CCSS Assessments

For English Language Learners:

For Learners with Cognitive Disabilities:

  • Dynamic Learning Maps Alternate Assessment Consortium (DLM) is also developing assessments for learners with cognitive disabilities.  There are two types of assessments that are being developed for DLM. The first is a stand-alone summative assessment that is adaptive. This test will be given in the spring of the year to assess what knowledge and skills have been learned throughout the year. The second is an instructionally embedded assessment that will be given throughout the year. (About the DLM System)
  • National Center and State Collaborative developed common alternate assessments in English language arts and math for its partner states and curriculum/instructional resources to support teaching the Common Core State Standards to students with significant cognitive disabilities that can be used in any state.  Also see the NCSC resources at its wiki.

Read more on K-12 Student Assessment Programs at the Educational Testing Service: K-12 Center.


All States:

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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.  The NAEP mathematics assessment is given every two years to students at grades 4 and 8, and approximately every four years at grade 12.  An overview of NAEP and major findings from past assessments are included. NAEP reports that 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.  The test does not measure any one particular student's performance, rather it provides a composite assessment.  Gerald Bracey (2009) reported 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) noted 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 includes information about its state tests.

Alaska: Assessments

Arizona: Assessment section. Also see the AzM2 Portal for Sample Tests.

Arkansas: Arkansas Department of Education Learning Services: Assessment

California: California Department of Education Smarter Balanced Practice Tests

Colorado: Colorado Assessment Division Colorado also includes samples of its performance assessments.

Connecticut: Connecticut State Department of Education: Comprehensive Assessment Program Portal includes practice and training tests.

Delaware: Delaware Mathematics Assessment Aligned to the Common Core

Florida: Florida K-12 Student Assessment at the Florida Department of Education.  Get released test questions and Florida practice tests for math grades 3-8, algebra 1, and geometry.  Note: the Florida Department of Education, the National Science Foundation, and FCR-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 standards.  You'll find curriculum, activity, and general resources and an extensive collection of lesson plans, and more.

Georgia: Georgia Department of Education Testing/Assessment Milestone Resources include experience with online testing.  Also see the Mathematics section at for additional resources.

Hawaii: Hawaii Statewide Assessment Program Portal

Idaho: Idaho Department of Education: ELA/Literacy and Math Assessment includes practice and training tests.  Math sample items are listed for grades 3-8 and high school in their portal: 

Illinois: Illinois State Board of Education: Assessment includes assessment resources.

Indiana: Indiana Department of Education has resources and sample test items in its ILEARN portal.

Iowa: Iowa Department of Education: Student Assessment.  See the Math Practice Tests for grades 3-11.

Kansas: Kansas State Department of Education Note: See the Kansas State Department of Education Assessment Literacy Project available online with 21 modules appropriate for all educators.  W. James Popham provided 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: Assessments: Measuring Resuslts includes an assessment library.

Maine: Maine's Comprehensive Assessment System

Maryland: Maryland State Department of Education  See practice tests for mathematics in grades 3-8, algebra I, geometry, and algebra II.

Massachusetts: Massachusetts State Department of Education released test questions and practice tests from its comprehensive assessment system

Michigan: Michigan Department of Education Student Assessment Program includes sample questions at the website.

Minnesota: Minnesota Department of Education indicates testing resources, including item samplers and Pearson’s Perspective, are available on the PearsonAccess Next website.

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: Assessment Resources and Resources for College-and-Career Readiness

Montana: Montana Office of Public Instruction: Statewide Testing  Montana uses SmarterBalanced Practice and Training items.

Nebraska: Nebraska Statewide Assessment contains sampler items for math for grades 3-8.  Also see practice tests for grades 3-8 at the Nebraska Student Center Assessment System.  Nebraska uses the ACT exam for high school learners and has an ACT exam prep site

Nevada: Nevada Department of Education Standards and Assessments--Nevada uses SBAC and its practice tests in grades 3-8 and ACT and its practice tests in grade 11.  Note: The Southern Nevada Regional Professional Development Program includes math resources for elementary, middle, and high school.  These latter contain content units with notes (many indicating alignments with Common Core math standards), worksheets, quizzes, practice tests.

New Hampshire: New Hampshire Statewide Assessment System includes its practice and training tests.

New Jersey: New Jersey Department of Education: Assessment

New Mexico: New Mexico Standards Based Assessments

New York:

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

North Dakota: North Dakota State Assessment Program


Bullseye GifTarget 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.  Ohio's OGT will continue to be administered until 2022 for those who need to pass one or more parts of the exam.

Oklahoma: Oklahoma Department of Education: Office of Assessments Assessment materials 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.

Oregon: Oregon Department of Education Student Assessment includes sample items and training tests for math.

Pennsylvania: Pensylvania Department of Education Standards Aligned System (SAS) contains an Assessment section with options such as: Project-based assessment, the state's Keystone Exams with high school sample questions in algebra 1, algebra 2, and geometry, an Assessment Creator, Reference Materials (e.g., formative assessment), and more.

Rhode Island: Rhode Island Department of Education: Instruction & Assessment: Mathematics contains released items and practice tests.

South Carolina: South Carolina State Department of Education The section on Assessment Information includes Quick Links for Teachers with sample test items for math in grades 3-8 and algebra 1.

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

Tennessee: Student Assessment in Tennessee You'll find pdf files of released test items in the section for TNReady.

Texas: Texas Education Agency: Student Assessment and STAAR Released Test Questions

Utah: Utah State Office of Education: Assessment.

Vermont: The Vermont Agency of Education includes an assessment section within Student Learning with a portal to Smarter Balanced.

Virginia: Released Tests and Item Sets are available in mathematics for grades 3-8, algebra I, algebra II, and geometry.

Washington: State of Washington Test Questions and Practice/Sample Tests

West Virginia: WV Department of Education: Assessment includes assessment resources.

Wisconsin: Wisconsin Department of Public Instruction assessment resources include sample items from various tests given by the state, including for the Wisconsin Forward Exam.

Wyoming: Wyoming Department of Education Statewide Assessment System


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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:

ACT provides online test prep for this exam and tips for success. 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).  You'll also find an SAT Resource Center for Educators.  Note: Effective Spring 2016, the College Board implemented a revised SAT.  The College Board and Khan Academy have a SAT Practice site designed to help learners prepare for the revised test.  Key features for math  include the following:

"The Math Test focuses in-depth on three essential areas of math: Problem Solving and Data Analysis, the Heart of Algebra, and Passport to Advanced Math. Problem Solving and Data Analysis is about being quantitatively literate. It includes using ratios, percentages, and proportional reasoning to solve problems in science, social science, and career contexts. The Heart of Algebra focuses on the mastery of linear equations and systems, which helps students develop key powers of abstraction. Passport to Advanced Math focuses on the student’s familiarity with more complex equations and the manipulation they require." (About section: Key Content Features)

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.

Dr. Roger's Math Neighborhood on YouTube includes video solutions to past SAT questions to help students prepare for this exam, including from SAT practice tests offered by the College Board.  Of value is that there are playlists grouped by topic, such as geometry, systems of equations, probability and statistics.  You'll also find a series of video solutions to Math Level 1 and Math Level 2 questions.

Education Galaxy is a game-based program designed to help K-8 learners prepare for state testing.  Users select their state to access questions aligned to the state's standards.  Per the site, "Education Galaxy is a great tier 1 solution for practice, instruction, and assessment."  A free basic account for teachers is available, and there are paid options.  A program called Liftoff Adaptive Intervention is also available to help struggling and at-risk learners.

HOT for AP Students: Fiveable provides free test prep resources for students taking AP courses.  AP Calculus AB/BC and AP Statistics are among those.  Resources include study plans, live streams, study guides, free response help, practice questions.  You'll find information on the upcoming exam--what's on it, how it will be graded, and what to focus on in your test prep.  Of value is that students can practice with others who will take the exam.

Formative Assessment Item Bank at Instructure includes assessment coverage for K-12 Math, English Language Arts, Science, and Social Studies.  Assessments are aligned to state, Next Generation Science Standards, and Common Core standards.  Item types include multiple choice, constructed response with rubrics, writing prompts with rubrics, and technology-enhanced items.

HOT for CCSS: Illustrative Mathematics was founded in 2011 at the University of Arizona.  Since then the project has yielded "a comprehensive suite of math curricula, designed to encourage engaging mathematical discussion, supported by tasks, lesson plans, and professional learning."  Tasks align with the Common Core State Standards for Mathematics.  Illustrative tasks are available for the K-8 and High School standards.  The project is an initiative of the Institute for Mathematics and Education at the University of Arizona 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, algebra 1, algebra 2, geometry, precalculus, and calculus.  The site provides a colorful, engaging environment for mastering skills.  The service is subscription based, but there is a free trial for teachers.  Full benefits (e.g., student progress tracking and reports; and an awards system for learners who reach their goals) are gained with membership.  IXL includes a diagnostic for six strands in math and also for a working math grade level.

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.

Khan Academy: SAT Test Prep: The College Board has teamed up with Khan Academy for free SAT Test Prep materials.  Students will find hundreds of questions and a set of videos with step-by-step solutions to help prepare for this exam.

MathDrills by Elias Saab 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.

New Meridian includes released test items for grades 3-8 math and high school algebra 1, algebra 2, geometry, and integrated math among its resources.  New Meridian indicates its item banks are aligned to the Common Core State Standards and compatible standards.

Shmoop offers fee-based test prep for multiple tests (e.g., SAT, ACT, AP exams, Common Core, PARCC, Smarter Balanced, GED).  Some learning resources are free, including study guides and videos for math--well worth examining.

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, BC1, and BC2.  Other subjects are also included at this site. has a series of video lessons to help prepare learners for standardized tests.  Among those are GED Math (73 lessons); AP Calculus Exam Prep (173 lessons); PSAT: Practice & Study Guide (241 lessons); SAT: Practice & Study Guide (305 lessons); and ACT: Practice & Study Guide (381 lessons on multiple subjects, including math).

Study Island is a standards-based formative assessment and practice program in your state for elementary, middle, and high school grade levels and exit exams or end of course exams--whatever your state requires.  It includes 12 technology enhanced item types.  Study Island is a product of Edmentum, which stated "Students can work through questions using a standard test format, an interactive game format, printable worksheets, or a classroom response system."  Pricing is available for the home, and schools/districts. has free ACT practice tests.  The site developers have gathered or written over 5,000 practice questions the for ACT.  The practice tests are automatically scored and come with answer explanations.  You'll also find official practice tests from ACT.  Additional resources for study tips, subject-specific strategies and more are also available.  Test-Guide also provides test prep resources for other major standardized tests.

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.

TIMSS Explore Your Knowledge Frog Logo GifTrends 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 prepare high school, middle school, and elementary students for standardized testing. Materials include diagnostic assessments, performance tracking, practice questions (e.g., multiple choice, free response), games, interactive skill work, performance tasks, video content, instant feedback, and more.  Free trials are available to qualified educators.  Review products are aligned to individual state standards, including the Common Core (Take A Tour section, Engaging Content).

Varsity Tutors: Practice Tests is a free section of the Varsity Tutors website where you will find practice test questions and flashcards in multiple subject areas.  When viewing math tests, for example, learners can select the concept to practice.  Explanations for answers are included.  Among K-12 math practice tests are grades K-8, basic geometry, algebra 1, algebra 2, trigonometry, precalculus, calculus (including AP), and more.  You'll also find math related to the ACT, GED, CLEP, GMAT, GRE, HSPT, ISEE, and SAT exams.


Know the Purpose of the Test You Take!

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According to W. James Popham (2016), we need to acknowledge that "validity depends on the purpose for which a test is to be used" (p. 46).  There are three primary purposes of tests:

  • Comparison among test takers, which can be made on student-by-student basis (e.g., "percentile-based status in relation to that of a norm group) or group-by-group status (e.g., "assigning students to such qualitatively distinct categories as advanced, proficient, basic, or below basic")
  • Improvement of ongoing instruction and learning, which is integral to formative assessment of the same students
  • Evaluation of instruction (p. 47).

There are two phrases describing tests of student achievement that are discussed in the literature: norm-referenced and criterion-referenced.  Mark O'Shea (2005) provided a difference between the two:

  • Norm-referenced standardized tests are used "to compare the performance of a student or group of students with the performance of a population of other students, typically a state or national population, [but] they serve no purpose in measuring student achievement of the content of the standards."
  • Criterion-referenced standards-based tests "measure the performance of a student or a group of students in relation to skills and knowledge of state standards and frameworks." This type of test is now used by many states. (p. 41)

Although O'Shea (2005) noted two kinds of standardized tests, Popham (2014) indicated: "Although test developers may build tests they believe will provide accurate norm-referenced or criterion-referenced inferences, a test itself should never be characterized as norm-referenced or criterion referenced" (p. 64).  It's a common misconception.  "What's criterion referenced or norm-referenced is the inference about, or the interpretation of a test taker's score" (p. 64).  This clarification is important if one is using precise language.  To emphasize, "it's score-based inferences--not tests--that are criterion-referenced or norm-referenced" (p. 64).  Thus, educators should know how test results will be interpreted.  According to Popham, "To support actionable instructional decisions about how best to teach students, norm referenced inferences simply don't cut it" (p. 64).

Per Popham (2016), "the primary purpose of a particular educational test ... should dominate the decision making of those who are building the test as well as those who are evaluating it.  Currently, emphasis on purpose is absent from U.S. educational testing" (p. 49).

Become Familiar with Standardized Testing Terms

The following will help you to better understand terms associated with standardized testing: Glossary of Standardized Testing Terms from the Educational Testing Service.

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.  Data Recognition Corporation (2017) developed Guidelines to 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. 5). 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. 6). 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. 7).  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.

Have you made appropriate accommodations for students with disabilities or English language learners?

The National Center for Educational Outcomes provides a list of State Websites for Accommodations Information.

The Metropolitan Center for Research on Equity and the Transformation of Schools has developed bilingual Glossaries for ELLs/MLLs Accommodations.  They include key terms in ELA, math, science, and social studies translated into multiple languages.  These serve as accommodations for learners who need them for testing and can be used in instruction throughout the year.  The bilingual glossaries are an expected test accommodation in New York, for example.  Math glossaries include elementary school, middle school, high school integrated algebra, high school geometry, high school algebra 2, high school calculus, an addenda for high school Common Core math terms, and supplementary math glossaries.  They can be downloaded, printed, and disseminated to educators, learners, and parents.

SBAC Assessments

The Smarter Balanced Assessment Consortium (SBAC) assessments include summative assessments for accountability purposes and optional interim assessments for instructional use and will use computer adaptive testing to the greatest extent possible.  Assessments go beyond multiple choice questions to include extended response and technology enhanced items, as well as performance tasks that allow students to demonstrate critical-thinking and problem-solving skills.

Read SBAC updates for Accessibility and Accommodations that outline the kinds of testing supports and tools that will be made available to all students, and particularly those with disabilities and English-language learners for the Common Core assessments.




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Tutoring Guidelines


Man tutoring a studentTutoring can be provided in a variety of ways, including in both face-to-face and online settings.  For example, Pellegrini, Lake, Inns, and Slavin (2018) noted programs have been used in one-to-one tutoring by teachers, paraprofessionals, and paid volunteers; one to small-group tutoring by teachers and small group tutoring by paraprofessionals.

Although most would agree that tutoring is a valuable service for learners who need it, Robert Slavin (2018) pointed out four shockers in recent findings on tutoring gleaned from three studies.  "One is a review of research on programs for struggling readers in elementary schools by Amanda Inns and colleagues (2018).  Another is a review on programs for secondary readers by Ariane Baye and her colleagues (2017).  Finally, there is a review on elementary math programs by Marta Pellegrini et al. (2018)."  The four shockers that follow challenge common beliefs about tutoring and have implications for tutoring programs.  As Slavin stated:

  1. In all three reviews, tutoring by paraprofessionals (teaching assistants) was at least as effective as tutoring by teachers.

  2. Volunteer tutoring was far less effective than tutoring by either paras or teachers.

  3. Inexpensive substitutes for tutoring have not worked.

  4. Certain whole-class and whole-school approaches work as well or better for struggling readers than tutoring, on average.

Slavin's (2018) "theory to account for the positive effects of tutoring in light of the four “shockers” is this:

Just as in the classroom, tutors need to be qualified and have subject-matter expertise.  Although certification and prior teaching experience are valued, Slavin (2020) noted that "teaching assistants, with proven materials and expert professional development, can obtain outcomes as good as those obtained by certified teachers working as tutors" (para. 9).

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.

In his commentary on Designing an Effective System of Services for Struggling Students, Slavin (2021) stated:

"There are two policies that are needed to provide a system of services capable of substantially improving student achievement.  One is to provide services during the ordinary school day and year, not in an after school or summer school.  The second is to strongly emphasize the use of programs proven to be highly effective in rigorous research."

Among rationals for providing tutoring during a school day is that there is an increase likelihood that students will attend those sessions, as they are expected to be in school, as opposed to sessions during non-school time.  Services during the school day (e.g., tutoring) are easier to integrate with other educational services and "entail far fewer non-educational costs" (Slavin, 2021).  Further, Barshay (2021) noted:

"Education researchers have a particular kind of tutoring in mind, what they call “high-dosage” tutoring. Studies show it has produced big achievement gains for students when the tutoring occurs every day or almost every day" (Tutoring section).

"High-dosage" tutoring is also called "high-impact" tutoring.  The National Student Support Accelerator (n.d.) program of the Annenberg Institute at Brown University is devoted to providing comprehensive resources for those who are interested in implementing high-impact tutoring.  "Research shows that high-impact tutoring — tutoring delivered three or more times a week by consistent, trained tutors using quality materials and data to inform instruction — is one of the most effective academic interventions, providing an average of more than four months of additional learning in elementary literacy and almost 10 months in high school math" (About: What is the Accelerator? section).

Note: The Every Student Succeeds Act of 2015 does not mandate tutoring.  Within Section 1004: Direct Student Services, a local education agency applying for funding "may include high quality academic tutoring" among components for a "personalized learning approach" (114th Congress, 2015, p. S.1177-18). In determining who can provide "high quality academic tutoring" the local education agency may select from "a variety of providers of such tutoring that are selected and approved by the State and appear on the State’s list of such providers" (pp. S. 1177-18 - S. 1177-19).

Tutoring Programs

Evidence for ESSA includes research-based math programs for struggling students that have been rated for their effectiveness for tutoring.  The following are among those and rated as "strong."


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114th Congress of the United States. (2015). Every Student Succeeds Act.

Barshay, J. (2021, August 25). The science of catching up. The Hechinger Report.  

Beilock, S., & Maloney, E. (2015). Math anxiety: A factor in math achievement not to be ignored. Policy Insights from the Behavioral and Brain Sciences, 2(1), 4-12. doi: 10.1177/2372732215601438. 

Blazer, C. (2011). Strategies for reducing math anxiety. Information Capsule IC1102. Miami, FL: Miami Dade County Public Schools, Research Services, Office of Assessment, Research, and Data Analysis.

Bracey, G. (2009). The big tests: What ends do they serve? Educational Leadership, 67(3), 32-37.

Carey, E., Hill, F., Devine, A., & Szücs, D.(2016, January) The chicken or the egg? The direction of the relationship between mathematics anxiety and mathematics performance. Frontiers in Psychology, 6, article 1987. doi: 10.3389/fpsyg.2015.01987.

Croft, M. (2014, October). The end of erasures: Updating test security laws and policies for computerized testing.

Data Recognition Corporation. (2017). Guidelines to inclusive test administration. Maple Grove, MN: Author.

Digitale, E. (2012, March 21). Imaging study reveals differences in brain function for children with math anxiety. Stanford, CA: Stanford University School of Medicine.

Doorey, N. (2014). The common core assessments: What you need to know. Educational Leadership, 71(6), 57-60.

Gewertz, C. (2013, March 5). Assessment consortium releases testing time estimates.

Gordon, E. (2006, November 29). America needs to wise up about need for quality tutoring. Chicago Sun-Times.

Gullen, K. (2014). Are our kids ready for computerized tests? Educational Leadership, 71(6), 68-71.

Herman, J. L., & Baker, E. L. (2005). Making benchmark testing work. Educational Leadership, 63(3), 48-54.

Howard-Jones, P. (2014, January). Neuroscience and education: A review of educational interventions and approaches by neuroscience. London, UK: Education Endowment Foundation. 

Jenifer, J. B., Rosek, C. S., Levine, S. C., & Beilock, S. L. (2022, March 14). Effort(less) exam preparation: Math anxiety predicts the avoidance of effortful study strategies. Journal of Experimental Psychology: General. Advance online publication.

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.

Mehrens, W. A. (1989). Preparing students to take standardized achievement tests. Practical Assessment, Research & Evaluation, 1(11).

Miller, A. (2014, April 24). School CIO: It's bigger than the backbone: 4 steps to prepare teachers for CCSS assessments.  

National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.

National Student Support Accelerator. (n.d.). What is the Accelerator? Annenberg Institute at Brown University.

O'Shea, M. (2005). From standards to success. Alexandria, VA: ASCD.

Pellegrini, M., Lake, C., Inns, A., & Slavin, R. E. (2018, October). Effective programs in elementary mathematics: A best-evidence synthesis. Baltimore, MD: Center for Research and Reform in Education, Johns Hopkins University.

Popham, W. J. (2014). Criterion-referenced measurement: Half a century wasted? Educational Leadership, 71(6), 62-66.

Popham, W. J. (2016). Standardized tests: Purpose is the point. Educational Leadership, 73(7), 44-49.

Ramirez, G., & Beilock, S. (2011). Writing about testing worries boosts exam performance in the classroom. Science, 331, 211-213.

Reeves, D. (2004). Accountability for learning: How teachers and school leaders can take charge. Alexandria, VA: ASCD. ISBN: 0-87120-833-4.

Silver, H., Strong, R., & Perini, M. (2007). The strategic teacher: Selecting the right research-based strategy for every lesson. Alexandria, VA: ASCD.

Slavin, R. (2018, April 5). New findings on tutoring: Four shockers. Robert Slavin's Blog.

Slavin, R. (2019, April 11). Benchmark assessments: Weighing the pig more often? Robert Slavin's Blog.

Slavin, R. (2020, April 23). A Marshall plan for post COVID-19 recovery. Robert Slavin's Blog.

Slavin, R. (2021, February 11). Avoiding the errors of supplemental educational services (SES). Robert Slavin's Blog.

Stanford University Medical Center. (2015, September 8). Tutoring relieves math anxiety, changes fear circuits in children. ScienceDaily.

Tomlinson, C. A. (2000). Reconcilable differences? Standards-based teaching and differentiation. Educational Leadership, 58(1), 6-11.

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.



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Binoculars GifGo to Preparing Your Students for the Ohio Graduation Test in Mathematics


Binoculars GifSee related topics: Math Resources and Math Manipulatives.