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Standardized Test Preparation and
Tips for Success

Test Prep Advice, Math Anxiety, and Tutoring

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Standardized Test Preparation and Tips for Success includes two pages of resources:

Test Prep Resources (Page 1) address the following:

Arrow: You are hereTest Prep Resources (Page 2):

 

Bullseye GifTarget your test prep with CT4ME resources!

 

Sunshine gif with smiling mask and pencil marking correct test answerSee 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.

Our extensive collection of math resources for elementary, middle, and high school are also beneficial to help learners master concepts within state standards.

CT4ME developed a free Test-Prep KWL Chart for students to use to help them monitor their test preparation progress.

 

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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.

Six Steps to Success Puzzle Pieces GifTest prep is a reality and there are steps you can follow to ensure success.

1. Become Familiar with Updated Policies for Computerized Testing

Step 1 Diagnostic ToolComputerized 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.

2. Use Effective Test Prep Strategies with Learners

Step 2 Textbook Reading TipsGood instruction is the best test preparation!  So how does one plan for good instruction?  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).

Use standards, benchmarks, and a diagnostic tool.  For many teachers, instruction has come to mean addressing as many standards as possible.  A standard is the goal that we wish students to attain and the benchmark is the assessment used to test a student's progress toward reaching the goal.  It identifies the student's strengths and weaknesses and is then used to inform future instruction.  However, state exams do not test every benchmark annually.

Benchmarking tests could be given periodically, perhaps every nine weeks, to monitor progress in mastering standards and objectives.  Such tests might be developed by districts.  However, the best test-prep will include that teachers integrate the kinds of questions that learners will encounter into their every day lessons.

A diagnostic tool, or a formative assessment tool (screening, progress, and diagnostic) will help educators identify specific areas of weakness that students might have, and will also help educators to tailor their classroom instruction to meet the needs of students.  It can also be used before planning a unit of instruction.  The Northwest Evaluation Association's Measures of Academic Progress is a possible tool.  These are Common Core-aligned assessments that provide information about student achievement and growth.

Although a diagnostic test with item analyses reveals weaknesses in concepts and content related to strands tested, teachers will still need to delve deeper into an analysis of why students missed certain questions.  At a second level, student literacy skills might have played a role in not answering a question correctly.

To assist teachers with providing good instruction leading to improved student outcomes, Mark 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.  In Making Benchmark Testing Work, they provided the following six criteria to help educators make benchmark testing effective:

  1. Alignment: Standards and benchmark assessments should be aligned from the beginning of test development.
  2. Diagnostic Value: Enhance the diagnostic value of assessment results through initial item and test structure design.  Distracters should be built into multiple choice items to reveal common student misunderstandings.  Likewise, extended response items should reveal students' potential misconceptions.
  3. Fairness: To ensure fairness for all students, including English language learners and students with disabilities, language used should not be unnecessarily complex.  Contexts used should be familiar to student subgroups and not hinder them from demonstrating what they know.  The test should provide "useful feedback for instructional planning for individuals and groups."
  4. Technical Quality: Data should reveal technical quality and include psychometric indices that reveal the reliability of the assessments.  This ensures you can trust the scores (e.g., reliability, inter-rater reliability, validity).
  5. Utility: Reports should be user-friendly so that educators can easily interpret results.  Schools might need to provide additional guidance and support for teachers to use the results (e.g., pedagogical knowledge, alternative materials, teams to analyze results).  To be useful, the key here is to provide test results quickly and train users to interpret information correctly.
  6. Feasibility: Benchmark testing should be worth the time and money.  The test should focus attention on student performance and provide solid information on which to base improvement efforts.  Such tests require systematic design and continual evaluation to improve their quality.  "Like state assessments, benchmark tests will fulfill their promise only if we monitor their consequences."

Provide tips for how to read and learn from a math textbook.  Inspite of having a math textbook, students don't necessarily read it and depend on their teachers to provide all the "how-to's."  In keeping with Silver, Strong, and Perini (2007), students need reading and study skills.  Consider providing students with tips for How to Learn from a Math Book, suggested by Cynthia Arem and Paul Nolting:

How-to-study.com also has tips for reading a math textbook.

In order to "make sense of abstract academic vocabulary" per Silver, Strong, and Perini (2007) and do well on standardized tests, students need to know and understand what those key vocabulary terms are.  You might ask students to note specialized math terminology used within questions posed when solving problems and ask them to define these in their own words.  You might be amazed at how many students have difficulty with the key action words and math vocabulary.

If students do not know the meaning of words within test items, they cannot complete the problems successfully.  Marileee Sprenger (2021) created "a list of 25 essential high-frequency words that are used in standardized assessments and other academic contexts across states and grade levels."  They Include: "analyze, cite, compare, contrast, demonstrate, describe, details, determine, develop, distinguish, evaluate, evidence, explain, infer, interpret, main idea, paraphrase, persuade, point of view, relevant, structure, summarize, support, theme, and trace" (Introduction section).  Such words are not typical of everyday speech.  Encourage students to use correct mathematical vocabulary in discussion and in their writing.

Review problem solving strategies.  Emphasize that often there is more than one way to solve a problem.  Provide students with problems that use those strategies, which generally fall into the following categories:

Problem Solving Strategies
Compute or simplify Use a formula Make a model
Make a table, list, or chart Guess, check, and revise Determine if problem requires a single-step or multiple-steps to solve
Solve a simpler case or work backwards Look for a pattern Write an equation
Eliminate possible solutions and/or extra information Draw a picture or diagram Use logical reasoning

As Reeves recommended, extensive writing is the best preparation for state tests (2004).  Writing helps students to make sense of mathematics and helps them to identify what they know or don't know.  As students tackle problems, stress George Polya's (author of "How to Solve It") problem solving steps:  The four steps are:

Visual students might then appreciate the How to Solve It Mind Map posted at GoGeometry.com.  It is interactive illustrating Polya's steps with key questions to consider at each stage in problem solving.

Use online resources for each strand to reinforce understanding and for concept development, including paper and online practice tests.  Select resources related to any weaknesses students have demonstrated on benchmark and formative testing.  CT4ME has numerous resources related to each strand in the Common Core math standards for high school learners to help in your selection.  For each, you will find technology-enhanced investigations, multiple choice and constructed response questions, and performance tasks.

When students feel confident that they have mastered objectives, they should complete a few practice tests and released test items from your state.  Practice tests should be scored using the same rubric as will be used on the actual test.  CT4ME has links to K-12 testing in each state and additional resources with other tips and test prep materials.

Review techniques for test-taking, including overcoming anxiety.  As noted in Kercheval and Newbill (2002), effective test preparation included direct instruction in test-taking skills.  As such, students should know the testing format, test instructions, and procedures they will follow on test day.  They should know how test items will be scored.  Review techniques for completing multiple choice, short-answer and extended response questions, as the math exam will contain these three types.  Learners need to know about the mechanics of test taking, such as distracters, adhering to time limits, working with bubble sheets or online testing formats, reading and following test directions, and using deductive thinking to eliminate incorrect answers.

For multiple choice questions, remind learners to read the entire question before attempting to answer it, try to answer the question without looking at the choices first, and not to keep changing an answer because usually learners' first choice is the right one, unless they did not read the question correctly.  Beyond reading directions carefully, tips for short-answer and extended response questions include to not give personal opinion when the question asks for facts, reread the response after completing it to ensure it addresses all parts of the question and is accurate.  Learners should focus on one main idea per paragraph.  If there is time remaining, proofread work and correct any errors.  To accurately answer short-answer and extended response questions, students also should know the meaning of specific performance verbs, such as those presented in Sprenger (2021) (e.g., analyze, compare, describe, evaluate, explain, formulate, infer, predict, summarize, support, trace).

As learners prepare for the actual test, they might have some test anxiety.  How-to-study.com has a short assessment to determine whether you have test anxiety and what to do about it.  Cuesta College provides relaxation techniques and how to overcome negative self-talk in How to Reduce Test Anxiety.  You'll also find other test taking and study strategies for math.  There's more on math anxiety below.

3. Ensure Learners Acquire Technology Skills

Kid on a computer imageStep 3 Problem Solving StrategiesWhat 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.

4. Teach to the Standards, Not to the Test

Taming the Test iconStep 4 Test TechniquesWe 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 or your state standards.  Teachers have been doing it for as long as standardized tests have been used to make important educational decisions.

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

Ethical:

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

Typically Ethical:

  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).

Unethical:

  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.

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).

Ultimately, students should have clear knowledge of which benchmarks they have not yet mastered.  Consider posting standards and benchmarks for mastery in your classroom and providing each student with a copy from which they can monitor their progress.  However, keep in mind that posting standards and benchmarks in your classroom and just reading them does not mean that students understand what mastery means.  For them to take responsibility, they must be able to self-assess and self-adjust their learning from standards that are broken down into meaningful components.  A good way to do this would be to provide students with K-W-L charts to help them keep track of the standard and benchmark, the resource(s) they used to address it, what they know, would like to know, and what they learned from the resource they used.  CT4ME developed a free Test-Prep KWL Chart for this purpose. 

 

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.

 

5. Consider the Big Picture--Everyone Counts

Step 5 Use Web ResourcesA 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 illustrated a culture change that must take place within districts to focus on student outcomes and illustrated that test preparation and standards-based instruction are 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.

6. Use Strategies to Minimize Math Anxiety

Step 6 Practice TestsMuch has been written about the role of math anxiety and how it affects a student's performance in mathematics.  Fortunately, there are instructional strategies that teachers can use to help minimize it and strategies that students can use, which you will find in the next section devoted to it.

Test SuccessFinally, the above strategies should lead to TEST SUCCESS!  But, after all this preparation, remind students to get a good rest the night before and to eat a good breakfast on test day.  These strategies have given them the confidence they need to do well.

 

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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)

Symptoms

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 Mathpower.com.  How-to-study.com 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. 9).  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. 16-17).  "His team’s observations show[ed] that math anxiety is neurobiologically similar to other kinds of anxiety or phobias" (para. 11).  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 youcubed.org 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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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, the Stanford University Medical Center (2015) has found that "Anxiety about doing math problems can be relieved with a one-on-one math tutoring program. ... The tutoring fixed abnormal responses in the brain's fear circuits."  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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References

114th Congress of the United States. (2015). Every Student Succeeds Act. https://www.ed.gov/esea

Barshay, J. (2021, August 25). The science of catching up. The Hechinger Report. https://hechingerreport.org/the-science-of-catching-up/  

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. https://www.semanticscholar.org/paper/Math-Anxiety-:-A-Factor-in-Math-Achievement-Not-to-Beilock-Maloney/eb27c4852d9adfeec98814f0b76de62832e88283 

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. http://drs.dadeschools.net/InformationCapsules/IC1102.pdf

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.  https://www.frontiersin.org/articles/10.3389/fpsyg.2015.01987/full

Croft, M. (2014, October). The end of erasures: Updating test security laws and policies for computerized testing. https://www.act.org/content/dam/act/unsecured/documents/End-of-Erasures-Issue-Brief.pdf

Digitale, E. (2012, March 21). Imaging study reveals differences in brain function for children with math anxiety. Stanford, CA: Stanford University School of Medicine.  https://med.stanford.edu/news/all-news/2012/03/imaging-study-reveals-differences-in-brain-function-for-children-with-math-anxiety.html

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. https://www.edweek.org/teaching-learning/assessment-consortium-releases-testing-time-estimates/2013/03

Gordon, E. (2006, November 29). America needs to wise up about need for quality tutoring. Chicago Sun-Times. https://www.pressreader.com/usa/chicago-sun-times/20061129/281964603226358

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. https://www.ascd.org/el/articles/making-benchmark-testing-work

Howard-Jones, P. (2014, January). Neuroscience and education: A review of educational interventions and approaches by neuroscience. London, UK: Education Endowment Foundation. https://educationendowmentfoundation.org.uk/public/files/Presentations/Publications/EEF_Lit_Review_NeuroscienceAndEducation.pdf 

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. http://dx.doi.org/10.1037/xge0001202

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. http://technical.allofe.com/gen/corp_generated_bin/documents/basic_module/Indiana_Effective_Practices.pdf

Mehrens, W. A. (1989). Preparing students to take standardized achievement tests. Practical Assessment, Research & Evaluation, 1(11). https://scholarworks.umass.edu/pare/vol1/iss1/11/

Miller, A. (2014, April 24). School CIO: It's bigger than the backbone: 4 steps to prepare teachers for CCSS assessments. https://www.techlearning.com/news/school-cio-its-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. https://files.eric.ed.gov/fulltext/ED500486.pdf

National Student Support Accelerator. (n.d.). What is the Accelerator? Annenberg Institute at Brown University. https://studentsupportaccelerator.com

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. https://web.archive.org/web/20200331134549/http://www.bestevidence.org/word/elem_math_Oct_8_2018.pdf

Ramirez, G., & Beilock, S. (2011). Writing about testing worries boosts exam performance in the classroom. Science, 331, 211-213. https://science.sciencemag.org/content/331/6014/211/tab-pdf

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. https://robertslavinsblog.wordpress.com/2018/04/05/new-findings-on-tutoring-four-shockers/

Slavin, R. (2020, April 23). A Marshall plan for post COVID-19 recovery. Robert Slavin's Blog. https://robertslavinsblog.wordpress.com/2020/04/23/a-marshall-plan-for-post-covid-19-recovery/

Slavin, R. (2021, February 11). Avoiding the errors of supplemental educational services (SES). Robert Slavin's Blog. https://robertslavinsblog.wordpress.com/2021/02/11/avoiding-the-errors-of-supplemental-educational-services-ses/

Sprenger, M. (2021). The essential 25: Teaching the vocabulary that makes or breaks student understanding. Alexandria, VA: ASCD.

Stanford University Medical Center. (2015, September 8). Tutoring relieves math anxiety, changes fear circuits in children. ScienceDaily. https://www.sciencedaily.com/releases/2015/09/150908180441.htm

Tomlinson, C. A. (2000). Reconcilable differences? Standards-based teaching and differentiation. Educational Leadership, 58(1), 6-11. https://www.ascd.org/el/articles/reconcilable-differences-standards-based-teaching-and-differentiation

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. https://files.eric.ed.gov/fulltext/ED508674.pdf

 

 

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