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CASE STUDY UNIT

Mathematics: Identifying and Addressing

Student Errors

Created by Janice Brown, PhD, Vanderbilt UniversityKim Skow, MEd, Vanderbilt University

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The contents of this resource were developed under a grant from the U.S. Department of Education, #H325E120002. However, those contents do not necessarily represent the policy of the U.S. Department of Education, and you should not assume endorse- ment by the Federal Government. Project Officer, Sarah Allen

Mathematics: Identifying and Addressing Student Errors

Contents: Page

Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ii Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv STAR Sheets

Collecting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Identifying Error Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Word Problems: Additional Error Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Determining Reasons for Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Addressing Error Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Case Studies Level A, Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Level A, Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Level B, Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Level B, Case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Level C, Case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Answer Key . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

TABLE OF CONTENTS

* For an Answer Key to this case study, please email your full name, title, and institutional affiliation to the IRIS Center at iris@vanderbilt .edu .

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To Cite This Case Study Unit

Brown J ., Skow K ., & the IRIS Center . (2016) . Mathematics: Identifying and addressing student errors. Retrieved from http:// iris .peabody .vanderbilt .edu/case_studies/ics_matherr .pdf

Content Contributors

Janice Brown Kim Skow

Case Study Developers

Janice Brown Kim Skow

Editor Jason Miller

Reviewers

Diane Pedrotty Bryant David Chard Kimberly Paulsen Sarah Powell Paul Riccomini

Graphics Brenda KnightPage 27- Geoboard Credit: Kyle Trevethan

Mathematics: Identifying and Addressing Student Errors

CREDITS

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Mathematics: Identifying and Addressing Student Errors

STANDARDS

Licensure and Content Standards This IRIS Case Study aligns with the following licensure and program standards and topic areas .

Council for the Accreditation of Educator Preparation (CAEP) CAEP standards for the accreditation of educators are designed to improve the quality and effectiveness not only of new instructional practitioners but also the evidence-base used to assess those qualities in the classroom .

• Standard 1: Content and Pedagogical Knowledge

Council for Exceptional Children (CEC) CEC standards encompass a wide range of ethics, standards, and practices created to help guide those who have taken on the crucial role of educating students with disabilities .

• Standard 1: Learner Development and Individual Learning Differences

Interstate Teacher Assessment and Support Consortium (InTASC) InTASC Model Core Teaching Standards are designed to help teachers of all grade levels and content areas to prepare their students either for college or for employment following graduation .

• Standard 6: Assessment • Standard 7: Planning for Instruction

National Council for Accreditation of Teacher Education (NCATE) NCATE standards are intended to serve as professional guidelines for educators . They also overview the “organizational structures, policies, and procedures” necessary to support them

• Standard 1: Candidate Knowledge, Skills, and Professional Dispositions

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Error analysis is a type of diagnostic assessment that can help a teacher determine what types of errors a student is making and why . More specifically, it is the process of identifying and reviewing a student’s errors to determine whether an error pattern exists—that is, whether a student is making the same type of error consistently . If a pattern does exist, the teacher can identify a student’s misconceptions or skill deficits and subsequently design and implement instruction to address that student’s specific needs . Research on error analysis is not new: Researchers around the world have been conducting studies on this topic for decades . Error analysis has been shown to be an effective method for identifying patterns of mathematical errors for any student, with or without disabilities, who is struggling in mathematics .

Steps for Conducting an Error Analysis An error analysis consists of the following steps: Step 1. Collect data: Ask the student to complete at least 3 to 5 problems of the same type (e .g .,

multi-digit multiplication) . Step 2. Identify error patterns: Review the student’s solutions, looking for consistent error patterns

(e .g ., errors involving regrouping) . Step 3. Determine reasons for errors: Find out why the student is making these errors . Step 4. Use the data to address error patterns: Decide what type of instructional strategy will best

address a student’s skill deficits or misunderstandings .

Benefits of Error AnalysisBenefits of Error Analysis An error analysis can help a teacher to:

• Identify which steps the student is able to perform correctly (as opposed to simply marking answers either correct or incorrect, something that might mask what it is that the student is doing right)

• Determine what type(s) of errors a student is making • Determine whether an error is a one-time miscalculation or a persistent issue that

indicates an important misunderstanding of a mathematic concept or procedure • Select an effective instructional approach to address the student’s misconceptions and

to teach the correct concept, strategy, or procedure

Mathematics: Identifying and Addressing Student Errors

INTRODUCTION

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References Ashlock, R . B . (2010) . Error patterns in computation (10th ed .) . Boston: Allyn & Bacon . Ben-Zeev, T . (1998) . Rational errors and the mathematical mind . Review of General Psychology,

2(4), 366–383 . Cox, L . S . (1975) . Systematic errors in the four vertical algorithms in normal and handicapped

populations . Journal for Research in Mathematics Education, 6(4), 202–220 . Idris, S . (2011) . Error patterns in addition and subtraction for fractions among form two students .

Journal of Mathematics Education, 4(2), 35–54 . Kingsdorf, S ., & Krawec, J . (2014) . Error analysis of mathematical word problem solving across

students with and without learning disabilities . Learning Disabilities Research & Practice, 29(2), 66–74 .

Radatz, H . (1979) . Error analysis in mathematics education . Journal for Research in Mathematics Education, 10(3), 163–172 .

Riccomini, P . J . (2014) . Identifying and using error patterns to inform instruction for students struggling in mathematics. Webinar slideshow .

Yetkin, E . (2003) . Student difficulties in learning elementary mathematics . ERIC Clearinghouse for Science, Mathematics, and Environmental Education. Retrieved from http://www .ericdigests . org/2004-3/learning .html

References for the Following Cases Ashlock, R . B . (2010) . Error patterns in computation (10th ed .) . Boston: Allyn & Bacon . Sherman, H . J ., Richardson, L . I ., & Yard, G . J . (2009) . Teaching learners who struggle with

mathematics: Systematic invervention and remediation (2nd ed .) . Upper Saddle River, NJ: Merrill/Pearson .

Chapin, S . H . (1999) . Middle grades math: Tools for success (course 2): Practice workbook. New Jersey: Prentice-Hall .

☆ What a STAR Sheet isWhat a STAR Sheet is A STAR (STrategies And Resources) Sheet provides you with a description of a well- researched strategy that can help you solve the case studies in this unit .

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Mathematics: Identifying and Addressing Student Errors Collecting Data

STAR SHEET

About the Strategy Collecting data involves asking a student to complete a worksheet, test, or progress monitoring measure containing a number of problems of the same type .

What the Research and Resources Say • Error analysis data can be collected using formal (e .g ., chapter test, standardized test) or

informal (e .g ., homework, in-class worksheet) measures (Riccomini, 2014) . • Error analysis is one form of diagnostic assessment . The data collected can help teachers

understand why students are struggling to make progress on certain tasks and align instruction with the student’s specific needs (National Center on Intensive Intervention, n .d .; Kingsdorf & Krawec, 2014) .

• To help determine an error pattern, the data collection measure must contain at a minimum three to five problems of the same type (Special Connections, n .d .) .

Identifying Data Sources To conduct an error analysis for mathematics, the teacher must first collect data . She can do so by using a number of materials completed by the student (i .e ., student product) . These include worksheets, progress monitoring measures, assignments, quizzes, and chapter tests . Homework can also be used, assuming the teacher is confident that the student completed the assignment independently . Regardless of the type of student product used, it should contain at a minimum three to five problems of the same type . This allows a sufficient number of items with which to determine error patterns .

Scoring To better understand why students are struggling, the teacher should mark each incorrect digit in a student’s answer, as opposed to simply marking the entire answer incorrect . Evaluating each digit in the answer allows the teacher to more quickly and clearly identify the student’s error and to determine whether the student is consistently making this error across a number of problems . For example, take a moment to examine the worksheet below . By marking the incorrect digits, the teacher can determine that, although the student seems to understand basic math facts, he is not regrouping the “1” to the ten’s column in his addition problems . Note: Marking each incorrect digit might not always reveal the error pattern . Review the STAR Sheets Identifying Error Patterns, Word Problems: Additional Error Patterns, and Determining Reasons for Errors to learn about identifying the different types of errors students make .

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TipsTips • Typically, addition, subtraction, and multiplication problems should be

scored from RIGHT to LEFT . By scoring from right to left, the teacher will be sure to note incorrect digits in the place value columns . However, division problems should be scored LEFT to RIGHT .

• If the student is not using a traditional algorithm to arrive at a solution, but instead using a partial algorithm (e .g ., partial sums, partial products) then addition, subtraction, multiplication, and division problems should be scored from LEFT to RIGHT .

References Kingsdorf, S ., & Krawec, J . (2014) . Error analysis of mathematical word problem solving across

students with and without learning disabilities . Learning Disabilities Research and Practice, 29(2), 66–74 .

National Center on Intensive Intervention . (n .d .) . Informal academic diagnostic assessment: Using data to guide intensive instruction. Part 3: Miscue and skills analysis . PowerPoint slides . Retrieved from http://www .intensiveintervention .org/resource/informal-academic-diagnostic- assessment-using-data-guide-intensive-instruction-part-3

Riccomini, P . J . (2014) . Identifying and using error patterns to inform instruction for students struggling in mathematics . Webinar series, Region 14 State Support Team .

Special Connections . (n .d .) . Error pattern analysis . Retrieved from http://www .specialconnections . ku .edu/~specconn/page/instruction/math/pdf/patternanalysis .pdf

The University of Chicago School Mathematics Project . (n .d .) . Learning multiple methods for any mathematical operation: Algorithms. Retrieved from http://everydaymath .uchicago .edu/about/ why-it-works/multiple-methods/

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STAR SHEETSTAR SHEET Mathematics: Identifying and Addressing Student Errors

Identifying Error Patterns

About the Strategy Identifying error patterns refers to determining the type(s) of errors made by a student when he or she is solving mathematical problems .

What the Research and Resources Say Three to five errors on a particular type of problem constitute an error pattern (Howell, Fox, & Morehead, 1993; Radatz, 1979) . Typically, student mathematical errors fall into three broad categories: factual, procedural, and conceptual . Each of these errors is related either to a student’s lack of knowledge or a misunderstanding (Fisher & Frey, 2012; Riccomini, 2014) . Not every error is the result of a lack of knowledge or skill . Sometimes, a student will make a mistake simply because he was fatigued or distracted (i .e ., careless errors) (Fisher & Frey, 2012) . Procedural errors are the most common type of error (Riccomini, 2014) . Because conceptual and procedural knowledge often overlap, it is difficult to distinguish conceptual errors from procedural errors (Rittle-Johnson, Siegler, & Alibali, 2001; Riccomini, 2014) .

Types of Errors 1. Factual errors are errors due to a lack of factual information (e .g ., vocabulary, digit identification,

place value identification) . 2. Procedural errors are errors due to the incorrect performance of steps in a mathematical process

(e .g ., regrouping, decimal placement) . 3. Conceptual errors are errors due to misconceptions or a faulty understanding of the underlying

principles and ideas connected to the mathematical problem (e .g ., relationship among numbers, characteristics, and properties of shapes) .

FYI FYI Another type of error that a student might make is a careless error . The student fails to correctly solve a given mathematical problem despite having the necessary skills or knowledge . This might happen because the student is tired or distracted by activity elsewhere in the classroom . Although teachers can note the occurrence of such errors, doing so will do nothing to identify a student’s skill deficits . For many students, simply pointing out the error is all that is needed to correct it . However, it is important to note that students with learning disabilities often make careless errors .

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Common Factual Errors Factual errors occur when students lack factual information (e .g ., vocabulary, digit identification, place value identification) . Review the table below to learn about some of the common factual errors committed by students .

Factual Error Examples

Has not mastered basic number facts: The student does not know basic mathematics facts and makes errors when adding, subtracting, multiplying, or dividing single-digit numbers .

3 + 2 = 7 7 − 4 = 2 2 × 3 = 7 8 ÷ 4 = 3

Misidentifies signs 2 × 3 = 5 (The student identifies the multiplication sign as an addition sign .) 8 ÷ 4 = 4 (The student identifies the division sign as a minus sign .)

Misidentifies digits The student identifies a 5 as a 2 .

Makes counting errors 1, 2, 3, 4, 5, 7, 8, 9 (The student skips 6 .)

Does not know mathematical terms (vocabulary)

The student does not understand the meaning of terms such as numerator, denominator, greatest common factor, least common multiple, or circumference .

Does not know mathematical formulas The student does not know the formula for calculating the area of a circle .

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Procedural Error Examples Regrouping Errors

Forgetting to regroup: The student forgets to regroup (carry) when adding, multiplying, or subtracting .

77 + 54

121

The student added 7 + 4 correctly but didn’t regroup one group of 10 to the tens column .

123 − 76

53

The student does not regroup one group of 10 from the tens column, but instead subtracted the number that is less (3) from the greater number (6) in the ones column .

56 × 2 102

After multiplying 2 × 6, the student fails to regroup one group of 10 from the tens column .

Regrouping across a zero: When a problem contains one or more 0’s in the minuend (top number), the student is unsure of what to do .

304 − 21

323

The student subtracted the 0 from the 2 instead of regrouping .

Performing incorrect operation: Although able to correctly identify the signs (e .g ., addition, minus), students often subtract when they are suppose to add, or vice versa . However, students might also perform other incorrect operations, such as multiplying instead of adding .

234 − 45

279

The student added instead of subtracting .

3 + 2

6

The student multiplied instead of adding .

Fraction Errors Failure to find common denominator when adding and subtracting fractions

3 1 4 — + — = — 4 3 7

The student added the numerators and then the denominators without finding the common denominator .

Failure to invert and then multiply when dividing fractions 1 1 2 2

— ÷ 2 = — × — = — = 1 2 2 1 2

The student did not invert the 2 to before multiplying to get the correct answer of .

Failure to change the denominator in multiplying fractions 2 5 10 — × — = — 8 8 8

The student did not multiply the denominators to get the correct answer .

Incorrectly converting a mixed number to an improper fraction

1 4 1— = — 2 2

To find the numerator, the student added 2 + 1 + 1 to get 4, instead of following the correct procedure ( 2 × 1 + 1 = 3 ) .

Common Procedural Errors Procedural knowledge is an understanding of what steps or procedures are required to solve a problem . Procedural errors occur when a student incorrectly applies a rule or an algorithm (i .e ., the formula or step-by-step procedure for solving a problem) . Review the table below to learn more about some common procedural errors .

1 4

1 2

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Common Conceptual Errors Conceptual knowledge is an understanding of underlying ideas and principles and a recognition of when to apply them . It also involves understanding the relationships among ideas and principles . Conceptual errors occur when a student holds misconceptions or lacks understanding of the underlying principles and ideas related to a given mathematical problem (e .g ., the relationship between numbers, the characteristics and properties of shapes) . Examine the table below to learn more about some common conceptual errors .

Conceptual Error Examples Misunderstanding of place value: The student doesn’t understand place value and records the answer so that the numbers are not in the appropriate place value position .

67 + 4

17

The student added all the numbers together ( 6 + 7 + 4 = 17 ), not understanding the values of the ones and tens columns .

10 + 9

91

The student recorded the answer with the numbers reversed, disregarding the appropriate place value position of the numbers or digits .

Write the following as a number:

When expressing a number beyond two digits, the student does not have a conceptual understanding of the place value position .

a) seventy-six b) nine hundred seventy-

four c) six thousand, six

hundred twenty-four

Student answer: a) 76 b) 90074 c) 600060024

Procedural Error cont Examples cont Decimal Errors

Not aligning decimal points when adding or subtracting: The student aligns the numbers without regard to where the decimal is located .

120 .4 +

63 .21 75 .25

The student did not align the decimal points to show digits in like places . In this case, .4 and .2 are in the tenths place and should be aligned .

Not placing decimal in appropriate place when multiplying or dividing: The student does not count and add the number of decimal places in each factor to determine the number of decimal places in the product . Note: This could also be a conceptual error related to place value.

3 .4 × .2

6 .8

As with adding or subtracting, the student aligns the decimal point in the product with the decimal points in the factors . The student did not count and add the number of decimal places in each factor to determine the number of decimal places in the product

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Conceptual Error cont . Examples cont .

Overgeneralization: Because of lack of conceptual understanding, the student incorrectly applies rules or knowledge to novel situations .

321 −

245 124

Regardless of whether the greater number is in the minuend (top number) or subtrahend (bottom number), the student always subtracts the number that is less from the greater number, as is done with single-digit subtraction .

Put the following fractions in order from smallest to largest .

The student puts fractions in the order , , , because he doesn’t understand the relation between the numerator and its denominator; that is, larger denominators mean smaller fractional parts .

Overspecialization: Because of lack of conceptual understanding, the student develops an overly narrow definition of a given concept or of when to apply a rule or algorithm .

Which of the triangles below are right triangles?

The student chooses a because she only associates a right triangle with those with the same orientation as a .

a)

b)

c) both

Student answer: a

90˚

12 200

1 351

77 486

12 200

1 351

77 486

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References Ashlock, R . B . (2010) . Error patterns in computation (10th ed .) . Boston: Allyn & Bacon . Ben-Hur, M . (2006) . Concept-rich mathematics instruction . Alexandria, VA: ASCD . Cohen, L . G ., & Spenciner, L . J . (2007) . Assessment of children and youth with special needs (3rd

ed .) . Upper Saddle River, NJ: Pearson . Educational Research Newsletter and Webinars . (n .d .) . Students’ common errors in working with

fractions . Retrieved from http://www .ernweb .com/educational-research-articles/students- common-errors-misconceptions-about-fractions/

El Paso Community College . (2009) . Common mistakes: Decimals. Retrieved from http://www . epcc .edu/CollegeReadiness/Documents/Decimals_0-40 .pdf

El Paso Community College . (2009) . Common mistakes: Fractions . Retrieved from http://www . epcc .edu/CollegeReadiness/Documents/Fractions_0-40 .pdf

Fisher, D ., & Frey, N . (2012) . Making time for feedback . Feedback for Learning, 70(1), 42–46 . Howell, K . W ., Fox, S ., & Morehead, M . K . (1993) . Curriculum-based evaluation: Teaching and

decision-making. Pacific Grove, CA: Brooks/Cole . National Council of Teachers of Mathematics . (2000) . Principles and standards for school

mathematics . Reston, VA: Author . Riccomini, P . J . (2014) . Identifying and using error patterns to inform instruction for students

struggling in mathematics . Webinar series, Region 14 State Support Team . Radatz, H . (1979) . Error analysis in mathematics education . Journal for Research in Mathematics

Education, 10(3), 163–172 . Rittle-Johnson, B ., Siegler, R . S ., & Alibali, M . W . ( 2001) . Developing conceptual understanding

and procedural skill in mathematics: An iterative process . Journal of Educational Psychology, 93(2), 346–362 .

Sherman, H . J ., Richardson, L . I ., & Yard, G . J . (2009) . Teaching learners who struggle with mathematics: Systematic intervention and remediation (2nd ed .) . Upper Saddle River, NJ: Merrill/Pearson .

Siegler, R ., Carpenter, T ., Fennell, F ., Geary, D ., Lewis, J ., Okamoto, Y ., Thompson, L ., & Wray, J . (2010) . Developing effective fractions instruction for kindergarten through 8th grade: A practice guide (NCEE #2010-4039) . Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U .S . Department of Education . Retrieved from http://ies .ed .gov/ncee/wwc/pdf/practice_guides/fractions_pg_093010 .pdf

Special Connections . (n .d .) . Error pattern analysis. Retrieved from http://www .specialconnections . ku .edu/~specconn/page/instruction/math/pdf/patternanalysis .pdf

Yetkin, E . (2003) . Student difficulties in learning elementary mathematics. ERIC Clearinghouse for Science, Mathematics, and Environmental Education . Retrieved from http://www .ericdigests . org/2004-3/learning .html

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STAR SHEETSTAR SHEET Mathematics: Identifying and Addressing Student Errors

Word Problems: Additional Error Patterns

About the Strategy A word problem presents a hypothetical real-world scenario that requires a student to apply mathematical knowledge and reasoning to reach a solution .

What the Research and Resources Say • Students consider computational exercises more difficult when they are expressed as word

problems rather than as number sentences (e .g ., 3 + 2 =) (Sherman, Richardson, & Yard, 2009) .

• When they solve word problems, students struggle most with understanding what the problem is asking them to do . More specifically, students might not recognize the problem type and therefore do not know what strategy to use to solve it (Jitendra et al ., 2007; Sherman, Richardson, & Yard, 2009; Powell, 2011; Shin & Bryant, 2015) .

• Word problems require a number of skills to solve (e .g ., reading text, comprehending text, translating the text into a number sentence, determining the correct algorithm to use) . As a result, many students, especially those with math and/or reading difficulties, find word problems challenging (Powell, Fuchs, Fuchs, Cirino, & Fletcher, 2009; Reys, Lindquist, Lambdin, & Smith, 2015) .

• Word problems are especially difficult for students with learning disabilities (Krawec, 2014; Shin & Bryant, 2015) .

Common Difficulties Associated with Solving Word Problems A student might solve word problems incorrectly due to factual, procedural, or conceptual errors . However, a student might encounter additional difficulties when trying to solve word problems, many of which are associated with reading skill deficits, such as those described below . Poor vocabulary knowledge: The student does not understand many mathematics terms (e .g ., difference, factor, denominator) . Limited reading skills: The student has difficulty reading text with vocabulary and complex sentence structure . Because of this, the student struggles to understand what is being asked . Inability to identify relevant information: The student has difficulty determining which pieces of information are relevant and which are irrelevant to solving the problem . Lack of prior knowledge: The student has limited experience with the context in which the problem is embedded . For example, a student unfamiliar with cooking might have difficulty solving a fraction problem presented within the context of baking a pie . Inability to translate the information into a mathematical equation: The student has difficulty translating the information in the word problem into a mathematical equation that they can solve . More specifically, the student might not be able to put the numbers in the correct order in the equation or determine the correct operation to use .

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Example The word problem below illustrates why students might have difficulty solving this type of problem .

Jonathan would like to buy a new 21-speed bicycle. The bike costs $119.76. Jonathan received $25 for his birthday. He also worked for 3 months last summer and earned $59.50. Find the difference between what the bike costs and the amount of money Jonathan has.

In addition to solving this word problem incorrectly due to factual, procedural, or conceptual errors, the student might struggle for reasons related to reading skill deficits .

• Poor vocabulary knowledge—The student might be unfamiliar with the term difference . • Limited reading skills—The student might struggle with the problem’s final sentence because of

its complex structure . If the student doesn’t understand some of the vocabulary (e .g ., received, earned), it might impede his or her ability to solve the problem .

• Inability to identify relevant information—The student might attend to irrelevant information, such as the type of bicycle or the number of months Jonathan worked, and therefore solve the problem incorrectly .

• Lack of prior knowledge—The student might have limited knowledge about the process of making purchases .

• Inability to translate information into a mathematical equation—The student might have difficulty determining which operations to perform with which numbers . This situation might be made worse in cases involving problems with multiple steps .

References Jitendra, A . K ., Griffin, C . C ., Haria, P ., Leh, J ., Adams, A ., & Kaduvettoor, A . (2007) . A

comparison of single and multiple strategy instruction on third-grade students’ mathematical problem solving . Journal of Educational Psychology, 99(1), 115–127 .

Krawec, J . L . (2014) . Problem representation and mathematical problem solving of students of varying math ability . Journal of Learning Disabilities, 47(2), 103–115 .

Powell, S . R . (2011) . Solving word problems using schemas: A review of the literature . Learning Disabilities Research & Practice, 26(2), 94–108 .

Powell, S . R ., Fuchs, L . S ., Fuchs, D ., Cirino, P . T ., & Fletcher, J . M . (2009) . Do word-problem features differentially affect problem difficulty as a function of students’ mathematics difficulty with and without reading difficulty? Journal of Learning Disabilities 20(10), 1–12

Reys, R ., Lindquist, M . M ., Lambdin, D . V ., & Smith, N . L . (2015) . Helping children learn mathematics (11th ed .) . Hoboken, NJ: John Wiley & Sons .

Sherman, H . J ., Richardson, L . I ., & Yard, G . J . (2009) . Teaching learners who struggle with mathematics: Systematic intervention and remediation (2nd ed .) . Upper Saddle River, NJ: Merrill/Pearson .

Shin, M ., & Bryant, D . P . (2015) . A synthesis of mathematical and cognitive performances of students with mathematics learning disabilities . Journal of Learning Disabilities, 48(1), 96–112 .

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Mathematics: Identifying and Addressing Student Errors Determining Reasons for Errors

CASE STUDY

About the Strategy Determining the reason for errors is the process through which teachers determine why the student is making a particular type of error .

What the Research and Resources Say • To help them to improve their mathematical performance, teachers must first identify and

understand why students make particular errors (Radatz, 1979; Yetkin, 2003) . • Typically, a student’s errors are not random; instead, they are often based on incorrect

algorithms or procedures applied systematically (Cox, 1975; Ben-Zeev, 1998) . • Knowing what a student is thinking when she is solving a problem can be a rich source of

information about what she does and does not understand (Hunt & Little, 2014; Baldwin & Yun, 2012) .

Helpful Strategies Determining exactly why a student is making a particular error is important in that it informs the teacher’s instructional response . Though it is sometimes obvious why a student is making a certain type of errors, at other times determining a reason proves more difficult . In these latter instances, the teacher can use one or more of the following strategies . Interview the student—It is sometimes unclear why a student is making a particular type of error . For example, it can be difficult for a teacher to distinguish between procedural or conceptual errors . For this reason, it can be beneficial to ask a student to talk through his or her process for solving the problem . Teachers can ask general questions such as “How did you come up with that answer?” or prompt the student with statements such as “Show me how you got that answer .” Another reason teachers might want to interview the student is to make sure the student has the prerequisite skills to solve the problem . Observe the student—A student might also reveal information through nonverbal means . This can include gestures, pauses, signs of frustration, and self-talk . The teacher can use information of this type to identify at what point in the problem-solving task that the student experiences difficulty or frustration . It can also help the teacher determine which procedure or set of rules a student is applying and why . Look for exceptions to an error pattern—In addition to looking for error patterns, a teacher should note instances when the student does not make the same error on the same type of problem . This, too, can be informative because it might indicate that the student has partial or basic understanding of the concept in question . For example, Cammy completed a worksheet on multiplying whole numbers by fractions . She seemed to get most of them wrong; however, she correctly answered the problems in which the fraction was . This seems to indicate that, though Cammy conceptually understands what of a whole is, she most likely does not know the process for multiplying whole numbers by fractions .

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Considerations for Students with Learning Disabilities Approximately 5–8% of students exhibit mathematics learning disabilities . Therefore, it is important to understand that their unique learning differences might impact their ability to learn and correctly choose and apply solution strategies to solve mathematics problems . A few characteristics that teachers might notice with students with learning disabilities is that these students often:

• Have difficulty mastering basic number facts • Make computational errors even though they might have a strong conceptual understanding • Have difficulty making the connection between concrete objects and semiabstract (visual

representations) or abstract knowledge or mathematical symbols • Struggle with mathematical terminology and written language • Have visual-spatial deficits, which result in difficulty visualizing mathematical concepts (although

this is quite rare)

References Baldwin, E . E ., & Yun, J . T . (2012) . Mathematics curricula and formative assessments: Toward an

error-based approach to formative data use in mathematics. Santa Barbara, CA: University of California Educational Evaluation Center .

Ben-Zeev, T . (1998) . Rational errors and the mathematical mind . Review of General Psychology, 2(4), 366–383 .

Cox, L . S . (1975) . Systematic errors in the four vertical algorithms in normal and handicapped populations . Journal for Research in Mathematics Education, 6(4), 202–220 .

Garnett, K . (n .d .) . Math learning disabilities . Retrieved from http://www .ldonline .org article/ Math_Learning_Disabilities

Hunt, H . H ., & Little, M . E . (2014) . Intensifying interventions for students by identifying and remediating conceptual understandings in mathematics . Teaching Exceptional Children, 46(6), 187–196 .

PBS, & the WGBH Educational Foundation . (2002) . Difficulties with mathematics. Retrieved from http://www .pbs .org/wgbh/misunderstoodminds/mathdiffs .html

Radatz, H . (1979) . Error analysis in mathematics education . Journal for Research in Mathematics Education, 10(3), 163–172 .

Sherman, H . J ., Richardson, L . I ., & Yard, G . J . (2009) . Teaching learners who struggle with mathematics: Systematic intervention and remediation. Upper Saddle River, NJ: Pearson .

Shin, M ., & Bryant, D . P . (2015) . A synthesis of mathematical and cognitive performances of students with mathematics learning disabilities . Journal of Learning Disabilities, 48(1), 96–112 .

Special Connections . (n .d .) . Error pattern analysis. Retrieved from http://specialconnections . ku .edu/~specconn/page/instruction/math/pdf/patternanalysis .pdf

Yetkin, E . (2003) . Student difficulties in learning elementary mathematics . ERIC Clearinghouse for Science, Mathematics, and Environmental Education . Retrieved from http://www .ericdigests . org/2004-3/learning .html

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STAR SHEET Mathematics: Identifying and Addressing Student Errors

Addressing Error Patterns

About the Strategy Addressing error patterns is the process of providing instruction that focuses on a student’s specific error .

What the Research and Resources Say • Students will continue to make procedural errors if they do not receive targeted instruction to

addresses those errors . Simply providing more opportunities to practice working a given problem is typically not effective (Riccomini, 2014) .

• By conducting an error analysis, the teacher can target specific misunderstandings or missteps, rather than re-teaching the entire skill or concept (Fisher & Frey, 2012) .

• Without intervention, students have been shown to continue to apply the same error patterns one year later (Cox, 1975) .

• Addressing a student’s conceptual errors might require the use of concrete or visual representations, as well as a great deal of re-teaching . Students can often use concrete objects to solve problems that they initially answered incorrectly (Riccomini, 2014; Yetkin, 2003) .

• Simply teaching the formula or the steps to solve a mathematics problem is typically not sufficient to help students gain conceptual understanding (Sweetland & Fogarty, 2008) .

How To Address Student Errors After the teacher has determined what types of error(s) a student is making, he or she can address the error in the following way . Discuss the error with the student: After the teacher has interviewed the student and examined work products, the teacher should briefly describe the student’s error and explain that they will work together to correct it . Provide effective instruction to address the student’s specific error: The teacher should target the student’s specific error instead of re-teaching how to work this type of problem in general . For example, if a student’s error is related to not regrouping during addition, the teacher should focus on where exactly in the process the student makes the error . The teacher must pinpoint the instruction to focus on the error and help the student to understand what he is doing incorrectly . Simply re-teaching the lesson will not ensure that the student understands the error and how to correctly solve the problem . Use effective strategies: With the type of error in mind, the teacher should select an effective strategy that will help to correct the student’s misunderstandings or missteps . Below are two effective strategies that teachers might find helpful to address some—if not all—error patterns .

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Manipulatives Manipulatives are concrete objects—for example, base-ten blocks, a geoboard, or integer chips—that a student can use to develop a conceptual understanding of mathematic topics . These objects help a student to represent the mathematical idea she is trying to learn or the problem she is trying to solve . For example, the teacher might demonstrate the idea of fractions by using fraction blocks or fraction strips . It is important that the teacher make explicit the connection between the concrete object and the abstract or the symbolic concept being taught . After a student has gained a basic understanding of the mathematical concept, the concrete objects should be replaced by visual representations such as images of a number line or geoboard (a small board with nails on which students stretch rubber bands to explore a variety of basic geometry concepts) . The goal is for the student to eventually understand and apply the concept with numerals and symbols . It is important that the teacher’s instruction match the needs of the student . Teachers should keep in mind that some students will need concrete objects to understand a concept, whereas others will be able to understand the concept using visual representations . Additionally, some students will require the support of concrete objects longer than will other students .

FYIFYI Recall that students with learning disabilities sometimes have visual-spatial deficits, which makes it difficult for them to learn concepts using visual representations . For these students, teachers should teach concepts using concrete materials accompanied by strong, precise verbal descriptions or explanations .

Keep in MindKeep in Mind The type of instruction a teacher uses to correct conceptual errors will likely differ from that used to address factual or procedural errors . Simply teaching a student the formula or the steps to solve a mathematics problem will not help the student gain conceptual understanding .

Geoboard Credit: Kyle Trevethan

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Explicit, systematic instruction Explicit, systematic instruction involves teaching a specific skill or concept in a highly structured environment using clear, direct language and incorporating the components listed in the table below .

Components of Explicit Instruction Modeling • The teacher models thinking aloud to demonstrate the completion of

a few sample problems . • The teacher leads the student through more sample problems . • The teacher points out difficult aspects of the problems .

Guided Practice • The student completes problems with the help of either teacher or peer guidance .

• The teacher monitors the student’s work . • The teacher offers positive corrective feedback .

Independent Practice

• The student completes the problems independently . • The teacher checks the student’s performance on independent

work . Adapted from Bender (2009), pp. 31–32

Reassess student skills: After providing instruction to correct the student’s error(s), the teacher should conduct a formal or informal assessment to make sure that the student has mastered the skill or concept in question .

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Instructional Tips • Check for prerequisite skills: Make sure the student has the prerequisite skills needed to solve

the problem with which he has been struggling . For example, if the student is making errors while adding two-digit numbers, the teacher needs to make sure the student knows basic math facts . If the student lacks the necessary pre-skills, the teacher should begin instruction at that point .

• Model examples and nonexamples: Be sure to model the completion of a minimum of three to five problems of the kind the student is struggling with . Add at least one nonexample of the error pattern to prevent overgeneralization (incorrectly applying the rule or knowledge to novel situations) and overspecialization (developing an overly narrow definition of the concept of or when to apply a rule or procedure) . For example, in the case of a student who does not regroup when subtracting, a teacher modeling how to solve this type of problem should also include problems that do not require regrouping .

• Pinpoint error: During modeling and guided practice, focus only on the place in the problem where the student makes an error . It is not necessary to work through the entire problem . For example, if the student’s error pattern is that she fails to find the common denominator when adding and subtracting fractions, the teacher would only model the process and explain the underlying conceptual knowledge of finding the common denominator . She would stop at that point, as opposed to completing the problem because the student knows the process from that point forward . The teacher should then continue in same manner for the remaining problems .

• Provide ample opportunities for practice: As with modeling, provide a minimum of three to five problems for guided practice, making sure to include a nonexample .

• Start with simple problems: During modeling and guided practice, begin with simple problems and gradually progress to more difficult ones as the student gains an understanding of the error and how to correctly complete the problem .

• Move the error around: When possible, move the error around so that it does not always occur in the same place . For example, if the student’s error is not regrouping when multiplying, the teacher should include examples that require regrouping in the ones and tens column, instead of always requiring the regrouping to occur in the ones column .

1 1 — + — 4 2

1 2 — + — 4 4

[Stop at this point because you have addressed the error pattern; the student knows how to add fractions.]

Problems 1 and 3 are examples that require regrouping, whereas problem 2, which does not require regrouping, is a nonexample . 121 231 376 − 17 − 120 − 229

1 . 2 . 3 .

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References Colarussso, R ., & O’Rourke, C . (2004) . Special education for all teachers (3rd ed .) . Dubuque, IA:

Kendall Hunt . Cox, L . S . (1975) . Systematic errors in the four vertical algorithms in normal and handicapped

populations . Journal for Research in Mathematics Education, 6(4), 202–220 . Fisher, D ., & Frey, N . (2012) . Making time for feedback . Feedback for Learning, 70(1), 42–46 . Riccomini, P . J . (2014) . Identifying and using error patterns to inform instruction for students

struggling in mathematics. Webinar series, Region 14 State Support Team . Retrieved from http://www .ohioregion14 .org/perspectives/?p=1005

Sweetland, J ., & Fogarty, M . (2008) . Prove it! Engaging teachers as learners to enhance conceptual understanding . Teaching Children Mathematics, 68–73 . Retrieved from http://www . uen .org/utahstandardsacademy/math/downloads/level-2/5-2-ProveIt .pdf

Yetkin, E . (2003) . Student difficulties in learning elementary mathematics. ERIC Clearinghouse for Science, Mathematics, and Environmental Education . Retrieved from http://www .ericdigests . org/2004-3/learning .html

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Background Student: Dalton Age: 12 Grade: 7th

Scenario Mrs . Moreno, a seventh-grade math teacher, is concerned about Dalton’s performance . Because Dalton has done well in her class up to this point, she believes that he has strong foundational mathematics skills . However, since beginning the lessons on multiplying decimals, Dalton has performed poorly on his independent classroom assignments . Mrs . Moreno decides to conduct an error analysis on his last homework assignment to determine what type of error he is making .

Possible Strategies • Collecting Data • Identifying Error Patterns

! ! AssignmentAssignment 1 . Read the Introduction. 2 . Read the STAR Sheets for the possible strategies listed above . 3 . Score Dalton’s classroom assignment below . For ease of scoring, an answer key has been provided . 4 . Examine the scored worksheet and determine Dalton’s error pattern .

Answer Key 1) 7 .488 2) 3 .065 3) 0 .5976 4) .00084 5) .5040 6) 2 .6724 7) .006084 8) 7 .602 9) .00183 10) 4 .6098 11) $39 .00 12) 732 .48 cm

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Mathematics: Identifying and Addressing Student Errors Level A • Case 1

CASE STUDY

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Background Student: Madison Age: 8 Grade: 2nd

Scenario Madison is a bright and energetic third-grader with a specific learning disability in math . Her class just finished a chapter on money, and her teacher, Ms . Brooks, was pleased with Madison’s performance . Ms . Brooks believes that Madison’s success was largely due to the fact that she used play money to teach concepts related to money . As is noted in Madison’s individualized education program (IEP), she more easily grasps concepts when using concrete objects (i .e ., manipulatives such as play coins and dollar bills) . In an attempt to build on this success, Ms . Brooks again used concrete objects—in this case, cardboard clocks with movable hands—to teach the chapter on telling time . The class is now halfway through that chapter, and to Ms . Brooks’ disappointment, Madison seems to be struggling with this concept . Consequently, Ms . Brooks decides to conduct an error analysis on Madison’s most recent quiz .

Possible Stragegies • Collecting Data • Identifying Error Patterns

! ! AssignmentAssignment 1 . Read the Introduction . 2 . Read the STAR Sheets for the possible strategies listed above . 3 . Score Madison’s quiz below by marking each incorrect response . 4 . Examine the scored quiz and determine Madison’s error pattern .

Answer Key

1) 3:00 2) 9:25 3) 7:15 4) 5)

6) 7) 8) 9)

10)

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Mathematics: Identifying and Addressing Student Errors Level A • Case 2

CASE STUDY

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Mathematics: Identifying and Addressing Student Errors Level B • Case 1

CASE STUDY

Background Student: Shayla Age: 10 Grade: 5th

Scenario Shayla and her family just moved to a new school district . Her math class is currently learning how to add and subtract fractions with unlike denominators . Shayla’s math teacher, Mr . Holden, is concerned because Shayla is performing poorly on assignments and quizzes . Before he can provide instruction to target Shayla’s skill deficits or conceptual misunderstandings, he needs to determine why she is having difficulty . For this reason, he decides to conduct an error analysis to discover what type of errors she is making .

Possible Strategies • Collecting Data • Identifying Error Patterns • Word Problems: Additional Error Patterns

! ! AssignmentAssignment 1 . Read Introduction . 2 . Read the STAR Sheets for the possible strategies listed above . 3 . Score Shayla’s assignment below by marking each incorrect digit . 4 . Examine the scored assignment and discuss at least three possible reasons for Shayla’s error pattern .

4 8

3 18

6 12

1 10

5 6

7 8

3 4

1 4

7 16

2 6

5 8

3 6

Answer Key

1) 2) 3) 4) 5)

6) 7) 8) 0 9) 10)

11) 12) 13)

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Mathematics: Identifying and Addressing Student Errors Level B • Case 2

CASE STUDY

Background Student: Elías Age: 7 Grade: 2nd

Scenario A special education teacher at Bordeaux Elementary School, Mrs . Gustafson has been providing intensive intervention to Elías, who has a learning disability, and collecting progress monitoring data for the past six weeks . His data indicate that he is not making adequate progress to meet his end-of- year goals . Mrs . Gustafson has decided that she needs to conduct a diagnostic assessment to identify areas of difficulty and to determine specific instructional needs . As part of the diagnostic assessment, Mrs . Gustafson conducts an error analysis using Elías’ progress monitoring data .

Possible Activities • Collecting Data • Identifying Error Patterns • Determining Reasons for Errors

! ! AssignmentAssignment 1 . Read the Introduction . 2 . Read the STAR Sheets for the possible strategies listed above . 3 . Score Elías’ progress monitoring probe below by marking each incorrect digit . 4 . When Mrs . Gustafson scores the probe, she finds two possible explanations . One is that Elías is

making a conceptual error, and the other is that he doesn’t understand or is not applying the correct procedure .

a . Assume that his error pattern is procedural . Describe Elías’ possible procedural error pattern .

b . Assume that his error pattern is conceptual . Describe Elías’ possible conceptual error pattern .

5 . Because the instructional adaptations Mrs . Gustafson will make will depend on Elías’ error pattern, she must be sure of the reasons for his errors . Explain at least one strategy Mrs . Gustafson could use to determine Elías’ error type .

Answer Key

1) 40 2) 87 3) 45 4) 22 5) 42

6) 34 7) 5 8) 122 9) 5 10) 80

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For illustrative purposes, only 10 of the 25 problems are shown .

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Mathematics: Identifying and Addressing Student Errors Level C • Case 1

CASE STUDY

Background Student: Wyatt Age: 12 Grade: 6th

Scenario Mr . Goldberg has been teaching a unit on fractions . He was pleased that all of his students seemed to quickly master adding and subtracting two fractions . However, when he began teaching the students how to multiply fractions, a small number of them did not readily learn the content . But after a quick mini-lesson, it appears that all but three students seem to understand how to solve the problems . One of these students, Wyatt, seems to be really struggling . Mr . Goldberg determines that he needs to collect some data to help him decide what type of error Wyatt is making so that he can provide appropriate instruction to help Wyatt be successful . To do so, he decides to evaluate Wyatt’s most recent independent classroom assignment .

! ! AssignmentAssignment 1 . Read the Introduction. 2 . Read the STAR Sheets . 3 . Score Wyatt’s classroom assignment below by marking each incorrect digit . 4 . Review Wyatt’s scored assignment sheet .

a . Describe Wyatt’s error pattern . b . Discuss any exceptions to this error pattern . What might these indicate?

5 . Based on Wyatt’s error pattern, which of the two strategies described in the Addressing Error Patterns STAR Sheet would you recommend that Mr . Goldberg use to remediate this error? Explain your response .

1 8

2 9

14 48

12 25

21 56

12 121

24 108

48 48

2 6

1 3

1 4

2 12

6 12

Answer Key

1) 2) 3) 4) 5)

6) 7) 8) or 1 9) or 10)

11) 12)

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Oncology South: Oncology Navigator Intake Form Name: MRN: D.O.B.:

ONCOLOGY NURSE NAVIGATION NEW PATIENT BARRIERS TO CARE and PSYCHOSOCIAL ASSESSMENT

The Oncology Nurse Navigator (ONN) introduced self to the patient and gave a brief explanation of the nurse navigator role. Contact information was provided. The ONN obtained a verbal consent for navigation assessment and follow-up.

Tell me about yourself:

▪ Who does your family consist of? ▪ What is your marital status? ▪ With whom do you live? ▪ What is your occupation? ▪ Are you in school? ▪ What do you enjoy doing in your spare time?

Chief complaint: Tell me what you know about your diagnosis so far… (Use direct quotes when possible) Family History of Cancer: Smoking History: Exposure History:

ACCESS TO CARE ASSESSMENT

Was it difficult for you to schedule your first appointment at UACC? NO YES ▪ Tell me more about how the process was difficult for you…

What is the name of your PCP? Who referred you to UACC?

Lack of a PCP is a barrier to cancer care. YES ▪ Refer to MERCK Resource Navigators to help patient obtain a PCP

NUTRITIONAL ASSESSMENT

Is Nutritional Status a barrier to care? NO YES

Malnutrition Screening Tool (MST): (If indicated)

Weight loss:

1. Have you recently lost weight without trying?

Yes or No?

0 = No

2 = I am not sure

2. If yes, how much have you lost? 1 = 2 to 13 lb. 2 = 14 to 23 lb. 3 = 24 to 33 lb. 4 = 34 lb. or more

Appetite:

3. Have you been eating poorly because of decreased appetite?

0 = No

1 = Yes

4. MST Score (weight loss + appetite)

Total score ______. Referral to Nutritionist should be made with a score of 2 or greater.

LEARNING ASSESSMENT – Document in Cerner

Do you have any Communication /Language barriers? NO YES

▪ In what language do you want to get your medical information? Any barriers to learning? NO YES

▪ Memory issues ▪ Dyslexia ▪ Impairment: hearing, eye site ▪ Cognitive Deficits ▪ Cultural Barrier ▪ Difficulty concentrating ▪ Emotional state ▪ Financial concerns ▪ Health Literacy ▪ Desire/Motivation

Preferred Learning Style: Demonstration, Printed materials, Verbal explanation, Video, Internet

PHYSICAL BARRIERS ASSESSMENT

Do you have any challenges accomplishing your Activities of Daily Living? NO YES

▪ Do you have any problems with mobility (walking/getting around)? ▪ Do mobility challenges make it difficult for you to get out of the house for errands or

appointments? ▪ Do you need any assistive devices? ▪ Self-care: bathing, dressing, cooking, etc.

Do you have family care responsibilities that limit your ability to be away from home for several hours at a time? NO YES

▪ How many dependents (children, older adults) do you care for? Ages? ▪ Are you the primary caretaker? ▪ What support do you have for caring for your dependents?

Do you expect to have difficulties obtaining transportation to your appointments? NO YES

▪ What is your primary mode of transportation? ▪ Is your transportation reliable? ▪ Do you expect there to be any transportation difficulties for your appointments? ▪ Is there someone who can drive you to your appointments if necessary?

Is housing/lodging a barrier? NO YES

▪ Do you have safe place to live? ▪ If you come from out of town, do you need a place to stay while you are in Tucson? ▪ If you were to need radiation therapy every day for some weeks, would you need a

place to stay close by?

Would you say that your current financial situation including your insurance coverage will be a barrier to your receiving medical care for your cancer diagnosis? NO YES

▪ Do you have difficulty affording your current bills? ▪ Who provides the main source of income for your household? ▪ Do you have health insurance? Name? ▪ Are you worried about your health insurance being adequate to cover cancer-related

services?

If you were to need cancer treatment, would you anticipate there being any problems getting time off from work or school? NO YES

▪ Does your job allow for time off for being sick? ▪ FMLA? Other programs? ▪ Will you get a pay check if you cannot work?

SOCIAL HABITS ASSESSMENT

Let me ask you about social habits: Do you smoke?

▪ Never ▪ Quit; How many years ago? ▪ Yes; How many PPD? How many years? ▪ Are you interested in quitting? ▪ Do you know about ASHLine? 1-800-55-66-222

Are you in the habit of using recreational drugs or drinking alcohol? And if so, have you had any problems as a result? NO YES

▪ Have you ever been stopped for driving under the influence? ▪ Do you have difficulty keeping a schedule after drinking/using recreational drugs?

PSYCHOSOCIAL BARRIERS ASSESSMENT

Do you worry about having enough social support to help you during stressful times? NO YES

▪ Who can you rely on to help you at home or outside of your home?

▪ Is there someone that can attend appointments with you? Who?

Do you have any religious and/or spiritual beliefs or cultural practices that may impact your health care decisions and that your health care team should be aware of? NO YES Would you say that you have difficulty trusting the medical system or medical providers? NO YES

Learning that you have a cancer diagnosis can certainly be frightening. Do you anticipate that fear of cancer or its treatment might affect your willingness to get care? NO YES Have you ever been diagnosed with anxiety, depression or other mental health condition? NO YES

▪ What was the specific diagnosis? ▪ Are you currently under a doctor’s care? ▪ Do you take any medications? What are they? ▪ How long ago were you diagnosed?

Would you say that you are having difficulty coping with your diagnosis at this time? NO YES

▪ How have you coped with stressors in the past? ▪ Would you find it helpful to speak to a counselor who can help with coping strategies?

DISTRESS THERMOMETER: On a scale of 0-10, with 10 being “extreme”, how much distress have you been experiencing in the past week including today? ____ Is there anything else that you want to share with me that you think might make it difficult for you to get access to care or is a barrier for you? NO YES

Distress Thermometer Score: ________________ Number of Barriers: _________________ Patient Acuity Score: _________________

NAVIGATION PLAN

1. Referrals:

2. Patient Education Plan: : At her initial visit, this patient will receive the ASCO Guide to Lung

Cancer and an orientation packet containing the UACC Living with Cancer Guide book. If a

decision to go to surgery is made, she will receive a surgical education packet. At subsequent

visits, she will receive Krames or Chemocare Handouts on any systemic antineoplastic agents

prescribed.

3. Navigation Follow-up Plan for Barrier Resolution (based on Acuity Score): Per the GREEN

YELLOW ORANGE RED protocol, I will make future contact to reassess and offer further

navigation as needed.

4. Hand-off: This note was routed to the Clinical Nurse Coordinator for Dr. who will take

over care during the treatment phase.

Barrier and Distress Resolution Protocol 1. GREEN (Normal) Within 5 business days of MD visit, ONN will call to assess understanding of the plan of care and reassess acuity. If patient remains at this acuity, no additional calls will be made unless new issues develop. If acuity increases, the number of FU calls will increase to that acuity level protocol. 2. YELLOW (Low) Within 5 business days of MD visit, ONN will call to assess understanding of the plan of care and reassess acuity. If patient remains at this acuity, at least one additional FU call will be made. If acuity increases, the number of FU calls will increase to that acuity level protocol. If acuity decreases, the number of FU calls will decrease to that acuity level protocol. 3. ORANGE (Medium) Within 5 business days of MD visit, ONN will call to assess understanding of the plan of care and reassess acuity. If patient remains at this acuity, at least two additional FU calls will be made. If acuity increases, the number of FU calls will increase to that acuity level protocol. If acuity decreases, the number of FU calls will decrease to that acuity level protocol. 4. RED (High) Within 5 business days of MD visit, ONN will call to assess understanding of the plan of care. If patient remains at this acuity, at least three additional FU calls will be made. If acuity decreases, the number of FU calls will decrease to that acuity level protocol.

Oncology North: Navigator Intake Paper Form

© 2021. Grand Canyon University. All Rights Reserved.

Integrated Case Study

Overview:

Throughout this course, you will use this case study to demonstrate knowledge of the following

course content:

• Clinical decision support

• Assessing user needs

• Analyzing and documenting workflow

• Designing and customizing fields, forms, and templates

• User testing

• Evaluation metrics

• Designing user documentation and training

In a series of assignments, you will use this case study to integrate user interface design

(including usability/human factor principles) into a design document, analyze and develop

workflows, evaluate users’ needs (including their involvement in user testing), develop

evaluation metrics, and design end user training materials.

The case study, which will be used throughout the course, will focus on various components of

the course topics. It focuses specifically on the unique needs of oncology patients and the health

care needs of oncology navigators and prior authorization/financial coordinators.

The Case:

Universal Health is a large not-for-profit health care system with 12 hospitals in three states and

two large oncology programs in Arizona. One of the oncology programs is affiliated with

Academic Hospital and the other with a larger national oncology health care system. Although

both oncology locations are part of Universal Health, there are significant differences in how

each of the locations operates due to a recent merger/acquisition of the Academic Hospital

oncology program (Oncology South) and the affiliation of the other oncology program

(Oncology North) with a national oncology health care system. To compound these operational

issues, Oncology North had been part of Universal Health for 8 years, so its Electronic Health

Record (EHR) was Chrystal, which was the EHR platform for Universal Health and became the

model used to convert Oncology South off its EHR to align with the rest of the organization.

Management of oncology patients is quite complex and there was significant concern from

Oncology South about the EHR conversion, as well as changes that would affect its operating

model. Previously, both oncology programs worked relatively independently with IT to create

custom solutions, but now would need to work together to create a standardized oncology

solution for Universal Health.

2

If a merger/acquisition of a large academic hospital and its oncology program was not complex

enough, adding the conversion of an EHR certainly made the situation more difficult. Also

compounding the issue, Oncology North—although it had been on the EHR Chrystal for almost

8 years—had significant issues with the current build and felt that there were several gaps related

to functionality for oncology clinicians to service its unique population. Since Universal Health

was in the process of converting the EHR at Academic Hospital and Oncology program, the

EHR vendor, Chrystal, was actively involving its alignment specialists to assist in the

conversion. One of the key first steps of the Chrystal alignment specialists was to do a gap

analysis and prioritization of EHR functionality for oncology as well as throughout Universal

Health.

The gap analysis done by Chrystal found that the oncology build for Universal Health overall did

not align to its recommendation for oncology specialties in several areas within the EHR. As a

result, a focused team (including a project manager, nursing informatics, Universal Health IT

resources, Chrystal oncology alignment specialists, and Chrystal oncology IT experts) was

created to systematically address the recommendations from the Chrystal oncology gap analysis.

Although there were recommendations globally related to Universal Health’s overall EHR build,

there were some specific recommendations related to the build of the oncology platform within

Chrystal. Some of the initial focus was related to concerns related to prior authorization/financial

gaps and the functionally/workflow of all the oncology providers/clinicians, but also the

oncology navigators who really did not have any oncology functionality within Chrystal.

Servicing an oncology population is a significant part of the patient demographics of any large

health care organization. Oncology patients have unique needs due to the frequency of their

visits and the length of their treatments and follow-up, which can last a lifetime. A cancer

diagnosis is life changing and can cause great emotional, physical, and financial stress. Oncology

navigators exist to assess and assist patients and their families during their cancer treatment and

hopefully into remission/survivorship. Unfortunately, cancer treatment can be costly, and dealing

with insurance companies for prior authorization is an unfortunate reality in the current health

care system. For health care providers, there is great financial responsibility in providing cancer

treatment, so obtaining authorization from insurance companies and ensuring that patients are

aware of their own financial responsibility are essential for both the patient and the organization.

After a patient receives a cancer diagnosis, the next step is usually a referral to an oncology

specialist/program like Oncology North or Oncology South. That referral can come from a

patient calling an oncology specialist/program directly or from the diagnosing physician

contacting an oncology specialist/program. Oncology South and Oncology North both have

dedicated intake referral specialists who work directly with patients, families, and referring

physicians to get patients scheduled with an oncology specialist based on their diagnosis. Before

the patient sees the oncology specialist for the first time, many documents need to be sent to the

prior authorization team for review to ensure that the appropriate prior authorization is obtained

from the insurance company, as well as making sure that the patient will be seen by the most

appropriate oncology specialist for the specifically diagnosed cancer. These documents vary

from pathology reports, diagnostic results, and referring physician notes that can be sent to the

prior authorization specialist at different times for different patients. It is essential to have a

standard workflow and expectation of standard documentation in a certain place in the EHR, so

that everyone involved in the initial authorization and clinical care knows what steps have been

taken and what actions are pending. While these financial steps are occurring behind the scenes

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and are important details that need to be secured before a patient’s first appointment, it is worth

noting that at this juncture patients have just received some of the worst news in their life and

they just want to get treatment as soon as possible.

Oncology navigators are nurses that specialize in assisting patients navigate their cancer journey

from diagnosis through treatment and into survivorship. After the first contact with the oncology

intake specialists, oncology navigators are the next foundational step in the patient’s journey

towards treatment and recovery. After the initial documentation is completed by the intake

specialist who provides some basic information, including name of person calling, contact

information, referral sources, provider information, and diagnosis information, such as type of

cancer. Based upon the type of cancer on the intake documentation, an oncology navigator who

specializes in that cancer type is notified of the new patient and contacts the patient to initiate a

custom navigation plan based upon assessment of needs. The oncology navigator role is an

extremely important part of the oncology team. However, oncology navigators were identified as

being significantly underdeveloped within Universal Health EHR based upon Chrystal’s gap

analysis, so there needed to be focused attention on this group within the organization.

As a result, a dedicated team needed to be formed to include individuals from nursing

informatics from Universal Health, Chrystal oncology alignment and IT specialists, Chrystal IT

staff, and oncology navigators from both Oncology North and Oncology South. This team would

be responsible documenting workflow, assessing end user needs, and submitting a final design

recommendation (including training materials) to the Universal Health IT build team. The

completion deadline for the design document is 8 weeks.

Assessing current state and understanding end user needs must be one of the first goals of this

dedicated team. Two days were dedicated for onsite observations of oncology navigators at

Oncology South and Oncology North, during which it was discovered from the observations that

even though the oncology navigators at both locations performed the same role, they had some

significant differences that needed to be overcome to be able to collaborate and create a single

oncology navigator solution. The grid below outlines some of the differences.

Operations Differences Oncology South Oncology North

Initial Contact With Patient Phone interview within 3 days Initial physician clinic visit

Patient Oversight

All oncology patients Only oncology patients that

have identified needs

Documentation

Paper form: See document: Nav

Assessment 2018

Paper form: See document:

Oncology North

Although each location has operational differences, they also have several similarities in how

they used some of the tools in the EHR, as well as their need for data and the ability to

track/trend the outcomes of their patients. One key request was to make it easier for all oncology

clinicians to be able to see their documentation within Chrystal. These foundational similarities

aligned to what Chrystal oncology specialists had implemented at other institutions, having

already created an Oncology Navigator Recommended Design Document that could be used at

Universal Health. The table below provides some similarities between Oncology North and

Oncology South.

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Operations Similarities Oncology North and Oncology South

Position Navigator/Coordinator RN

Data Request Wanted discrete data for reports

Electronic Documentation Used same two electronic methods to chart:

1. Electronic forms shared by all types of navigators (e.g., ortho, pulmonary)

2. Free-text note also shared by same navigators above

Electronic Documentation Wanted it to be easier to find specific oncology navigator

documentation

Health care is all about data. In addition to using EHR for recording documentation, it is used to

extract data to evaluate outcomes. Data in the EHR can come from discrete data from

ICD10/ICD9 used by providers/coders, SNOMED, IMO codes used clinicians, but also directly

from forms and flowsheets from discrete data fields. Understanding the unique data requirements

of the oncology navigators, as well the initial prior authorization team, is foundational to creating

the appropriate discrete fields or using existing data fields like ICD10 to help sort and organize

data.