in meaning from the original test. For example, the substitution of
hold for fight in “fight back the tears” is semantically correct and
does not alter meaning. However, the substitution of ready for right in
“he’ll be all right” does change the sense of the passage.
Miscues that produce changes in meaning can be further analyzed.
For example, the student’s miscue and the original text can be
compared in these three ways:
Graphic Similarity: How much do the two words look alike?
Sound Similarity: How much do the two words sound alike?
Grammatical Function: Is the grammatical function of the reader’s word the same as the grammatical function of the text word?
Informal Assessment of Mathematics
Math is a relatively easy subject to assess using informal
methods. The areas that are usually assessed include:
The assessment should be combined with both task
analysis and error analysis to determine specific problem
areas. These problem areas should be further assessed by
using probes to determine the specific difficulty.
Interviewing the student is also helpful in determining
how the student is reasoning through a problem.
Methods of Informal Math Assessment
Informal Inventories—Informal inventories survey a variety of skills to determine where the student’s strengths and weaknesses lie. Inventories usually have only one or two examples of each type of math problem so further analysis of errors is necessary in more specific probes.
Criterion-Referenced Tests--CRTs are used to assess mastery of specific mathematics skills (e.g. multiplication by 9).
Error Analysis—Error analysis is a process of looking at the student’s responses to determine why a mistake was made and to see if there is a pattern of repeated types of errors. Error analysis differentiates between systematic computation errors and errors that are random or careless mistakes.
Diagnostic Probes—Probes are in-depth assessments of the mastery of a specific skill or sub-skill; typically a probe contains several items focused on the same skill.
Clinical Math Interviews—Clinical interviews elicit information about the procedures that students use to arrive at their answers. The student is observed going about the mathematics task and then the student is interviewed to find out the cognitive strategies he or she used to accomplish the task.
Portfolio Assessment—A portfolio should contain several examples of the student’s work, including classroom quizzes or assignments, group or individual projects, written math reports or math logs, or artwork related to mathematics. Portfolios may also contain results of standardized tests and informal assessments, student self-assessments, and student interest surveys and questions. Teachers might include checklists of student progress, graphs of results from CBA measures and records of clinical math interviews.
Example of an Informal Inventory
6 3 4 10 8 11 17 33 67
+2 + 5 + 0 + 5 + 3 + 4 + 5 +15 +71
6 3 4 17 98 47 10 14 27
-4 -3 -0 -3 -4 -32 -3 -6 -24
3 2 2 6 33 22 3 232 204
x 2x2x8 x0x 4x 422x3x 4
Example of Math CRT Criterion for Mastery: 100% (10/10) correct
Directions: Round off each number to the nearest
Math Error Analysis
The teacher examines the student’s work and observes how the student goes about solving the problems. The teacher can then analyze what types of errors the student is making. Common types of errors include:
Incorrect number fact
Errors in place value
Failure to follow sequence of
Placement (working from right to left)
Copying or handwriting errors
Error Analysis Practice For each of the following problems, analyze and describe the types of errors the student is making. Note that within the same box, all of the problems display the same error.
83 66 476 753
1410 815 148 1113
67 58 627 861
17 16 261 428
More Error Analysis
175 185 632 523 563
- 54- 22 -147-366-382
1111 1513 495 167 181
17 46 1206 divided by 6 = 21
x 4x 8
Teacher-made probes can be used to identify specific problem areas. Mixed
probes are used to locate areas that need further assessment or instruction.
In the probe on the following page, each of the following categories
has nine items:
basic addition facts of sums to 9 (first item and then every fourth item),
two-digit numbers plus two-digit numbers with no regrouping (second
item and then every fourth item),
two-digit number plus one-digit number with no regrouping (third item and then every fourth item), and
basic addition facts of sums to 18 (fourth item and then every fourth item).
When scoring a probe, the student receives one point for every correct digit
in the correct place. On this probe, the student can obtain a maximum score
of 63 correct digits with no errors. After three times, a high score of 40 or
more correct digits per minute with no errors is a reasonable criterion for
Could the student do the steps of the problem in proper sequence?
Were the student’s calculations accurate?
Diagnostic Questions for Analysis of Problem Solving
______ ______ Decodes words correctly in story problem
______ ______ Understands the meaning of the situation described in the story problem
______ ______ Identifies the relevant and irrelevant information in the problem
______ ______ Can illustrate the components of the problem
______ ______ Selects the appropriate operation (addition, subtraction, multiplication or division)
______ ______ Writes down the computational problem correctly
______ ______ Remembers number facts correctly
______ ______ Selects the appropriate computational algorithm
______ ______ Estimates the correct answer
______ ______ Determines is answer “makes sense”
Informal Assessment of Written Expression
Written expression includes a complex array of
skills which all must be working relatively well in
order for the written product to be legible,
understandable, and persuasive. Informal probes
of writing skills can be done in each of the
important areas, including handwriting, writing
mechanics, spelling, and composition. On the
next slide is a chart showing common methods of
informal writing assessment by category.
Common Informal Methods of Assessing Writing
Analysis of handwriting sample (copy 100 word passage)
CRTs of punctuation, capitalization, and grammar
Paper and pencil dictation test
Rating scales and checklists of skills
Rating handwriting sample according to grade level template (e.g., shape, slant, spacing, size, smoothness)
Informal surveys of punctuation, capitalization, and grammar
Writing sample analysis (write for 15 minutes on a topic or from a story starter)
Inventories and CRTs (e.g., Denver Handwriting Analysis, Brigance)
(choose the correct spelling)
Spontaneous writing sample
Observation and clinical interview
Inventories of regular words, irregular words and homophones
Criterion-referenced test (usually of grade level words
the peopol of englind didn’t the cherch roals. So a group
of pepol got to gether and desided to live. So after a lot of
comfermising. The king gov them 3 ships and they set sail
for a mew land. They sailed a long ways for a to long tine.
Then they saw it land it was North amareca. They landid
on plymouth rock. There they started to beld the ferst
coliny. The firs winter wase the hardes a lot peopl dide
from being sick. Afte the winter was over the ingin’s
becom frinds with them and to them how to hunt and
What kinds of errors do you see in this composition? What is your error analysis?
Excerpt from a Writing Checklist
______ ______ Does the writing clearly communicate an idea or ideas to the reader?
______ ______ Is the content adequately developed?
______ ______ Is the content interesting to the potential reader?
______ ______ Does the writer select appropriate words to communicate his/her ideas?
______ ______ Does the writer use precise/vivid vocabulary?
______ ______ Does the writer effectively use verbs, nouns, adjectives and adverbs?
______ ______ Does the vocabulary meet acceptable standards for written English (e.g., isn’t vs. ain’t)?
______ ______ Are the sentences complete (subject and predicate)?
______ ______ Are run-on sentences avoided?
______ ______ Are exceptionally complex sentences avoided?
______ ______ Are the sentences grammatically correct (e.g., word order, subject-verb agreement)?
______ ______ Do the sentences in the paragraph relate to one topic?
______ ______ Are the sentences organized to reflect the relationships between ideas within the paragraph?
______ ______ Does the paragraph include a topical, introductory or transition sentence?
Sample Writing Interview Questions
You’ve finished your composition. Tell me about what you’ve written.
When you finished, did you read over what you had written? Did you make any changes?
What did you change?
Did you have anyone else read your paper? Did you change your paper on the basis of suggestions that someone else made?
While you were writing, what did you think about? Did you consider the ideas you were writing about? What should come first, second, and so on? Choosing the exact words to express your meaning? Spelling the words correctly, using correct punctuation, and following all the rules for correct grammar?
Do you think that you’ve accomplished your purpose in writing? Why or why not? If not, what do you need to change?
Do you think your writing will be understandable for your audience? Is the vocabulary suitable? The tone? If not, what do you need to change?
A short informal spelling test can be designed by selecting
grade level words from a frequency-of-use word list. The
grade list until three words in a grade list are missed. The
student’s spelling level can be estimated as that at which
two or fewer words are missed.
Common Types of Spelling Errors
Dysphonetic errors. Spelling errors which reflect inaccurate spellings without regard to phonics. Words may have some correct letters, but the letters are placed in bizarre positions, such as ronaeg for orange. Students with this problem read and spell primarily through visualization.
Dyseidetic errors. Spelling errors reflect phonic-equivalent errors (e.g., pese for peace, det for debt).
What kinds of spelling errors do you see in the essay on
Summary of Methods of Informal Assessment
Criterion Referenced Tests—tests of one skill with a designated level of accuracy in order for the skill to be considered mastered
Curriculum-Based Assessments—informal tests using content from the curriculum
Probes—tests of specific skills or sub-skills with multiple examples of the same skill to determine strengths and weaknesses of the student
Checklists—lists of academic or behavioral skills
Questionnaires—questions about a student’s behavior or academicperformance that can be answered by the student or by a parent or teacher
Work Samples—samples of a student’s classroom work
Permanent Products—products made by the student that can be analyzed for academic or behavioral performance
Performance assessment--assessment that requires the student to create an answer or product to demonstrate knowledge
Authentic assessment--assessment that requires the student to apply knowledge in the real world
Portfolio assessment--evaluating student progress, strengths, and weaknesses using a collection of different measurements and work samples
samples of student writing
examples of student problem solving
informal inventories and probes
results of standardized tests
reading log or reading list
artwork, project papers, photographs, and other products
group work, papers, projects, and products
letters to pen pals, letters exchanged with teacher
out-of-school writing and artwork
unit and lesson tests
math computation exercises
Elements of High Quality Assessment
Authentic and valid
Encompass the whole child
Involve repeated observations of patterns of behavior
Ongoing and continuous
Use a variety of methods
Provide a means for feedback
Provide an opportunity for students, teachers, and parents to discuss progress