Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________
1) Record the main components of the lesson, using these codes.
Use multiple codes only if class is separated into distinct groups with different modes
(e.g., 10 advanced Ss work ahead in the book while T leads review for 20 others).
TI
TM
SD
WP
WC
GP
GC
IP
IC
T/Q
U
O
teacher presentation of behavioral directives or task instructions (nonmathematical)
teacher presentation of math content (minimal or no student input)
student demonstration (more significant than verbal answer from seat)
whole-class discussion to review/apply learned procedures (significant student input)
whole-class discussion to co-construct new concepts or procedures
pair or small-group work practice of learned procedures
pair or small-group concept development (e.g., discovery activity/lab/project)
individual practice of learned procedures
individual concept development (e.g., discovery activity/lab/project)
test/quiz
activity or discussion unrelated to math or implementation of the lesson
other (write in)
Start
Stop
time
time
Example:
8:35 am 8:40 am
Elapsed
time
5:00
Component
(use codes)
TM
Description
T demonstrates example problem with some low-level
questioning of Ss; choral response.
Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________
TI
TM
SD
WP
WC
GP
GC
IP
IC
T/Q
U
O
Start
time
teacher presentation of behavioral directives or task instructions (nonmathematical)
teacher presentation of math content (minimal or no student input)
student demonstration (more significant than verbal answer from seat)
whole-class discussion to review/apply learned procedures (significant student input)
whole-class discussion to co-construct new concepts or procedures
pair or small-group work practice of learned procedures
pair or small-group concept development (e.g., discovery activity/lab/project)
individual practice of learned procedures
individual concept development (e.g., discovery activity/lab/project)
test/quiz
activity or discussion unrelated to math or implementation of the lesson
other (write in)
Stop
time
Elapsed
time
Component
(use codes)
Description
Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________
2) Describe and number each different incidence (including homework) of nontrivial uses of these
practices. Afterwards, rate the overall role of each practice: (S) Significant, (M) Marginal, (N) None.
Practice
a) T asks question or poses
task with a high level of
cognitive demand
(S must do one or more of:
 decide/invent approach
 meaningfully connect
ideas or rep. forms
 analyze/synthesize/
evaluate ideas/strategies
 apply math in a real
problem setting
 deepen conceptual
understanding)
b) Ss are given authority to
judge the mathematical
soundness of publicly
presented solution or method
(rather than the T or text)
c) T connects (or poses task
that prompts S to connect)
the featured math topic to
another math topic
d) T connects (or poses task
that prompts S to connect)
the featured math topic to
another academic topic
e) T connects (or poses task
that prompts S to connect)
the featured math topic to a
real-life situation or object
Description
Rating
Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________
f) Ss allowed or encouraged
to choose among solving
methods or present
alternative methods
g) T or Ss use technology,
manipulatives, body
movement, or other
nonverbal support for a math
concept
h) Specific attention paid to
developing writing,
reading, or speaking skills
i) T uses or encourages S to
use multiple forms of
representation (English,
symbolic, graph, table,
diagram, physical model) for
the same problem
Example:
i) T uses or encourages S to
use multiple forms of
representation . . . for the
same problem
1) Task requires Ss to translate from table to graph
2) T asks Ss to diagram a word problem
3) T asks S to describe the action in a graph
S
Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________
Observation Overview (complete immediately after the class has ended)
1) Overall impression of student engagement level:
Mathematical depth? Widespread involvement? Overall impression of impact on student learning:
Any evidence that students learned new concepts or behaviors?
2) Overall impression of the nature of teacher talk:
Mainly information giving? Problem posing? Facilitating student talk and work? Managing
behavior?
3) Overall impression of student talk:
Mainly short answer to teacher questions? Explanations of procedures? Mathematical
justifications? Choral response or individuals? Student-to-student?
4) Overall impression of the sequencing of lesson sections:
Logical? Developmentally responsive? Logistically motivated (e.g., fits available time)?
Internally connected? Strategic?
5) Overall impression of power dynamics:
Who has authority over how and what math gets done? Who has responsibility for teaching,
evaluating, choosing methods or tasks? How autonomous are students?
6) Overall ratings of importance of each mode as a source of content (check one rating for each source):
Source
Teacher presentation
Textbook or other published print materials
Individual student construction of ideas/procedures
Small-group construction of ideas/procedures
Whole-class construction of ideas/procedures
Other:
Other:
dominant
significant
minimal
none
Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________
EXAMPLES
TI
teacher presentation of behavioral directives or task instructions (nonmathematical)
TM teacher presentation of math content (minimal or no student input)
 Teacher lectures about content and/or gives a visual, physical, or technological demonstration, as
students listen and/or take notes.
 Teacher may invite student input, but it is minimal: short answers that mainly require recall and seem
solicited primarily to maintain student attention rather than to engage deep thinking and develop
concepts. Rarely will students directly respond to each other in this mode.
SD
student demonstration (more significant than verbal answer from seat)
 Student displays work on the board or overhead projector for the class to examine (as opposed to
individual white-boards, which are usually for the teacher only). Student may verbally explain her
displayed work.
 Student gives extended, prepared verbal explanation of work in front of class.
 Student presents the results of a project, verbally, on a poster, or in some other fashion.
X Not example: Student gives a short answer from seat in response to a teacher or classmates’ question.
X Not example: Student gives an explanation or justification for a solution or idea, but it is part of the
flow of the discussion, not a prepared work.
WP whole-class discussion to review/apply learned procedures (significant student input)
 Whole class is supposed to be attending to the same conversation, and student input is significant.
Much of the information about how to carry out or apply the procedures comes from student
comments.
 Students may respond directly to each other, supporting or challenging each other’s ideas.
 Teacher may press students to justify their ideas or procedures.
X Not example: Teacher describes how to carry out procedures and asks students for only minimal, lowlevel input.
WC whole-class discussion to co-construct new concepts or procedures
 Same as WP, but the topic of discussion is a new concept or an extension of one already learned.
 Student comments are significant and reflect mental work to make sense of and explore the concept.
 Much of the information about the new concept comes from student comments.
GP
pair or small-group work practice of learned procedures
 Students are seated in pairs or small groups and allowed or directed to interact over the task
 Actual interaction may be minimal; students may essentially decide to work independently
 Teacher may give varying degrees of autonomy; groups may be required to struggle alone or teacher
may offer heavy guidance and instruction for groups or individual students
GC
pair or small-group concept development (e.g., discovery activity/lab/project)
Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________

Same as GP, but the task is to discover a new concept or extend understanding of one already learned.
IP
individual practice of learned procedures
 Students are not seated in groups and are mainly expected to work alone; minimal collaboration may
be allowed (e.g., “Help the person next to you if you get done early”)
 Or students are seated in groups because the class is normally arranged like this, but for this task
students are explicitly instructed to work alone
IC
individual concept development (e.g., discovery activity/lab/project)
 Same as IP, but the task is to discover a new concept or extend understanding of one already learned.
T/Q test/quiz
 For a grade or for diagnosis. Some type of scoring will be done, but it might not “count.”
X Not example: Seatwork for practice, punishment, fun.
U
activity or discussion unrelated to math or implementation of the lesson
O
other (write in)
Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________
2) Describe and number each different incidence (including homework) of nontrivial uses of these
practices. Afterwards, rate the overall role of each practice: (S) Significant, (M) Marginal, (N) None.
Practice
a) T asks question or poses
task with a high level of
cognitive demand
(S must do one or more of:
 decide/invent approach
 meaningfully connect
ideas or rep. forms
 analyze/synthesize/
evaluate ideas/strategies
 apply math in a real
problem setting
 deepen conceptual
understanding)
b) Ss are given authority to
judge the mathematical
soundness of publicly
presented solution or method
(rather than the T or text)
c) T connects (or poses task
that prompts S to connect)
the featured math topic to
another math topic
d) T connects (or poses task
that prompts S to connect)
the featured math topic to
another academic topic
e) T connects (or poses task
that prompts S to connect)
the featured math topic to a
Examples
(See Stein et al. materials)

T does not pronounce publicly presented work as “correct” or not, but asks
Ss to judge it.
 T asks Ss to determine which of multiple solutions is the best one and why.
 S takes it on herself to judge the mathematical soundness of the idea or
method of a classmate, the T, or published materials.
X If T immediately follows up with a judgment, this may cancel out the Ss’
Authority and invalidate what at first looked like an incident of this practice.
 T relates featured topic to one previously learned but perhaps to Ss not
obviously related, e.g., how the constant of variation in a direct variation is
like (and not like) the slope of a line, when slope was studied weeks ago.
 T foreshadows an upcoming topic and how the featured topic relates, e.g.,
when teaching that the volume of a box can be expressed as (Area Base)(h),
T says this formulation will be helpful later when finding the volume of
other solids.
X Nearly all topics build gradually from others. Don’t count as an incident T
building the topic from more basic versions, e.g., T relates factoring a
trinomial with a leading coefficient to factoring without one, taught the day
before, or T starts the lesson with a reminder of yesterday’s lesson on
exponent rules, then shows how to use them with fractional exponents.
 T poses problem that has a scientific context, e.g., has Ss interpret a graph of
the temperature of a cooling liquid over time.
 T has Ss work with data from a historical event, e.g., casualties of various
wars.
 T poses a math task or makes explicit reference to the link between math and
the content of another course she knows students are taking, e.g., “I know
you’re talking about genetics in biology. We’re going to use probability to
find out the chances of two blue-eyed parents having a blue-eyed child.”
 T asks Ss to come up with connections between the featured topic and
another course.
X This practice may be hard to distinguish from a connection to a real-life
situation, especially if T doesn’t explicitly reference another course. Count
here a connection that people are likelier to encounter in an academic course
or scholarly work than in everyday life or employment.
 T poses a word problem that relates to a situation from everyday life or
work, e.g., to find the interest earned in an investment.
 T gives a project where Ss collect real data and analyze them, e.g., heights of
Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________
real-life situation or object
kids and adults.
 T uses a real object or situation to illustrate a concept, e.g., sub-zero
temperatures to illustrate negative numbers, or a soup can to show volume.
 T asks Ss to connect the featured math topic to real situations.
X Don’t count manipulatives or tools designed to demonstrate math concepts,
such as algebra tiles, spinners, dice, fraction blocks, etc. Hands-on does not
automatically equal real-world.
f) Ss allowed or encouraged
 T does not complain when Ss present different solving methods, and T does
to choose among solving
not imply that Ss should only pay attention to one.
methods or present
 T solicits alternative methods after one has been presented.
alternative methods
 T presents multiple methods and suggests that Ss may choose which they
like, or advises that different methods may be more efficient for different
problems or purposes and that Ss should try to make the best choice.
 T praises S for coming up with a new method.
g) T or Ss use technology,
manipulatives, body
movement, or other
nonverbal support for a math
concept



h) Specific attention paid to
developing writing,
reading, or speaking skills


i) T uses or encourages S to
use multiple forms of
representation (English,
symbolic, graph, table,
diagram, physical model) for
the same problem
 Task requires Ss to translate from table to graph.
 T asks Ss to diagram a word problem.
 T asks S to describe the action in a graph.
X Avoid trivial or unavoidable incidents, e.g., a lesson about how to plot points
on a coordinate plane (don’t count as a translation from a table to a graph),
or the solving of a word problem (don’t count as a translation from words to
symbols).
Calculators, computers, PowerPoint.
Mathematical tools (ruler, protractor)
Commercial or homemade manipulatives (algebra tiles, fraction blocks),
probability tools (dice, spinners), real-world props (product packages for
finding volume, round household items for finding pi).
 Movement more significant than a fleeting gesture to illustrate a concept,
e.g., Ss playing the part of points on a coordinate plane, T walking forward
and backward to represent adding signed numbers, Ss crossing their arms to
represent vertical angles.
X Do not count the conventional classroom tools: blackboard, chalk, paper and
pencil, overhead projector, unless they are used in unconventional ways (e.g.,
Scotch tape “constructions,” overhead projector to cast shadows for a lab on
proportions, tossed chalk to represent projectile motion).
Task requires Ss to write an extended response.
Task requires Ss to analyze a reading passage, with explicit attention paid to
the language or vocabulary used.
 Task designed to polish mathematical vocabulary (e.g., contribute to a Word
Wall, look up definitions of terms, create definitions)
 T critiques language or expressive features of S’s oral or written presentation
(e.g., clarity of writing, voice tone, eye contact)
X Many new concepts come with new vocabulary; do not count the standard
introduction and definition of a new math term. These incidents should
reflect deliberate literacy-building strategies.
Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________
Summary of Observation Data
Lesson
component
Total
elapsed
time
TI
TM
SD
WP
WC
GP
GC
IP
IC
T/Q
U
O
Important notes regarding these lesson-component data:
Important notes regarding these practice data:
Practice
a) High level of cognitive demand
b) Ss given authority
c) T connects to another math topic
d) T connects to another academic topic
e) T connects to real-life
f) Ss choose among solving methods
g) Technology, manipulatives, etc.
h) Developing language skills
i) Multiple forms of representation
Rating
Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________
Teachers for a New Era
Evidence of the impact of Preservice Preparation on Classroom Practices
and Pupil Learning
Teacher Practices and Rationales: Observations and Interviews
Post-Observation Interview Questions
Script: “I just had the opportunity to observe your lesson. Thank you very much. Now I have some
questions for you about your class, experiences in teacher education at CSUN, and specifically about
today’s lesson. You may skip any question if it causes any stress. Remember that your comments are
strictly confidential and none of your remarks will be associated with you by name.
In your consent form, you indicated your permission to allow tape recording of this interview. If that is
still agreeable to you, I would like to turn on the recorder and begin our interview. Do you have any
questions before we begin?”
Background Demographics of Class/Students
a. Observer
b. Date and day/time of the class
c. Teacher/school
d. Course Name/grades
e. Unit topic
f. Learning objective
g. Instructional materials
h. Relationship to previous or forthcoming lessons
i. Number of students officially enrolled in the class
j. Number of special education students
k. Language/ethnic/cultural characteristics including English Language learners
l. Transitory nature of the students (i.e. are there many recent immigrants or do students only
spend a short time in the school before moving?)
m. Other comments (such as “is there anything unusual or special about the students I
observed?”
Background Demographics of Teacher
a. Describe your previous teaching experience.
b. Did you take all your credential coursework at CSUN? Yes No ; if no, how did you satisfy
your subject matter competence?
c. What additional coursework have you taken relevant to math teaching?
d. Do you speak any languages other than English? If so, which ones and what is your level of
fluency (such as completely fluent, somewhat fluent, conversational).
e. How would you identify yourself in terms of a cultural and/or ethnic group?
f. What motivated you to become a teacher? (try to get as much detail and nuances as possible).
g. Does being a teacher have a special meaning for you? Please explain.
Lesson Planning
A. In planning and teaching today’s lesson, what experiences were you drawing upon?
With prompts…
Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________
1)
2)
3)
4)
How you were taught in the same grade/course in high school
Experiences within your family (as a sibling, mother, daughter, father, son)
Previous work (either with or without children)
Lessons from your coursework, reading, or professors at CSUN. Be specific if the class
was in the field of math, of educational psychology (such as Psychological
Foundations, classroom management) or content knowledge such as math courses.
5) Lessons from your clinical practice, supervised fieldwork aligned with CSUN
6) Suggestions from people at your school – principal, math chairperson, other teachers
7) Professional Development such as those run by the school, district, or conferences
(please describe)
8) Other university coursework
9) Your own reading about teaching
10) Other
B. In general, what technologies and/or manipulatives have you used in your
teaching? How often do you use each? What encourages or prevents you from using them?
Perceptions of the Observed Lesson
I just had the opportunity to observe a lesson in your class.
Tell me your thoughts about it or anything that might be useful for me to know
1. Did this lesson turn out different from what you planned? If so, in what ways?
2. Was this a typical example of your teaching? Why or why not? (note use of group work,
technology and /or manipulatives)
3. Was this a typical example of your students’ behavior? Why or why not?
4. What do you think the students learned from this lesson? How do you know?
5. What went through your mind when [event]? What were your options for actions or responses?
Why did you choose to respond as you did? Did it work out or would you have responded
differently in hindsight?
Perceptions of Students’ Learning
1. What things help your students learn best? (probe for three responses)
2. How did you come to know these are helpful in learning?
3. How do you use to determine successful learning?
4. What challenges do your students encounter in their learning?
Perceptions of Teacher Education program at CSUN
1. What were the most useful or influential courses or experiences you had at CSUN that have
impacted your teaching? Describe how and why these were especially useful. (Probe for three
responses)
2. Was there anything that happened at CSUN that was particularly encouraging to you in pursuing a
career in teaching?
3. Was there anything that happened at CSUN that was particularly discouraging to you in pursuing a
career in teaching?
4. Given what you now know about teaching, what do you think should have been part of your
CSUN program but were not? Be specific and tell why these would have been useful in math
education.
5. Do you plan to stay in teaching? Why or why not?
Observation of:___________________ Date: _____ Course:___________ Grade(s):_______ Observer:_________
Additional Comments
Is there anything else you would like to tell me about your experience in teacher education at CSUN
or about the lesson today?
Some indicators from Weaver, Dick & Ringelman (2005)