The Consistency of Teaching Beliefs and Practices;

A Case Study

Ryan O’Block

Phys4460

12 December, 2011

Introduction:

Is it enough to change the way teachers think about their teaching? Can teacher beliefs

alone inform their employed teaching practices? Is it possible that there is a disconnect between

teachers’ beliefs about teaching and how they actually teach? These were the questions that came

up during my time observing at Boulder high school. My observations led me to conduct a case

study of an experienced high school physics teacher. The purpose of this case study is twofold.

First, it tests the plausibility of examining complicated classroom qualities such as agency,

possibly informing future efforts of a similar nature. Second, this study sets out to investigate the

consistency between a teacher's expressed beliefs and their classroom practices. The results of

which have possible implications for future teacher education.

Background:

This semester long case study was conducted in two algebra based physics classes in

Boulder high school. These physics classes were general level, high school physics courses taken

up by juniors and seniors. Each class contained about 26 students that were taught during back to

back classes in the first and second periods of the day. The teacher observed, Allen (pseudonym),

has almost a decade of experience in aerospace engineering prior to enter the teaching profession.

He has been teaching at the high school level for almost two decades. Allen had been identified

by many people in boulder educational community as a top notch teacher.

Method:

To investigate the alignment of teacher beliefs and practices a framework had to be

developed. This was done in collaboration with Ben Spike and Noah Finkelstein of the

University of Colorado PER group. While there are many different aspects of teacher student

interacts that could be analyzed, this study focused upon two. The first dimension of the

classroom to be analyzed is agency. Merriam-Webster defines agency as "the capacity, condition,

or state of acting or of exerting power." To determine who had agency within the class room two

questions were asked. Who is active in the learning process? Who is in control of what is to be

learned and how? Since activities in this high school classroom varied widely, a number of

different rubrics to assess agency in these different situations were created. The first rubric was

applied to the student-teacher interactions during either lecture or one on one. The rubric focuses

on agency surrounding the solving of problems or discussion of concepts. The second rubric was

used for laboratory type activities. This rubric focused on how the lab was designed and

facilitated to allow students to interact with the physics material. The third rubric was used for in

class demonstrations. This rubric focused on how the demonstration used facilitated students

access to physics concepts. All rubrics are shown on the next two pages.

The second dimension of the classroom that was analyzed is activity goal. Activity goal

is focused on the outcome of an activity or interaction. At first approach this dimension seems

extremely vague and subjective. To focus the evaluation of this dimension I specifically looked

at whether the activity was encouraging the students to engage in sense-making or

answer-making. In other words, was the value of the activity surrounding the outcome or

“answer” or was the reasoning process behind that answer valued. This is distinct from agency

because either the teacher or student could be in charge of activity goal. For example, it is

possible for students to be working on an activity on their own, allowed to discuss with

neighbors, and where the teacher does not interfere with or engage the students. This would be

classified under student agency. If in this activity, the students’ only task and goal was to get the

correct answer, the activity would be classified under answer-making for the activity goal.

Agency Rubrics Rubric 1 (Lecture, one-on-one student teacher interaction)

Student (+1) Mixed (0) Teacher (-1) Facilitate discussion Summarize student

points Give complete answer

Let students discuss Confirm & correct student ideas

Show how I would do it

Listen to discussion Clarify the question Tell/explain correct reasoning

Let students think Provide real-world examples

Start from scratch

Know when to stop/not interact

Rubric 2 (Lab activities) Student (+1) Mixed (0) Teacher (-1)

Determine topic or driving question of lab

Students determine part of the driving question

No freedom from given procedure

Help determine the accuracy of result

Students compare result to one given by teacher

Teacher determines if results are correct

Investigation of phenomenon where theory is derived

Students investigating preexisting theory

Lab is just demonstrating theory, no real question asked

Rubric 3 (Class demonstrations) Student (+1) Mixed (0) Teacher (-1)

Make open ended predictions

Students select from teacher provided predictions

Give complete answer

Students’ observations/ measurement judge results

Teacher moderates what students observe

Show how I would do it

It is the left to the student to connect the physics ideas

Teacher guides/ clarifies physics explanation

Tell/explain correct reasoning

Activity Goal Rubric

Rubric 4 (Sense-making vs Answer-making) Sense-Making (-1) Mixed (0) Answer-Making (-1)

More emphasis is place upon reasoning behind solution

Both answer and reasoning is given equal emphasis

Teacher focuses solely upon mechanics when solving a problem

Students are engaged in discussion surrounding concepts

Only the solution is requested/ displayed with no explanation

Teacher uses open ended questions such as how do you know?

In order to measure Allen’s beliefs against his practices, a variety of sources were

analyzed. The main tool used to flush out Allen’s self-expressed beliefs about teaching was an

interview. The questions used in the interview were: What is your role as a teacher? What is the

role of the Student, how does a student learn best? How do you become a better teacher, what do

you do to improve your teaching? What are the external constraints on your teaching? If you

didn’t have any external constraints how would you teach differently? The next source used to

investigate Allen’s beliefs was his syllabus. It is important to note that only statements that more

explicitly expressed to his beliefs of physics or teaching were analyzed. It was not attempted to

extract beliefs from course policies or assignment lists, as they are just the mechanics of the

course and more subject to interpretation. The final source used to determine Allen’s

self-expressed beliefs about teaching was his comments to me outside of classroom activities.

Since Allen knew that I am an aspiring high school physics teacher he would often comment

about his teaching practices. This proved to be small, but valuable source of data. The source of

data used to evaluate Allen’s teaching practices was detailed in-class field notes. These field

notes were usually taken by hand Monday mornings, but occasionally I would also observe

Friday mornings as well.

After the completion of the semester I coded all the data sources for both dimensions.

Using the established rubrics, I assigned a value of either 1 or -1 to one of the extremes and value

of 0 to mixed category. After the data sources were coded, the numbers were averaged to give a

value between 1 and -1. The goal of this approach was to place the overall teacher’s beliefs and

actions along a sliding scale. For agency, the scale ranged from student’s having agency (+1) or

the teacher having agency (-1). The activity goal the scale ranged from answer-making (+1)

activity to sense-making (-1) activity. Also, to see how diverse Allen’s beliefs and approaches

were, the standard deviation was taken and plotted on the sliding scale.

Results:

Upon analysis of Allen’s self-expressed beliefs it was found that his beliefs span the

spectrum in both dementions. It was also found that although he expresses a variety of beliefs, he

strongly favors student agency and sense-making activities. Below is a table of examples

statements taken from the interview, syllabus, and in-class comments and categorized.

Agency Beliefs

Student (+1) Mixed (0) Teacher (-1) Interview “[They need to be]

mentally engaged in the process, so that they are performing the role of the scientist or physicist. They are solving problems, I am not doing it for them

“I have to provide a motivation for them to perhaps be interested in [physics].I have to clarify difficulties…”

“I need to maintain a sense of order, a sense of control”

Syllabus “Another important thing for youth practice is how to find information on your own”

…purpose of this class is to show you what physics is and what physicist do

In-class Comments “I plan on letting nature tell them if they are right or wrong. Then they can go back a figure out where they went wrong”

“I was hoping everyone would finish their lab today. I wanted them to compare their numbers with the ones I calculated.”

“You give them f=ma and they just stare back at you blankly. You just have to keep walking them through it.”

The data collected from describing Allen’s self-expressed beliefs about agency was then

compared to the in class field notes. It was found that although the data still spanned the

spectrum, his in class actions favored the mixed to teacher agency. Below are some examples

from what was noted in class.

Agency Related Practices

Student (+1) Mixed (0) Teacher (-1) Lecture and student/teacher interactions

Allows and encourages students to work in groups to solve the problem together. Walks around room allowing students to work on problem.

Takes student suggestions/ number values as he works problem on the front board

Comes back up to the front of the room, quickly runs through how problem is performed on board.

Labs Decided where to place person catching ball, based on calculations, if they missed they were given a chance to return and reexamine calculations. “Let nature decide who was right/wrong.”

“These are the values you should have gotten and if you didn't you need to explain why in your lab book.”

Practically does a groups calculations for group 1 "so we take the sign of that and get about 16…and that should fix your problem…37 feet should be good"

Demos “What do you think is going to happen?” leaves open ended

“Do you think the ball will land in position 1,2,3,4 or 5.”

Tell the class, "as you can see whatever horizontal velocity I have, the ball has the same horizontal velocity" emphasizes that they know this.

Agency Beliefs

Student (1) Mixed (0) Teacher (-1) 11 8 3

Agency Practices

Student (1) Mixed (0) Teacher (-1) 42 27 72

Comparing Agency Beliefs to Practices

Upon averaging the data from the beliefs and practices surrounding agency one can

see a shift from the student agency toward teacher agency. The difference between Allen’s

beliefs and practices surrounding agency is 0.577. This is a fairly large discrepancy considering

that it is almost half of the possible discrepancy from his original beliefs. The standard deviation

in Allen’s agency beliefs is + 0.36. The standard deviation in his agency practice is + 0.44. These

spreads are represented by the colored arrows extending to either side of the average on the scale.

It is important to remember that the standard deviations in this case do not represent error bars,

but how diverse Allen’s beliefs/ practices are.

Next, the data of Allen’s beliefs and practices surrounding activity goal was

analyzed. Some examples of coded beliefs and practices are shown below.

Activity Goals Beliefs Sense-making (+1) Mixed (0) Answer making (-1)

Interview “My goal might be for them to do an awful lot of thinking, and if I'm overly clear their not doing that.”

Syllabus “Physics is mostly about figuring things out” “There is virtually nothing to memorize in physics… The primary goal of this class is to improve your analytical thinking…”

In-class comments In response to the question of why teach graphical solving method instead of constant acceleration equations: "They do not allow for a grasp for what is actually going on. You can give a 10 year old E=MC^2, E and M and they can solve for E. Doesn't meant they understand E=MC^2.

Activity Goal Practices Sense-making (+1) Mixed (0) Answer making (-1)

Teacher models multiple ways to approach test question #2. Spends much of the time explaining WHY. Allen asks group to explain if the final calculated distance in their projectile lab made sense Asks students to come up and label forces on the free body diagram. Students then engage in debate to why labels are correct or incorrect.

Quickly solves problem explaining reasoning along the way. Does not check for understanding, just moves on. Allen gives values of what students “should have gotten” students must say why their values are different from his values…observe students recording Allenʼs values as “correct results”, “right answer”, …

Students observed working on a page filled with algebra problems. Some worked in groups, some on own. Many students observed to using phone to look up answer. Some copying off each other…. Tells result of demo, no reasoning, observations, or argumentation behind it. "The important thing to remember is that motion in the horizontal motion and motion in the vertical direction are COMPLETELY INDEPENDENT! Remember this"

Activity Goal Beliefs

Sense-making (1)

Mixed (0)

Answer-making (-1)

14 1 0

Activity goal Practices

Sense-making (1)

Mixed (0)

Answer-making (-1)

29 12 41

Comparing Activity Goal Beliefs to Practices

After averaging Allen’s beliefs and practices surrounding activity goal on can see

that there is a major discrepancy between his beliefs and practices. His belief average places him

as 0.933 which is very close to a complete focus on sense making. Allen’s practices on the other

hand place him at -0.146 on the answer- making side of a mixed approach. The discrepancy

between his beliefs and practices surrounding activity goals is about 1.08. This is a large swing

considering the scale has a total length of 2. The standard deviation of Allen’s beliefs is + 0.13

and the standard deviation of his practice is + 0.45. This shows that although Allen has a very

narrow belief about activity goal, his actual approach is much more diverse.

Conclusion:

In this case study it was observed that teacher’s self-expressed beliefs does not

necessarily match their practice. In both dimensions of agency and activity goal there was a large

discrepancy between the observed teacher’s expressed beliefs and classroom practices. Although

the data agrees with my personal experience in the class, there are possible effects exaggerating

the differences between Allen’s beliefs and practices. The first is data availability. The majority

of the semester that I was observing Allen’s class I was focusing on a similar, but different

research question. This being the case, the majority of my field notes did not possible identity

evidence informing the agency and activity goal dimensions of the class. Also, because field

notes were taken by hand, not all of the classroom activities could be documented. This could

possibly cause a source of bias in terms of what I chose to document. The second possible source

of error is the fact that that all events were weighted equally. This means that a comment by the

teacher could possibly be weighted the same as a 5 minute long activity. Attempts to address

these issues will be discussed in the next section of the paper.

This case study is foreseen to have two possible implications. The first is the

framework developed here could possibly be used in evaluating more complicated teaching

qualities. Instead of comparing beliefs with practices one could compare practices to a teaching

quality standard. This could be utilized in teacher education programs, for professional

development, or in a state’s evaluation of teaching. Although due to the time investment it takes

to analyze a single dimension, there would have to be a more streamlined system developed.

The second possible implication of this study pertains to the dissemination model of

professional development. Within the discipline-based STEM education research community,

findings and instructional strategies tend to be exported through dissemination (Henderson et.

All, 2010). This method assumes that solely convincing teachers that an instructional practice is

beneficial is enough to create change. Even if the two problems of teacher buy in and

environmental/structural constraints addressed in the Henderson article are accounted for, it is

still possible to see a discrepancy between practice and belief. I would argue that the amount that

a teacher reflects, using actual class data, upon his/her teaching is correlated with this

discrepancy between belief and practice.

Future directions of this study:

The hypothesis of teacher reflection is possible direction for future work on this

topic. But before one continues on to try and fix this problem, I feel that it needs to be identified

as a problem in the first place. Currently the literature is split on whether or not teacher’s beliefs

are consistent with their practice (Raymond, 1997).More research could be done to provide

clarity on this issue. Also, I feel that one should see if inconsistency itself is a problem. Is

agreement between belief and practice connected to student learning or attitude, or is the only

thing that matters teacher practice? All in all, there is not yet enough research to provide clear

answers.

If this research project were to be continued, I would recommend a couple of

changes to the methodology. First, there needs to be a way to assign weight to different activities.

Currently, this study’s approach views a 15 min time block allotted for peers to discuss a

problem the same as the teacher spending 2 minutes solving the same problem. Yes, if the

teacher has additional interactions during that 15 min peer instruction time, then those are taken

ingot account. It is still possible that if the majority of the class time is spent doing activities that

focus on student agency, but there is the same number of activities focused on teacher agency

this approach won’t show this. What I would recommend is videotaping class sessions. This

allows the evaluation of different class dimensions using time-on-task analysis. While there is

still some tinkering that needs to be done, I feel that this is a valuable study to inform us about

teachers’ consistency between their beliefs and practices.

References

Henderson,  C.,  Finkelstein,  N.  &  Beach  A.  (2010).  Beyond  Dissemination  in  College  science  teaching:  An  Introduction  to  Four  Core  Change  Strategies,  Journal  of  College  Science  Teaching,  39  (5),  18-­‐25.  

Raymond,  Anne  M  (1997).  Inconsistancy  Between  a  Beginning  Elementary  School  Teacher’s  

Mathematics  Beliefs  and  Teaching  Practices,  Journal  for  Research  in  Mathematics  Education,  39(28),  550-­‐576