Afl research proposal

ASSESSMENT FOR LEARNING 1

Assessment for Learning: What Assessment Methods Do Teachers of Mathematics Use and Why

Yulia Shadyrya

University of Washington Bothell


Research Topic

In her book What’s Math Got to Do With It?: Helping Children Learn to Love Their

Least Favorite Subject, Jo Boaler describes the gloomy state of mathematics in the United States.

Our country’s ranking in math, when compared to thirty-nine other countries around the world, is

as low as twenty-eighth (and plummets down to fortieth if we take into account the amount of

spending on education). The number of students graduating with a major in mathematics at four-

year colleges has decreased by nineteen percent over the last ten years and almost half of all

master’s degrees and more than a third of all bachelor’s degrees in engineering, mathematics,

and information science are attained by nonresident aliens (2008). Among the main reasons for

such depressing data, the author points out, is the fact that American schools use standardized

high stakes tests and other forms of summative assessment, which is a form of assessment of

learning. Wikipedia’s definition of the assessment of learning is: assessment that is accompanied

by a number or letter grade, assessment that compares one student’s achievement with standards,

and assessment that occurs at the end of the learning unit. Boaler suggests that American

teachers need to learn to practice assessment for learning. The concept of the assessment for

learning ―is based upon the principle that student should have a full and clear sense of what they

are learning, of where they are in the path toward mastery, and of what they have to do to

become successful‖ (p. 98).

In related literature the term assessment for learning is often used interchangeably with

the term formative assessment, which might lead readers to believe that they are the same thing.

However, according to Richard Stiggins, the founder of the Assessment Training Institute of

Pearson Education, Inc. and the author of multiple publications on assessment, assessment for

learning is not limited to formative assessment. In addition to frequent testing and revising their


teaching styles based on testing information, teachers must involve students in the process of

assessment. Stiggins recommends a list of actions to teachers, who want to use the assessment to

advance student learning. These actions include: explaining achievement targets to students,

educating themselves on accurate uses of assessment and on using it to strengthen students’

confidence as learners, translating assessment into frequent feedback, adjusting instruction based

on assessment, engaging students in self-assessment, and teaching students to communicate with

them and with family members regarding their learning progress (2002). Dylan William, the

deputy director of the Institute of Education in London, and education researcher of many years,

who specifically focuses on formative assessment research wrote about very specific techniques

of assessment for learning: rich questioning, feedback, and learner’s role in assessment (1999).

Rich questioning refers to questioning technique that requires students to analyze problem,

instead of just guessing an answer which teacher will like. Mathematical problems that confuse

students are usually avoided by teachers. However ―tricky‖ questions are a valuable part of rich

questioning because they provoke deep thinking, and help teachers in assessing their pupils’ true

understanding of math. Other techniques of rich questioning include: allowing for long

conversations to grow from one student’s question, giving ample time for students to think about

a question, asking students to come up with questions, and framing questions as statements to

provoke discussions. Feedback given to students can take different forms. Based on clear

research, William suggests letting students know what they need to do to improve, instead of

praising them or comparing to others, and design feedback so it instills in students belief that

they can improve their mathematical skills with practice. He also insists that students have an

important role in assessment for learning. Thus, sharing assessment criteria with students and

letting them monitor their own progress is essential.


In addition to the obvious benefits of assessment for learning, in my opinion a major

advantage of assessment for learning lies in relating classroom setting to real life. In real life we

rarely get grades for our actions. Constructive criticism and help is more relevant and useful than

grades. To illustrate my point, I will share an example from my own work experience. Once I

worked at a firm that did not give proper training or any feedback of its employees’ performance.

I was satisfied with my pay and position at that time, and did not wonder why the company

promoted several other workers before me. Luckily, one of the managers was observing my work

for several months. She had a lot of work experience and was a top performer at that company.

Only through conscious observation was she able to notice and truly assess my performance.

After I spent some time training with her, I was able to correct a few mistakes, and master skills

necessary for me to be successful. It turned out that due to poor training and the absence of

feedback, many new employees were underperforming, and, as a result either quit or got fired.

Some employees, who were able to overcome poor reviews, became stuck at the same positions,

and only a few employees moved up the corporate ladder. Needless to say, that the company

morale as well as productivity suffered because of such a poor feedback system. Today, many

students in American schools are stuck in a situation that is not unlike the one described above.

Unlike adults, who have more experience in life, students often do not try to figure out what is

the real reason behind their poor grades, and merely accept the label of being ―stupid in math.‖

Literature Review

The importance of assessment for learning (improved formative assessment) was shown

by Paul J. Black and Dylan William in 1998. Their study is referenced by most authors who

wrote about the subject of assessment for learning. Black and William examined more than 160

journals, 580 articles or chapters on assessment and together with the experts from all over the


world, concluded that a lot of evidence exists to the fact that formative assessment improves

learning standards, that there is room for improvement, and that there is information available on

how to improve formative assessment. The authors illustrate their argument by stating that

improved formative assessment could help an average student to move to the top 35% of their

class and an average ranking country, like the United States, could rise to be in the top 5%.

Moreover, the study also shows that improved formative assessment tends to help lower

achieving students more so than average or high achieving students, which has tremendous

implications for closing the achievement gap present in the United States. One of the two biggest

areas where assessment needs to be improved, that the authors list is the teaching practice, where

currently assessment is proven ineffective and even damaging to students. The study suggests

that in order to make a positive difference, formative assessment needs to be improved by

focusing on the following: self-esteem of pupils, which is improved by moving away from

competitive classroom culture and helping individual students with specific problems; self-

assessment by students, which is only possible and greatly beneficial when students have a clear

picture of where their learning goals are; and the evolution of effective teaching, which involves

revising whole teaching plan instead of just one of its aspects, which is assessment.

The authors emphasize that the strategy for improving formative assessment needs to

focus on the ―inside of the black box,‖ in other words, in the classroom. Neither more traditional

research nor large implementation programs will help with the implementation of assessment for

learning. Rather ―each teacher must find his or her own ways of incorporating the lessons and

ideas set out above into his or her own patterns of classroom work and into the cultural norms

and expectations of a particular school community‖ (1998, p. 12,). Specific steps include

learning from development, which means having plenty of real life examples for teachers on how


to implement assessment for learning, such examples must be specific to subject areas; and

practitioner research, one example of which is investigating ways teachers are dealing with

balancing formative and summative assessment in their classrooms. Moreover, in 1999 William

publishes three studies that describe specific strategies that can be used by teachers in their

classrooms. These studies include rich questioning, feedback, and the learner’s role in

assessment (for more description see introduction). Beyond these recommendations, the author

provides evidence gathered from research. For example, one of the articles references an

experiment done by Ruth Butler, where 200 fifth- and sixth-graders were given four kinds of

assessment: comments, grades, praise, and no feedback. This study showed that the interest as

well as performance of students increased after comments, and stayed the same after grades,

praise, or no feedback (1987).

More current literature suggests that the problem of inadequate assessment still exists in

the United States. Richard Stiggins conveys the urgency of assessment reform in the U.S.A.,

which would balance assessment of learning with assessment for learning (2002). He describes

the attitude of our nation toward assessment as: ―obsessed with the belief that the path to school

improvement is paved with better, more frequent and more intense standardized testing‖ (p. 759).

As a result, he states, there are no resources left to support teachers in ongoing classroom

assessment. Only a small portion of states require teachers to be skilled in assessment, and

almost no states require that of school administration. Stiggins argues that instead of constantly

increasing challenge in attempt to motivate students, the country should balance and improve

assessments of and for learning. He lists relevant position statements from such groups as

American Foundation of Teachers, National Education Association, National Council on

Measurement in Education, American Association of School Administrators, and others.


Popham, W. explains that No child Left Behind (NCLB) and its measurement system of

adequate yearly progress (AYP) pressures teachers to teach to the test, and consequently get in

the way of attempts to instill assessment for learning. The author insists that states needs to

develop instructionally sensitive tests, which measure teaching as well as learning (2006). It

must be noted that although the two sources listed above agree with the urgency of the situation,

they both are focused on the strategies on large scale, which is contrary to the recommendations

of Black and William.

Finally, as described in introduction, the subject of mathematics needs special

consideration when making changes in assessment strategies. Jo Boaler describes that most

mathematics students, who are being evaluated in traditional ways, cannot even describe what

they are learning beyond the names of the chapters in textbook or problem numbers. Those who

suffer the most from the standardized testing are usually children from low income families and

students who are English language learners. Moreover, students who are low achievers in

schools are not being helped, but are instead merely labeled as ―below average,‖ which further

discourages them from learning mathematics (2008). My work experience taught me that having

a mentor skilled in assessment for learning is invaluable. Teachers, who have the opportunity to

observe their students directly and often, are at a perfect position to become such mentors and

empower students to take learning in their own hands.

Research Questions

Here are some aspects connected to assessment that I would like to investigate in the process

of my research: 1) What are the current techniques of assessing students’ knowledge of

mathematics? Are the elements of assessment for learning present? 2) What factors do


mathematics teachers in a particular school consider when developing assessment plans?

According to the section above on literature review, American students are suffering from the

overwhelming presence of judgmental feedback in the form of grades, and would instead benefit

from the presence of meaningful assessment—assessment that could help them take charge of

their learning. Clearly, mathematics is a subject in need of special attention. There is a lot of

information about how to improve formative assessment.. Here are some ways my research

might contribute to theoretical development of the concept of the assessment for learning:

 simply raising such important questions might make teachers re-think their assessment

techniques or even their personal teaching philosophies

 data gathered in the process can be used in further research of what elements of the

formative assessment American teachers currently practice (if at all), and to compare it to similar

data collected in the past in order to measure the progress(or lack thereof) of the formative

assessment in American classrooms or in a particular school

 information about different types of assessment can be used in future practitioner

research projects. One such project could evaluate the effect of different types of assessment on

student learning and self-esteem in a particular school, which in turn might influence school

policies to support teachers with assessment for learning

 increase in the assessment for learning in a particular school and whole America, will

lead to overall increase in student learning and to decreasing the achievement gap between low

and high achieving students

Considering the recommendation of Black and William, it is clear that practitioner research is

crucial in implementing assessment for learning in schools. Therefore these research questions


are aimed at investigating assessment situations in one particular school by either a teacher or

someone else, who is able to work with teachers regularly. The combined analysis of both

questions should help mathematics teachers of this particular school in their daily practice,

because it will allow them to see what the overall assessment strategy of the mathematics

department is as a whole, and it will allow them to see what some of the most important

constrains are as perceived by teachers and the administration. It will also help each teacher to

take an objective look at his or her own assessment approaches and to judge whether these

assessment approaches assist student learning. Separate teachers, as well as the whole

mathematics department, will be able to revise assessment strategies if necessary, whether it will

be by adding more elements of the assessment for learning, or by reconstructing the whole

approach based on the most important constrains. Having information about constrains can also

help with releasing potentially damaging findings, according to Robinson and Lai (2006).

Research Setting Design

This research project is designed to be conducted by a group of student-teachers in the

school of their placement. Each student-teacher will primarily collect information on their

cooperating teacher, but in general research, planning, and analysis will be done by these student

teachers as a group. Prior to initiating research, student-teachers will have a discussion meeting

with teachers in order to explain the general purpose of this research. Student-teachers will be

very explicit about what they will do. A question might arise as to whether it is appropriate to tell

teachers that this research focuses on assessment for learning, as it might influence the way

teachers normally evaluate their student. However, in my opinion, one of the great advantages of

practitioner research is that it is able to improve teaching practices in its process. Even if teachers


will start to include elements of assessment for learning, objective descriptions of their

assessment styles with these alterations will still be beneficial, because it is not as important for

us to know past actions of teachers as it is to promote assessment for learning techniques.

Another concern is that teachers might feel like they are being judged by researchers if they

reveal their intention of finding out whether teachers’ assessment techniques are assessment for

learning or not. Explaining that part of research is intended to discover constrains which shape

assessment strategies, might help in relieving this tension.

The student-teacher position fits very well with this type of research, because a lot of

initial responsibility of student-teachers is to observe their cooperating teachers. In addition,

student-teachers will be working in close contact with cooperating teachers and with all the

students, which will give student-teachers better understanding of the set of assessment and

related constrains teachers face. On the other hand, because student-teachers will be new to the

setting, they might have less bias in their assessment of the situation. Putting this research in the

hands of student-teachers is also practical: every student-teacher will have only one cooperating

teacher to follow, which is very helpful with keeping the load of work under control.

Consent forms will need to be signed by parents or guardians of all student participants.

Final and intermediate results will be open to all participating teachers. Any explanations and

corrections will be welcome. In case the research will be published, pseudonyms will be used for

schools and all participants. Preparations for this research will take about two months, including

writing the research proposal, talking to teachers, and collecting consent forms. Therefore,

according to 40-20-40 rule described by Robinson and Lai(2006), the optimal time frame for

data collection should be one month, and for results – two months.


Methods for Collecting Information

1) What are current techniques of assessing students’ knowledge of mathematics? Are the

elements of assessment for learning present?

These questions can be thought of as exploratory in nature, because student-teachers will

be investigating different assessment techniques used by mathematics teachers. However, the

ultimate goal of raising these questions is to encourage teachers to think of assessment as

something that should improve student learning, and, while collecting information, researchers

will look for specific indicators of assessment for learning. For this purpose we will think of

these questions as both exploratory and checking. The process of information collection will start

as exploratory, and as clear patterns of assessment develop, observation notes, questions, and

other inquiries will become checking.

In order to investigate these questions, student-teachers will conduct interviews with all

mathematics teachers, and two or three students from each teacher’s class. Student-teachers will

also conduct observations of each participating classroom once a week throughout the quarter,

and look at examples of assignments (homework, group work, tests, etc). Classroom

observations will be done two class hours a week, alternating days and classes to assure broad

coverage of collected information. One week student-teachers will swap cooperating teachers in

order to increase validity. During classroom observations student-teachers will take notes--

writing down every instance teacher is giving any type of verbal feedback to students or that of

students giving feedback to each other whether prompted or not. Copies of various assignments

will be made for analysis.

Interviews will be conducted after classroom observations are done and assignments

studied, in order to ask teachers and students for any clarifications or elaborations. Interviews


will start with a general question: Please describe way in which you assess your students’

understanding of mathematical concepts? If necessary, more specific questions will follow: What

instruments do you use to assess your student’s knowledge (tests, dialogue, projects, etc)? How

do you give them feedback on each of these instruments (grade, comments, grade and comments,

praise, credit, etc)? How often do you assess each of your students (every day, week, month,

etc)? Do you use such techniques as self-assessment and peer-assessment by students? Students

will be asked some questions that are similar, for example: How often do you receive feedback

from your teacher and what kind of feedback is it (grade, comment, etc)? Some questions will be

quite different, for example: Did your teacher clearly communicate the learning objectives for

this week(unit)? Does your teacher explicitly tell you where you are and what you need to do to

achieve class objectives? Does your teacher encourage you to discuss your learning progress

with your teacher and your family? In order to increase validity, student-teachers will switch

their observed teachers once in two weeks, and audio- or videotape all interviews, and will

transcribe and analyze them together.

2) What factors do mathematics teachers in a particular school need to take into account when

developing assessment plans?

This question will be asked at interviews with teachers and will be also posed to

administrators. All answers will be listed, and a follow-up questionnaire will ask teachers and

administrators to assign significance value to each factor: very important, important, not very

important, or unimportant.

Methods for Analyzing Information

During analysis I will be looking for these elements of assessment for learning: presence


of rich questioning as described by Dylan William(1999); teacher commenting on students’

progress without giving a grade or praise; presence and quality of self and peer assessment by

students; quality of classroom discussions (Does teacher often answer her own questions? Are

students allowed to discuss answers among themselves?); frequency of tests; general openness of

the teacher to discussing students’ learning progress with the student and his or her family.

Transcribed interviews with teachers will be scanned for any information on assessment

tools and classroom observation notes will be analyzed for any evidence of assessment, such as:

teacher taking notes on where her students are, teacher giving evaluative comments to her

students, students evaluating each other with and without prompt from a teacher, and any other

such instances. This information will be organized in portfolios for each separate teacher, in a

form of a time line one quarter in length. In my opinion measuring assessments against time is

relevant, because a crucial part of assessment for learning is giving students timely feedback.

Each instrument of assessment will be listed on timeline with a detailed description of such

things as what the main purpose of the assessment was (reporting to the state, teacher’s insight

to students understanding, letting student know where she stands, etc), feedback to student, and

so on.

Transcribed interviews with students will be analyzed for two things: whether students

are have a feel about where they are in the process of learning based on their teacher’s

assessment and whether or not discussion of their learning process with their teacher and families

is encouraged by their teacher. Depending on how clear the data will be, the data might be

quantified and added to teacher’s portfolios in form of a simple table or if additional information

is discovered, descriptions of how students perceive their assessment. Together with the


information from the teacher, a picture will be formed illustrating what a particular teacher’s

assessment techniques are, and which techniques can be classified as assessment for learning.

One list of constraints on assessment strategies will be developed for all mathematics

teachers and administration separately. All constraints will be marked as: very important,

important, not very important, unimportant. This information should help to see what are the

most important constrains considered in this particular school’s math department. Constraints

perceived as important by teachers might be compared to those perceived important by

administration.

Reflection

The most important realization I have made while working on this research proposal is

how important it is for a teacher to think like a researcher. While I knew that a good teacher must

be reflective, all this meant to me was that a teacher must look critically at his or her own work

and must be open to change. It was difficult for me to imagine how I would measure the

effectiveness of my teaching and to know what criteria I would use to gauge myself. While I

knew that it is important for a teacher to work in collaboration with other teachers, I could not

imagine the process of collaboration to be anything more than discussing student related

problems. Working on this project gave me an idea of how practitioner research might establish a

framework for self-reflection as well as for collaboration with other teachers.

When working on developing research questions, I realized that knowing what you want

to research is only one part of research preparation. The way research questions are formed

defines what the research project will have a potential to accomplish. In my case, I was very

interested in researching something relating to assessment for learning, since I was convinced


that this approach can really influence student learning. However, when deciding on what

exactly can and should be researched, I realized how many factors needed to be considered. First,

I had to do preliminary research of relevant literature and somehow classify all available

information deciding which to consider when developing research questions. It was very

important for me to imagine a situation that was possible, and for this proposal to be for

practitioner research. Therefore, I picked a realistic setting: student-teaching placement; and

designed research considering such details as practicality, ethics, and validity. I asked myself

such questions as: How much time can I dedicate to this research? How can I discuss this

research with a cooperating teachers without offending him or her? What can I do in my position

of student-teacher? Forming research questions with all these questions in mind was,

surprisingly, the most difficult part of this proposal.

Searching for relevant information, I came across some great and not-so-great projects. I

realized that a valid topic, well formed research questions, and a solid research design can lead to

a study that many teacher researches will find useful. Being in the position of student teacher

means having access to great data and knowing what research topics are significant. Learning

about and practicing research means being able to design a study that will bring useful results.

However, in such setting researchers must be very careful about preparing, conducting, and

analyzing their research. They need to remember that they are new in the school; and before

starting any such activity it is necessary to study school’s environment. I learned that even if all

participants are eager to help, it is important to know that information provided by them is only

their perception. In my research project, I tried to establish a process of triangulation, where I

look at one issue from the eyes of teachers, administration, students, and researchers. Finally,

preparing this proposal, I imagined how much different information will be gathered in the


process, and how important it is to collect it using appropriate research techniques, which could

make the difference between groundbreaking revelations and ―oops, never mind‖ kind of

research

References

Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom

assessment. The Phi Delta Kappan, 80(2), 139-148. Retrieved

from http://www.jstor.org/stable/20439383

Boaler, J. (2008). What’s math got to do with it?: Helping children learn to love their least

favorite subject –and why it’s important for America. London: Penguin Group.

Butler, R. (1987). Task-involving and ego-involving properties of evaluation: Effects of different

feedback conditions on motivational perceptions, interest, and performance. Journal of

Educational Psychology, 79(4), 474-482. doi:10.1037/0022-0663.79.4.474.

Doganay, A., & Bal, A. P. (2010). The measurement of students' achievement in teaching

primary school fifth year mathematics classes. Educational Sciences: Theory and

Practice, 10(1), 199-215. Retrieved

from http://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ882727&site=

ehost-live

Popham, W. (2006). Assessment for Learning: An Endangered

Species? Educational Leadership, 63(5), 82-3. Retrieved from


http://vnweb.hwwilsonweb.com.offcampus.lib.washington.edu/hww/results/getResults.jh

tml?_DARGS=/hww/results/results_common.jhtml.33

Stiggins, R. J. (2002). Assessment crisis: The absence of assessment FOR learning. The Phi

Delta Kappan, 83(10), 758-765. Retrieved fromhttp://www.jstor.org/stable/20440249

William, D. (1999) Formative assessment in mathematics. Part 1: Rich questioning. Equals:

Mathematics and special educational needs, 5(2). Retrieved from

http://eprints.ioe.ac.uk/1150/1/Wiliam1999Formativepart115.pdf.

William, D. (1999) Formative assessment in mathematics. Part 2: Feedback. Equals:


https://docs.google.com/viewer?url=http://eprints.ioe.ac.uk/1148/1/Wiliam1999Formativ

epart2_8.pdf

William, D. (1999) Formative assessment in mathematics. Part 3: The learner’s role. Equals:


http://eprints.ioe.ac.uk/1149/1/Wiliam1999Formativepart3_19.pdf.

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