What Is Research, and Why Do People Do It?

Abstract

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Every day people do research as they gather information to learn about something of interest. In the scientific world, however, research means something different than simply gathering information. Scientific research is characterized by its careful planning and observing, by its relentless efforts to understand and explain, and by its commitment to learn from everyone else seriously engaged in research. We call this kind of research scientific inquiry and define it as “formulating, testing, and revising hypotheses.” By “hypotheses” we do not mean the hypotheses you encounter in statistics courses. We mean predictions about what you expect to find and rationales for why you made these predictions. Throughout this and the remaining chapters we make clear that the process of scientific inquiry applies to all kinds of research studies and data, both qualitative and quantitative.

Full text

1
Chapter 1
What Is Research, andWhy Do People
Do It?
Part I.What Is Research?
Have you ever studied something carefully because you wanted to know more about
it? Maybe you wanted to know more about your grandmother’s life when she was
younger so you asked her to tell you stories from her childhood, or maybe you
wanted to know more about a fertilizer you were about to use in your garden so you
read the ingredients on the package and looked them up online. According to the
dictionary denition, you were doing research.
Recall your high school assignments asking you to “research” a topic. The
assignment likely included consulting a variety of sources that discussed the topic,
perhaps including some “original” sources. Often, the teacher referred to your prod-
uct as a “research paper.”
Were you conducting research when you interviewed your grandmother or wrote
high school papers reviewing a particular topic? Our view is that you were engaged
in part of the research process, but only a small part. In this book, we reserve the
word “research” for what it means in the scientic world, that is, for scientic
research or, more pointedly, for scientic inquiry.
This book is about scientic inquiry—what it is and how to do it. For starters,
scientic inquiry is a process, a particular way of nding out about something that
involves a number of phases. Each phase of the process constitutes one aspect of
scientic inquiry. You are doing scientic inquiry as you engage in each phase, but
Exercise 1.1
Before you read any further, write a denition of what you think scientic
inquiry is. Keep it short—Two to three sentences. You will periodically update
this denition as you read this chapter and the remainder of the book.
© The Author(s) 2023
J. Hiebert et al., Doing Research: A New Researcher’s Guide,
Research in Mathematics Education,
https://doi.org/10.1007/978-3-031-19078-0_1

2
you have not done scientic inquiry until you complete the full process. Each phase
is necessary but not sufcient.
In this chapter, we set the stage by dening scientic inquiry—describing what
it is and what it is not—and by discussing what it is good for and why people do it.
The remaining chapters build directly on the ideas presented in this chapter.
A rst thing to know is that scientic inquiry is not all or nothing. “Scienticness”
is a continuum. Inquiries can be more scientic or less scientic. What makes an
inquiry more scientic? You might be surprised there is no universally agreed upon
answer to this question. None of the descriptors we know of are sufcient by them-
selves to dene scientic inquiry. But all of them give you a way of thinking about
some aspects of the process of scientic inquiry. Each one gives you different
insights.
In this book, we reserve the word “research” for what it
means in the scientific world, that is, for scientific re-
search, or, more pointedly, for scientific inquiry.
Creating anImage ofScientic Inquiry
We will present three descriptors of scientic inquiry. Each provides a different
perspective and emphasizes a different aspect of scientic inquiry. We will draw on
all three descriptors to compose our denition of scientic inquiry.
Descriptor 1. Experience Carefully Planned inAdvance
Sir Ronald Fisher, often called the father of modern statistical design, once referred
to research as “experience carefully planned in advance” (1935, p.8). He said that
humans are always learning from experience, from interacting with the world
around them. Usually, this learning is haphazard rather than the result of a deliberate
process carried out over an extended period of time. Research, Fisher said, was
learning from experience, but experience carefully planned in advance.
This phrase can be fully appreciated by looking at each word. The fact that
scientic inquiry is based on experience means that it is based on interacting with
the world. These interactions could be thought of as the stuff of scientic inquiry.
Exercise 1.2
As you read about each descriptor below, think about what would make an
inquiry more or less scientic. If you think a descriptor is important, use it to
revise your denition of scientic inquiry.
1 What Is Research, andWhy Do People Do It?

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In addition, it is not just any experience that counts. The experience must be care-
fully planned. The interactions with the world must be conducted with an explicit,
describable purpose, and steps must be taken to make the intended learning as likely
as possible. This planning is an integral part of scientic inquiry; it is not just a
preparation phase. It is one of the things that distinguishes scientic inquiry from
many everyday learning experiences. Finally, these steps must be taken beforehand
and the purpose of the inquiry must be articulated in advance of the experience.
Clearly, scientic inquiry does not happen by accident, by just stumbling into some-
thing. Stumbling into something unexpected and interesting can happen while
engaged in scientic inquiry, but learning does not depend on it and serendipity
does not make the inquiry scientic.
Descriptor 2. Observing Something andTrying toExplain Why It Is
theWay It Is
When we were writing this chapter and googled “scientic inquiry,” the rst entry
was: “Scientic inquiry refers to the diverse ways in which scientists study the natu-
ral world and propose explanations based on the evidence derived from their work.”
The emphasis is on studying, or observing, and then explaining. This descriptor
takes the image of scientic inquiry beyond carefully planned experience and
includes explaining what was experienced.
According to the Merriam-Webster dictionary, “explain” means “(a) to make
known, (b) to make plain or understandable, (c) to give the reason or cause of, and
(d) to show the logical development or relations of” (Merriam-Webster, n.d.). We
will use all these denitions. Taken together, they suggest that to explain an obser-
vation means to understand it by nding reasons (or causes) for why it is as it is. In
this sense of scientic inquiry, the following are synonyms: explaining why, under-
standing why, and reasoning about causes and effects. Our image of scientic
inquiry now includes planning, observing, and explaining why.
Our image of scientific inquiry now includes planning, ob-
serving, and explaining why.
We need to add a nal note about this descriptor. We have phrased it in a way that
suggests “observing something” means you are observing something in real time—
observing the way things are or the way things are changing. This is often true. But,
observing could mean observing data that already have been collected, maybe by
someone else making the original observations (e.g., secondary analysis of NAEP
data or analysis of existing video recordings of classroom instruction). We will
address secondary analyses more fully in Chap. 4. For now, what is important is that
the process requires explaining why the data look like they do.
Part I.What Is Research?

4
We must note that for us, the term “data” is not limited to numerical or quantita-
tive data such as test scores. Data can also take many nonquantitative forms, includ-
ing written survey responses, interview transcripts, journal entries, video recordings
of students, teachers, and classrooms, text messages, and so forth.
“Data” is not limited to numerical or quantitative data
such as test scores. Data can also take many nonquantita-
tive forms, including written survey responses, interview
transcripts, journal entries, video recordings of students,
teachers, and classrooms, text messages, and so forth.
Descriptor 3. Updating Everyone’s Thinking inResponse toMore
andBetter Information
This descriptor focuses on a third aspect of scientic inquiry: updating and advanc-
ing the eld’s understanding of phenomena that are investigated. This descriptor
foregrounds a powerful characteristic of scientic inquiry: the reliability (or trust-
worthiness) of what is learned and the ultimate inevitability of this learning to
advance human understanding of phenomena. Humans might choose not to learn
from scientic inquiry, but history suggests that scientic inquiry always has the
potential to advance understanding and that, eventually, humans take advantage of
these new understandings.
Before exploring these bold claims a bit further, note that this descriptor uses
“information” in the same way the previous two descriptors used “experience” and
“observations.” These are the stuff of scientic inquiry and we will use them often,
sometimes interchangeably. Frequently, we will use the term “data” to stand for all
these terms.
An overriding goal of scientic inquiry is for everyone to learn from what one
scientist does. Much of this book is about the methods you need to use so others
have faith in what you report and can learn the same things you learned. This aspect
of scientic inquiry has many implications.
Exercise 1.3
(a) What are the implications of the statement that just “observing” is not
enough to count as scientic inquiry? Does this mean that a detailed
description of a phenomenon is not scientic inquiry?
(b) Find sources that dene research in education that differ with our posi-
tion, that say description alone, without explanation, counts as scientic
research. Identify the precise points where the opinions differ. What are
the best arguments for each of the positions? Which do you prefer? Why?
1 What Is Research, andWhy Do People Do It?

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One implication is that scientic inquiry is not a private practice. It is a public
practice available for others to see and learn from. Notice how different this is from
everyday learning. When you happen to learn something from your everyday expe-
rience, often only you gain from the experience. The fact that research is a public
practice means it is also a social one. It is best conducted by interacting with others
along the way: soliciting feedback at each phase, taking opportunities to present
work-in-progress, and benetting from the advice of others.
A second implication is that you, as the researcher, must be committed to sharing
what you are doing and what you are learning in an open and transparent way. This
allows all phases of your work to be scrutinized and critiqued. This is what gives
your work credibility. The reliability or trustworthiness of your ndings depends on
your colleagues recognizing that you have used all appropriate methods to maxi-
mize the chances that your claims are justied by the data.
A third implication of viewing scientic inquiry as a collective enterprise is the
reverse of the second—you must be committed to receiving comments from others.
You must treat your colleagues as fair and honest critics even though it might some-
times feel otherwise. You must appreciate their job, which is to remain skeptical
while scrutinizing what you have done in considerable detail. To provide the best
help to you, they must remain skeptical about your conclusions (when, for example,
the data are difcult for them to interpret) until you offer a convincing logical argument
based on the information you share. A rather harsh but good-to-remember statement
of the role of your friendly critics was voiced by Karl Popper, a well- known twentieth
century philosopher of science: “. . . if you are interested in the problem which I
tried to solve by my tentative assertion, you may help me by criticizing it as severely
as you can” (Popper, 1968, p.27).
A nal implication of this third descriptor is that, as someone engaged in scien-
tic inquiry, you have no choice but to update your thinking when the data support
a different conclusion. This applies to your own data as well as to those of others.
When data clearly point to a specic claim, even one that is quite different than you
expected, you must reconsider your position. If the outcome is replicated multiple
times, you need to adjust your thinking accordingly. Scientic inquiry does not let
you pick and choose which data to believe; it mandates that everyone update their
thinking when the data warrant an update.
Doing Scientic Inquiry
We dene scientic inquiry in an operational sense—what does it mean to do scien-
tic inquiry? What kind of process would satisfy all three descriptors: carefully
planning an experience in advance; observing and trying to explain what you see;
and, contributing to updating everyone’s thinking about an important phenomenon?
We dene scientic inquiry as formulating, testing, and revising hypotheses about
phenomena of interest.
Part I.What Is Research?

6
Of course, we are not the only ones who dene it in this way. The denition for
the scientic method posted by the editors of Britannica is: “a researcher develops
a hypothesis, tests it through various means, and then modies the hypothesis on the
basis of the outcome of the tests and experiments” (Britannica, n.d.).
We define scientific inquiry as formulating, testing, and re-
vising hypotheses about phenomena of interest.
Notice how dening scientic inquiry this way satises each of the descriptors.
“Carefully planning an experience in advance” is exactly what happens when for-
mulating a hypothesis about a phenomenon of interest and thinking about how to
test it. “Observing a phenomenon” occurs when testing a hypothesis, and “explain-
ing” what is found is required when revising a hypothesis based on the data. Finally,
“updating everyone’s thinking” comes from comparing publicly the original with
the revised hypothesis.
Doing scientic inquiry, as we have dened it, underscores the value of accumu-
lating knowledge rather than generating random bits of knowledge. Formulating,
testing, and revising hypotheses is an ongoing process, with each revised hypothesis
begging for another test, whether by the same researcher or by new researchers. The
editors of Britannica signaled this cyclic process by adding the following phrase to
their denition of the scientic method: “The modied hypothesis is then retested,
further modied, and tested again.” Scientic inquiry creates a process that encour-
ages each study to build on the studies that have gone before. Through collective
engagement in this process of building study on top of study, the scientic commu-
nity works together to update its thinking.
Before exploring more fully the meaning of “formulating, testing, and revising
hypotheses,” we need to acknowledge that this is not the only way researchers
dene research. Some researchers prefer a less formal denition, one that includes
more serendipity, less planning, less explanation. You might have come across more
open denitions such as “research is nding out about something.” We prefer the
tighter hypothesis formulation, testing, and revision denition because we believe it
provides a single, coherent map for conducting research that addresses many of the
thorny problems educational researchers encounter. We believe it is the most useful
orientation toward research and the most helpful to learn as a beginning researcher.
A nal clarication of our denition is that it applies equally to qualitative and
quantitative research. This is a familiar distinction in education that has generated
much discussion. You might think our denition favors quantitative methods over
qualitative methods because the language of hypothesis formulation and testing is
often associated with quantitative methods. In fact, we do not favor one method over
1 What Is Research, andWhy Do People Do It?

7
another. In Chap. 4, we will illustrate how our denition ts research using a range
of quantitative and qualitative methods.
Unpacking theTerms Formulating, Testing,
andRevising Hypotheses
To get a full sense of the denition of scientic inquiry we will use throughout this
book, it is helpful to spend a little time with each of the key terms.
We rst want to make clear that we use the term “hypothesis” as it is dened in
most dictionaries and as it used in many scientic elds rather than as it is usually
dened in educational statistics courses. By “hypothesis,” we do not mean a null
hypothesis that is accepted or rejected by statistical analysis. Rather, we use
“hypothesis” in the sense conveyed by the following denitions: “An idea or expla-
nation for something that is based on known facts but has not yet been proved”
(Cambridge University Press, n.d.), and “An unproved theory, proposition, or sup-
position, tentatively accepted to explain certain facts and to provide a basis for fur-
ther investigation or argument” (Agnes & Guralnik, 2008).
We distinguish two parts to “hypotheses.” Hypotheses consist of predictions and
rationales. Predictions are statements about what you expect to nd when you
inquire about something. Rationales are explanations for why you made the predic-
tions you did, why you believe your predictions are correct. So, for us “formulating
hypotheses” means making explicit predictions and developing rationales for the
predictions.
“Testing hypotheses” means making observations that allow you to assess in
what ways your predictions were correct and in what ways they were incorrect. In
education research, it is rarely useful to think of your predictions as either right or
wrong. Because of the complexity of most issues you will investigate, most predic-
tions will be right in some ways and wrong in others.
By studying the observations you make (data you collect) to test your hypothe-
ses, you can revise your hypotheses to better align with the observations. This means
revising your predictions plus revising your rationales to justify your adjusted pre-
dictions. Even though you might not run another test, formulating revised hypoth-
eses is an essential part of conducting a research study. Comparing your original
and revised hypotheses informs everyone of what you learned by conducting your
Exercise 1.4
Look for ways to extend what the eld knows in an area that has already
received attention by other researchers. Specically, you can search for a pro-
gram of research carried out by more experienced researchers that has some
revised hypotheses that remain untested. Identify a revised hypothesis that
you might like to test.
Part I.What Is Research?

8
study. In addition, a revised hypothesis sets the stage for you or someone else to
extend your study and accumulate more knowledge of the phenomenon.
We should note that not everyone makes a clear distinction between predictions
and rationales as two aspects of hypotheses. In fact, common, non-scientic uses of
the word “hypothesis” may limit it to only a prediction or only an explanation (or
rationale). We choose to explicitly include both prediction and rationale in our de-
nition of hypothesis, not because we assert this should be the universal denition,
but because we want to foreground the importance of both parts acting in concert.
Using “hypothesis” to represent both prediction and rationale could hide the two
aspects, but we make them explicit because they provide different kinds of informa-
tion. It is usually easier to make predictions than develop rationales because predic-
tions can be guesses, hunches, or gut feelings about which you have little condence.
Developing a compelling rationale requires careful thought plus reading what other
researchers have found plus talking with your colleagues. Often, while you are
developing your rationale you will nd good reasons to change your predictions.
Developing good rationales is the engine that drives scientic inquiry. Rationales
are essentially descriptions of how much you know about the phenomenon you are
studying. Throughout this guide, we will elaborate on how developing good ratio-
nales drives scientic inquiry. For now, we simply note that it can sharpen your
predictions and help you to interpret your data as you test your hypotheses.
We define a hypothesis to include both a prediction and a
rationale. Both parts act in concert, and they provide dif-
ferent kinds of information. We discuss predictions in
more detail in Chapter 2 and we detail how to build ra-
tionales in Chapter 3.
Hypotheses in education research take a variety of forms or types. This is because
there are a variety of phenomena that can be investigated. Investigating educational
phenomena is sometimes best done using qualitative methods, sometimes using
quantitative methods, and most often using mixed methods (e.g., Hay, 2016; Weis
etal. 2019a; Weisner, 2005). This means that, given our denition, hypotheses are
equally applicable to qualitative and quantitative investigations.
Hypotheses take different forms when they are used to investigate different kinds
of phenomena. Two very different activities in education could be labeled conduct-
ing experiments and descriptions. In an experiment, a hypothesis makes a prediction
about anticipated changes, say the changes that occur when a treatment or interven-
tion is applied. You might investigate how students’ thinking changes during a
particular kind of instruction.
A second type of hypothesis, relevant for descriptive research, makes a predic-
tion about what you will nd when you investigate and describe the nature of a situ-
ation. The goal is to understand a situation as it exists rather than to understand a
1 What Is Research, andWhy Do People Do It?

9
change from one situation to another. In this case, your prediction is what you
expect to observe. Your rationale is the set of reasons for making this prediction; it
is your current explanation for why the situation will look like it does.
You will probably read, if you have not already, that some researchers say you do
not need a prediction to conduct a descriptive study. We will discuss this point of
view in Chap. 2. For now, we simply claim that scientic inquiry, as we have dened
it, applies to all kinds of research studies. Descriptive studies, like others, not only
benet from formulating, testing, and revising hypotheses, but also need hypothesis
formulating, testing, and revising.
One reason we dene research as formulating, testing, and revising hypotheses
is that if you think of research in this way you are less likely to go wrong. It is a
useful guide for the entire process, as we will describe in detail in the chapters
ahead. For example, as you build the rationale for your predictions, you are con-
structing the theoretical framework for your study (Chap. 3). As you work out the
methods you will use to test your hypothesis, every decision you make will be based
on asking, “Will this help me formulate or test or revise my hypothesis?” (Chap. 4).
As you interpret the results of testing your predictions, you will compare them to
what you predicted and examine the differences, focusing on how you must revise
your hypotheses (Chap. 5). By anchoring the process to formulating, testing, and
revising hypotheses, you will make smart decisions that yield a coherent and
well- designed study.
Learning fromDoing Scientic Inquiry
We noted earlier that a measure of what you have learned by conducting a research
study is found in the differences between your original hypothesis and your revised
hypothesis based on the data you collected to test your hypothesis. We will elabo-
rate this statement in later chapters, but we preview our argument here.
Exercise 1.5
Compare the concept of formulating, testing, and revising hypotheses with
the descriptions of scientic inquiry contained in Scientic Research in
Education (NRC, 2002). How are they similar or different?
Exercise 1.6
Provide an example to illustrate and emphasize the differences between
everyday learning/thinking and scientic inquiry.
Part I.What Is Research?

10
Even before collecting data, scientic inquiry requires cycles of making a pre-
diction, developing a rationale, rening your predictions, reading and studying
more to strengthen your rationale, rening your predictions again, and so forth.
And, even if you have run through several such cycles, you still will likely nd that
when you test your prediction you will be partly right and partly wrong. The results
will support some parts of your predictions but not others, or the results will “kind
of” support your predictions. A critical part of scientic inquiry is making sense of
your results by interpreting them against your predictions. Carefully describing
what aspects of your data supported your predictions, what aspects did not, and
what data fell outside of any predictions is not an easy task, but you cannot learn
from your study without doing this analysis.
Even before collecting data, scientific inquiry requires cy-
cles of making a prediction, developing a rationale, refin-
ing your predictions, readingand studying more to
strengthen your rationale, refining your predictions again,
and so forth.
Analyzing the matches and mismatches between your predictions and your data
allows you to formulate different rationales that would have accounted for more of
the data. The best revised rationale is the one that accounts for the most data. Once
you have revised your rationales, you can think about the predictions they best jus-
tify or explain. It is by comparing your original rationales to your new rationales
that you can sort out what you learned from your study.
Suppose your study was an experiment. Maybe you were investigating the effects
of a new instructional intervention on students’ learning. Your original rationale was
your explanation for why the intervention would change the learning outcomes in a
particular way. Your revised rationale explained why the changes that you observed
occurred like they did and why your revised predictions are better. Maybe your
original rationale focused on the potential of the activities if they were implemented
in ideal ways and your revised rationale included the factors that are likely to affect
how teachers implement them. By comparing the before and after rationales, you
are describing what you learned—what you can explain now that you could not
before. Another way of saying this is that you are describing how much more you
understand now than before you conducted your study.
Revised predictions based on carefully planned and collected data usually exhibit
some of the following features compared with the originals: more precision, more
completeness, and broader scope. Revised rationales have more explanatory power
and become more complete, more aligned with the new predictions, sharper, and
overall more convincing.
1 What Is Research, andWhy Do People Do It?

11
Part II.Why Do Educators Do Research?
Doing scientic inquiry is a lot of work. Each phase of the process takes time, and
you will often cycle back to improve earlier phases as you engage in later phases.
Because of the signicant effort required, you should make sure your study is worth
it. So, from the beginning, you should think about the purpose of your study. Why
do you want to do it? And, because research is a social practice, you should also
think about whether the results of your study are likely to be important and signi-
cant to the education community.
If you are doing research in the way we have described—as scientic inquiry—
then one purpose of your study is to understand, not just to describe or evaluate or
report. As we noted earlier, when you formulate hypotheses, you are developing
rationales that explain why things might be like they are. In our view, trying to
understand and explain is what separates research from other kinds of activities, like
evaluating or describing.
One reason understanding is so important is that it allows researchers to see how
or why something works like it does. When you see how something works, you are
better able to predict how it might work in other contexts, under other conditions.
And, because conditions, or contextual factors, matter a lot in education, gaining
insights into applying your ndings to other contexts increases the contributions of
your work and its importance to the broader education community.
Consequently, the purposes of research studies in education often include the
more specic aim of identifying and understanding the conditions under which the
phenomena being studied work like the observations suggest. A classic example of
this kind of study in mathematics education was reported by William Brownell and
Harold Moser in 1949. They were trying to establish which method of subtracting
whole numbers could be taught most effectively—the regrouping method or the
equal additions method. However, they realized that effectiveness might depend on
the conditions under which the methods were taught—“meaningfully” versus
“mechanically.” So, they designed a study that crossed the two instructional
approaches with the two different methods (regrouping and equal additions). Among
other results, they found that these conditions did matter. The regrouping method
was more effective under the meaningful condition than the mechanical condition,
but the same was not true for the equal additions algorithm.
What do education researchers want to understand? In our view, the ultimate
goal of education is to offer all students the best possible learning opportunities. So,
we believe the ultimate purpose of scientic inquiry in education is to develop
understanding that supports the improvement of learning opportunities for all stu-
dents. We say “ultimate” because there are lots of issues that must be understood to
improve learning opportunities for all students. Hypotheses about many aspects of
education are connected, ultimately, to students’ learning. For example, formulating
and testing a hypothesis that preservice teachers need to engage in particular kinds
of activities in their coursework in order to teach particular topics well is, ultimately,
connected to improving students’ learning opportunities. So is hypothesizing that
school districts often devote relatively few resources to instructional leadership
Part II.Why Do Educators Do Research?

12
training or hypothesizing that positioning mathematics as a tool students can use to
combat social injustice can help students see the relevance of mathematics to
their lives.
We do not exclude the importance of research on educational issues more
removed from improving students’ learning opportunities, but we do think the argu-
ment for their importance will be more difcult to make. If there is no way to imag-
ine a connection between your hypothesis and improving learning opportunities for
students, even a distant connection, we recommend you reconsider whether it is an
important hypothesis within the education community.
Notice that we said the ultimate goal of education is to offer all students the best
possible learning opportunities. For too long, educators have been satised with a
goal of offering rich learning opportunities for lots of students, sometimes even for
just the majority of students, but not necessarily for all students. Evaluations of suc-
cess often are based on outcomes that show high averages. In other words, if many
students have learned something, or even a smaller number have learned a lot, edu-
cators may have been satised. The problem is that there is usually a pattern in the
groups of students who receive lower quality opportunities—students of color and
students who live in poor areas, urban and rural. This is not acceptable. Consequently,
we emphasize the premise that the purpose of education research is to offer rich
learning opportunities to all students.
One way to make sure you will be able to convince others of the importance of
your study is to consider investigating some aspect of teachers’ shared instructional
problems. Historically, researchers in education have set their own research agen-
das, regardless of the problems teachers are facing in schools. It is increasingly
recognized that teachers have had trouble applying to their own classrooms what
researchers nd. To address this problem, a researcher could partner with a teacher—
better yet, a small group of teachers—and talk with them about instructional prob-
lems they all share. These discussions can create a rich pool of problems researchers
can consider. If researchers pursued one of these problems (preferably alongside
teachers), the connection to improving learning opportunities for all students could
be direct and immediate. “Grounding a research question in instructional problems
that are experienced across multiple teachers’ classrooms helps to ensure that the
answer to the question will be of sufcient scope to be relevant and signicant
beyond the local context” (Cai etal., 2019b, p.115).
As a beginning researcher, determining the relevance and importance of a
research problem is especially challenging. We recommend talking with advisors,
other experienced researchers, and peers to test the educational importance of pos-
sible research problems and topics of study. You will also learn much more about
the issue of research importance when you read Chap. 5.
Exercise 1.7
Identify a problem in education that is closely connected to improving learn-
ing opportunities and a problem that has a less close connection. For each
problem, write a brief argument (like a logical sequence of if-then statements)
that connects the problem to all students’ learning opportunities.
1 What Is Research, andWhy Do People Do It?

13
Part III.Conducting Research asaPractice
ofFailing Productively
Scientic inquiry involves formulating hypotheses about phenomena that are not
fully understood—by you or anyone else. Even if you are able to inform your
hypotheses with lots of knowledge that has already been accumulated, you are
likely to nd that your prediction is not entirely accurate. This is normal. Remember,
scientic inquiry is a process of constantly updating your thinking. More and better
information means revising your thinking, again, and again, and again. Because you
never fully understand a complicated phenomenon and your hypotheses never pro-
duce completely accurate predictions, it is easy to believe you are somehow failing.
The trick is to fail upward, to fail to predict accurately in ways that inform your
next hypothesis so you can make a better prediction. Some of the best-known
researchers in education have been open and honest about the many times their
predictions were wrong and, based on the results of their studies and those of others,
they continuously updated their thinking and changed their hypotheses.
A striking example of publicly revising (actually reversing) hypotheses due to
incorrect predictions is found in the work of Lee J.Cronbach, one of the most dis-
tinguished educational psychologists of the twentieth century. In 1955, Cronbach
delivered his presidential address to the American Psychological Association.
Titling it “Two Disciplines of Scientic Psychology,” Cronbach proposed a rap-
prochement between two research approaches—correlational studies that focused
on individual differences and experimental studies that focused on instructional
treatments controlling for individual differences. (We will examine different
research approaches in Chap. 4). If these approaches could be brought together,
reasoned Cronbach (1957), researchers could nd interactions between individual
characteristics and treatments (aptitude-treatment interactions or ATIs), tting the
best treatments to different individuals.
In 1975, after years of research by many researchers looking for ATIs, Cronbach
acknowledged the evidence for simple, useful ATIs had not been found. Even when
trying to nd interactions between a few variables that could provide instructional
guidance, the analysis, said Cronbach, creates “a hall of mirrors that extends to
innity, tormenting even the boldest investigators and defeating even ambitious
designs” (Cronbach, 1975, p.119).
As he was reecting back on his work, Cronbach (1986) recommended moving
away from documenting instructional effects through statistical inference (an
approach he had championed for much of his career) and toward approaches that
probe the reasons for these effects, approaches that provide a “full account of events
in a time, place, and context” (Cronbach, 1986, p.104). This is a remarkable change
in hypotheses, a change based on data and made fully transparent. Cronbach under-
stood the value of failing productively.
Closer to home, in a less dramatic example, one of us began a line of scientic
inquiry into how to prepare elementary preservice teachers to teach early algebra.
Teaching early algebra meant engaging elementary students in early forms of
Part III.Conducting Research asaPractice ofFailing Productively

14
algebraic reasoning. Such reasoning should help them transition from arithmetic to
algebra. To begin this line of inquiry, a set of activities for preservice teachers were
developed. Even though the activities were based on well-supported hypotheses,
they largely failed to engage preservice teachers as predicted because of unantici-
pated challenges the preservice teachers faced. To capitalize on this failure, follow-
up studies were conducted, rst to better understand elementary preservice teachers’
challenges with preparing to teach early algebra, and then to better support preser-
vice teachers in navigating these challenges. In this example, the initial failure was
a necessary step in the researchers’ scientic inquiry and furthered the researchers’
understanding of this issue.
We present another example of failing productively in Chap. 2. That example
emerges from recounting the history of a well-known research program in mathe-
matics education.
Making mistakes is an inherent part of doing scientic research. Conducting a
study is rarely a smooth path from beginning to end. We recommend that you keep
the following things in mind as you begin a career of conducting research in education.
First, do not get discouraged when you make mistakes; do not fall into the trap
of feeling like you are not capable of doing research because you make too
many errors.
Second, learn from your mistakes. Do not ignore your mistakes or treat them as
errors that you simply need to forget and move past. Mistakes are rich sites for
learning—in research just as in other elds of study.
Third, by reecting on your mistakes, you can learn to make better mistakes,
mistakes that inform you about a productive next step. You will not be able to elimi-
nate your mistakes, but you can set a goal of making better and better mistakes.
Exercise 1.8
How does scientic inquiry differ from everyday learning in giving you the
tools to fail upward? You may nd helpful perspectives on this question in
other resources on science and scientic inquiry (e.g., Failure: Why Science is
So Successful by Firestein, 2015).
Exercise 1.9
Use what you have learned in this chapter to write a new denition of scien-
tic inquiry. Compare this denition with the one you wrote before reading
this chapter. If you are reading this book as part of a course, compare your
denition with your colleagues’ denitions. Develop a consensus denition
with everyone in the course.
1 What Is Research, andWhy Do People Do It?

15
Part IV.Preview ofChap. 2
Now that you have a good idea of what research is, at least of what we believe
research is, the next step is to think about how to actually begin doing research. This
means how to begin formulating, testing, and revising hypotheses. As for all phases
of scientic inquiry, there are lots of things to think about. Because it is critical to
start well, we devote Chap. 2 to getting started with formulating hypotheses.
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Part IV. Preview of Chap. 2