What are they asking? An analysis of the questionsplanned by prospective teachers when integratingliterature in mathematics

Barbara Purdum-Cassidy • Suzanne Nesmith • Rachelle D. Meyer •

Sandi Cooper

� Springer Science+Business Media Dordrecht 2014

Abstract Questioning is considered a powerful tool in mediating students’ knowledge

construction and conceptual understanding. In this qualitative study, the mathematics-

focused lesson plans of elementary education prospective teachers provided data to

determine the ways that the approach of literature integration in mathematics influenced

prospective teachers’ planned questions. All prospective teachers were required to incor-

porate children’s literature within the mathematics lessons they planned and presented

during a field-based teaching experience. Analysis revealed variances in the numbers,

types, and foci of prospective teachers’ planned questions. These findings allow specula-

tion that the utilization of mathematics literature integration allowed many of the pro-

spective teachers to create reform-oriented, constructivist mathematics-focused questions

and experiences for their students.

Keywords Teacher education � Mathematics instruction � Questioning �Field-based experience

Introduction

Teacher questioning is a powerful instructional strategy and has been identified as a critical

and challenging part of teachers’ work (Boaler and Brodie 2004). The act of asking a good

question is cognitively demanding because it requires considerable pedagogical content

knowledge and necessitates that teachers know their students well (Boaler and Brodie

2004; Ong et al. 2010). Research has found that differences in students’ mathematical

thinking and reasoning could be attributed to the type of questions that teachers ask (Boaler

and Brodie 2004; Kazemi and Stipek 2001; Wood 2002). Studies confirm that many

teachers ask ‘‘lower order’’ questions that make minimal demands on student thinking,

B. Purdum-Cassidy (&) � S. Nesmith � R. D. Meyer � S. CooperBaylor University, One Bear Place #97314, Waco, TX 76798, USAe-mail: Barbara_Purdum-Cassidy@baylor.edu

123

J Math Teacher EducDOI 10.1007/s10857-014-9274-7

even though ‘‘higher order’’ questions have been identified as important tools in developing

student understanding (Hiebert and Wearne 1993; Klinzing et al. 1985).

Developing questioning skills for mathematical understanding and content knowledge is

an important part of learning to teach and assess mathematics. An integral aspect of

effective instructional planning is determining the questions to pose in class. Asking good

questions is a complex skill that requires practice and thoughtful planning, as well as

reflection on and analysis of the mathematical and pedagogical goals of the lesson (Ma-

nouchehri and Lapp 2003). Nicol (1999) concluded that novice teachers experience dif-

ficulty related to planning questions that probe students’ thinking versus planning questions

that assess students’ thinking.

According to Moyer and Milewicz (2002), there is little recent empirical evidence that

investigates the development of teacher questioning techniques among novice teachers.

Crespo (2003) suggested that novice teachers may learn and construct meaning from their

experiences when they actively engage in authentic activities that help them learn to think

and act in a community of practice. Recognizing the importance of knowing the right

question to ask and when to ask it, as well as understanding that verbal questioning is a

skill that must be practiced before it can be effectively used (Vogler 2005), prompted the

research in this study. The study in this paper investigates the questions prospective

teachers plan to incorporate within mathematics lessons that utilize children’s literature.

Various aspects of the approach of integrating literature in mathematics have been

researched and documented in mathematics and literacy journals, yet this study aims to

identify the ways that the approach influences the number, types, and focus of prospective

teachers’ planned questions.

Rationale for study

Questioning has been found to deeply influence the processing of instructional materials,

and questioning remains one of the most commonly utilized instructional techniques

(Andre 1979; Hamilton 1985). Yet, as determined by Hannel (2009), most K-12 teachers

have not had practical, substantial training in the art and science of effective questioning.

‘‘Most have received snippets about questioning—stems to consider or recitations of

Bloom’s Taxonomy as a scaffold for questioning—but few have been taught a practical

pedagogy for questioning’’ (pp. 65–66). Additionally, due to their limited training and

experiences in questioning pedagogy as well as their novice status, prospective teachers

fail to evenly distribute their questions over a variety of categories, move from one

question to the next very quickly with very little follow-up, and rarely allow previous

student responses to inform subsequent questions (Henning and Lockhart 2003).

Recognition of the inherent benefits of quality questioning techniques alongside the

realization that the questioning skills of most prospective teachers are reflective of their

novice status and are often poorly developed, especially in mathematics, prompted the

research described in this study (Buschman 2001; Mewborn and Huberty 1999; Moyer and

Milewicz 2002). Previous studies have investigated the distinctions between questions and

discourse initiated by inservice and prospective teachers (Henning and Lockhart 2003;

Moyer and Milewicz 2002), variances in questions posed in traditional and reform-oriented

mathematics classrooms (Baird and Northfield 1992; NCTM, National Council of Teachers

of Mathematics 2000; National Research Council 2001), and the relationship between

teachers’ questions and students’ opportunities to reason mathematically (Boaler and

Brodie 2004; Kazemi and Stipek 2001; Stein et al. 2007). Yet no prior studies have

B. Purdum-Cassidy et al.

123

explored these elements through the lens of literature-based mathematics instruction. One

question guided the study: When utilizing literature integration in mathematics, what kind

of questions do prospective teachers plan in order to scaffold children’s understanding of

the mathematics concepts presented through the text?

Theoretical underpinnings

The principal theoretical framework underlying this study is social constructivism. Central

to social constructivism is a belief that knowledge is constructed in the social context of the

classroom through language and other semiotic processes (Vygotsky 1978). Conceptual

knowledge first occurs between learners (interpsychological) and then moves within the

learner (intrapsychological). Thus, teachers have the opportunity to support student

learning and performance through the ‘‘zone of proximal development’’ by guiding the

discourse that occurs at the interpsychological plane. As questions are key to classroom

discourse, the theory of social constructivism suggests that teachers’ questions represent a

powerful tool in mediating students’ knowledge construction and conceptual

understanding.

Related literature

Types, styles, and roles of questioning

The types and levels of knowledge that students construct during instruction is impacted by

the types and levels of questions posed by the teacher. Teachers who are better able to

recognize and effectively utilize questions of varying types at various levels within the

cognitive domain are also better able to differentiate and promote a wide range in breadth

and depth of students’ thinking (Moyer and Milewicz 2002). Relative to question types and

levels, numerous researchers have categorized the types of questions that teachers ask.

Many of these classification systems are based upon the seven category question taxonomy

(knowledge, comprehension, application, analysis, synthesis, and evaluation) developed in

Bloom’s Taxonomy of Educational Objectives, Handbook I Cognitive Domain (Bloom

1956). Gallagher (1965) developed an analysis system (cognitive-memory, convergent

thinking, evaluative thinking, divergent thinking, and routine) which described the thinking

level called for in teachers’ questions and Sanders (1966) developed a taxonomy of

teachers’ questions (memory, translation, interpretations, application, analysis, synthesis,

and evaluation) that offered guidelines for expanding students’ thinking skills and pro-

viding opportunities for students to learn how to think. Herber’s (1978) classification

focused on comprehension levels (literal, interpretive, and applied comprehension) and

Smith (1969) revealed that questions could be classified as either convergent or divergent.

Utilizing Smith’s classification system but expanding the system to include the function of

all questions posed by teachers within a classroom, Blosser (1973, 2000) identified

questions as falling into one of four categories: managerial, rhetorical, open, and closed.

Blosser concluded that managerial questions serve a classroom operation function, rhe-

torical questions serve a reinforcement/emphasis role, closed questions provide a means for

checking students’ retention of previously learned information, and open questions are

utilized in promoting discussion and student interaction. By their very nature, closed

questions require students to think convergently by focusing on a single fact, defining a

What are they asking?

123

particular term, or attending to specific elements of an object or event. In contrast, open

questions trigger divergent thinking by requiring students to engage broad portions of their

schema while considering a wide array of possibilities.

Along with promoting breadth and depth in student’s thinking, it has been determined

that the consistent utilization of effective oral questioning techniques that employ various

types and levels of questions yields the accrual of numerous additional benefits. These

benefits include enhanced opportunities to garner and maintain students’ attention, increase

engagement and motivation, promote thinking, encourage discourse, enhance curiosity and

creativity, facilitate classroom management, and increase comprehension (Borich 1992;

Cerdan et al. 2009; Lorber 1996; Parker and Hurry 2007; Ralph 1999a, b). Moreover, when

educators combine effective questioning with the listening, probing, and clarifying of

students’ responses, the added benefits of consistent, reliable monitoring and assessment of

the learner’s acquisition of knowledge and understanding emerge (Martino and Maher

1999; White 2000, 2003).

Despite the documented research citing the importance of utilizing varying types and

levels of questions within the classroom, the vast majority of teacher-posed questions

consist of short answer, low-level questions that require students to recall rules, facts, and

procedures (Gall et al. 1971; Graesser and Person 1994), instead of high-level questions

that involve students in inferring and synthesizing ideas (Hiebert and Wearne 1993; Webb

et al. 2006). Additionally, although questioning that promotes discourse between students

and between the teacher and students is an essential component of social constructivism,

teacher talk often dominates classroom discourse (Cazden 2001), and students rarely ask

questions of the teacher or each other (Graesser and Person 1994). These findings have

remained consistent through more than two decades of questioning research (e.g., Cazden

1986; Doyle 1985; Gall 1984; Mehan 1985).

Questioning and discourse in mathematics

Mathematics classrooms are often classified based upon the manner and style in which

content, assessment, and instructional practices are addressed. Representing the two ends

of the mathematics classroom continuum are traditional mathematics classrooms and

reform-oriented mathematics classrooms. In a traditional mathematics classroom, teachers

generally behave in a didactic manner, providing information to students and viewing the

learning of mathematics as a series of memorizing facts and procedures (National Research

Council 2001). Often referred to as textbook driven, traditional mathematics curricula

emphasize computational skills, rules, and procedures and encourage learning that is

‘‘inflexible, school-bound, and of limited use’’ (Boaler 1998, p. 60; Murphy 1999). The

textbook or adopted curriculum is viewed as a source of irrefutable fact, thereby prohib-

iting the need for any form of discussion or for the sharing of alternative opinions or ideas

(Freeman and Pearson 1998). It is perceived that students within these classrooms learn

best by ‘‘listening to teachers’ demonstrations, attending carefully to their modeling

actions, and practicing the steps in the procedures until they can complete them without

substantial effort’’ (Freeman and Pearson 1998, p. 391).

The purpose of teacher questioning in traditional mathematics lessons is to evaluate

what students know about mathematical procedures. The teacher asks closed, information-

seeking questions that require students to use recall or lower-order cognitive thinking

levels in their articulation of predetermined short answers. Correct answers are praised,

students are discouraged from examining and articulating their thought processes, and any

challenge to the teacher’s questions is viewed as a threat (Baird and Northfield 1992).

B. Purdum-Cassidy et al.

123

While the prevailing psychological view of traditional mathematics learning is behav-

iorism, reform-oriented mathematics focuses on a constructivist perspective. In direct

opposition to the content-oriented focus of traditional mathematics, reform-oriented

mathematics highlights students’ understanding of mathematical concepts and processes

[National Council of Teachers of Mathematics (NCTM) 2000] and recognizes that

‘‘individuals approach a new task with prior knowledge, assimilate new information, and

construct their own meaning’’ (Amit and Fried 2002, p. 360). More specifically, a reform-

oriented mathematics classroom can be described as one in which a teacher uses problem

solving activities that build on and deepen students’ abilities to reason and communicate

mathematically. Teachers who support a reform-oriented classroom generally behave in an

interactive manner, mediating classroom interactions and discussions and highly valuing

students’ questions (National Council of Teachers of Mathematics 2000). Consequently,

the nature of questioning in a reform-oriented, constructivist-based mathematics classroom

differs from that found in a traditional mathematics classroom.

Within reform-oriented classrooms, the purpose of questioning is to elicit information

regarding students’ thinking, to encourage true dialog, to assist students in constructing

conceptual knowledge, and, when needed, to bring about conceptual change (Lemke 1990;

Smith et al. 1993). Such questions are more open, require students to provide longer, one-

or two-sentence responses, encourage elaboration, promote student participation, and

engage students in higher order thinking (Baird and Northfield 1992).

Types and levels of questions within mathematics classrooms can be further delineated

based upon the distinction between understanding of mathematical concepts and knowl-

edge of mathematical procedures. Procedural knowledge in mathematics focuses on the

rules and procedures used in carrying out mathematical processes, and procedural ques-

tions are those that require the recitation of those rules and procedures. Conversely,

conceptually-based questions are those that attempt to forge understanding of the rela-

tionships and foundational ideas of a mathematics topic.

A growing body of research suggests that the type and cognitive level of teachers’

mathematics questions effects the degree of student engagement, shapes the classroom

environment, and influences the opportunities for learning high-level mathematics (Boaler

and Brodie 2004; Kazemi and Stipek 2001; Smith 2000; Stein et al. 2007). Mirroring the

findings of general content questioning research, questions posed within many mathe-

matics classrooms across the globe fail to provide students with opportunities to reason

about mathematical concepts or to explore mathematical connections (Hiebert et al. 2003;

Perry et al. 1993; Stigler and Hiebert 1999). A study comparing the questions asked by

Asian and American teachers indicated that Japanese students were engaged by their

teachers in a significantly greater proportion of lessons containing conceptual knowledge

questions than were Chinese or United States students, and Chinese students were engaged

in a significantly greater proportion than were United States students (Perry et al. 1993).

Results from Stigler and Hiebert’s (1999) Trends in International Mathematics and Science

Study (TIMSS) video study of mathematics lessons in Germany, Japan, and the United

States indicated that teachers in Japan posed questions that emphasized students’ mathe-

matical thinking while teachers in Germany and the United States posed questions that

promoted students’ development of mathematical skills. Similar findings were reported in

the TIMSS 1999 video analysis of seven countries—Australia, the Czech Republic, Hong

Kong SAR, Japan, the Netherlands, Switzerland, and the United States. Japanese teachers

asked significantly more describe/explain questions than did the teachers in all the other

participating countries (Kawanaka et al. 1999). Comparisons between the countries also

revealed the following: (a) teachers in the Czech Republic and the United States utilized

What are they asking?

123

the most class time per lesson posing questions for the purpose of reviewing previously

learned content; (b) teachers in Hong Kong SAR and the United States used the most class

time for public interactions and discussions of mathematics, yet the teachers in these two

countries talked significantly more than their students during these discussion; (c) Dutch

teachers placed a great amount of responsibility on their students for selecting and posing

questions geared toward what needed to be discussed during the lesson; and (d) teachers in

the United States most often employed a sequence of rapid fire questions that required one-

word responses and were geared toward the acquisition of isolated facts (Hiebert et al.

2003; Stigler and Hiebert 1999). When examined collectively, mathematics-questioning

research reveals the importance of formulating an appropriate balance between the various

types and levels of questions posed to students. Reform-oriented, constructivist mathe-

matics classrooms designed to foster students’ mathematical understanding must give

precedence to challenging, high-level questions that promote conceptual understanding but

must also include questions that build students’ knowledge and abilities to effectively

utilize mathematical procedures (Franke et al. 2009; Perry et al. 1993).

Prospective teacher’s use of questioning

Napell (2001) suggested that teachers who have learned the skills of effective questioning

are able to teach by their own example how to acquire and classify information and to think

logically, thereby creating active participants in the learning process. Yet, according to

Wasserman (1991), ‘‘teachers do not learn the art of questioning from any serious study of

questioning strategies during the teacher education programs,’’ (p. 257) and Wilen (2001)

exposed as a myth the often-cited and firmly-held educator belief that questioning is a

natural teaching behavior that requires little to no practice or planning.

Nilssen et al. (1995) conducted research specific to mathematics questioning and found

that utilizing an interactive dialog structure in teaching mathematics was difficult for both

inservice and prospective teachers alike because ‘‘when open ended questioning is used

and there are many right answers, the learning environment becomes complex and less

predictable as teachers attempt to interpret and understand children’s responses’’ (p. 296).

Furthermore, prospective teachers have the added difficulty of being unable to interpret and

respond to students’ unexpected answers because of their limited background and expe-

rience with understanding how students think and reason mathematically. Investigating the

types of questions asked by prospective teachers, Moyer and Milewicz (2002) found that

prospective teachers often utilized a ‘‘check listing’’ procedure for asking questions. This

procedure resulted in fast paced questions that lacked follow-up and one- or two-word

verbalizations that indicated to the child that it was no longer necessary to continue

thinking about the question. Moreover, Henning and Lockhart (2003) indicated that pro-

spective teachers often posed few follow-up questions and, when employed, follow-up

questions tended not to be ‘‘informed by any of the previous student responses and did not

necessarily encourage the students to expand their answer in any significant way’’ (p. 50).

According to Nicol (1999), prospective teachers frequently struggle not only with

posing questions but with planning what questions they might ask and for what purpose.

Nicol concluded that novices experience difficulties related to planning questions that

probe students’ thinking versus planning questions that assess students’ thinking. Addi-

tionally, research comparing questions planned by inservice and prospective teachers

revealed that prospective teachers commonly planned a series of questions similar to the

type employed on mathematics worksheets. In utilizing these questions, the prospective

B. Purdum-Cassidy et al.

123

teachers moved from one question to the next with few follow-up questions being asked

(Henning and Lockhart 2003).

Children’s literature in mathematics

Children’s literature has long been used in classroom settings to support children’s social,

emotional, and intellectual development. When integrating literature within any subject

area, the goal of the instruction should be the development of comprehension. Specific to

mathematics, comprehension of mathematical text is critical to students’ abilities to ‘‘do’’

mathematics well (Van Garderen 2004), and mathematical success is contingent upon

attaining and utilizing reading skills related to all components of mathematical language

(Adams 2003). Draper (2002) claimed that only those mathematics teachers who attend to

their students’ literacy needs are fulfilling their responsibility to truly educate students, and

Moyer (2000) determined that teachers who separate language and mathematics instruction

are creating unnatural learning experiences for children.

The use of literature in teaching mathematics has been found to actively engage students

in meaningful mathematical contexts (Bentz and Moore 2003; Keat and Wilburne 2009;

Whitin 1992), nurture students’ imagination (Keat and Wilburne 2009; Yopp and Yopp

2001), enhance students’ enjoyment, interest, motivation, and enthusiasm toward mathe-

matical tasks (Ducolon 2000; Keat and Wilburne 2009; Whitin and Whitin 2004; Yopp and

Yopp 2001; Young and Marroquin 2006), promote students’ problem solving and problem

posing abilities (Whitin and Whitin 2004; Young and Marroquin 2006), support students’

mathematical reasoning (Whitin 1992) and critical thinking (Young and Marroquin 2006),

and encourage students’ justification and communication of mathematics results (Young

and Marroquin 2006). It has also been asserted that because books present mathematical

ideas in a low-key, nonthreatening manner, students’ confidence in their mathematical

abilities are enhanced (Whitin 1992) and their mathematical anxiety is reduced (Zambo

2005).

Within the realm of literature integration in mathematics, there presents a variety of

formats from which an educator may choose when making integration decisions. Welch-

man-Tischler (1992) suggested that there are a variety of ways that children’s literature can

be integrated into mathematics lessons, and, since that time, numerous others have pro-

vided similar suggestions with minor variations in classification. The seven types of uses

for children’s literature in mathematics include the following: (a) provide a context,

(b) introduce manipulatives, (c) model a creative experience, (d) pose an interesting

problem, (e) prepare for a concept or skill, (f) develop a concept or skill, and (g) provide a

context for review (see Table 1). It has also been indicated that children’s literature can

serve as a ‘‘springboard’’ for posing questions and creating mathematical opportunities for

students (Whitin and Whitin 2004). The type and number of questions as well as the form

and level of explanation required while reading the book varies according to the children’s

needs and book’s characteristics (van den Heuvel-Panhuizen et al. 2008; Elia et al. 2010).

Methodology

Context

The study took place in an initial teaching certification program at a private university in

the central United States. Fourteen elementary prospective teachers were the participants in

What are they asking?

123

this study. All participants were enrolled in one section of a junior-level field-based

practicum course and were assigned to an elementary professional development school

(PDS) for the experience. PDSs are innovative institutions formed through partnerships

between professional education programs and P-12 schools. PDS partnerships focus on the

preparation of new teachers, faculty development, inquiry directed at the improvement of

practice, and enhanced student achievement (Teitel 2003). Six of the participants were

enrolled in the required field-based practicum course during the fall semester, and eight

participants were enrolled during the spring semester. As a requirement of the practicum

course, all participants planned and taught a 1-hour mathematics lesson, 4 days each week

for 13 weeks, to a small group of elementary students.

All prospective teacher participants were assigned in pairs to classroom teachers at the

third- and fourth-grade levels, and all of the assignments were in self-contained, non-

departmentalized classrooms. As specified within the PDS contracts, all of the classroom

teachers had at least 1 year previous teaching experience and at least 1 year of teaching

experience at the PDS. Thus, though some of the prospective teacher participants were

placed with classroom teachers relatively new to the profession and the PDS experience

others were placed with veteran classroom teachers well-versed and experienced with the

PDS model. As all of the classroom teachers were responsible for teaching mathematics,

the diversity in their teaching experience was also expressed through the classroom

teachers’ varied experiences specific to mathematics instruction.

The professor for the field-based practicum course was situated at the PDS campus and

was responsible for assigning and evaluating all practicum course assignments. The

practicum course professor conducted regular observations of the prospective teachers

while they were actively involved in teaching experiences and met daily with the

Table 1 Welchman-Tischler (1992) ways to integrate children’s literature

Welchman-Tischler’s sevenways

Children’s book Possible use

Provide a context Divide and ride (Murphy 1997) Children at an amusement park have to makedecisions about how to organize their group toride various rides

Introducemanipulatives

The penny pot (Murphy 1998b) Students can use coins as manipulatives to organizeas the story is read about gathering enough moneyfor face-painting at the carnival

Model a creativeexperience

One hundred hungry ants(Pinczes 1993)

After 100 ants reorganize themselves in variousways on their journey to a picnic, students cancreate their own combinations in a new story witha different number of ants

Pose aninterestingproblem

Counting on Frank (Clement1991)

A young boy’s wonderings provide severalinteresting problems that could be exploredfurther

Prepare for aconcept or skill

The doorbell rang (Hutchins1986)

Sharing cookies with friends and neighbors preparesstudents for the concept of division

Develop aconcept or skill

Sir Cumference and the firstround table (Neuschwander1997)

Sir Cumference’s quest to find the best shape for atable, leads to the discovery of the properties ofcircles

Provide a contextfor review

Pigs on a blanket (Axelrod1996)

Following the family of pigs in their journey to thebeach allows students to review elapsed time

B. Purdum-Cassidy et al.

123

prospective teachers to provide pedagogical instruction, support, and feedback relative to

their teaching and assignments. Pedagogical instruction during practicum seminars

included planning and implementing effective lessons and the role of questioning. Specific

seminar topics associated with the development of effective questioning techniques

included the role of open-ended questioning, helping students make connections through

questioning, and supporting student inquiry. During both semesters of the study, one

specific requirement of the practicum course was to incorporate children’s literature within

at least three of the mathematics lessons that the prospective teachers designed and taught

to elementary students.

Concurrent with their enrollment and participation in the field-based practicum course,

all prospective teacher participants were enrolled in a mathematics methods course. During

the mathematics methods course, the prospective teachers were exposed to lessons and

strategies connecting mathematics and children’s literature books. These can best be

described as books with short passages, a predominance of illustrations, and designed to

share in a short time frame. Some of these books are designed as a narrative with a story,

while others may be more didactic, presenting a more instructive format. Many of the

children’s literature books presented in this course, whether narrative or didactic, had an

intentional mathematics focus. In an early class session during each semester, there was a

presentation of the seven ways to integrate children’s literature, as outlined by Welchman-

Tishchler (1992), including examples for each. Additionally, throughout the semester,

several children’s books were shared with the prospective teachers and the methods course

professor would point out the different ways to incorporate the texts within the elementary

mathematics classroom setting. For example, the professor would select the literature book,

The Greedy Triangle (Burns 1994), begin reading the book, then stop to show a particular

picture that could be used to ‘‘prepare’’ a geometry concept related to regular polygons. At

other times, the professor would actually have the prospective teachers engage in math-

ematical activities that were stimulated from a particular literature book so that they could

see how the connection between literature and mathematics could be used to teach various

mathematical concepts. When sharing The Penny Pot (Murphy 1998b) the prospective

teachers would organize coins into a ‘‘pot’’ as illustrated in the story to better understand

the combination of coins needed. These experiences also allowed the methods course

professor to share with the prospective teachers the ways and means to utilize questioning

to support the connection between the literature and mathematics and to build mathe-

matical understanding.

Data sources

The required literature connected mathematics lessons formed the basis of the study. It is

noted that not all of the 14 prospective teachers prepared, presented, and submitted the

required three lessons. One prospective teacher incorporated children’s literature within

five mathematics lessons, one utilized mathematics children’s literature within two lessons,

and three prospective teachers utilized and submitted only one lesson plan in which they

utilized children’s literature. Decisions regarding the content of the mathematics lesson and

the choice of the children’s literature books were left to the prospective teacher. Yet, as

with all of the mathematics lessons that the prospective teachers designed and shared

during the entirety of the field experience, the classroom teacher provided input as well as

final approval. The prospective teachers were expected to write questions on their math-

ematics lesson plans that they intended to ask students throughout the lesson. For the

purposes of this study, a decision was made to incorporate every question written by the

What are they asking?

123

prospective teachers as recorded in the submitted lesson plans. While it is recognized that

this data may not be correlated to the actual questions asked by the prospective teachers

during the delivery of the mathematics lessons, the study’s purpose reflects our desire to

explore the prospective teachers’ planned questions within the context of literature

integration.

Data analysis

The best fit for this investigation was the qualitative, naturalist paradigm. This research

method allows for an investigation relative to how individuals react in and to the world

around them as they construct a personalized meaning to that particular world. As sug-

gested by Lincoln and Guba (1985), only through holistic, contextually situated inquiry

emphasizing processes, meanings, and the qualities of entities, can an understanding of

those realities be determined with any degree of trustworthiness. Additionally, a decision

was made to utilize deductive analysis ‘‘where the data are analyzed according to an

existing framework’’ as opposed to inductive analysis where themes, categories, and

patterns emerge ‘‘out of the data, through the analyst’s interactions with the data’’ (Patton

2002, p. 453). As the purpose of the study was to determine the influence of the approach

of literature integration in mathematics on prospective teachers’ planned questions, the

decision was made to use both a general question and a mathematics-specific question

classification system. The general question classification system was based upon Blosser’s

(1973) and Smith’s (1969) closed convergent and open divergent scheme, and the math-

ematics-specific classification system was based upon the delineation between procedural

and conceptual mathematics.

As mentioned earlier, prospective teachers were expected to write questions on their

mathematics lesson plan that they intended to ask students throughout the lesson. For the

purposes of this study, a decision was made to incorporate every question written by the

prospective teachers as recorded in the submitted lesson plans. While it is recognized that

this data may not be correlated to the actual questions asked by the prospective teachers

during the delivery of the mathematics lessons, the study’s purpose reflects our desire to

explore the prospective teachers’ planned questions within the context of literature

integration.

Determinations of question classifications involved several readings, comparisons, and

verifications of the data by the four researchers. Each researcher independently read and

coded the data set based upon a specific predetermined classification system. Once each

researcher had completed their independent coding of all questions based upon this clas-

sification, the researchers met to compare coding. Coding was considered valid when three

out of four researchers agreed on the coding of the individual questions. Questions were

categorized first as mathematics or literacy focused questions. Because the study’s focus

was on mathematical understanding, the researchers decided to focus solely on those

questions determined to be mathematics focused. All mathematics questions were first

classified according to their text dependency. Questions classified as text-dependent

required the elementary students to have either read or listened to the children’s literature

book, and the students’ ability to answer the question was dependent upon their prior

interaction with the text. Questions coded as text-independent were those not specifically

linked to the text and, therefore, did not require prior interaction with the text in the

formulation of a response. Although text dependency is not related to mathematical

knowledge or understanding, this classification was instigated because the study is built

B. Purdum-Cassidy et al.

123

upon the influence of the approach of literature integration in mathematics on prospective

teachers’ planned questions.

The mathematics-focused questions were then classified as closed convergent or open

divergent questions. Closed convergent questions were defined by researchers as those

questions framed so that several students would arrive at the same, limited number of

answers, while open divergent questions were defined as open-ended, multiple response

questions that required students to engage in critical, creative thinking in the formulation of

a response. Questions were then further delineated as being procedural or conceptual. The

agreed upon definition of procedural questions was any question focused on rules and

computational processes associated with determining the correct answer to a posed

problem. The accepted definition of conceptual questions was a question designed to assess

students’ understanding of mathematical relationships. Questions that could not be coded

based upon the categories described above were labeled as poor mathematics questions.

Questions within this category were those that could result in student confusion because of

poor wording, a lack of connection between the question and the mathematical task or

concept, or the inclusion of an incorrect mathematical statement/concept.

In addition to reporting qualitative data, results are also presented by the quantity and

typology of planned questions. This method of reporting should not be construed as an

attempt to construct or portray a quantitative study but merely as a means of providing an

additional measure for comparing the types of questions planned by the prospective

teachers.

Results

An examination of mathematics focused, literature integrated lesson plans created by

prospective teachers and incorporated within elementary classrooms provided data relevant

to the ways in which a specific approach influenced the prospective teachers’ planned

utilization of questions. For the purposes of this study, every planned question was

examined and the researchers coded and categorized each mathematics question in mul-

tiple ways in order to provide insights into the depth and strength of prospective teachers’

mathematics questioning pedagogy.

Utilizing the 37 literature integration mathematics lesson plans submitted by the pro-

spective teachers, the total number of questions planned and recorded within the lessons as

well as the number of questions planned in each lesson was determined. With 246 total

planned questions, there revealed great variance in the number of questions planned by

individual lesson and by individual prospective teacher. One submitted lesson plan

included no planned questions while another lesson plan contained 25 questions. The

average number of planned questions per lesson was nearly seven, and there was a broad

standard deviation due to the substantial range. Examination of the questions planned by

each prospective teacher also revealed a high level of variance. One prospective teacher

planned an average of approximately 16 questions per lesson while another prospective

teacher planned an average of one question per lesson, with the average number of

questions per lesson by prospective teacher being approximately six. When the questions

were examined by semester, the six prospective teachers who participated in the study

during the fall semester planned a total of 133 or 54 % of the total questions, while the

eight spring semester participants planned a total of 113 or 46 % of the total questions.

In all subsequent reporting of results, only 241 total planned questions will be reported

because, through the previously delineated multi-tiered validation process, five of the

What are they asking?

123

prospective teachers’ planned questions (2 % of the total) could not be validated and were

thus removed from the data set. The first level of question classification utilized was

content focus; a determination was made as to whether the focus of the question was

mathematical, literary, or did not fit in either of the aforementioned categories. Findings

revealed that 201 (83 %) of the total planned questions focused on mathematics while 40

(17 %) of the questions had a literary focus. Moreover, nineteen of the mathematics

questions planned by the prospective teachers (approximately 9 %) were determined to be

poor mathematics questions (see Table 2). These questions were poorly worded, not

connected to mathematics, or included an incorrect mathematical concept. The following

planned questions are representative of these poor mathematics question types: ‘‘How

would you make sure that you have guessed correctly?’’ ‘‘What is your favorite thing about

probability?’’, and ‘‘When you divide zero into a number, what is your answer?’’ In all

subsequent classifications and reporting of results, the nineteen poor mathematics ques-

tions were removed from the data set, resulting in 182 total planned mathematics questions.

Researchers determined that these poorly formulated questions constituted a distinct subset

of the prospective teachers planned mathematics questions and, thus, there was no need for

further classification.

An examination of these 182 planned mathematics-focused questions revealed that 81

(45 %) of the questions were text-dependent and 101 (55 %) of the questions were text-

independent. Examination of each submitted lesson plan indicated that the prospective

teachers varied greatly in their utilization of text-dependent questions. Some prospective

teachers planned almost all of their questions based upon information found within the text

while others devised lesson plans in which no text-dependent questions were formulated.

Examples of text-dependent questions submitted by one prospective teacher and based

upon The Doorbell Rang (Hutchins 1986) included multiple iterations of ‘‘How many

cookies does each child have now?’’ and text-independent examples based on the same text

included ‘‘What is a row?’’ ‘‘What is a column?’’, and ‘‘How did you determine the number

of cookies in your array using the rows and columns?’’

All mathematics questions were then classified as being either closed convergent or

open divergent. Representing 73 % of the total mathematics questions planned by the

prospective teachers, 133 of the questions were closed, convergent questions, and 27 % (49

questions) were open divergent questions (see Table 3). The closed convergent questions

ranged in length from brief, single sentence questions (‘‘How many tiny black bugs were

there in all?’’) to longer, multiple sentence questions (‘‘There are 3 families with 4 people.

There are 8 families with 5 people. My family has 3 people. How many people is that all

together?’’). It was also noted that of the 133 closed convergent questions, 21 (16 %) were

yes/no questions.

Additional analysis of the prospective teachers’ planned closed questions revealed that

although the questions triggered convergent thinking, many were planned in a manner that

Table 2 Prospective teachers’ planned questions

Question type Overall Literacy focused Mathematics focused

Satisfactory quality Poor quality

Non-validated questions 5

Validated questions 241 40 (17 %) 182 (76 %) 19 (8 %)

Total 246

B. Purdum-Cassidy et al.

123

required students to formulate more than a single word response. Questions such as ‘‘What

did Sheri have to do with the bar [graph] now that the number of cups is 24?’’ posed during

the reading of Lemonade for Sale (Murphy 1998a), exemplified a majority of the closed

convergent mathematics-focused questions planned by the prospective teachers. Yet, while

a rarity, and utilized by only one prospective teacher within one lesson, 24 of the planned

closed mathematics questions came directly from a worksheet provided to the prospective

teacher in advance of the lesson. Every question prompted from the worksheet could be

answered with a single word or single numerical response, and the prospective teacher

planned only three additional questions within the lesson, with two of those being closed

mathematics questions as well.

Similar to the closed convergent questions, the 49 planned open divergent questions

also varied in length. When utilizing the book Counting on Frank (Clement 1991), one

prospective teacher planned both brief (‘‘How much do you think you grow in a year?’’)

and more lengthy (‘‘How long do you think it would take for the faucets you use in the

bathroom at your home to fill up your bathroom?’’) open-ended questions. These examples

reveal that even when open divergent questions are of short length, they still allow for

multiple, varied responses from students. Deeper inspection of open divergent mathematics

questions revealed that questions of this type fell almost exclusively within two catego-

ries—questions requiring students to relate the mathematics to real life and questions

directly related to the text. An example of the first type, utilized during a lesson which

incorporated the text Spaghetti and Meatballs for All (Burns 1997), was ‘‘What are some

other ways we can use area and perimeter in real life?’’ and an example of the second type,

utilized during a lesson incorporating the text On the Scale—A Weighty Tale (Cleary

2008), was ‘‘What is something else besides a slice of bread that might weigh an ounce?’’

The prospective teachers’ planned mathematics-focused questions were further cate-

gorized as being either procedural or conceptual. Of the 133 questions determined to be

closed convergent, 67 were classified as procedural, and an almost equal number, 66, were

classified as conceptual. However, all but one of the 49 open divergent mathematics-

focused questions were ascertained as being conceptual (see Table 3). ‘‘We have 80

pounds [of tomatoes], how many more do we need [to make 88 pounds]?’’ ‘‘Would a

kilogram of rice weight more, less, or the same as a kilogram of cheese?’’ and ‘‘How do

you know it [the shape] is symmetrical?’’ are consecutively representative of the pro-

spective teachers’ closed procedural, closed conceptual, and open conceptual questions.

The special case of an open divergent procedural question occurred during a lesson

incorporating the text Coyotes All Around (Murphy 2003). In planning the question, ‘‘Why

did he move the 8 to the 10 and the 12 to the 10?’’ the prospective teacher was attempting

to assess students’ understanding of rounding numbers to the nearest ten. While the

question allowed students to construct and provide numerous correct responses, it forced

students to focus on the process of rounding.

Table 3 Satisfactory quality planned mathematics questions

Question type Overall Type of knowledge assessed

Procedural Conceptual

Closed convergent 133 (73 %) 67 66

Open divergent 49 (27 %) 1 48

Total 182 68 (37 %) 115 (63 %)

What are they asking?

123

Discussion

Recognizing the importance of utilizing questioning within the classroom while also

acknowledging that prospective teachers often struggle with designing and incorporating

questions, the researchers chose to explore the kinds of questions prospective teachers plan

when utilizing literature in mathematics lessons to scaffold children’s understanding of the

mathematics concepts presented through the text. The first component analyzed was the

number of questions planned by the prospective teachers within each of the submitted

lesson plans. Results revealed that some of the prospective teachers possessed a limited

recognition of or ability to incorporate questioning when planning lessons. Additionally,

with some of the prospective teachers submitting lesson plans with such a limited number

of planned questions, it was impossible for these prospective teachers to have incorporated

an even distribution of question types so as to support and assess student thinking and

understanding, As revealed by Moyer and Milewicz (2002), it is only those teachers who

incorporate questions at various levels who are capable of probing and discerning the range

and depth of students’ thinking.

As the research question guiding the study addressed the kinds of questions prospective

teachers planned when integrating literature in mathematics lessons, there presented a need

to analyze the planned questions based upon their dependency and utilization of said

literature. While some of the prospective teachers planned multiple questions at varied

levels in a manner designed to forge and strengthen the relationship between the mathe-

matics in the text and the mathematics in the students’ lives, others failed to plan even one

text-dependent question within their lesson. The power of the approach of literature

integration in mathematics is built upon literature’s ability to reveal to students that

mathematics is intrinsic in human thinking and is applicable to their lives (Haury 2001;

Murphy 1999); therefore, if no questions were designed so as to formulate the link between

the mathematics in the text and the mathematics in the students’ lives, the approach was

not utilized in a manner that allowed the prospective teacher nor the students to reap its

benefits.

An examination of the content focus of questions revealed that a majority of the total

planned questions were focused on mathematics. This data corresponded to the fact that the

prospective teachers were participating in a mathematics practicum course associated with

a mathematics field experience and were required to create mathematics lesson plans with

literature integration being a secondary requirement. Thus, it is not surprising that math-

ematics-focused questions dominated the questions planned by the prospective teachers.

Content focus data presented further revelations through an analysis of the questions

determined to lie outside the mathematics and literary categories. Although only a small

percentage of the total planned questions were categorized as poor mathematics questions,

this result is indicative of the prospective teachers’ novice level. The prospective teachers

planned, wrote, and submitted questions that lacked clarity, were limited in mathematical

connectivity, or included incorrect mathematical concepts. While it is highly likely that

some of the impromptu questions formulated by educators in response to student discourse

will be poorly worded and will subsequently require rephrasing, questions that are planned

in advance should be well devised and articulated so as to construct and assess students’

mathematical understanding. More specifically, the four questions within this category

determined to include incorrect mathematical concepts are of concern because inclusion of

even one question of this type can be problematic in a mathematics classroom. The

problem of developing mathematics misconceptions is compounded in the elementary

classroom because, although the questions may not produce an immediate impact on

B. Purdum-Cassidy et al.

123

students, as they progress to higher-level mathematics, the seed of misconception may

grow so as to eventually create a critical situation. Additionally, because three of the four

incorrect mathematics questions were planned by one prospective teacher for utilization

within a single division lesson, both the prospective teacher and the students with whom

the lesson was shared could experience a multitude of future mathematics difficulties.

Research has revealed that employing an array of closed convergent and open divergent

questions stimulates students’ creative/critical thinking and challenges students’ ideas and

beliefs (Ralph 1999a). Therefore, this classification data presents as an important venue for

analyzing the planned questions of prospective teachers. Seventy-three percent of the total

planned mathematics questions were categorized as closed convergent. This percentage is

slightly higher than that determined by Gall et al. (1971) who found that 60 % of the

questions posed by teachers solely require the recall of facts. However, upon closer

inspection of these questions, a direct contrast to the TIMSS report of Stigler and Hiebert

(1999) was revealed; many of the prospective teachers’ closed convergent mathematics

questions were not rapid fire questions that required one-word responses but were ques-

tions that required students to formulate longer, more detailed responses.

Henning and Lockhart (2003) indicated that worksheet questions, whether planned by

the prospective teacher or provided to the prospective teacher, are problematic because

prospective teachers pose these questions quickly and with little or no follow-up. Con-

sistent with these research findings, and thus prompting concern, one prospective teacher

asked numerous closed convergent mathematics-focused questions within one lesson and

almost all of these questions came directly from a worksheet. The prospective teacher in

question was provided the worksheet as a possible lesson resource, and it appears that she

failed to consider how the sole utilization of these closed convergent worksheet questions

could negatively impact student learning and understanding. As a result, she made no

attempt to incorporate additional questions within the lesson or to consider additional ways

to connect the literature with the lesson.

Of additional concern was the number of yes/no questions planned by the prospective

teachers. Yes/no questions represent a specific type of closed, convergent question that

should be avoided because they can promote guessing and have low diagnostic power

(Groisser 1964; Wilen 2001). Moreover, yes/no questions have been found to severely

limit students’ thinking and teachers’ abilities to assess student understanding because

there are only two possible answer options (Napell 2001). When yes/no questions are

utilized, the teacher is unable to determine when or if a student response is a guess, a

correct response with or without understanding, or an incorrect response with limited or no

understanding.

Examination of the prospective teachers’ open divergent mathematics questions

revealed findings contrary to prior research. Gall et al. (1971) discerned that 20 % of the

questions posed by teachers stimulate student thinking, and Nicol (1999) indicated that

prospective teachers have difficulty planning questions to learn what students are thinking.

The prospective teachers involved in the study planned approximately one out of every

four questions in a manner that encouraged their elementary students to think mathe-

matically, thereby allowing the prospective teachers to explore students’ thought processes

during their construction of mathematical understanding.

Numerous studies have found that traditional classrooms emphasize and laud students’

abilities to memorize facts, follow rules, plug in formulas, and execute procedures (Battista

1994; Brandy 1999; Hiebert 2003), yet results of this study revealed both an elevated

percentage of open divergent questions as well as a high percentage of conceptually-based

questions. Subsequently, data revealed that when utilizing the approach of literature

What are they asking?

123

integration in mathematics, the prospective teachers involved in the study went against the

aforementioned trend. Also indicated within the presented data was that although closed

convergent procedural questions did represent the highest number and the highest per-

centage of mathematics-focused questions, there was only a one question difference

between this category and the closed convergent conceptually-based question category.

Accordingly, there presented a good balance between the two question types and, as

documented by mathematics researchers and educators alike, a mix of both procedural and

conceptual questions is required and appropriate within the mathematics classroom

(Bransford et al. 2000; Franke et al. 2009; National Mathematics Advisory Panel 2008;

NCTM 2000; Van de Walle et al. 2010).

Recommendations and implications

At a time when research indicates that as many as 50,000 questions are asked by teachers

annually with most of these questions focusing on information recall while ignoring issues

of substance, educators at all levels must realize that an exploration and analysis of the

questioning skills and habits of educators is essential (Watson and Young 2003). Within

this study, the researchers chose to examine the questions planned by prospective teachers

when integrating literature in mathematics lessons. The results signify areas of concern,

need, revelation, and optimism.

Based upon the results of this study, there are implications and recommendations for

both classroom teachers and teacher educators alike to consider when making determi-

nations relative to the mathematics classroom, course, and field experience. Although all

the prospective teachers in this study were novices, they revealed a great deal of variance

in their incorporation of questions within lessons integrating literature in mathematics.

Much of this variance could be attributed to individual differences between the prospective

teachers, and, as such, it is important for teacher educators to be aware of the distinct

characteristics and needs of individual students. However, when prospective teachers are

involved in field-based experiences, it is important that teacher educators also consider the

existence of possible external forces when developing, assessing, and evaluating assign-

ments directly linked to those field experiences. These external factors include such ele-

ments as the expectations, requirements, and background experiences of a specific campus,

principal, or classroom teacher. Variances in these factors could result in the cessation or

limitation of the prospective teachers’ abilities to complete an assignment to required

specifications. Relative to this study the researchers recognized that the classroom teacher

greatly influenced the number of mathematics lessons that utilized children’s literature that

the prospective teachers were able to plan and incorporate in the classroom as well as the

level of support and assistance provided to the prospective teachers relative to the lesson.

When examining the written lesson plans for the types of questions prospective teachers

were planning to pose when integrating literature within their mathematics lesson, it was

surprising that prospective teachers planned a higher percentage of text-independent than

text-dependent questions. It appeared that the text dependency of the questions was closely

related to both the type of text utilized and the way in which the prospective teacher

utilized the text. Some prospective teachers incorporated the text as an integral part of the

lesson while others chose to include the text in a manner that was separate from the

purpose of the assigned task. Additionally, some prospective teachers’ utilized didactic

texts while others utilized narratives. Because all the prospective teachers had participated

in experiences within their mathematics methods course wherein literature integration was

B. Purdum-Cassidy et al.

123

utilized with suitable texts in an appropriate text-dependent manner with appropriate

corresponding questions, this finding is reflective of the developmental nature of the act of

teaching. In their initial attempt to apply the approach of literature integration in mathe-

matics and to utilize questions designed to scaffold students’ understanding of the math-

ematics concepts presented through the text, the prospective teacher participants revealed

that their attempts represented developing approximations of their abilities to both

understand and to apply that understanding (Cambourne 2001). Teacher educators must

recognize that prospective teachers’ attempts to implement instructional approaches are

developing approximations, and without the provision of multiple opportunities and spe-

cific feedback, those approximations will never progress beyond the initial phase. More-

over, when those opportunities and accompanying feedback are linked to actual classroom-

based experiences with students, teacher educators can further guide and propel the

development of these approximations (Nicol 1999).

Prospective teachers involved in the study planned numerous mathematics questions

that provided evidence of their novice level and the resulting need to provide courses in

which there is presented the pedagogical underpinnings as well as the modeling of

effective questioning skills. An examination of the numerous planned yes/no questions

revealed that many of these questions could be easily modified so as to move the question

from the closed convergent category to the open divergent category. Within all content

pedagogy coursework, prospective teachers should be exposed to information related to the

closed nature of yes/no questions, the inability of yes/no questions to assess student

understanding, and the practice of revising yes/no questions to the creation of open

divergent questions. Additionally, although the number of questions in this study that

incorporated incorrect mathematics concepts was limited, it is of concern and must be

addressed. Prospective teachers at the elementary level must participate in mathematics

content courses where their mathematics misconceptions and limited conceptions can be

identified and addressed. Furthermore, within mathematics methods courses, prospective

teachers must be introduced to the nature and impacts of mathematics misconceptions on

student learning and understanding. They must then acquire the skills and abilities required

in identifying and reconceptualizing those misconceptions.

Wasserman (1991) postulated that prospective teachers do not learn questioning from

any serious study of questioning strategies during their teacher education programs but,

instead, learn it as a byproduct of their own student days. With most prospective teachers

being byproducts of very traditional, procedurally bound mathematics classrooms, a logical

presumption follows that these future educators would develop and utilize traditional,

procedural questioning strategies (Smith et al. 2002). However, in direct contrast to

Wasserman’s study and the previously indicated presumption, it appears that the utilization

of the approach of integrating literature in mathematics provided the experience and the

bridge that allowed many of the prospective teachers in the study to break from their

personal mathematics experiences to create reform-oriented, constructivist questions and

experiences for their students.

The researchers recognize that the study was limited by its sole utilization of the

questions planned within prospective teachers’ submitted lesson plans. Yet we believe that

an examination of planned questions is valid because ‘‘Quality questioning cannot be

created on the fly during instruction, nor can the task of question formulation be separated

from lesson planning…their design cannot be left to chance’’ (Walsh and Sattes 2011).

Additionally, we recognize that future studies aimed at investigating the questions pro-

spective teachers both plan and ask their students, as well as the impact of these questions

on mathematical discourse, are warranted. Questioning has been and will continue to be a

What are they asking?

123

mainstay in classrooms across the country, and, subsequently, an examination of the

questioning strategies of teachers and prospective teachers is an arena affording numerous

research opportunities. Asking questions and leading discussions can have a positive effect

on student learning by providing students with opportunities to reason about mathematical

concepts or to explore mathematical connections (Hiebert et al. 2003). However, good

questions and classroom discussions do not just happen. Verbal questioning is a skill, and

like any skill, must be practiced before it is mastered (Vogler 2005).

References

Adams, T. L. (2003). Reading mathematics: More than words can say. Reading Teacher, 56(8), 786–795.Amit, M., & Fried, M. N. (2002). Research, reform, and times of change. In L. D. English (Ed.), Handbook

of international research in mathematics education (pp. 355–381). Mahwah, NJ: Erlbaum.Andre, T. (1979). Does answering higher-level questions while reading facilitate productive learning?

Review of Educational Research, 49, 280–318.Axelrod, A. (1996). Pigs on a blanket. New York, NY: Simon & Schuster Books for Young Readers.Baird, J. R., & Northfield, J. R. (Eds.). (1992). Learning from the PEEL experience. Melbourne: Monash

University Printing.Battista, M. (1994). Teacher beliefs and the reform movement in mathematics education. Phi Delta Kappan,

75, 462–463.Bentz, W. P., & Moore, S. D. (2003). Using literature to teach factorials. Mathematics Teaching in the

Middle School, 8(9), 461–465.Bloom, B. S. (1956). Taxonomy of educational objectives: The classification of educational goals.

(Handbook I: Cognitive domain). New York, NY: David McKay Company, Inc.Blosser, P. E. (1973). Handbook of effective questioning techniques. Worthington, OH: Education

Associates.Blosser, P. E. (2000). How to ask the right questions. Arlington, VA: National Science Teachers

Association.Boaler, J. (1998). Open and closed mathematics: Student experiences and understanding. Journal for

Research in Mathematics Education, 29(1), 41–62.Boaler, J., & Brodie, K. (2004). The importance of depth and breadth in the analyses of teaching: A

framework for analyzing teacher questions. Proceedings of the 26th meeting of the North AmericanChapter of the International Group for the Psychology of Mathematics Education. Toronto, Ontario,Canada.

Borich, G. (1992). Effective teaching methods (2nd ed.). New York, NY: Merrill.Brandy, T. (1999). So what? Teaching children what matters in math. Portsmouth, NH: Heinemann.Bransford, J., Brown, A., & Cocking, R. (Eds.). (2000). How people learn: Brain, mind, experience, and

school: Expanded edition. Washington, DC: National Academy Press.Burns, M. (1994). The greedy triangle. New York, NY: Scholastic Press.Burns, M. (1997). Spaghetti and meatballs for all. New York, NY: Scholastic Press.Buschman, L. (2001). Using student interviews to guide classroom instruction: An action research project.

Teaching Children Mathematics, 8(4), 222–227.Cambourne, B. (2001). Conditions for literacy learning: Why do some students fail to learn to read?

Ockham’s razor and the conditions of learning. The Reading Teacher, 54(8), 784–786.Cazden, C. B. (1986). Classroom discourse. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd

ed., pp. 432–463). New York, NY: Macmillan.Cazden, C. B. (2001). Classroom discourse: The language of teaching and learning (2nd ed.). Portsmouth,

NH: Heinemann.Cerdan, R., Vidal-Abarca, E., Martinez, T., Gilabert, R., & Gil, L. (2009). Impact of question–answering

tasks on search processes and reading comprehension. Learning and Instruction, 19, 13–27.Cleary, B. P. (2008). On the scale—A weighty tale. Minneapolis, MN: Millbrook Press.Clement, R. (1991). Counting on Frank. Milwaukee WI: Gareth Stevens.Crespo, S. (2003). Learning to pose mathematical problems: Exploring changes in preservice teachers’

practices. Educational Studies in Mathematics, 52, 243–270.

B. Purdum-Cassidy et al.

123

Doyle, W. (1985). Classroom organization and management. In M. C. Wittrock (Ed.), Handbook of researchon teaching (3rd ed., pp. 392–431). New York, NY: Macmillan.

Draper, R. J. (2002). School mathematics reform, constructivism, and literacy: A case for literacy instructionin the reform-oriented math classroom. Journal of Adolescent and Adult Literacy, 45(6), 520–529.

Ducolon, C. K. (2000). Quality literature as a springboard to problem solving. Teaching Children Mathe-matics, 6(7), 442–446. Retrieved from http://www.jstor.org/stable/i40051648.

Elia, I., van den Heuvel-Panhuizen, M., & Georgiou, A. (2010). The role of pictures in picture books onchildren’s cognitive engagement with mathematics. European Early Childhood Education ResearchJournal, 18(3), 125–147.

Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning toelicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education,60(4), 380–392.

Freeman, E. B., & Person, D. G. (1998). Connecting informational children’s books with content arealearning. Boston, MA: Allyn and Bacon.

Gall, M. (1984). Synthesis of research on teachers’ questioning. Educational Leadership, 42, 40–47.Gall, M., Dunning, B., & Weathersby, R. (1971). Minicourse nine: Higher cognitive questioning, teachers

handbook. Beverly Hills, CA: Macmillan Educational Services.Gallagher, J. J. (1965). Productive thinking of gifted children. U. S. Department of Health, Education, and

Welfare, Office of Education, Cooperative Research Project, No 965. Urbana, UL: University ofIllinois.

Graesser, A. C., & Person, M. K. (1994). Question asking during tutoring. American Educational ResearchJournal, 31, 104–137.

Grossier, P. (1964). How to use the fine art of questions. Englewood Cliffs, NJ: Prentice-Hall.Hamilton, R. J. (1985). A framework for the evaluation of the effectiveness of adjunct questions and

objectives. Review of Educational Research, 55, 47–85.Hannel, I. (2009). Insufficient questioning. Phi Delta Kappan, 91(3), 65–69.Haury, D. L. (2001). Literature-based mathematics in elementary school. Retrieved May 15, 2006 from

Ohio State University, Eric Digest Web site: http://www.ericse.org.Henning, J. E., & Lockhart, A. (2003). Acquiring the art of classroom discourse: A comparison of teacher

and prospective teacher talk in a fifth grade classroom. Research for Educational Reform, 8(3), 46–57.Herber, H. L. (1978). Teaching reading in the content areas. Englewood Cliffs, NJ: Prentice Hall.Hiebert, J. (2003). What research says about the NCTM standards. In J. Kilpatrick, W. G. Martin, & D.

Schifter (Eds.), A research companion to principles and standards for school mathematics (pp. 1–23).Reston, VA: National Council of Teachers of Mathematics Inc.

Hiebert, J., Gallimore, R., Garnier, H., Givving, K. B., Hollingsworth, H., Jacobs, J., et al. (2003). Teachingmathematics in seven countries: Results from the TIMSS 1999 video study. Washington, DC: NationalCenter for Education Statistics.

Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30, 393–425.

Hutchins, P. (1986). The doorbell rang. New York, NY: Greenwillow Books.Kawanaka, T., Stigler, J., & Hiebert, J. (1999). Studying mathematics classrooms in Germany, Japan, and

the United States: Lessons from TIMSS videotape study. In G. Kaiser, E. Luna, & I. Huntley (Eds.),International comparisons in mathematics education (pp. 86–203). Philadelphia, PA: Falmer Press.

Kazemi, E., & Stipek, D. (2001). Promoting conceptual thinking in four upper-elementary mathematicsclassrooms. Elementary School Journal, 102, 59–80.

Keat, J. B., & Wilburne, J. M. (2009). The impact of storybooks on kindergarten children’s mathematicalachievement and approaches to learning. US-China Education Review, 6(7), 61–67.

Klinzing, H. G., Klinzing-Eurich, G., & Tisher, R. P. (1985). Higher cognitive behaviors in classroomdiscourse: Congruencies between teachers’ questions and pupils’ responses. The Australian Journal ofEducation, 29(1), 63–75.

Lemke, J. L. (1990). Talking science: Language, learning and values. Norwood, NJ: Ablex.Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic inquiry. Newbury Park, CA: Sage.Lorber, M. (1996). Objectives, methods, and evaluation for secondary teaching (4th ed.). Boston, MA: Allyn

and Bacon.Manouchehri, A., & Lapp, D. A. (2003). Unveiling student understanding: The role of questioning in

instruction. Mathematics Teacher, 96(8), 562–566.Martino, A. M., & Maher, C. A. (1999). Teacher questioning to promote justification and generalization in

mathematics: What research practice has taught us. Journal of Mathematics Behavior, 18, 53–78.Mehan, H. (1985). The structure of classroom discourse. In T. A. Van Dijk (Ed.), Handbook of discourse

analysis (Vol. 3, pp. 119–131). London: Academic Press.

What are they asking?

123

Mewborn, D. S., & Huberty, P. D. (1999). Questioning your way to the standards. Teaching ChildrenMathematics, 6(4), 226–227.

Moyer, P. S. (2000). Communicating mathematically: Children’s literature as a natural connection. TheReading Teacher, 54(3), 246–256.

Moyer, P. S., & Milewicz, E. (2002). Learning to question: Categories of questioning used by preserviceteachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5,293–315.

Murphy, S. J. (1997). Divide and ride. New York, NY: Harper Collins.Murphy, S. J. (1998a). Lemonade for sale. New York, NY: Harper Collins.Murphy, S. J. (1998b). The penny pot. New York, NY: Harper Collins.Murphy, S. J. (1999). Learning math through stories. School Library Journal, 45(3), 122–124.Murphy, S. J. (2003). Coyotes all around. New York, NY: Harper Collins.Napell, S. M. (2001). Using questions to enhance classroom learning. Education, 99(2), 188–197.National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.

Reston, VA: National Council of Teachers of Mathematics.National Mathematics Advisory Panel. (2008). Foundations for success. Jessup, MD: United States

Department of Education.National Research Council. (2001). The state of school mathematics in the United States, Chapter 2. In J.

Kilpatrick, J. Swafford & B. Findell (Eds.), Adding it up: Helping children learn mathematics (pp.31–70). Washington, DC: National Academy Press.

Newschwander, C. (1997). Sir Cumference and the first round table: A math adventure. Watertown, MA:Charlesbridge.

Nicol, C. (1999). Learning to teach mathematics: Questioning, listening and responding. EducationalStudies in Mathematics, 37, 45–66.

Nilssen, V., Gudmundsdottir, S., & Wangsmo-Cappelen, V. (1995). Unexpected answers: Case study of astudent teacher derailing in a math lesson. Paper presented at the annual meeting of the AmericanEducational Research Association, San Francisco, CA.

Ong, E. G., Lim, C. S., & Ghazali, M. (2010). Examining the changes in novice and experienced mathe-matics teachers’ questioning techniques through the lesson study process. Journal of Science andMathematics Education in Southeast Asia, 33(1), 86–109.

Parker, M., & Hurry, J. (2007). Teachers’ use of questioning and modeling comprehension skills in primaryclassrooms. Educational Review, 59(3), 299–314.

Patton, M. (2002). Qualitative research and evaluation methods (3rd ed.). Thousand Oaks, CA: Sage.Perry, M., VanderStoep, S. W., & Yu, S. L. (1993). Asking questions in first-grade mathematics classes:

Potential influences on mathematical thought. Journal of Educational Psychology, 85(1), 31–40.Pinczes, E. (1993). One hundred hungry ants. New York, NY: Houghton Mifflin Company.Ralph, E. G. (1999a). Developing novice teachers’ oral-questioning skills. McGill Journal of Education,

34(1), 29–47.Ralph, E. G. (1999b). Oral-questioning skills of novice teachers: Any questions? Journal of Instructional

Psychology, 26(4), 286–296.Sanders, N. M. (1966). Questions: What kinds?. New York, NY: Harper and Row.Smith, R. (1969). Questions for teachers: Creative reading. The Reading Teacher, 22(5), 430–434.Smith, M. S. (2000). Balancing old and new: An experienced middle school teacher’s learning in the context

of mathematics instructional reform. Elementary School Journal, 100(4), 351–375.Smith, P. S., Banilower, E., McMahon, K., & Weiss, I. (2002). The national survey of science and math-

ematics education: Trends from 1977 to 2000. Chapel Hill, NC: Horizon Research, Inc. Retrieved fromhttp://2000survey.horizon-research.com/reports/trends/trends_report.pdf.

Smith, E. L., Blakeslee, T. D., & Anderson, C. W. (1993). Teaching strategies associated with conceptualchange learning in science. Journal of Research in Science Teaching, 10, 111–126.

Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F.J. Lester Jr (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319–369).Charlotte, NC: Information Age.

Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improvingeducation in the classroom. New York, NY: The Free Press.

Teitel, L. (2003). The professional development schools handbook: Starting, sustaining, and assessingpartnerships that improve student learning. Thousand Oaks, CA: Corwin Press Inc.

Van de Walle, J. A., Karp, K., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics.Teaching developmentally (7th ed.). Boston, MA: Pearson Education Inc.

van den Heuvel-Panhuizen, M., van den Boogaard, S., & Doig, B. (2008). Picture books as an impetus forkindergarteners’ mathematical thinking. Mathematical Thinking and Learning, 10, 341–373.

B. Purdum-Cassidy et al.

123

Van Garderen, D. (2004). Reciprocal teaching as a comprehension strategy for understanding mathematicalword problems. Reading & Writing Quarterly, 20, 225–229. doi:10.1080/10573560490272702.

Vogler, K. E. (2005). Improve your verbal questioning. The Clearing House, 79(2), 98–103.Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge,

MA: Harvard University Press.Walsh, J. A., & Sattes, B. D. (2011). Thinking through quality questioning: Deepening student engagement.

Thousand Oaks, CA: Sage.Wasserman, S. (1991). The art of the question. Childhood Education, 67(4), 257–259.Watson, K., & Young, B. (2003). Discourse for learning in the classroom. In S. Murphy & C. Dudley-

Marling (Eds.), Literacy through language arts: Teaching and learning in context (pp. 39–49). Urbana,IL: National Council of Teachers of English.

Webb, N. M., Nemer, K. M., & Ing, M. (2006). Small-group reflections: Parallels between teacher discourseand student behavior in peer-directed groups. Journal of the Learning Sciences, 15, 63–119.

Welchman-Tischler, R. (1992). How to use children’s literature to teach mathematics. Reston, VA: TheNational Council of Teachers of Mathematics Inc.

White, D. Y. (2000). Reaching all students mathematically through questioning. In M. Strutchens, M.L. Johnson, & W. F. Tate (Eds.), Changing the faces of mathematics: Perspectives on AfricanAmericans (pp. 21–32). Reston, VA: NCTM.

White, D. Y. (2003). Promoting productive mathematical classroom discourse with diverse students. TheJournal of Mathematical Behavior, 22(1), 37–53.

Whitin, D. (1992). Explore mathematics through children’s literature. School Library Journal, 38(8), 24–28.Whitin, D. J., & Whitin, P. E. (2004). New visions for linking literature and mathematics. Urbana, IL: The

National Council of Teachers of English.Wilen, W. W. (2001). Exploring myths about teacher questioning in the social studies classroom. The Social

Studies, 92(1), 26–32.Wood, T. (2002). What does it mean to teach differently? In B. Barton, K. Irwin, M. Pfannuch & M. Thomas

(Eds.), Mathematics education in the South Pacific: Proceedings of the twenty-fifth annual conferenceof the Mathematics Education Research Group of Australasia (Vol. 1, pp. 61–67). Auckland, NewZealand: MERGA.

Yopp, R. H., & Yopp, H. K. (2001). Literature-based reading activities (3rd ed.). Boston, MA: Allyn andBacon.

Young, E., & Marroquin, C. (2006). Posing problems from children’s literature. Teaching ChildrenMathematics, 12(7), 362–366.

Zambo, R. (2005). The power of two: Linking mathematics and literature. Mathematics Teaching in theMiddle School, 10(8), 394–399.

What are they asking?

123