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Teacher implementation profiles for integrating computational thinking into elementary mathematics and science instruction


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Incorporating computational thinking (CT) ideas into core subjects, such as mathematics and science, is one way of bringing early computer science (CS) education into elementary school. Minimal research has explored how teachers can translate their knowledge of CT into practice to create opportunities for their students to engage in CT during their math and science lessons. Such information can support the creation of quality professional development experiences for teachers. We analyzed how eight elementary teachers created opportunities for their students to engage in four CT practices (abstraction, decomposition, debugging, and patterns) during unplugged mathematics and science activities. We identified three strategies used by these teachers to create CT opportunities for their students: framing, prompting, and inviting reflection. Further, we grouped teachers into four profiles of implementation according to how they used these three strategies. We call the four profiles (1) presenting CT as general problem-solving strategies, (2) using CT to structure lessons, (3) highlighting CT through prompting, and (4) using CT to guide teacher planning. We discuss the implications of these results for professional development and student experiences.
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Teacher implementation profiles for integrating
computational thinking into elementary mathematics
and science instruction
Kathryn M. Rich
&Aman Yadav
&Rachel A. Larimore
Received: 12 November 2019 /Accepted: 21 January 2020/
#Springer Science+Business Media, LLC, part of Springer Nature 2020
Incorporating computational thinking (CT) ideas into core subjects, such as mathemat-
ics and science, is one way of bringing early computer science (CS) education into
elementary school. Minimal research has explored how teachers can translate their
knowledge of CT into practice to create opportunities for their students to engage in CT
during their math and science lessons. Such information can support the creation of
quality professional development experiences for teachers. We analyzed how eight
elementary teachers created opportunities for their students to engage in four CT
practices (abstraction, decomposition, debugging, and patterns) during unplugged
mathematics and science activities. We identified three strategies used by these teachers
to create CT opportunities for their students: framing, prompting, and inviting reflec-
tion. Further, we grouped teachers into four profiles of implementation according to
how they used these three strategies. We call the four profiles (1) presenting CT as
general problem-solving strategies, (2) using CT to structure lessons, (3) highlighting
CT through prompting, and (4) using CT to guide teacher planning. We discuss the
implications of these results for professional development and student experiences.
Keywords Computational thinking .Integration .Elementary school .STEM .Teacher
1 Introduction
In recent years, there have been increasing calls across the globe to bring quality computer
science (CS) instruction to all students in primary and secondary schools (Grover and Pea
2013; Yadav et al. 2016). This has led to efforts such as CSforAll in the United States,
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*Kathryn M. Rich
Michigan State University College of Education, East Lansing, MI, USA
Computing at School in the UK, and several other efforts to introduce CS ideas to young
learners. Many are in favor of exposing students to CS concepts and practices through
computational thinking (CT), which is loosely defined as the mental tools, such as abstrac-
tion and decomposition, used within computer science to solve problems (Wing 2006).
Motivated, in part, by the need to fit computational thinking instruction into an
already full school day, several recent efforts at the elementary school level have aimed
to integrate computational thinking ideas into core subjects such as mathematics (e.g.,
Israel et al. 2015;Richetal.2017). While knowledge is beginning to emerge about
how elementary teachers see CT as connected to their existing teaching practices
(Yadav et al. 2018;Richetal.2019), there are few detailed descriptions of how CT
is integrated into core subjects in elementary classrooms. In this paper, we present
strategies and profiles detailing how eight elementary teachers created opportunities for
their students to engage in CT during mathematics and science lessons.
2 Background
2.1 Computational thinking
As proliferation of technology continues to have profound impact and change the way we
operate in the world, providing all students with access and opportunities to engage with
computer science ideas is critical (Wing 2006). While preparation for jobs that increas-
ingly require knowledge of computing is one benefit of including CS education in K-12,
the benefits are broader (Israel et al. 2015). Exposure to the problem-solving processes
used in computer science has the potential to prepare K-12 students to be engaged problem
solvers both in their careers and in their everyday lives as citizens (Gretter and Yadav
2016). This is true even if they do not choose careers directly related to computer science.
In recent years, the CS education field has been exploring ways to communicate that
CS is more than something only computer scientists do, and learning CS is more than
strictly learning to program. The term computational thinking (CT) has gained popu-
larity as a name for the practice-based, conceptually oriented aspects of computer
science (Bocconi et al. 2016;Denning2017). Specific definitions of computational
thinking and the kinds of thinking processes it includes remain under debate, although
certain processes appear across many definitions and descriptions. In a review article,
Grover and Pea (2013) identified nine elements of CT including abstraction and pattern
generalization, structured problem decomposition, and debugging and systematic error
correction. To frame their proposed model for integrating CT into preservice teacher
education, Yadav et al. (2017) highlighted four processes embedded within Wings
(2006) seminal description of CT: decomposition, algorithms, abstraction, and auto-
mation. Similarly, a European Union report aimed at guiding development of CT in
compulsory education identified six core CT skills: abstraction, algorithmic thinking,
automation, decomposition, debugging, and generalization (Bocconi et al. 2016).
This paper reports on one aspect of the CT4EDU project, a research-practitioner
partnership between researchers and elementary teachers to co-develop and implement
math and science lessons that integrate CT into teachersexisting teaching practices. In
an effort to focus our work with teachers on understanding how they implement CT
and not on defining and redefining CTwe focused the project on four CT practices:
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abstraction, decomposition, debugging, and patterns. We chose to emphasize decom-
position and patterns because interviews with our participating teachers suggested they
saw many connections between these practices and their mathematics and science
teaching (Rich et al. 2019). We chose to emphasize debugging because, although
teachers were not initially familiar with the term, a focus on finding and correcting
mistakes appealed to them. Finally, we chose to focus on abstraction because although it
was unfamiliar to our partner teachers, it has been identified as a particularly important
CT practice by several CS education researchers (Armoni 2013;Hazzan2008;Kramer
2007). Thus, we sought to find ways to make this practice useful and meaningful to
elementary students and teachers. Table 1provides our definitions of each of these four
practices, in both teacher-facing and student-facing language. The student-facing lan-
guage was developed by our partner teachers for use on classroom posters.
2.2 Integration as a path to CT instruction in elementary school
Some approaches to bringing computational thinking instruction into K-12 education
focus on developing standalone CS/CT courses. For example, the Exploring Computer
Science program (Goode et al. 2012) and the advanced placement Computer Science
principles course (Astrachan et al. 2011) each emphasize problem solving and appli-
cations within the context of a computer science course. Another approach to bringing
CT into K-12 education is to integrate CT ideas into instruction in other subjects.
Mathematics and science may offer particularly fruitful opportunities for CT integra-
tion, given the inclusion of mathematics and computational thinking as a practice in the
Next Generation Science Standards (NGSS 2013) and connections between CT and the
Common Cores Standards for Mathematical Practice (Common Core State Standards
Initiative 2010). Advocates of an integrated approach also argue that incorporating CT
into a core subject helps to ensure the instruction reaches all students (Weintrop et al.
2016) and allows teachers to build on their existing content and pedagogical knowledge
as they begin to introduce CT in their classrooms (Rich et al. 2019).
Studies focused specifically on CT in elementary school have suggested that integra-
tion of CT into core subjects may be the most successful pathway to providing CT to this
age level (Duncan et al. 2017; Israel et al. 2015). After being introduced to CT concepts in
professional development (PD), primary teachers in New Zealand created lessons that
integrated CT into several other subjects (Duncan et al. 2017). The researchers credited
Table 1 Focus CT practices and descriptions
Practice Teacher-Facing Description Student-Facing Description
Abstraction Reducing complexity by focusing on important
elements of a problem or situation
Focusing on the information I need while
ignoring unnecessary details
Decomposition Breaking apart a complex problem or situation to make
it more manageable
Breaking something down into smaller,
more manageable parts
Debugging Systematically finding and correcting problems and
Finding and fixing errors or mistakes
Patterns Looking for similarities between new problems and
problems that have already been solved
Looking for similarities and patterns
between things
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this tendency to the particular situation of primary teachers, who teach multiple subjects to
their students and therefore are in a position to facilitate connections across subjects. In a
U.S.-based study of a school-wide initiative to incorporate CT into the curriculum, many
of the classroom teachers chose to integrate CT into other subjects because the pace of the
curriculum was too rapid to allow time for an entirely new subject (Israel et al. 2015). The
researchers described integration as key to successful implementationof CT (Israel et al.
2015, p. 268). For these reasons, our efforts focused on supporting our partner teachers,
who all taught at the elementary level, in integrating CT into their mathematics and
science teaching. In an effort to stay close to teachersexisiting practices, we took an
unpluggedapproach and worked with teachers to incorporate CT into math and science
lessons that did not involve using computers.
2.3 Teacher knowledge and models of implementation
Teachers use multiple forms of knowledge as they plan and implement instruction,
including content knowledge of the topic of instruction, pedagogical content knowl-
edge about how to effectively teach that content, and curricular knowledge of available
instructional resources and approaches (Shulman 1986). Decades of research has
illustrated the complex ways in which teachersknowledge affects their instruction
(Toom 2017). For example, teacherscontent knowledge is related to how they specify
learning goals for their lessons (Hiebert et al. 2007), and knowledge of how people
learn is necessary in order for teachers to make informed decisions about how to
proceed when their instruction is not initially successful (Darling-Hammond 2006). As
such, it is not surprising that much of the existing research on elementary school
teachers integrating CT in their instruction focuses on the ways teachers thought about
CT and related it to other subject matter. Duncan et al. (2017) described ways primary
teachers connected CT to other curriculum topics and misconceptions the teachers had
about CT and computer science as a field. Yadav et al. (2018) reported how elementary
teachersunderstanding of CT became more elaborate and nuanced over the course of a
year of PD focused on integrating CT in science inquiry. Hestness et al. (2018)found
that teachers in a professional development workshop made connections between CT
and their existing knowledge of students, curriculum, and their school contexts.
While this emerging body of research is important, it is incomplete. Certainly, knowledge
of how teachers connect CT to other knowledge has implications for the design of effective
professional development for elementary teachers looking to integrate CT into their teach-
ing, as it supports the identification for learning goals for teachers as well as strategies for
helping teachers meet those learning goals (Duncan et al. 2017; Yadav et al. 2018).
However, effective professional development must not only have goals for teacher learning,
but also specific goals for teaching practice (Loucks-Horsley et al. 2010). The development
of teacher content knowledge is of little use if teachers do not know how to translate this new
knowledge into practice (Toom 2017). One way to support teachers to translate knowledge
into practice is by including examination of examples of teaching and learning of new
content in professional development (Loucks-Horsley et al. 2010). In addition to providing
models for how teachers might incorporate what they have learned into their teaching,
studying examples of implementation can illustrate for teachers the impact the new content
and teaching styles have on students, thereby increasing teacher motivation to try new
practices (Guskey 2002).
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Research examining not only what teachers learn about CT from professional develop-
ment, but also how they translate that knowledge into classroom practices, will guide the
creation of professional development experiences that support additional teachers in trans-
lating CT knowledge into practice. While such studies are scarce, a few are emerging. Israel
et al. (2015) described how elementary teachers implemented integrated CT instruction,
focusing on the amount of explicit instruction teachers provided and whether they utilized
whole-class or center-based instruction. In a case study of one teacher incorporating CT into
science inquiry, Krist et al. (2017) described how the teacher took ownership of particular
thinking strategies, such as using a flow chart, that she identified as computational thinking.
In this study, we aim to add to this existing work by documenting specific pedagogical
strategies elementary teachers used to provide opportunities for their students to engage in
CT during math and science lessons. Further, we describe the various ways the teachers
coordinated these strategies by grouping teachers into profiles of CT implementation.
2.4 Theoretical framework and research question
To guide our examination of teacher implementation, we used Carrolls(1963,1989)
concept of opportunities to learn. In his model of school learning, Carroll defined a
students opportunity to learn a topic, practice, or idea as the amount of time that student
was exposed to that idea in the classroom. While acknowledging many other factors,
including the quality of instruction and the students motivation, would also affect
student learning, Carroll argued that if any learning is to occur, students have to be
given time for such learning. Teachers play a critical role in providing time for learning.
Providing opportunities to learn is closely tied to finding ways to support teachers to
translate their knowledge of CTand how it connects to their curriculuminto practice.
To support the ultimate goal of students becoming proficient computational thinkers,
teachers must provide opportunities in the classroom for students to learn how to use CT.
The following research question guided this study: How do elementary school teachers
create opportunities for their students to engage in CT practices during mathematics and
science lessons? For our particular context and area of interest, we operationalized
opportunities to learn as instances of students being given opportunities to engage in
tasks and thinking that reflected the ways their teacher described our four CT practices.
3 Methods
3.1 Participants
This study included eight elementary teachers from five schools in a large intermediate
school district just outside an urban area in the Midwest United States. The district included a
total of 168 elementary schools and served a dense suburban area with a total population of
1.2 million. As mentioned above, the teachers were part of a researcher-practitioner
partnership that focused on integrating computational thinking within elementary class-
rooms. A summary of the teacher and school demographics is in Table 2.Theiryearsof
teaching experience and school demographics varied, but the schools were chosen, in part,
based on high percentages of minority students, students from low-income families, or
English-language learners as compared to the national distributions of students enrolled in
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public schools. In fall of 2015, 51% of students enrolled in K-12 public schools in the United
States were non-White and 10% were identified as English-language learners. Overall, 15%
of children under 18 were living in poverty (National Center for Education Statistics 2019).
Tab le 2shows that each school exceeded these overall percentages in at least one category.
3.2 Materials
To support various aspects of this study, we developed a number of resources, for both
teacher and student use, related to our four focal CT practices: abstraction, decompo-
sition, debugging, and patterns (see Table 1). We include descriptions of the materials
here because the completed lesson planning tools were one source of data for this study,
and some of the materials for classroom implementation are referenced in the classroom
video analyzed for this study.
3.2.1 Materials for professional development and lesson planning
To assist teachers in making connections between each of the four CT practices and their
own classroom practice, we developed two teacher-facing tools. First, the CT Lesson
Screener was developed to help teachers identify elements of CT already present in the
lesson. Second, the CT Lesson Enhancer was developed to help teachers plan and implement
lessons in ways that would make existing CT ideas more explicit or embed new opportunities
for CT. Teachers used these tools during professional development workshops (described
further below). These tools are available on the project website at
3.2.2 Materials for classroom implementation
In addition to the lessons co-developed during the professional development workshop
(described further below), we provided teachers with three resources to support the
introduction of CT into their classrooms: (1) a CT teacher toolkit that served as a pocket
reference for how each CT practice related to elementary mathematics and science (Yadav
Table 2 Participant teaching experience and school demographics
Tea ch er
Year s o f
% Non-White % Free &
Allen 4 20+ Harwood 66.3 58.6 **
Burgess 5 *
Connors 5 20+
Danson 2 20+ Whitfield 52.7 76.0 3.9
Ellis 4 15
Foster 3 4 Spring Hill 22.7 50.2 18.7
Gaines 5 5 Mapleview 41.8 62.5 **
Hawthorne 5 3 Harrington 61.5 48.8 15.4
*This teacher did not disclose how long he had been teaching.
**Percent ELL for these schools was not available.
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et al. 2019); (2) a set of student-facing CT classroom posters, developed by one of the
teacher participants, which provided a definition, example, and list of facilitating questions
for each practice (available at; and (3) two classroom-ready activities
designed to introduce students to the four CT practices in an informal, playful way.
3.3 Procedures
3.3.1 Professional development
Prior to implementing CT lessons in their classrooms, teachers participated in three
professional development workshops. In Spring of 2018, they received a preliminary
introduction to computational thinking and discussed the ways in which CT ideas might
apply to their mathematics and science teaching. In early Summer of 2018, they were
formally introduced to four computational thinking ideas on which the remainder of the
project would focus: abstraction, decomposition, patterns, and debugging.
In late Summer of 2018, teachers came to the third workshop with examples of their
existing mathematics or science lessons (often from a district-provided textbook or
other resource) that they felt were good candidates for CT integration. Working in small
groups that included 23teachers,12 members of the research team, and sometimes a
member of the school district staff, study participants used the CT Lesson Screener and
CT Lesson Enhancer tools to create lesson plans to be implemented in the first few
months of school. They spent one day planning a mathematics lesson, one day planning
a science lesson, and one day sharing with the group the lesson plans they had created.
3.3.2 Implementation
When the school year started, each teacher chose when and how to formally introduce the
CT practices in their classroom. All eight teachers displayed the CT classroom posters in
their classrooms. At least three of them used the playful classroom activities (described
under Materials) to introduce students to the four practices. After introducing the CT
practices to students, each teacher implemented at least one CT lesson during the first half
of the 20182019 school year. Some of the lessons extended across two class periods. We
used tablets mounted on rotating tripods to record video of each lesson implementation.
Teachers wore microphones that were synced to the recording devices, so the tripod base
rotated to allow the camera to follow the teachers as they moved around their classrooms.
One author was present at each implementation. Observers took field notes both during and
immediately after implementation. The number of minutes of each day of instruction ranged
from 25 to 81, with a median lesson length of 54 min.
3.4 Data sources
The observation notes and classroom videos of the CT lessons teachers planned during
professional development are the main data source for this study. However, we also drew
upon the teacherscompleted CT Screener and Enhancer tools (lesson plans) to aid us in
defining and identifying how teachers created opportunities for CT in their classrooms. As
described below, we used each teachers descriptions of each of the CT practices, present in
either the lesson plans or the classroom video, to guide the video coding.
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3.5 Analysis
3.5.1 Developing CT descriptions
In order to identify and describe the ways teachers translated their conceptions of CT
into practice, we first needed to understand how each teacher thought about each
practice. To accomplish this, we reviewed each participants lesson plans and classroom
video and documented each time the teacher provided an explicit description of the
meaning of a CT practice. Each teacher described each of the four CT practices at least
once, except two teachers (Foster and Gaines) did not describe decomposition. As an
example, the list of descriptions from one teacher (Ellis) is provided in Table 3.
3.5.2 Identifying CT opportunities in videos
Next, we used each teacherslist of descriptions as a coding scheme for his or her
classroom video(s). The first author identified segments of the videos that exemplified
teacher-provided opportunities for students in the classroom to engage in each practice.
For example, using the description in the first row in Table 3,segmentswereidentified
in Elliss classroom video where the teacher provided students with opportunities to
simplify a problem to make it easier to work with, or when students described
themselves as doing so. For each segment, the author also recorded whether the
description used to identify the CT segment was articulated within the lesson video
(within the segment or elsewhere) or only articulated in the lesson plans. Across 12 days
of instruction, there were 124 video segments containing CT opportunities.
3.5.3 Coding CT opportunities
After identifying the relevant video segments, hereafter called CT opportunities,we
developed codes to describe how the teacher provided students with opportunities to
engage in CT. First, we generated brief descriptions of individual opportunities (e.g.,
Teacher asks a student to look for a mistake, and afterward asks class to name the CT
practice just used) and recorded dimensions along which the opportunities differed
(e.g., immediacy with which students could engage in the practice, whether teacher
mention of the practice was before or after students used the practice). We then
Table 3 One teachers (Ellis) descriptions of the four CT practices
CT Practice Description Data Source(s)
Abstraction Simplifying a problem to make it easier to work with Lesson plan
Abstraction Ignoring details that dont matter to the problem Classroom video
Decomposition Breaking something down, such as breaking a number into place-value
Lesson plan;
Classroom video
Patterns Looking for similarities across situations or problems Classroom video
Patterns Looking for numbers that make addition easier (Given as an example
rather than a full description)
Lesson plan
Debugging Examining and discussing work to find and correct mistakes Classroom video
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iteratively grouped the opportunities according to these dimensions until we had a set of
techniques that were clearly described and mutually exclusive. We called these tech-
niques strategies for providing CT opportunities. The three strategies are summarized
in Table 4.
The first author tagged each CT opportunity with the name of the CT practice and
whether the name of the CT term was explicitly mentioned during the opportunity. If
the name of the CT practice was stated by a teacher or student, the opportunity was
coded as an explicit mention of CT, and if the name of the CT practice was not said
aloud, the opportunity was coded as an implicit use of CT. We also coded each
opportunity with the strategy the teacher used to provide the opportunity. The rightmost
columns of Table 4provide examples of explicit and implicit opportunities for each
strategy. The full coding scheme is in Table 5. Note there were a small number of video
segments (N= 12) where none of the teacher strategies applied. These were cases where
students independently engaged in a CT practice, without the teacher creating a specific
opportunity, and were coded as spontaneous by student.
After the first author coded all the video segments, she trained the third author to
code the videos using a written codebook using 12 (10%) of the coded video segments.
After training, the third author coded an additional 31 segments (25%) independently.
The segments used for training and for independent coding were randomly selected.
The second coder was given timestamps for the CT opportunities, but independently
coded them according to CT practice, Explicitness, and Strategy as a reliability check
on the first authors coded descriptions of the opportunities. After checking the
reliability of the first round of coding, the first author made minor adjustments to the
codebook, and the two coders each made adjustments to their codes accordingly. After
this adjustment, the Cohens Kappa values were 0.81, 0.94, and 0.71 for the three sets
of codes in Table 5, respectively. Given the moderate to strong agreement, we
proceeded with the first authorscoding.
3.5.4 Developing teacher prof iles
When coding was complete, we counted the number of times in each day of
instruction the teacher used each strategy, sorting the opportunities according to
whether or not the CT practice was named explicitly. We also developed brief
narrative descriptions of how each teacher used each strategy in their classroom
implementations. When describing the explicit versus implicit opportunities, we
were attentive to whether the CT opportunity was based on a description of CT
articulated elsewhere in the video. That is, we noted whether the description
was made available to students during the lesson or based only on a description
in the teachers lesson plans that was never communicated to students. We felt
this distinction was relevant, as it could impact whether the students were
aware of their own opportunities to engage in CT.
Using these numerical and narrative descriptions, along with counts of how many of
the CT practices were explicitly mentioned in each lesson, we looked for similarities
and differences across lessons and across teachers. Based on these similarities and
differences, we grouped teachers into four profiles of implementation and wrote
descriptions of each profile. Note that although four of the teachers had two videos
(either two lessons or two days of instruction on the same lesson), each with a different
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Table 4 Teacher strategies for creating CT opportunities
Strategy Description Examples of Teacher Talk
Explicit Mention of CT Implicit Use of CT
Framing Teacher describes an opportunity students will have to
engage in the practice later in the activity. These
descriptions frame the activity as requiring students
to use the practice, and could prime students to begin
thinking about how they might use the practice.
Allen: Today youregoingtolookforpatterns ... of
what happens when things are going on with
rounding, so we can come up with a strategy thats
more efficient.
Allen: Were going to generalize now. Were going to
create a strategy that we will always be able to use.
(This is consistent with how Allen describes
abstraction elsewhere in the video, but she does not
name it as abstraction here.)
Prompting Teacher prompts students to consider engaging in a CT
practice, with the presumption that students will
begin using the practice immediately or shortly after
the prompt.
Burgess: Maybe if you guys finish, check your
neighbors. Check each others. Do a little
Burgess: One of you want to go up and explain why
you disagreed and fix what she had?(This is
consistent with how Burgess describes debugging in
the video, but he does not name it as debugging
Teacher highlights ways in which students have already
engaged in a CT practice. These may include cases
where the teacher describes how students used a
practice and cases where the teacher asks students to
describe how they used a practice.
Gaines: (after a student talks about setting aside
denominators when adding fractions) Which word
was that? We talked about doing that [setting
information aside] yesterday, too. We have a word
for that.[Students answer abstraction.]
Gaines: We found that the 1 in that mixed number we
could kind of put away for now and look at the
fraction pieces.(This is consistent with how Gaines
describes abstraction elsewhere in the video, but she
does not name it as abstraction here.)
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quantitative and qualitative description, we did not see a great enough difference across
a single teachers videos to merit placing any of them in more than one profile.
As a preliminary examination of how the different teacher profiles lead to
differences in student experiences, we also calculated the average number of
CT opportunities per lesson for each profile. We also calculated how those
opportunities were distributed across the four CT practices. Additionally, we
noted the average number of instances of students spontaneously engaging in a
CT practice in each profile.
Tab le 6shows the quantitative summary of the CT opportunities provided by
each teacher in their CT lessons. The first column groups the teachers into the
four profiles. The shaded cells highlight the key features of each profile. The
narrative summary of each lesson is provided as an appendix Table 9.
Tab le 7summarizes the four profiles in terms of how the teachers used the
three strategies for providing CT opportunities for students. The sections that
follow describe each profile in greater detail. We first give an overall summary,
and then provide more detail about the way teachers in the profile used
framing, prompting, and inviting reflection to create CT opportunities for their
4.1 Profile A: Presenting CT practices as general problem-solving strategies
The four teachers in Profile A (Ellis, Burgess, Danson, and Connors) utilized all three
strategies for providing CT opportunities (i.e., framing, prompting, and inviting reflec-
tion) in their classrooms. Their use of the strategies reflected a conceptualization of the
CT practices as general problem strategies that could be applied to a variety of
problems. These teachers most often prompted students to use patterns or debugging
in the moment; however, they framed their lessons with reference to all four practices
and invited students to reflect on the use of all four practices. These teacherslessons
did not reflect significant focus on one particular practice. Rather, the teachers seemed
to bring up the practices in opportunistic ways as they became relevant to the discus-
sion. Additionally, almost all of these teachersuses of the strategies involved explicit
references to CT or implicit references that mirrored the meanings they made explicit to
students elsewhere in the lesson. We refer to this profile as presenting CT practices as
general problem-solving strategies.
Table 5 Full coding scheme for CT opportunities in lesson video
Category Codes
CT practice Abstraction, Decomposition, Debugging, Patterns
Explicitness Explicit mention of CT, Implicit use of CT
Strategy for providing opportunity Framing, Prompting, Inviting reflection, Spontaneous by student
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4.1.1 Prof ile A framing
As shown in Table 6, all of the framing present in these teacherslessons was explicit.
The ways in which the teachers thought about the CT practices were usually present in
the lesson plans, but they were also made clear to students during the lesson when the
teacher made a framing statementthat is, a statement that primed the students to begin
thinking about a particular CT practice.
The framing used by the teachers in Profile A took two forms. First, three of the four
teachers began their lessons by reviewing the four CT practices with students, and then
making a general statement about opportunities for students to use the practices during
the lesson. For example, after asking volunteers to describe each of the four practices,
Danson told her second graders, We are going to use, actually in this lesson were
going to do, were going to look at patterning for sure, abstraction for sure, possibly
Table 6 Quantitative summary of CT opportunities provided by class period
Teacher and Day or
Lesson (Grade)
No. CT
per Class
Framing Prompting
Exp. Imp. Exp. Imp. Exp. Imp.
CT as
Ellis (G4) 4 1 0 2 2 7 0
Burgess (G5) 4 4 0 2 6 3 4
Danson (G2) 4 1 0 6 2 6 1
Connors (G5) 4 2 0 5 0 6 1
CT to
Foster, Day 1 (G3) 1 0 2 0 6 1 1
Foster, Day 2 (G3) 1 2 0 0 3 0 0
Allen, Lesson 1 (G4) 2 3 1 2 5 0 0
Allen, Lesson 2 (G4) 3 3 0 1 0 1 0
Hawthorne, Lesson 1
Hawthorne, Lesson 2
CT for
Gaines, Day 1 (G5) 2 0 0 0 4 2 1
Gaines, Day 2 (G5) 1 0 0 0 0 1 0
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some debugging if we make a mistake, and breaking things downdecomposition.
This statement, used by Danson, and similar statements by Burgess and Ellis, seemed to
be intended to prime studentsthinking about the practices before they began the
lessons main activities.
Second, some of the Profile A teachersframing consisted of highlighting the way in
which students might use one specific practice as they engaged in the lesson activities.
For example, as Connors was introducing the days sunrise/sunset science lesson to his
fifth graders, he said, What I want to do is do some abstraction and think about,
what can we look at? What can we look at if we want to talk about day and night and
figure out whats happening?Students did not offer answers at that moment in the
lesson. Rather, Connorss question seemed to be intended to get students thinking in
terms of abstraction as they generated scientific explanations about the sunrise and
sunset. Ellis and Burgess also used similar statements or questions to frame their
lessons. For example, Ellis said, So what I want you to be looking for in your task
today is, is there an abstraction? Is there anything that you need to ignore?
4.1.2 Profile A prompting
The teachers in Profile A prompted students to use a CT practice between four and nine
times per lesson, and all prompts were focused on one CT practice at a time. All four
teachers used at least one prompt that contained an explicit reference to a CT practice.
For example, as his fifth-grade students worked on a problem, Burgess suggested they
compare with their partners or groups and do some debugging.Similarly, as her
students helped her complete a chart organizing their answers to rounding problems,
Danson prompted, Lets use that word pattern again. What patterns do you notice?
Three of the Profile A teachers also used some prompts that did not explicitly
mention a CT practice. All but one of these implicit prompts reflected an understanding
of the CT practice they expressed to students elsewhere in the video. For example, after
explicitly prompting his students to debug early in the lesson, Burgess asked a student
to fix what [another student] had,which is consistent with the way he talked about
debugging earlier in the lesson but not called out explicitly as debugging. Similarly,
Table 7 Summary of teacher profiles for providing CT opportunities
Profile Framing Prompting Inviting Reflection
A: CT as Problem-
Solving Strategies
Explicit framing statements
for all four or one CT
practice at a time.
Mix of explicit and implicit prompts.
Implicit prompts mostly reflected
earlier explicit mentions in video.
Mostly explicit invitations to
reflect on all four CT
practices, one at a time.
B: CT to Structure
Explicit framing of one or
two CT pra ctices.
Implicit prompts usually connected
to the CT practices that were
framed earlier or would be
reflected upon later.
Occasional explicit invitations
to reflect on one CT
C: CT through
Occasional implicit
Explicit prompting to use 12CT
Occasionalimplicit invitations
for reflection.
D: CT for Teacher
No framing. Implicit prompting to use 12CT
practices as written about in les-
son plans.
Occasional explicit invitations
to reflect on how students
used CT practices in earlier
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shortly after the explicit reference to patterns in the chart mentioned in the previous
paragraph, Danson implicitly suggested students look for patterns again by asking,
What do you notice?in reference to the more fully completed chart.
In one case, a teachers implicit prompt did not reflect a description from elsewhere
in the video, but rather only reflected what was written in the teacherslessonplan.
Specifically, one of Burgesss prompts reflected decomposition as articulated in his
lesson plan, where he wrote that students should, Decompose your groupsnumber
and write just your digits value on your board(emphasis added). As he planned, he
seemed to see breaking numbers into place value parts and thinking about one digit at a
time as an example of decomposition. In his classroom video, he told a student, You
can look at each place value at a time. So you can look at the tenths to tell whats
happening.He did not, however, explicitly note that doing so was an example of
decomposition as he spoke to the student.
4.1.3 Prof ile A inviting reflection
Each of the Profile A teachers invited students to reflect on how they had used CT
practices seven times per lesson. As shown in Table 6, 22 out of the 28 invitations to
reflect included explicit reference to a CT practice. While these invitations varied in
form, most often teachers asked students to describe how they used a particular CT
practice in an activity they just completed. At the end of her lesson, for example, Ellis
asked her students to reflect on what they did by asking, What about abstraction? Was
there anything that needed to be abstracted?All four teachers asked questions similar
to this. Ellis and Connors also occasionally asked students to name which CT practice
they had just used. For example, Connors asked a student What were you doing there
by looking at one smaller thing instead of the whole planet at once?The student
responded that she had used abstraction. With her second graders, Danson tended to
describe what a students had done in terms of one of the practices, rather than asking
the students to name the practice they had used. For example, as students modeled even
and odd numbers with linking cubes, she said, Were using decomposition. Were
breaking down our numbers into smaller parts.
While most of the invitations to reflect were explicit, there were six times when
Profile A teachers used implicit invitations to reflect on use of a CT practice. Five of
these implicit invitations to reflect mirrored ways of thinking about the practices that
were made explicit to students elsewhere in the video. For example, toward the end of
his lesson, Connors asked, What did we see between the two models? Was there
anything we were able to focus in on? Was there anything we might want to ignore?
This is consistent with how he described abstraction earlier in the lesson, but he did not
use the term abstraction in the invitation to reflect. The explicit and implicit invitations
to reflect on CT were spread across all four of the CT practices.
4.2 Profile B: Using CT to structure lessons
As shown in Table 6, the teachers in Profile B, Foster and Allen, tended to make
explicit statements to frame the CT in their lessons, and/or explicitly ask students to
reflect on their use of CT. They supplemented these strategies by implicitly prompting
students to use CT during the lesson. The CT opportunities they offered were
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distributed across two or three of the CT practices in each lesson, but each teacher
primarily focused on one particular practice. Their focus on one practice, combined
with their tendency to rely on framing, suggested they planned and implemented their
lessons with one practice in mind. We refer to this profile as using CT to structure
4.2.1 Prof ile B framing
Eight out of the 11 framing statements used by the Profile B teachers were explicit.
Both Foster and Allen described to students what they were going to do in the lesson,
connecting the activities to one particular CT practice. Foster, for example, asked
students to identify which CT practice they would be using. Students in her classroom
constructed cardboard rockets, called hopper poppers, that launched from their tables
powered by rubber bands. Foster framed the activity of testing and modifying the
hopper poppers as follows: You re going to have a chance to test your hopper popper.
The one you already made. And then youre going to have a chance to fix your hopper
popper. OK, looking up at my CT wall, after we test our hopper popper and we get a
chance to fix it, raise your hand if you see what CT skill were going to be using.The
CT wall refers to a section of the classroom wall showing the posters that highlighted
the four CT practices (see Section 3.2). In response to her question, a student identified
debugging as the relevant skill for the hopper popper testing. Similarly, Allen named
the CT practice within her lesson framing. For example, she framed one of her lessons
around patterns by saying, Today y oure going to look for patterns and youre going to
generalize for us a strategy of what happens when things are going on with rounding, so
we can come up with a strategy thatsmoreefficient.Foster framed her lesson around
debugging only, whereas Allen included framing statements about patterns and ab-
straction in one lesson, and abstraction and debugging in the other. The three implicit
framing statements used by the Profile B teachers reflected meanings and examples
reflected elsewhere in the videos.
4.2.2 Prof ile B prompting
In contrast to the explicit prompting used by teachers in Profile A, Table 6shows the
prompting used by teachers in Profile B was mostly implicit. Many of these implicit
prompts were consistent with the way a CT practice had been framed earlier in the
lesson. For example, after framing Day 2 of her lesson in terms of debugging (as
highlighted in Section 4.2.1), Foster implicitly prompted two of her third graders to
debug how they were using their hopper popper by asking, Look at my video. Look at
the way my hopper popper is. Do you see [whats different about yours]?Similarly,
after framing her lesson in terms of patterns (as highlighted in Section 4.2.1), Allen
implicitly prompted her students to look for patterns by asking questions such as,
What do you notice about these numbers?Interestingly, although Allen used a
framing statement about abstraction in this lesson, she did not prompt students to use
abstraction during the lesson.
During the first day of her lesson, Fosters implicit prompts did not correspond to an
explicit framing statement. Rather, her implicit uses of prompting on this day seemed to
serve two purposes. Some prompts seemed to be aimed at setting up a reflection
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opportunity at the end of a discussion. For example, after twice asking her students to
identify similarities between two videos they had just viewed, she referred to her
classroom CT posters and asked her students, What did we just look for? Which of
those CT skills did we just use?A student identified patterns as the CT practice and
described how they had used patterns. Some of Fosters other implicit prompts were
about debugging, which suggests her purpose was to foreshadow the more explicit
debugging she had planned for the second day of the lesson.
Although most of the implicit prompting used by the Profile B teachers reflected
meanings made explicit elsewhere in the lesson, there were a few examples of Foster
implicitly prompting students to engage in a practice as described in her lesson plans,
but never made explicit to students. For example, one activity in Fosters lesson was for
students to figure out how children could beat adults in a game of tug of war. In her
lesson plans, Foster identified the following question as an example of asking students
to engage in abstraction: What information was most important to come up with a
solution? (size, strength, number of students, etc.)She asked a very similar question in
her lesson video (What was an important piece? How could we beat an adult at tug of
war?), but never explicitly mentioned abstraction during her lesson.
4.2.3 Profile B inviting reflection
The teachers in Profile B occasionally provided CT opportunities for reflection. Foster
set up one opportunity for reflection via implicit prompting about patterns, as described
in Section 4.2.2 (What did we just look for? Which of those CT skills did we just
use?). She also invited students to reflect on debugging, without naming it as
debugging, on the first day of her lesson. During Allens second lesson, she had a
student share his guess-and-check strategy for solving a problem, then described the
strategy as a kind of debugging. She said, Guessing and checking is a wonderful
strategy. In fact, itsalsocalleddebugging.
4.3 Profile C: Highlighting CT through prompting
Like the teachers in Profile B, one fifth-grade teacher, Hawthorne, focused on a subset
of CT practices rather than all four. Unlike the Profile B teachers, however, Hawthorne
relied mostly on explicit prompting to provide CT opportunities to her students. In her
first lesson (see Table 6), Hawthornes explicit prompting was supplemented with
implicit framing and implicit opportunities to reflect. The implicit framing was con-
nected to the explicit prompts later in the lesson. Her invitations to reflect on CT,
however, were not connected to her prompting. Rather, they referred to other CT
practices not explicitly mentioned in the lesson. In her second lesson, Hawthorne used
only explicit prompting, with no framing or invitations to reflect. As such, there seems
to be less intentional structuring of Hawthornes lessons around CT than by the teachers
in Profile B. We call this profile highlighting CT through prompting.
4.3.1 Prof ile C framing
Hawthorne made one implicit framing statement in her first lesson. She was leading a
full-class discussion about a set of related problems for which the answers to earlier
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problems can often be helpful in solving later problemsknown as a problem string.
As she moved from the first to the second problem in the string, Hawthorne said,
Remember, how do these problem strings work? We use the first problem to do
what?When a student responded that the problems get harder and harder, she
confirmed that the problems build on each other.In her lesson plan, she had identified
the relationships among problems in problem strings as an example of patterning in CT,
as so we coded this as implicitly framing the lesson around patterns. She did not
explicitly mention patterns in her framing statement, although she did make the
connection to patterns explicit in her prompts later in the lesson.
4.3.2 Prof ile C prompting
Hawthorne used several explicit prompts in both of her lessons. In her first lesson, for
example, her explicit prompts related to the example of patterns discussed in her
implicit framing. After students had completed the second problem in the problem
string, she said, Remember, these build off of each other. Start looking for the pattern
as we go on to our next problem.In her second lesson, which was about ordered pairs
and coordinate grids, Hawthorne used explicit prompts for debugging and patterns. For
example, when a student forgot to write parentheses around an ordered pair, she said,
What are we missing, can we think about it for a second? Debug, look at it? What do
you think were missing?Additionally, after students completed a chart showing the
coordinates of vertices of shapes that were translated and rotated in the coordinate
plane, Hawthorne had students turn and talk to a partner about patterns they noticed in
the chart, then share their thoughts with the whole class.
4.3.3 Prof ile C inviting reflection
As shown in Table 6, Hawthorne implicitly invited reflection twice in her first lesson.
In the first case, she described what a student did in terms of the understanding of
decomposition she wrote into her lesson plan. Specifically, after a student described a
strategy for solving one of the problems in the problem string, she said, I see how
youre breaking it apart.In the other case, she encouraged a student to explain to the
class how he corrected a mistake, which was consistent with how she described
debugging in her lesson plan. However, in neither of these CT opportunities did
Hawthorne or a student say the name of the CT practice.
4.4 Profile D: Using CT to guide teacher planning
One fifth-grade teacher, Gaines, most commonly created CT opportunities via implicit
prompting for students to use one or two CT practices that were highlighted in her
lesson plans. She made few explicit references to CT practices during classroom
instruction. On occasion, she did provide explicit opportunities for students to reflect
on how they used CT, but these invitations to reflect most often referenced the previous
lessons, rather than ways students used CT within the same lesson. This lack of explicit
references to CT within the lesson being taught suggests that CT played a larger role in
planning than in classroom implementation. As such, we call this profile using CT to
guide teacher planning.
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4.4.1 Profile D framing
As shown in Table 6, Gaines did not use any explicit or implicit framing in her CT
4.4.2 Profile D prompting
Gainess lesson focused on abstraction through discussion of various represen-
tations of fractions. In her lesson plan, she noted that students would be
engaging in abstraction when they Look at visual representations of mixed
numbers, identifying the whole and the extra.On the first day of Gainess
lesson, she used prompts to provide two opportunities for her students to use
abstraction as she described it in her lesson plans. In the classroom video of
Day 1 of the lesson, Gaines asked students What do you see?and How
much do you see?about two different representations of fractions: a visual
model of 5/4 (two squares, each divided into fourths, with one entirely shaded
and one with one fourth shaded), and a sum of unit fractions for 5/3 (1/3 + 1/
3 + 1/3 + 1/3 + 1/3). During the discussion, she encouraged students who shared
answers to explain where they saw the 1 or the whole. For example, when a
student said the sum of unit fractions was equal to 1 2/3, Anderson asked,
Can you explain? Because I dont see a 1 anywhere up there, and I think
some other friends are like, where is he getting 1 from or where is 2/3 from?
The student came to the board and drew a ring around 1/3 + 1/3 + 1/3,
explaining that this was the same as 3/3, or 1. We coded this as an implicit
prompt to use abstraction because it reflected the process of identifying the
whole and the extra that Gaines had labeled as abstraction in her lesson plan.
The word abstraction, however, was not used by the teacher or the students.
Gainess thinking about patterns, as written into the lesson plan, was similarly
reflected in the classroom implementation without being named. (Gaines did not
use any prompting on Day 2 of her lesson.)
4.4.3 Profile D inviting reflection
Four times Gaines offered opportunities for her students to reflect on CT they
had already used, although in three out of the four cases, the previous use of
CT had occurred on a different day. For example, in the first day of her lesson,
Gaines said, We had, yesterday, kind of debugged those fractions that were
smaller than one.She also implicitly reminded students that on the previous
day, they had set aside the whole-number parts of mixed numbers, focusing just
on the fraction part. We coded this as an explicit reference to abstraction
because Gaines explicitly referred to a similar strategy as abstraction later on
in the lesson (see examples of inviting reflection in Table 4). Specifically, when
a student referenced focusing on just the numerators and temporarily ignoring
the denominators while adding fractions, Gaines explicitly invited students to
reflect on this as a CT practice. She asked, And which word was that? We
talked about doing that yesterday, too. We have a word for that.The students
then named the practice as abstraction.
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4.5 Comparison of profiles
Tab le 8compares the profiles in terms of the average number of CT opportunities
teachers created for students in each day of instruction and how those opportunities
were distributed across the four CT practices. The teachers in Profile A created the
highest number of CT opportunities for their students, with those opportunities distrib-
uted across all four CT practices. The teachers in Profiles B and C created fewer
opportunities, although the opportunities were focused on particular practices. The
teacher in Profile D created the fewest opportunities (4), with those opportunities
spread across two or three practices.
The available data did not allow us to analyze if or how students took up the CT
opportunities created by the teachers. However, some of the videos showed a few
instances of students engaging in the CT practices as described by the teachers
elsewhere in the lesson, without a specific prompt or invitation to reflect from the
teacher. The rightmost column of Table 8shows the average number of times per lesson
this occurred in each profile. It was an infrequent occurrence for all classrooms.
This study contributes to a growing body of research exploring how elementary
school teachers might translate their understanding of computational thinking
practices in their mathematics and science teaching (e.g., Israel et al. 2015;
Kristetal.2017). Specifically, we shared ways elementary teachers created
opportunities for students to engage in or reflect upon how they used CT
practices during unplugged mathematics and science lessons. We identified
three strategies teachers used to create CT opportunities for their students:
framing tasks and lessons as requiring the use of CT practices, prompting
students to engage in CT practices in the moment, and inviting students to
reflect on the ways they had already used CT practices in lesson activities.
Further, we grouped teachers into four profiles of CT implementation based on
how many of the four CT practices they incorporated into each lesson, how
Table 8 Summary of student CT opportunities by teacher profile
Profile Avg. No.
of Opportunities
per Day of
Distribution of
Opportunities across
CT Practices
Avg. No. of Times
Spontaneously Used
CT per Day of
A: CT as Problem- Solving
15.25 Distributed across all 4 1.25
B: CT to Structure Lessons 7.75 Focused on 1 with some
reference to 12 others
C: CT through Prompting 6 Focused on 1 with some
reference to 12 others
D: CT for Teacher Planning 4 Distributed across 231
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often they used each of the three strategies for creating CT opportunities, and
when and how they spoke explicitly about CT practices during their lessons.
Teachers who used Profile A, presenting CT as general problem-solving strategies,
utilized all three strategies (framing, prompting, and inviting reflection) to make their
thinking about all four CT practices explicit to students in each lesson. Teachers who
used Profile B, using CT to structure lessons, used framing and invitations to reflect to
make explicit connections to CT, and supplemented this with implicit prompting for
students to engage in the practices during the lesson. The teacher who used Profile C,
highlighting CT through prompting, relied mostly on explicit prompts to create oppor-
tunities for students to use CT. The teacher who used Profile D, using CT to guide
teacher planning, rarely made CT connections explicit to students, and instead used
implicit prompting and reflection opportunities to bring her ideas about CT into the
lesson. Although the Profile D teacher most often brought her ideas about CT into the
lesson implicitly, there were examples across all three of the other profiles where
teacher ideas about CT, as expressed in lesson plans, were embedded in the classroom
implementation but not made explicit to students.
The strategies and profiles we identified in this study provide concrete examples of
goals for teaching practice that could be incorporated in professional development
alongside goals for teacher and student learning (Loucks-Horsley et al. 2010). In this
section, we discuss how teachers might be best supported through professional devel-
opment to use the three strategies to engage students in CT practices within their
mathematics and science instruction. Further, we compare the profiles and discuss how
their use may lead to differences in the ways students experience CT in the classroom.
Our goal is not to advocate for one practice goal over another, but rather to highlight
relevant differences to help teachers and teacher educators select goals and strategies
that are a good fit for their context.
5.1 Implications for professional development: Supporting teachers in using
the strategies
The three strategies used by teachers in this study to create CT opportunities differ in
the learning opportunities they create for students. Specifically, framing and prompting
create opportunities for students to use CTwhere otherwise they may not have done so.
That is, they have the potential to increase the number of opportunities students have to
use CT practices. In contrast, inviting reflection does not, in and of itself, create an
opportunity to use CT. Rather, it creates an opportunity to recognize and name CT
when it has already been used. Implementation of these different strategies will require
different forms of teacher learning and support.
5.1.1 Framing and prompting
Framing of a lesson, and prompting within a lesson, can largely be planned in advance.
This was particularly evident with Profile B teachers who structured their lessons
around a particular CT practice and foreshadowed how students would use the CT
practice through framing statements early in the lesson. Additionally, it was clear that
the Profile D teacher had planned prompts in advance, as her verbal statements in the
lesson tended to mirror her plans closely. Thus, one way to support teachers in utilizing
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the framing and prompting strategies is to provide time in professional development
workshops to create lesson plans that incorporate framing statements and prompts
targeted to CT. Framing statements and questions (prompts) to ask students are
common elements in existing frameworks for creating teacher lesson plans (e.g.,
Smith et al. 2008). We found the screener and planner tools we developed to be useful
in focusing teachersattention on the CT practices as they created lesson plans.
Teacher participants in other studies focused on integrating CT into other subjects in
elementary school (Duncan et al. 2017;Israeletal.2015) designed their own lessons
without using a formalized template or framework, but the ways they organized their
lessons suggest that framing and prompting could fit well into their planning. For
example, several of the teachers in the Israel et al. (2015) study started their lessons
with whole-class instructionwhere framing statements could be usedand later
circulated as students worked independently or in groupswhere prompting could
be used. Teachers in the Duncan et al. (2017) study sometimes taught a CT-focused
lesson designed by the researchers, and then later connected the CT ideas to their
subsequent math lessons. Framing and prompting could be offered to these teachers (or
those following a similar model) as a way to explicitly connect CT ideas to mathemat-
ics or other subjects. Additionally, using the same kinds of framing statements and
prompts within computationally rich activities later in the curriculum may also provide
pathways for students to make connections between the exposure to CT practices they
had in unplugged contexts to using the ideas in plugged contexts.
An additional way to support teachers in creating CT opportunities through framing
and prompting is to support them in selecting or designing disciplinary tasks that are, in
and of themselves, rich in opportunities for student thinking and problem solving. In
our professional development workshops, we found that teachers had an easier time
incorporating CT into rich, open-ended, inquiry tasks for mathematics and science that
were intentionally designed to engage students in higher-level thinking. Teachers who
were working with such tasks easily used framing and prompting to foreground aspects
of the task and student thinking that aligned with their conceptions of the CT practices.
Unfortunately, many elementary curricula for mathematics and science do not provide
teachers with access to such tasks (Banilower et al. 2013; van Zanten and van den
Heuvel-Panhuizen 2018). As such, creating CT opportunities through framing and
prompting may first require teachers to design or redesign lessonsthis was the case
for some of our participating teachers. Although this made the co-design of lessons
more difficult than we anticipated, it also revealed an unexpected, but potentially
beneficial effect of teachers using CT practices as a lens for examining their existing
math and science lessons: CT provided affordances for teachers to think deeply about
their math and science instruction and how to allow more opportunities to engage their
students in rich tasks. While our end goal is to provide pathways for teachers to create
computationally rich activities for their students, the ways teachers used framing and
prompting to redesign their lesson tasks was encouraging, particularly in Profiles B and
D where the connections between lesson plans and implementation were clear. These
teachers took up CT in ways that supported productive changes in their disciplinary
Providing more intentional support to teachers in designing and redesigning lessons
may enhance these benefits, as well as support teachers and students in making
connections between unplugged math and science lessons and computationally rich
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activities. Designing a lesson is a fundamentally different task than planning a lesson,
as the former is focused on considering the purpose of the lesson and the latter is
focused on the details of how a lesson will be carried out (Hathaway and Norton 2019).
We intended for our CT Screener to focus teachersattention on considering which CT
practices to highlightas part of the design and purpose of the lessonand our CT
Planner to focus teachersattention on planning specific ways to bring CT into the
lesson. The mixed experiences of our teachers in PD in ease with which they found
ways to incorporate CT suggests that teachers needed greater support in the design
Hathaway and Norton (2019) developed guidelines to support teacherslesson
designs. They recommend that finished lesson designs have multiple elements, includ-
ing an explanation of the problem of practice the lesson is designed to solve, a clear list
of constraints and requirements, a statement of the design problem, and potential
learning activities. Engaging in a design process such as the one articulated by
Hathaway and Norton may support teachers in creating meaningful CT opportunities
for their students because it will provide an avenue for articulating the provision of CT
opportunities as part of the goal of the lesson. Co-design has been successfully used in
mathematics education as an element of professional development that supported
teacher learning and teacher creation of task sequences that prompted particular kinds
of thinking from students (Hansen et al. 2016). While this study provides a lens into
how elementary teachers use unplugged CT practices in their math and science
instruction, future research could examine how co-design during professional develop-
ment could support teachers to create computationally rich, plugged CT opportunities
for their students. There is limited work in this area, but one study by Finch et al. (2018)
found that when co-designing a classroom unit with high-school teachers that used
artistic sensor-data-driven representation of the garden, teachersaesthetics and scien-
tific aims motivated them to learn computing skills.
5.1.2 Inviting reflection
Although teachers can purposefully design opportunities for students to reflect on the
ways they have used CT, such as Fosters prompting in Profile B, our data suggests that
teachers can also spontaneously notice and name studentsuse of CT practices. For
example, Profile A teachers quite often either described what their students had just
done in terms of a CT practice or asked their students to name which CT practice they
had just used. Yet recognizing particular forms of student thinking is challenging task
for teachers, especially in the complex context of classroom instruction (Heritage et al.
2009). Three of the four Profile A teachers, who created the most frequent opportunities
for students to reflect on CT, had at least 15 years of teaching experience (and the fourth
teacher did not disclose how long he had been teaching), suggesting that recognizing
particular forms of student thinking is a skill developed with experience. Thus,
professional development that provides practice for teachers to recognize when students
are using CT practices could be helpful in supporting teachers to use the inviting
reflection strategy in their teaching. One relevant professional development activity
might be watching and discussing video of teaching, which has been shown to be
effective for supporting teachers in recognizing studentsmathematical thinking, and
importantly, also in supporting teachers in translating the skills they gained into practice
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(Sherin and van Es 2009). Future research could examine how observing and reflecting
on CT-related teaching practice could be used to support teachers in creating opportu-
nities for CT in their classrooms.
In our study, teachers created opportunities for reflection in a number of ways,
including labeling what a particular student did with a CT practice and revoicing what a
student did to highlight its connection to a CT practice. These modes of creating CT
opportunities were consistent with the pedagogical strategy of assigning competence,
or highlighting the intellectual value of a studentscontribution or thinking (Boaler
2006). Assigning competence has been shown to contribute to the development of
supportive relationships between elementary teachers and students, especially for
African American and Latinx students (Battey et al. 2016). Given the goal of broad-
ening participation in computing, helping teachers learn how to recognize and highlight
how students use CT practices may not only provide teachers with new contexts for
assigning competence, but also allow students from traditionally marginalized groups
to see that they can engage in CT ideas. Future research in this area should examine
whether and how integrating unplugged and plugged CT within elementary classrooms
influences studentsmotivation and interest in computer science.
5.2 Comparing profiles: Focus and explicitness
The four profiles for CT implementation we described in this study differ along several
dimensions. Two of these dimensions have the potential to impact both student
experiences and teachersprofessional development needs. These are focus and
5.2.1 Variation in focus across profiles
First, the profiles varied in the level of focus on particular CT practices. The teachers in
Profile A created CT opportunities that were distributed across all four CT practices. By
contrast, the teachers in Profiles B, C, and D limited the CT opportunities to two or
three practices, with the teachers Profiles B and C seeming to focus on creating
opportunities for one particular practice. The difference in focus seemed to relate to a
difference in both the quantity and the nature of CT opportunities created for students.
For example, the Profile A teachers, with a wider focus on multiple practices, created
an average of about 15 CT opportunities per day of instructionalmost twice as many
as any other profile. However, a narrower focus on one or two CT practices, as used by
the teachers in Profiles B, and C, resulted in fewer opportunities.
Regarding the nature of the opportunities, the opportunities created by the teachers
in Profile B and C were more likely to be related to each other. For example, the
implicit prompts used by the Profile B teachers tended to connect to either their framing
or their invitations to reflect. Although they were coded as separate CT opportunities in
this study, these connected opportunities could also be conceived as examples of single,
extended opportunities. By contrast, the teachers in Profiles A and D, who did not focus
on a particular practice, did not make connections across strategies. Their framing and
invitations to reflect were mostly disconnected from their prompting.
The classroom video data used in this study did not provide enough information for
us to systematically evaluate the quality of the CT opportunities provided to students or
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how students responded to the opportunities, but we suspect that extended opportuni-
ties may have greater benefits than isolated, brief opportunities. Indeed, research in
elementary science education suggests that extended opportunities to engage in scien-
tific argumentation supported students in improving their abilities to construct and
evaluate arguments (Ryu and Sandoval 2012). Thus, the variation in focus among the
profiles highlights a potential tension between providing fewer, but extended and
higher quality CT opportunities versus more, but briefer and less rich CT opportunities.
Future research could explore the benefits and costs of each side of this tension for
studentslearning of CT ideas and explore how providing CT experiences in plugged
versus unplugged environments helps to manage this tension. Additionally, future work
could address the ways in which teachers are able to leverage brief versus extended CT
opportunities provided in unplugged contexts to help students transition to plugged
The focus on individual practices and creation of extended opportunities to use that
practice, used by the teachers in Profiles B and C, may reflect a sense of comfort or
familiarity with the focal CT practices by the teachers. Similar to the way that the case
study by Krist et al. (2017) showed that the teacher took ownership of particular
strategies, some of the teachers in our study seemed to take greater ownership of some
CT practices than others. Future research could examine how teacherssenses of self-
efficacy related to the CT practices affects the length and nature of the CT opportunities
created for students.
The focused patterns of CT opportunities created by the teachers in Profiles B and C
may also reflect more significant changes to the ways teachers would have implement-
ed the lessons without attention to CT. The connectedness of the opportunities,
especially in Profile B, suggests a fundamental rethinking of the lesson and its goals.
On the other hand, the shorter, more frequent CT opportunities created by the teachers
in Profile A suggest minimal changes to the lessons. Thus, Profile A may be easier for
teachers to implement, especially when they teach in highly structured professional
environments that, for example, place a high value on standardized assessments
(Priestley et al. 2012; McGee et al. 2012). If the goal of integrating CT into elementary
mathematics and science is to provide students early, informal exposure to CT-related
vocabulary and concepts, the strategies used by the teachers in Profile A could be both
easy to implement and effective for this purpose. If the goal of integrating CT is, on the
other hand, to support students in using the CT practices independently, the strategies
used by teachers in Profile B may be a better option. Future research examining the
effect of each teacher profile on students knowledge of and attitudes about CT could
help to guide decisions about what level of focus on particular CT practices is helpful
and for what purposes. In particular, future research could unpack which profiles have
the greatest advantages for supporting students in transitioning from unplugged to
plugged contexts.
5.2.2 Variation in explicitness across profiles
The second dimension of variation among the profiles worthy of discussion is the explicit
mention versus implicit application of CT practices within lessons. The teachers in Patterns
A and C used primarily strategies that included explicit mention of at least one CT practice.
The teachers in Pattern B used explicit framing and invitations for reflection coupled with
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implicit prompting. The teacher in Pattern D used almost entirely implicit strategies. In their
study of how elementary teachers implemented CT instruction, Israel et al. (2015) noted that
teachers varied in the levels of explicit instruction they used in their CT lessons. In contrast to
looking at explicit use of CT vocabulary, however, these researchers described a contrast
between teachers who used didactic, full-class discussions and those who used open-ended,
student-directed tasks. The teachers in the study acknowledged the importance of both types
of instruction, but also all expressed worry that students would struggle with high-level CT
without explicit instruction (Israel et al. 2015). The teachers in the current study expressed
similar concerns about making high-level CT accessible to elementary students in their pre-
project interviews (Rich et al. 2019). The varying levels of their explicit references to the CT
practices may, therefore, reflect differing opinions about how to make the CT accessible.
Some teachers seemed to believe that explicitly referencing the CT practices would support
students in making sense of the practices, while others may have thought that emphasizing
the vocabulary would add an unnecessary layer of complexity. Future research should
examine the impact of explicit uses of CT terminology, in both unplugged and plugged
contexts, on studentsknowledge and skills.
6 Limitations
This study examined only one or two lessons implemented by each teacher in the study,
leaving us unable to determine if teachers used these profiles of implementation
consistently across the school year. We were also unable to analyze how students took
up the CT opportunities created by their teachers, or how the inclusion of CT may have
changed the nature of the mathematics and science taught or how students experienced
it. As such, we intend this study only to provide examples of how elementary teachers
take up CT as integrated with mathematics and science and their strategies for creating
opportunities for their students to engage in CT. In future research, we plan to collect
more student data to explore the differential impact of these implementation profiles
and specific strategies for how students think about CT and apply it in the context of
elementary mathematics and science. Longitudinal research could also examine the
ways in which different opportunities to engage in CT in elementary mathematics and
science impact studentsattitudes about computer science, the rates at which they enroll
in CS courses, and how they apply what they know about CT to CS courses.
Funding information This work is supported by the National Science Foundation under grant number
1738677. Any opinions, findings, and conclusions or recommendations expressed in this material are those of
the author(s) and do not necessarily reflect the views of the National Science Foundation.
Compliance with ethical Standards The authors declare that they have no conflict of interest. The
study was reviewed and approved by the Institutional Review Board at the university at which the study was
conducted. Informed consent was obtained from all teacher participants. No students were identified and no
student data was analyzed.
Conflict of interest The authors declare that they have no conflict of interest.
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Appendix 1
Table 9 Narrative description of CT opportunities provided by each teacher
Profile Teacher Framing Prompting Inviting Reflection
A: CT as Problem-
Solving Strate-
Ellis Framing of lesson
suggested students think
about all four CT
Several explicit prompts
to use debugging
Explicit opportunities to
reflect on all four CT
Burgess Explicit framing of
opportunities to use
debugging, patterns.
Explicit prompts to use
patterns and
debugging. Implicit
prompts to use all
four CT practices.
Explicit reflection
opportunity for
patterns, implicit for
other CT practices.
Danson Teacher reviewed terms at
beginning of lesson,
suggested students think
about using practices.
Explicit prompts to use
patterns and
Explicit reflection
opportunities for
abstraction and
Connors Explicit framing of
opportunities to use
abstraction, debugging,
Explicit prompts to use
all four CT practices.
Explicit reflection
opportunity for all
four CT practices.
B: CT to Structure
Foster Day 1 (G3) Implicit framing of
opportunity to use
Implicit prompts to use
Explicit opportunity to
reflect on patterns.
Foster Day 2 (G3) Explicit framing of
opportunities to use
Implicit prompts to use
debugging, patterns.
No reflection
Allen, Lesson 1
Explicit framing of patterns,
Implicit prompts to use
No reflection
Allen, Lesson 2
Explicit framing of
abstraction, debugging.
Explicit prompt to use
Explicit opportunity to
reflect on debugging.
C: CT through
Gaines, Day 1 (G5) No framing. Implicit prompts to use
patterns, abstraction.
Explicit opportunity to
reflect on abstraction,
Gaines, Day 2 (G5) No framing. No prompting. Explicit opportunity to
reflect on debugging.
D: CT for Teacher
One implicit framing of
opportunity to use
Explicit prompts to use
patterns, debugging.
Two implicit
opportunities to
reflect on debugging,
No framing. Explicit prompts to use
patterns, debugging.
No opportunities for
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... Several studies showed that primary school teachers are less qualified and knowledgeable, which might reduce their effectiveness in implementing STEM (DeCoito & Myszkal, 2018;Nesmith & Cooper, 2019). As a result, primary school teachers have difficulty accepting non-traditional teaching practices (Correia & Baptista, 2022) and organizing and designing their STEM lessons (Hamilton et al., 2021;Rich et al., 2020). Thus, primary school teachers require additional support in increasing their STEM knowledge and assisting them in implementing STEM integration in their lessons as well as developing their belief in teaching STEM (Arrington & Willox, 2021;Chen et al., 2020;Hamilton et al., 2021;Havice et al., 2018;Hourigan et al., 2021;Lee et al., 2021). ...
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In the Netherlands, mathematics textbooks are a decisive influence on the enacted curriculum. About a decade ago, Dutch primary school mathematics textbooks provided hardly any opportunities to learn problem solving. In this study we investigated whether this provision has changed. In order to do so, we carried out a textbook analysis in which we established to what degree current textbooks provide non-routine problem-solving tasks for which students do not immediately have a particular solution strategy at their disposal. We also analyzed to what degree textbooks provide ‘gray-area’ tasks, which are not really non-routine problems, but are also not straightforwardly solvable. In addition, we inventoried other ways in which present textbooks facilitate the opportunity to learn problem solving. Finally, we researched how inclusive these textbooks are with respect to offering opportunities to learn problem solving for students with varying mathematical abilities. The results of our study show that the opportunities that the currently most widely used Dutch textbooks offer to learn problem solving are very limited, and these opportunities are mainly offered in materials meant for more able students. In this regard, Dutch mainstream textbooks have not changed compared to the situation a decade ago. A textbook that is the Dutch edition of a Singapore mathematics textbook stands out in offering the highest number of problem-solving tasks, and in offering these in the materials meant for all students. However, in the ways this textbook facilitates the opportunity to learn problem solving, sometimes a tension occurs concerning the creative character of genuine problem solving.
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This framework for developing pre-service teachers' knowledge does not necessarily depend on computers or other educational technology.
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In the past decade, Computational Thinking (CT) and related concepts (e.g. coding, programing, algorithmic thinking) have received increasing attention in the educational field. This has given rise to a large amount of academic and grey literature, and also numerous public and private implementation initiatives. Despite this widespread interest, successful CT integration in compulsory education still faces unresolved issues and challenges. This report provides a comprehensive overview of CT skills for schoolchildren, encompassing recent research findings and initiatives at grassroots and policy levels. It also offers a better understanding of the core concepts and attributes of CT and its potential for compulsory education. The study adopts a mostly qualitative approach that comprises extensive desk research, a survey of Ministries of Education and semi-structured interviews, which provide insights from experts, practitioners and policy makers. The report discusses the most significant CT developments for compulsory education in Europe and provides a comprehensive synthesis of evidence, including implications for policy and practice.
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Developing students’ 21st century skills, including creativity, critical thinking, and problem solving, has been a prevailing concern in our globalized and hyper-connected society. One of the key components for students to accomplish this is to take part in today’s participatory culture, which involves becoming creators of knowledge rather than being passive consumers of information. The advancement and accessibility of computing technologies has the potential to engage students in this process. Drawing from the recent publication of two educational frameworks in the fields of computational thinking and media & information literacy and from their practical applications, this article proposes an integrated approach to develop students’ 21st century skills that supports educators’ integration of 21st century skills in the classroom.
Conference Paper
Computing curricula are being developed for elementary school classrooms, yet research evidence is scant for learning trajectories that drive curricular decisions about what topics should be addressed at each grade level, at what depth, and in what order. This study presents learning trajectories based on an in-depth review of over 100 scholarly articles in computer science education research. We present three levels of results. First, we present the characteristics of the 600+ learning goals and their research context that affected the learning trajectory creation process. Second, we describe our first three learning trajectories (Sequence, Repetition, and Conditionals), and the relationship between the learning goals and the resulting trajectories. Finally, we discuss the ways in which assumptions about the context (mathematics) and language (e.g., Scratch) directly influenced the trajectories.
Addressing unresolved questions concerning computational thinking.
Conference Paper
This paper reports on the preliminary results of an ongoing study examining the teaching of new primary school topics based on Computational Thinking in New Zealand. We analyse detailed feedback from 13 teachers participating in the study, who had little or no previous experience teaching Computer Science or related topics. From this we extract key themes identified by the teachers that are likely to be encountered when deploying a new curriculum, including unexpected opportunities for cross-curricula learning, development of students' social skills, and engaging a wide range of students. From here we articulate key concepts and issues that arise in the primary school context, based on feedback during professional development for the study, and direct feedback from teachers on the experience of delivering the new material in the classroom.