K-2 STUDENT'S COMPOSING OF LEGO STRUCTURES

Abstract

Block building activities help develop students' spatial reasoning, but few studies focus on the development of block building skills beyond preschool. We worked with four kindergarten, four first grade, and four second grade students to learn more about their Lego block building. We compared students' accuracy, building strategies, and spatial language as they used manuals versus pictures of final Lego structures (presented in color versus grayscale) to build two Lego structures. On the first structure, students using color manuals or pictures had an easier time choosing correct bricks but had difficulty correctly placing them; students using grayscale manuals or pictures had difficulty picking the correct bricks but placed them more accurately. By the second design, students did better with the manuals, regardless of color. Students need more support to use specific spatial language and building with depth versus height.

Full text

K-2 STUDENT’S COMPOSING OF LEGO STRUCTURES
Sezai Kocabas
Purdue University
Skocabas@purdue.edu
Yi Zhu
Purdue University
Zhu966@purdue.edu
Yiheng Liang
Purdue University
Liang273@purdue.edu
Laura Bofferding
Purdue University
Lbofferd@purdue.edu
Block building activities help develop students’ spatial reasoning, but few studies focus on the
development of block building skills beyond preschool. We worked with four kindergarten, four
first grade, and four second grade students to learn more about their Lego block building. We
compared students’ accuracy, building strategies, and spatial language as they used manuals
versus pictures of final Lego structures (presented in color versus grayscale) to build two Lego
structures. On the first structure, students using color manuals or pictures had an easier time
choosing correct bricks but had difficulty correctly placing them; students using grayscale
manuals or pictures had difficulty picking the correct bricks but placed them more accurately.
By the second design, students did better with the manuals, regardless of color. Students need
more support to use specific spatial language and building with depth versus height.
Keywords: Elementary School Education; Geometry and Spatial Reasoning; Instructional
Activities and Practices.
The K-2 mathematics standards in the United States emphasize geometric reasoning, which
includes the ability to identify and describe shapes and to create structures by analyzing and
predicting the outcome of composing and decomposing shapes (National Governors Association
Center for Best Practices & the Council of Chief State School Officers, 2010). Children use
geometric reasoning to make sense of the world through multiple practices (Goldenberg &
Clements, 2014). The first practice in making sense of the world is classification, which involves
children identifying the elements in the environment and establishing relationships among them.
Then, children might use spatial relationships, which help identify an object's location relative to
reference points by using spatial words (e.g., right, under, top) or numbers (e.g., 3 units away
from an object). Another practice to understand the environment is noticing the transformations
of objects at various orientations or distances (e.g., symmetry, rotation). Geometric reasoning
also entails measuring or counting to identify the relationships between objects in the
environment. To identify certain properties of the objects, direct measurements (e.g., length,
area, volume), indirect measurements (e.g., comparing an object to another object being
measured), or using various units (e.g., one-unit length, block should be placed in the middle)
might be utilized (Goldenberg & Clements, 2014).
Play with blocks is a popular early childhood activity that helps children develop a variety of
concepts, including geometric and spatial reasoning (Casey et al., 2008; Phelps & Hanline, 1999;
Ramani et al., 2014), part-whole relationships (Gura, 1992), and other early mathematics
concepts (e.g., aspect of numbers, lines, area surfaces, and volume; Cross et al., 2009; Gura,
1992; see also Kamii et al., 2004). There is also a 3D shape composition learning trajectory
(Clements & Sarama, 2009) focused primarily on preschoolers’ block-building; however,
research on block building beyond the preschool has been limited. Since the development of
Lischka, A. E., Dyer, E. B., Jones, R. S., Lovett, J. N., Strayer, J., & Drown, S. (2022). Proceedings of the forty-fourth annual meeting
of the North American Chapter of the International Group for the Psychology of Mathematics Education. Middle Tennessee
State University.
574

block-building skills may not be fully established until school age, more research on block-
building behaviors after preschool is needed (Tian et al., 2020).
Unstructured (free-play) and structured (guided) block building activities are two
pedagogical approaches to building blocks. Unstructured tasks are more open-ended, allowing
children to create their own structures without being given specific goals, i.e., “Build the best
thing you can with these blocks” (Caldera et al., 1999, p. 860). In structured activities, children,
on the other hand, copy and reproduce a specific structure from a design (Caldera et al., 1999;
Stiles & Stern, 2009). Structured activities focused on improving skills in sorting and classifying
blocks and sometimes focused on “...estimation, measurement, patterning, part-whole
relationships, visualization, symmetry, transformation, and balance” (Casey & Bobb, 2003, p. 2).
At the preschool level, Verdine et al. (2014) used the Test of Spatial Assembly (TOSA) to
measure students’ block building accuracy. For these tasks, students must copy a block design
(e.g., a three-piece Lego structure). However, Lego sets targeted at students ages 5-8 typically
range from having about 50 pieces to multiple hundred pieces, and the features (i.e., use of color,
types of pieces, orientation of pieces, placement of pieces) increase in complexity. Therefore, to
better understand K-2 students’ block building behaviors, we need more investigations into how
they coordinate these features and how pictures and manuals can support their efforts.
Framework
Worked examples are an instructional aid for helping students understand challenging
concepts. Worked examples show step-by-step solutions to problems that help students
understand the problem-solving process (Atkinson et al., 2000; Sweller & Cooper, 1985) while
reducing cognitive load (Paas et al., 2003; Sweller et al., 1998). Analyzing worked examples
promotes learning in different fields, such as in mathematics (Catrambone, 1998; Congdon et al.,
2018; Durkin & Rittle-Johnson, 2012) and programming (Bofferding et al., 2022; Joentausta &
Hellas, 2018; Margulieux & Catrambone, 2016). Congdon et al. (2018) investigated first-graders'
ability to measure using rulers starting at zero or a whole number. The students’ measurement
conceptions improved when they analyzed worked examples of taking measurements that were
not aligned with the zero point.
Worked examples organized by subgoals, on the other hand, may help students learn since
subgoals make problem steps explicit by explaining the purpose of each step and providing clues
on how to achieve them (Atkinson et al., 2003; Atkinson & Derry, 2000; Catrambone, 1998).
Additionally, students can concentrate on the important components in the worked examples
(Margulieux et al., 2016) and engage in more self-explanations (Catrambone, 1998; Renkl &
Atkinson, 2002).
Studies of young children’s block building provide some insight into factors that children pay
attention to (e.g., spatial language, see Bower et al., 2020; Cohen & Emmons, 2017; Pruden &
Levine, 2017) or struggle with when recreating block structures (e.g., placement, see Stiles &
Stern, 2009; Verdine et al., 2017). For example, Verdine et al. (2014) evaluated 102 children's
(38 to 48 months) spatial assembly skills beyond basic building accuracy as they attempted to
construct seven models using 2 to 4 Mega Blocks of various sizes and colors. When determining
if the children's constructions matched the models, the researchers created a dimensions score.
They scored the accuracy of blocks relative to the base block, taking into account the vertical
location of the blocks, rotation of the blocks, and the translation or horizontal location of the
blocks based on the child placing the blocks on the right studs. Based on children's decreasing
dimension scores, they had difficulty coordinating rotation and translation as the number of
pieces (e.g., 2 versus 3 pieces) or the spatial complexity (e.g., two blocks sharing the two-studs
Lischka, A. E., Dyer, E. B., Jones, R. S., Lovett, J. N., Strayer, J., & Drown, S. (2022). Proceedings of the forty-fourth annual meeting
of the North American Chapter of the International Group for the Psychology of Mathematics Education. Middle Tennessee
State University.
575

width of the base) increased.
Other researchers have investigated the language children use as they work with blocks for
insight into the factors they find important. Pruden and Levine (2017) investigated boys versus
girls’ (14-46 months) spatial language in terms of dimensions (e.g., big, little, tall, short), shape
terms (e.g., circle, square), and spatial features (e.g., curvy, bent). Compared with girls, boys
produced more spatial words in preschool years. On the other hand, Cohen and Emmons (2017)
investigated school aged children’s (4-12 years) production of spatial language during structured
block building activities. Like Pruden and Levine (2017), Cohen and Emmons (2017) identified
children’s spatial language regarding dimensions (e.g., big, wide, length), shapes (e.g., square),
and spatial features (e.g., vertical, flat, curvy, side, corner). Additionally, they identified
children’s spatial language regarding location/direction referring to relative position of blocks
(e.g., high, under, up), orientation/transformation referring to relative orientation or
transformation (e.g., rotate, upright, right side up), continuous amount (e.g., a lot, same, half,
inch), deictic (e.g., here, there, anywhere), and pattern (e.g., order, next, first, increase)(Cohen &
Emmons, 2017). Children were more likely to produce words in the location/direction category
than they were in the shape and orientation categories (Cohen & Emmons, 2017).
Current Study
Block features (e.g., length, color, shape, size) contribute to spatial complexity, especially as
the number of blocks increases. The preschool studies involved a few bricks (e.g., up to 4,
Verdine et al., 2014; up to 8, Stiles & Stern, 2009) and typically focused on children’s final
structures. Instead, we explored how school-aged children deal with spatial complexity by
concentrating on the process, particularly what is easy or difficult for them and what they pay
attention to in relation to language while building 30-40 piece Lego structures.
Structured (guided) block building can be interpreted as a form of using worked examples,
where the final structure is shown but also includes all information needed to build it (e.g.,
someone can trace the steps from bottom to top and see the needed pieces). Manuals, such as
those included in Lego sets, can be interpreted as a worked example with subgoals, where the
final structure is broken down into smaller chunks to help explain how the pieces fit together to
make the final structure. Subgoal labels may be of increasing importance as structures increase in
size and complexity because they make each step explicit. Likewise, colors might reduce
cognitive load when structural complexity increases by helping children distinguish among
pieces.
In this study, we explored: How do students’ composing of Lego structures compare when
they build with manuals of steps versus a picture of the final structures? (a) What spatial
language do they use? (b) Which Lego brick features (i.e., location, size, orientation, shape,
color) are most difficult to coordinate in their building?
Method
For this study, we analyzed data from four kindergarteners, four first graders, and four
second graders in an afterschool program at a Montessori school in the midwestern United
States. We tried to strike a balance in regard to students’ gender and background. During three
sessions of a Lego building project, the students composed, decomposed, and fixed Lego
structures. We met with students individually and video recorded them using two cameras to
capture the front and back of their Lego structure. Interviewers also asked students questions
about where they were looking in the picture or manual as they built, how they knew which brick
to use and where to place it. The data for this study comes from the composing portions of the
tasks from the project’s first two sessions.
Lischka, A. E., Dyer, E. B., Jones, R. S., Lovett, J. N., Strayer, J., & Drown, S. (2022). Proceedings of the forty-fourth annual meeting
of the North American Chapter of the International Group for the Psychology of Mathematics Education. Middle Tennessee
State University.
576

In the first session, the students either used a picture (as a worked example) or a step-by-step
manual (as a worked example with subgoals) to build a Lego structure (see Table 1). We showed
the picture or manual in color to half of the students and in grayscale to the other half. The
students built a different Lego structure in the second session but started with half of the
structure already built. Students who used a manual in the first session used a picture in the
second session (and vice versa). Likewise, students used a color picture or manual in the first
session used a grayscale one in the second session (and vice versa).
Table 1: Examples of Pictures and Manuals Used for Each Design
Design 1
Design 2
Order
1
Example color pictures
Example grayscale manual steps
Order
2
Example grayscale pictures
Example color manual steps
Order
3
Example color manual steps
Example grayscale pictures
Order
4
Example grayscale manual steps
Example color pictures
Analysis
In order to analyze students’ building process, we first recorded the number of differences
between students’ structures and the given picture or manual. Differences were divided into
several categories based on Verdine et al.’s (2014) coding scheme and included students using
the wrong brick, including an extra brick, leaving out a brick, placing a brick with an incorrect
Lischka, A. E., Dyer, E. B., Jones, R. S., Lovett, J. N., Strayer, J., & Drown, S. (2022). Proceedings of the forty-fourth annual meeting
of the North American Chapter of the International Group for the Psychology of Mathematics Education. Middle Tennessee
State University.
577

orientation, and placing a piece with an incorrect left-to-right, forward-to-backward, or vertical
placement. We took notes of the specific bricks students had difficulty with in order to identify
patterns. Next, we coded the students’ building process based on how they used the bricks,
pictures, and manuals (see Table 2 for description of codes). During this process, we also took
notes of changes students made as they built as well as any help they received from the
interviewers.
Table 2: Codes for How Students Composed the Lego Structure
Composing strategy
Description
Resource
Where students referred when building and explaining:
Picture of structure
The composed picture of the structure (solo picture/in manual)
Manual of steps
Steps in manual for how to compose the bricks
Lego structure
Parts of the Lego structure
Turning pieces
Turned the direction of bricks horizontally
Flipping pieces
Turned the direction of bricks vertically
Turning structure
Turned the direction of the Lego structure
Direction
Built the structure from bottom to top or top to bottom
Symmetric
Built one side and a similar brick on the other side (1 piece, 2 pieces,
or 3 pieces at a time)
One side
Built up more than 3 bricks of one side, then did the other side
Lines
Used the lines between bricks on the picture
Counting studs
Counted raised dots on bricks to decide the location or brick
Finally, we used Cohen and Emmons’ (2017) classification to code students’ spatial language
as they built and answered questions about the building of the Lego structures. We did not use
their pattern category, but we also included a separate color category given our design focus on
the role of color in building (see Table 3). We calculated the percent of students’ language for
each of the categories to look for trends.
Table 3: Codes for How Students Composed the Lego Structure
Language (Cohen &
Emmons, 2017)
Description
Dimension
Length and Width: Students reference the brick size using specific
numbers (4x2) or in generic terms (e.g., long, big, wide) Height:
Students reference the brick’s thickness (e.g., thick, thin) or how
tall it is.
Shapes
Specific: Students use shape words or names of the bricks (e.g.,
square, window, flower)
Generic: Students refer to the brick using “this” “that” or other
generic referents
Lischka, A. E., Dyer, E. B., Jones, R. S., Lovett, J. N., Strayer, J., & Drown, S. (2022). Proceedings of the forty-fourth annual meeting
of the North American Chapter of the International Group for the Psychology of Mathematics Education. Middle Tennessee
State University.
578

Location/Direction
Specific: Students use the number of studs on Lego bricks or
number of bricks to justify placement
Generic: Students refer to locations without using numbers (e.g.,
on the top, the other side, on the right)
Orientation/
Transformation
Students talk about turning or flipping bricks
Continuous amount
Students use number words to describe number of pieces or the
count pieces using numbers
Deictic
Students use generic language (e.g., here, there) to describe brick
placement
Spatial features
Students describe the appearance or features of the brick (e.g.,
sharp, slanted, curved, has a shadow, has an eye)
Generic: Students describe the appearance using vague language
and actions (e.g., “like this,” “the same,” “looks good”)
Color (we separated this
out from spatial features)
Students refer to the color or shading of a brick (e.g., red, darker)
Results
Design One
When building design 1, all students built from the bottom to the top and used the lines
between bricks to help guide their building. Further, one student composed several bricks into a
substructure on one side before building the same sub-structure on the other side; whereas, the
other 11 students built symmetrically (see Figure 1), placing bricks back and forth between sides.
Students used more spatial language as their grade level increased, but overall their language was
pretty generic. They referred to the bricks in general shape terms (27% of language terms) and
often paired it with a continuous amount (e.g., this one, those two; 24% of terms), leading to
those categories having the highest percentage. Their language involved specific location terms
11% of the time and general location terms (e.g., “there”) 13% of the time. Overall, students had
a median of six differences with the target structure (ranging from 2 to 17) when composing the
first Lego structure. Students who used the grayscale picture had a total of 38 differences, those
who used the color picture had 21 differences, those who used the color manual had 16
differences, and those who used the grayscale manual had 14 differences. Participants who had
the highest numbers of differences left out chunks of the structure (e.g., the window and
surrounding pieces or arch and surrounding pieces) and referred to the picture of the final
structure.
Figure 1: Second Grader Building Symmetrically
Lischka, A. E., Dyer, E. B., Jones, R. S., Lovett, J. N., Strayer, J., & Drown, S. (2022). Proceedings of the forty-fourth annual meeting
of the North American Chapter of the International Group for the Psychology of Mathematics Education. Middle Tennessee
State University.
579

Aside from general differences between students who built using the manual versus the
picture, there were interesting differences between students who used color pictures or manuals
and those who only used grayscale pictures or manuals. Students in the color conditions had
more difficulty placing Lego bricks in the correct spots; their typical difficulties in placing the
bricks aligned with students not making proper use of the forward/backward dimension (see
Figure 2). Students in the grayscale conditions had more difficulty using the correct Lego bricks;
their typical difficulties with pieces involved using the incorrect thickness of pieces, regular 2x2
bricks instead of taller 2x1 bricks, or incorrect dimensions (see Figure 3).
Incorrect: red brick
does not overhang
Correct overhang
for red bricks
Incorrect: window and
blue 4x2s set back
Correct placement of
window and blue 4x2s
Figure 2: Difficulty with Placing Lego Bricks
Incorrect: 4x2 curved
bricks instead of 3x2
Correct use of 3x2
curved bricks
Incorrect: 2 stacked
2x2 bricks on right
Correct use of tall
2x1 bricks on right
Figure 3: Difficulty with Choosing Lego Bricks
Design Two
In general, most students had fewer differences when they completed design 2, which was
not surprising since they only had to build half of the structure. Students also did not have much
difficulty figuring out where to start from the manual or general picture. They continued to build
symmetrically from the bottom up but only eight continued to use the lines between bricks to
guide them. As with the first design, they continued to use generic language, referring to bricks
in generic ways (21% of language terms) and paired this with continuous amounts (20% of
terms). They also continued to refer to locations in generic ways (13% of terms) and increased
their focus on the bricks’ colors or shading (e.g., darker; 11% of terms). Overall, students had a
median of two differences in their final designs (ranging from zero to six difficulties, excluding
one kindergartener who left off 10 bricks). Interestingly, there were fewer differences between
the color and grayscale conditions with this design. Rather, the biggest difference occurred
between students who used a manual (who had a total of six differences in their final structures)
versus those who used the picture (who had a total of 29 differences in their final structures).
Students’ difficulties were similar to those from the first design.
Lischka, A. E., Dyer, E. B., Jones, R. S., Lovett, J. N., Strayer, J., & Drown, S. (2022). Proceedings of the forty-fourth annual meeting
of the North American Chapter of the International Group for the Psychology of Mathematics Education. Middle Tennessee
State University.
580

Discussion
Overall, students who built the Lego structures using the manuals had fewer differences than
those who built the Lego structures using the pictures. Manuals (a kind of worked example with
subgoals) may reduce students' cognitive load by engaging them in more self-explanation
(Atkinson et al., 2003; Catrambone, 1998; Renkl & Atkinson, 2002) and helping them focus on
transformations (Goldenberg & Clements, 2014). There were benefits and drawbacks to
students’ building their first design using the color picture or manual. These students were
largely able to pick out the correct pieces, perhaps aided by the color (see also classification,
Goldenberg & Clements, 2014) and a reduction to cognitive load (Atkinson et al., 2000; Paas et
al., 2003; Sweller et al., 1998); however, they had difficulty placing them, especially in relation
to the forward-backward dimension (see also transformation, Goldenberg & Clements, 2014).
One potential reason may be that their focus was more on the correct use of pieces vertically in
relation to each other. Students who saw the pictures and manuals in grayscale may have looked
more closely at the placement to help them figure out both the pieces involved as well as how to
place them because they did not have the color cues. The Lego structures were designed to
emphasize the vertical element, so future work could explore if students have similar color-
placement difficulty with Lego structures that involve a stronger depth element and little vertical
change. Another possible avenue to explore would be to give students manuals where the pieces
for the sub-goals are in color but the composed structure is in grayscale. This change might help
students find the correct pieces but then encourage them to examine the picture more closely to
interpret how to place the pieces. In fact, by design 2, the advantage of having color appeared to
wane, and the benefits of the manual, with its sub-goals, took on more importance. Interestingly,
students were more likely to use general words than specific words to describe the bricks and
their locations, similar to findings from Cohen and Emmons (2017). Therefore, another fruitful
avenue may be to help students use specific language when building to determine if that helps
them have a better sense of the spatial dimensions in the pictures or manuals.
Acknowledgments
This research was supported by a Ross-Lynn grant through Purdue University.
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