Craig Cullen

Craig Cullen
Illinois State University | ISU · Mathematics Education

PhD
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About

29
Publications
15,769
Reads
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236
Citations
Citations since 2017
16 Research Items
195 Citations
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Introduction

Publications

Publications (29)
Article
We report on the process of children’s construction of a volume calculation algorithm for rectangular prisms. We provided third- and fourth-grade students with traditional volume tasks and a dynamic virtual manipulative to support their three-dimensional reasoning and use of unit cubes to structure space. We investigated the challenges faced, evolv...
Article
Full-text available
Measurement is a critical component of mathematics education, but research on the learning and teaching of measurement is limited. We previously introduced, refined, and validated a developmental progression – the cognitive core of a learning trajectory – for length measurement in the early years. A complete learning trajectory includes instruction...
Article
In this lesson, third graders were asked how many degrees is a full rotation around a circle. After we gave students time and space to disagree, to make and test conjectures, and to explore, they reasoned about angle as turn and determined a full rotation is 360 degrees.
Article
Full-text available
We present our findings with respect to our two research questions: 1) How well do children at the ICS and ARCS levels of the LT for area measurement estimate areas of rectangles and what is the nature of their estimates? And 2) To what extent can ICS and ARCS level children’s area estimation performance be quantitatively improved through targeted...
Article
We review literature relevant to using technology in the teaching/learning of mathematics to highlight four roles of effective technology use: (a) promoting cycles of proof; (b) presenting and connecting multiple representations; (c) supporting case-based reasoning; and (d) serving as a tutee. We then discuss how they intersect with good instructio...
Chapter
Full-text available
Designed to strengthen the teaching of mathematics in the elementary grades, this chapter focuses on helping teachers engage in instruction based on learning trajectories (LTs). We explain our experiences and key research-based findings working with teacher educators in which we created effective professional development around LTs for geometric me...
Article
Full-text available
We examine the effects of 3 interventions designed to support Grades 2-5 children's growth in measuring rectangular regions in different ways. We employed the microge-netic method to observe and describe conceptual transitions and investigate how they may have been prompted by the interventions. We compared the interventions with respect to childre...
Article
We evaluated the effects of three instructional interventions designed to support young children’s understanding of area measurement as a structuring process. Replicating microgenetic procedures we used in previous research with older children to ascertain whether we can build these competencies earlier, we also extended the previous focus on corre...
Book
Full-text available
Quantitative reasoning and measurement competencies support the development of mathematical and scientific thinking in children in the early and middle grades and are fundamental to science, technology, engineering, and mathematics (STEM) education. The sixteenth Journal for Research in Mathematics Education (JRME) monograph is a report on a four-y...
Article
A 14-year-old child with Acute Lymphoblastic Leukemia participated in 52 weeks of robotics task-based interviews. We present 3 of her tasks from Weeks 1, 20, and 46 along with an overview of the complete 52 weeks. We compare the data from the tasks to Brousseau's (1997) Theory of Didactical Situations of Mathematics to answer our research questions...
Book
Full-text available
This monograph is a report on a 4-year-long multisite longitudinal study in which we studied children’s thinking and learning about geometric measurement (i.e., length, area, and volume). The Children’s Measurement research team, as funded by the National Science Foundation between 2007 and 2012, completed the research reported in this monograph. D...
Conference Paper
Full-text available
We examined children's estimation performance, ages 9-10, to find the area of rectangular regions given a unit square for visual comparison. We found children generally underestimated, with approximately 40 percent error. We relied on prior research to establish a starting point of approximately 14 percent as the boundary beyond which it proved too...
Conference Paper
Full-text available
In this paper we report on five Grade 6 students’ responses to a proportional reasoning task. We conducted pair interviews within a longitudinal study focused on extending a hypothetical learning trajectory for length measurement. Results suggest that there exists a link between children’s level of conceptual and procedural knowledge for length mea...
Conference Paper
Full-text available
This report describes the longitudinal development of one student, Drew, in terms of his unit concepts in area and volume measurement situations across Grades 2 through 5. Data were collected during individual interviews and an open-response assessment within the context of a four-year longitudinal teaching experiment. Results indicate that Drew's...
Article
Full-text available
The NCTM Algebra Standard suggests that students use technology to explore the effects of varying the parameters in y = ax2 + bx + c. This article discusses an extension of this task that incorporates dynamic geometry software to engage students in generating, testing, and proving mathematical conjectures.
Article
Full-text available
We examined children's development of strategic and conceptual knowledge for linear measurement. We conducted teaching experiments with eight students in grades 2 and 3, based on our hypothetical learning trajectory for length to check its coherence and to strengthen the domain-specific model for learning and teaching. We checked the hierarchical s...
Conference Paper
Full-text available
This empirical study investigated the effects of an instructional sequence on pre-service secondary teachers' understanding of trigonometric functions. Guided by the APOS framework, we designed activities to promote a directed length interpretation of the six trigonometric functions using a dynamic geometry environment. Results of a paired t-test (...
Article
Full-text available
We examined ways of improving students’ unit concepts across spatial measurement situations. We report data from our teaching experiment during a six-semester longitudinal study from grade 2 through grade 5. Data include instructional task sequences designed to help children (a) integrate multiple representations of unit, (b) coordinate and group u...
Conference Paper
Full-text available
The purpose of this report is to compare three different unit eliciting task structures for measurement comparison tasks. Twelve students ranging from grade 2-4 were presented length, area, and volume tasks. Student responses were coded for correctness and comparison type. The results indicated that students were most successful with task structure...
Conference Paper
Full-text available
The purpose of this report is to compare the effects of presentation mode based on y use in measurement tasks. The same treatment was presented, either with a paper-and-pencil environment to 36 students (21 aged 4-5 years, and 15 aged 7-8 years. Changes in student strategy use were tracked by following a microgenetic method over 18 trials. The non-...

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Projects

Projects (2)
Project
How do children think and learn about geometric measurement—length, area, and volume? Funded by the National Science Foundation, this research and development project focuses on the learning and teaching of measurement in early and elementary education. Conducted in collaboration with Jeffrey Barrett (PI) and Craig Cullen from Illinois State University, we are producing research-based developmental progressions—descriptions of the levels of thinking children move through as they learn— in measurement across a seven-year span. These developmental progressions are the core of research-based learning trajectories—with full trajectories including instructional activities and teaching strategies (Sarama & Clements, 2009).