Learning Progression

Uncovering Middle School CS Students’ Understanding of Variables and Control Structures: A Cognitive Think-Aloud Approach

This poster presents findings on middle school students’ understanding of core computer science (CS) concepts, such as variables and control structures, using cognitive think-aloud interviews with eight students. Each student worked on 16-22 formative assessment tasks designed to assess understanding on the ‘Algorithms and Programming’ middle school CS standards. Our study describes students’ interpretations of the CS concepts and discusses potential factors influencing student interpretations. Significance and next steps are described.

Author/Presenter

Hui Yang

Satabdi Basu

Daisy Rutstein

Arif Rachmatullah

Carol Tate

Christopher Ortiz

Eliese Rulifson

Lead Organization(s)
Year
2023
Short Description

This poster presents findings on middle school students’ understanding of core computer science (CS) concepts, such as variables and control structures, using cognitive think-aloud interviews with eight students.

Exploring Middle School Students’ Understanding of Algorithms Using Standards-aligned Formative Assessments: Teacher and Researcher Perspectives

‘Algorithms’ is a core CS concept included in the K-12 CS standards, yet student challenges with understanding different aspects of algorithms are still not well documented, especially for younger students. This paper describes an approach to decompose the broad middle-school ‘algorithms’ standard into finer grained learning targets, develop formative assessment tasks aligned with the learning targets, and use the tasks to explore student understanding of, and challenges with, the various aspects of the standard.

Author/Presenter

Satabdi Basu

Daisy Rutstein

Carol Tate

Arif Rachmatullah

Hui Yang

Christopher Ortiz

Lead Organization(s)
Year
2023
Short Description

‘Algorithms’ is a core CS concept included in the K-12 CS standards, yet student challenges with understanding different aspects of algorithms are still not well documented, especially for younger students. This paper describes an approach to decompose the broad middle-school ‘algorithms’ standard into finer grained learning targets, develop formative assessment tasks aligned with the learning targets, and use the tasks to explore student understanding of, and challenges with, the various aspects of the standard.

Designing Standards-aligned Formative Assessments to Explore Middle School Students’ Understanding of Algorithms

'Algorithms’ is a core CS concept included in the K-12 CS learning standards, yet student challenges with understanding and using algorithms are still not well documented. This paper describes an approach to decompose the broad middle-school ‘algorithms’ standard into finer grained learning targets, develop formative assessment tasks aligned with the fine-grained learning targets, and use the tasks to explore student understanding of and challenges with the various concepts underlying the standard.

Author/Presenter

Satabdi Basu

Daisy Wise Rutstein

Arif Rachmatullah

Carol Tate

Hui Yang

Christopher Ortiz

Lead Organization(s)
Year
2023
Short Description

'Algorithms’ is a core CS concept included in the K-12 CS learning standards, yet student challenges with understanding and using algorithms are still not well documented. This paper describes an approach to decompose the broad middle-school ‘algorithms’ standard into finer grained learning targets, develop formative assessment tasks aligned with the fine-grained learning targets, and use the tasks to explore student understanding of and challenges with the various concepts underlying the standard.

Connecting Classroom Assessment with Learning Goals and Instruction Through Theories of Learning

In this report section, we discuss the importance of aligning classroom assessments with learning goals and instructional practices to both shape and evaluate students’ learning opportunities. We describe a plausible solution for improving alignment by integrating theories of learning in the design of classroom assessments. We discuss ways in which the specification of theories of learning as learning progressions can improve alignment between classroom assessments and instruction by focusing on the content, task design, and data generated from classroom assessments.

Author/Presenter

Leanne R. Ketterlin-Geller

Christopher J. Harris

Year
2023
Short Description

In this report section, we discuss the importance of aligning classroom assessments with learning goals and instructional practices to both shape and evaluate students’ learning opportunities.

Empirical Recovery of Learning Progressions Through the Lens of Educators

Learning progressions represent the relationship between concepts within a domain and how students develop increasingly sophisticated thinking therein. Typical evidence sources used to validate theorized learning progressions are also used to validate the use and interpretation of assessments, such as student cognitive interviews and psychometric analyses of item responses on assessments (Alonzo, 2018; Duschl et al., 2011).

Author/Presenter

Leanne R. Ketterlin-Geller

Yetunde Zannou

Anthony Sparks

Lindsey Perry

Year
2020
Short Description

In this manuscript, we propose that educators’ perspectives may serve as an independent source of evidence that can be integrated with traditional evidence sources (e.g., cognitive interviews with students, psychometric data). This manuscript describes two studies that used surveys to draw on educator knowledge of students to identify upper and lower bounds of a learning progression (MMaRS study) and to understand the order of intermediary phases of learning (ESTAR study).

NCTM Presentation Line of "Good" Fit in Grade 8 Classrooms

Lead Organization(s)
Year
2018
Short Description

This presntation addreses 4 research cquestions

 

What extant criteria do Grade 8 students use to choose the better line
of fit between two lines “fit” to a set of data, when both lines express
the trend of the data?
 
Is a residual criterion accessible and useful to Grade 8 students when
learning about line of fit?
 
How does introducing a residual criterion impact student
understanding of line of fit and their understanding mathematical
modeling process?
 
What stages of learning do students express as they engage in our
lesson?

LEAP: Learning through an Early Algebra Progression

Designed to be integrated with any curriculum, each grade level includes 18-20 one-hour lessons to be conducted throughout the school year. Each LEAP lesson lasts about an hour is designed to fit within a typical daily math instructional period.

LEAP early algebra curriculum for Grades K-5. Grades 3 and 4 currently available, with the remaining books for Grades K-2, 5 in press.

Blanton, M., Gardiner, A., Stephens, A., & Knuth, E. (2020). LEAP: Learning through an early algebra progression. Didax: Rowley, MA.

Author/Presenter

Maria Blanton

Angela Murphy Gardiner

Ana Stephens

Eric Knuth

Lead Organization(s)
Year
2020
Short Description

Designed to be integrated with any curriculum, each grade level includes 18-20 one-hour lessons to be conducted throughout the school year. Each LEAP lesson lasts about an hour is designed to fit within a typical daily math instructional period.

Length Measurement in the Early Years: Teaching and Learning with Learning Trajectories

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 instructional activities and pedagogical strategies, correlated with each level of the developmental progression. This study evaluated a portion of our learning trajectory, focusing on the instructional component.

Author/Presenter

Julie Sarama

Douglas H. Clements

Jeffrey E. Barrett

Craig J. Cullen

Aaron Hudyma

Yuly Vanegas

Lead Organization(s)
Year
2021
Short Description

This study evaluated a portion of our learning trajectory, focusing on the instructional component. We found that the instruction was successful in promoting a progression from one level to the next for 40% of the children, with others developing positive new behaviors (but not sufficient to progress to a new level).

The Role of Balance Scales in Supporting Productive Thinking about Equations Among Diverse Learners

This research focuses on ways in which balance scales mediate students’ relational understandings of the equal sign. Participants included 21 Kindergarten–Grade 2 students who took part in an early algebra classroom intervention focused in part on developing a relational understanding of the equal sign through the use of balance scales. Students participated in pre-, mid- and post-intervention interviews in which they were asked to evaluate true-false equations and solve open number sentences. Students often worked with balance scales while solving these tasks.

Author/Presenter

Ana Stephens

Yewon Sung

Susanne Strachota

Ranza Veltri Torres

Karisma Morton

Angela Murphy Gardiner

Maria Blanton

Eric Knuth

Rena Stroud

Year
2020
Short Description

This research focuses on ways in which balance scales mediate students’ relational understandings of the equal sign.