Number Sense

Does Use of a Hypothetical Learning Progression Promote Learning of the Cardinal-Count Concept and Give-n Performance?

The general aim of the research was to conduct a rare test of the efficacy of hypothetical learning progressions (HLPs) and a basic assumption of basing instruction on HLPs, namely teaching each successive level is more efficacious than skipping lower levels and teaching the target level directly. The specific aim was evaluating whether counting-based cardinality concepts unfold in a stepwise manner. The research involved a pretest—delayed-posttest design with random assignment of 14 preschoolers to two conditions.

Author/Presenter

Arthur J. Baroody

Douglas H. Clements

Julie Sarama

Year
2024
Short Description

The general aim of the research was to conduct a rare test of the efficacy of hypothetical learning progressions (HLPs) and a basic assumption of basing instruction on HLPs, namely teaching each successive level is more efficacious than skipping lower levels and teaching the target level directly. The specific aim was evaluating whether counting-based cardinality concepts unfold in a stepwise manner.

Accountable Assessment

There is widespread agreement about the importance of accounting for the extent to which educational systems advance student learning. Yet, the forms and formats of accountable assessments often ill serve students and teachers; the summative judgements of student performance that are typically employed to indicate proficiencies on benchmarks of student learning commonly fail to capture student performance in ways that are specific and actionable for teachers. Timing is another key barrier to the utility of summative assessment.

Author/Presenter

Richard Lehrer

Lead Organization(s)
Year
2021
Short Description

The author describes an innovative approach to assessment that aims to blend the productive characteristics of both summative and formative assessment. The resulting assessment system is accountable to students and teachers by providing actionable information for improving classroom instruction, and at the same time, it addresses the demands of psychometric quality for purposes of system accountability as it is currently practiced (in the US).

Language Systematizes Attention: How Relational Language Enhances Relational Representation by Guiding Attention

Language can affect cognition, but through what mechanism? Substantial past research has focused on how labeling can elicit categorical representation during online processing. We focus here on a particularly powerful type of language—relational language—and show that relational language can enhance relational representation in children through an embodied attention mechanism.

Author/Presenter

Lei Yuan

Miriam Novack

David Uttal

Steven Franconeri

Lead Organization(s)
Year
2024
Short Description

Language can affect cognition, but through what mechanism? Substantial past research has focused on how labeling can elicit categorical representation during online processing. We focus here on a particularly powerful type of language—relational language—and show that relational language can enhance relational representation in children through an embodied attention mechanism.

Second and Fifth Graders’ Use of Knowledge-Pieces and Knowledge-Structures When Solving Integer Addition Problems

In this study, we explored second and fifth graders’ noticing of negative signs and incorporation of them into their strategies when solving integer addition problems. Fifty-one out of 102 second graders and 90 out of 102 fifth graders read or used negative signs at least once across the 11 problems. Among second graders, one of their most common strategies was subtracting numbers using their absolute values, which aligned with students’ whole number knowledge-pieces and knowledge-structure.

Author/Presenter

Mahtob Aqazade

Laura Bofferding

Lead Organization(s)
Year
2021
Short Description

In this study, we explored second and fifth graders’ noticing of negative signs and incorporation of them into their strategies when solving integer addition problems. For both grade levels, the order of the numerals, the location of the negative signs, and also the numbers’ absolute values in the problems played a role in students’ strategies used. Fifth graders’ greater strategy variability often reflected strategic use of the meanings of the minus sign. Our findings provide insights into students’ problem interpretation and solution strategies for integer addition problems and supports a blended theory of conceptual change.

The Development and Assessment of Counting-based Cardinal Number Concepts

The give-n task is widely used in developmental psychology to indicate young children’s knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and the cardinal-count concept, which she argued is a more advanced cardinality concept that underlies the counting-out process required by the give-n task with larger numbers.

Author/Presenter

Arthur J. Baroody

Menglung Lai

Year
2022
Short Description

The give-n task is widely used in developmental psychology to indicate young children’s knowledge or use of the cardinality principle (CP): the last number word used in the counting process indicates the total number of items in a collection. Fuson (1988) distinguished between the CP, which she called the count-cardinal concept, and the cardinal-count concept, which she argued is a more advanced cardinality concept that underlies the counting-out process required by the give-n task with larger numbers. One aim of the present research was to evaluate Fuson’s disputed hypothesis that these two cardinality concepts are distinct and that the count-cardinal concept serves as a developmental prerequisite for constructing the cardinal-count concept. Consistent with Fuson’s hypothesis, the present study with twenty-four 3- and 4-year-olds revealed that success on a battery of tests assessing understanding of the count-cardinal concept was significantly and substantially better than that on the give-n task, which she presumed assessed the cardinal-count concept.

Teaching Practices for Differentiating Mathematics Instruction for Middle School Students

Three iterative, 18-episode design experiments were conducted after school with groups of 6–9 middle school students to understand how to differentiate mathematics instruction. Prior research on differentiating instruction (DI) and hypothetical learning trajectories guided the instruction. As the experiments proceeded, this definition of DI emerged: proactively tailoring instruction to students’ mathematical thinking while developing a cohesive classroom community.

Author/Presenter

Amy J. Hackenberg

Mark Creager

Ayfer Eker

Lead Organization(s)
Year
2020
Short Description

This study is a case of using second-order models of students’ mathematical thinking to differentiate instruction, and it reveals that inquiring into research-based knowledge and inquiring responsively into students’ thinking are at the heart of differentiating mathematics instruction.

Children’s Integer Understanding and the Effects of Linear Board Games: A Look at Two Measures

The purpose of this study was to identify affordances and limitations of using order and value comparison tasks versus number placement tasks to infer students’ negative integer understanding and growth in understanding. Data came from an experiment with kindergarteners (N = 45) and first graders (N = 48), where the experimental group played a numerical linear board game and the other group did control activities, both involving negative integers.

Author/Presenter

Laura Bofferding

Andrew Hoffman

Lead Organization(s)
Year
2019
Short Description

The purpose of this study was to identify affordances and limitations of using order and value comparison tasks versus number placement tasks to infer students’ negative integer understanding and growth in understanding.

Training Teachers in the Effective Mathematical and Pedagogical Uses of Software: Perspectives from the Dynamic Number and Dynamic Geometry in Classrooms Projects

Day
Thu

This presentation explores technology training in relation to two DR K-12 projects with a focus on increasing the mathematical and pedagogical content knowledge of teachers.

Date/Time
-
Session Type
Panel

How can professional development that is focused on technology move beyond the nuts and bolts of the particular tool to a deeper look into the mathematical and pedagogical opportunities afforded by the technology?     This presentation explores technology training in relation to two DR K–12 projects with a focus on increasing the mathematical and pedagogical content knowledge of teachers.