Papers by Linda Venenciano
Abstract: This book introduces students to the types of problems and processes used throughout th... more Abstract: This book introduces students to the types of problems and processes used throughout the" Reshaping Mathematics for Understanding" series. The problems in this unit deepen students' understanding of mathematics by encouraging them to clarify concepts ...
for the learning of mathematics, 2014
The design of the problem requires students to do more than merely count the number of squares in... more The design of the problem requires students to do more than merely count the number of squares in each figure. Part B requires reasoning about the relationship between two variables: the figure number and the number of squares needed to construct the figure. What experiences help students recognize the opportunity to use a more efficient, non-counting approach? What curriculum do students need in order to develop skills for solving numeric problems that demand more than counting? In this article, we highlight the importance of elementary mathematics in setting a foundation for student success with algebraic concepts and skills, and suggest an approach that takes into account work from Davydov (1966, 1975a, 1975b) to promote access to higher and more complex mathematics. Our aim is to offer a basis with which to clarify educational priorities in elementary mathematics to support algebraic understandings. In the first part of the article, we describe three major lines of thought that ...
In this study we explore possible long-term effects of an adaptation of the El’konin–Davydov ele... more In this study we explore possible long-term effects of an adaptation of the El’konin–Davydov elementary grades curriculum, Measure Up or MU. The objectives for the study are to assess how students relate an equation of nonnumeric quantities to a length representation, and if former MU students develop and retain a perspective characteristic of the curriculum. Data were collected from thirteen former MU students and a group of fourteen peers who were instructed together with the MU students in identical middle and high school programs, but did not receive MU instruction. Findings show that former MU students reasoned about lengths as generalized quantities, applied a method for marking and labeling quantities, and justified a representation of relationships given by an equation. Implications are discussed for how a measurement context in elementary mathematics supports meaning making in the later study of algebra, particularly with regard to variables and multiple representations.
Educational Studies in Mathematics, 2021
In many countries, the twentieth century philosophy and social sciences were marked by a dialecti... more In many countries, the twentieth century philosophy and social sciences were marked by a dialectical materialist understanding of humans and the world. This understanding revolves around the idea that human collective activity and material and ideational culture (e.g., symbols, language) play a central role in learning and development. In socialist Russia, dialectical materialist was the main philosophy that shaped research in psychology and education. This philosophy is the foundation of the work of L. S. Vygotsky and his followers, Vasil V. Davydov (1930-1998) among them. Davydov studied the philosophy of dialectical and historical materialism and the pedagogical psychology under the supervision of Piotr Galperin-one of the former students of Lev Vygotsky-at the Russian State University in Moscow. From 1953 Davydov worked together with Galperin, Daniil El'konin, and others to study, from the theoretical point of view, the psychological processes of conceptual knowledge acquisi...
The Mathematics Teacher
Use the Reversibility, Flexibility, Generalization (RFG) questioning framework to develop robust,... more Use the Reversibility, Flexibility, Generalization (RFG) questioning framework to develop robust, multifaceted, interconnected, and lasting mathematical comprehension.
Educational Studies in Mathematics
Investigations in Mathematics Learning
Mathematics Teaching in the Middle School
In a professional development session, teachers reflect on their mathematical practice following ... more In a professional development session, teachers reflect on their mathematical practice following the reading of the MTMS article, “12 Math Rules that Expire.” The ideas in the article elicited teachers' awareness of mathematics that they emphasize in instruction and implications for student learning.
Prior studies examined how students use quantitative reasoning and multiple representations to mo... more Prior studies examined how students use quantitative reasoning and multiple representations to model mathematical relationships. In this paper we will discuss how students attend to the structure of an equation and how they reason about the expressed quantities. The assessment was adapted from the elementary project, Measure Up, and administered to Grade 5 and Grade 12 students. Findings from this research can add to the understanding of a quantitative reasoning trajectory.
This paper describes the development of materials for a course for struggling ninth-grade student... more This paper describes the development of materials for a course for struggling ninth-grade students who need support while enrolled in an algebra course. The materials, called A Modeling Approach to Algebra (Olson, Olson, Slovin, Venenciano, and Zenigami, 2013b), focus on modeling, one of the conceptual categories of the high school standards, and the Standards for Mathematical Practice from the Common Core State Standards in Mathematics (CCSSM)
The Curriculum Research & Development Group has developed A Modeling Approach to Algebra, a curri... more The Curriculum Research & Development Group has developed A Modeling Approach to Algebra, a curriculum created to support ninth-grade students' effort to learn Algebra I. Funded by a contract with the Hawai'i State Department of Education, materials were developed to support struggling learners by emphasizing modeling mathematical content and practice as described in the Common Core Curriculum Standards for Mathematics. In this paper we discuss the curriculum research and development from a design research perspective.
Educational Studies in Mathematics, 2015
This paper describes the development of materials for a course for struggling ninth-grade student... more This paper describes the development of materials for a course for struggling ninth-grade students who need support while enrolled in an algebra course. The materials, called A Modeling Approach to Algebra (Olson, Olson, Slovin, Venenciano, and Zenigami, 2013b), focus on modeling, one of the conceptual categories of the high school standards, and the Standards for Mathematical Practice from the Common Core State Standards in Mathematics (CCSSM)
Prior studies examined how students use quantitative reasoning and multiple representations to mo... more Prior studies examined how students use quantitative reasoning and multiple representations to model mathematical relationships. In this paper we will discuss how students attend to the structure of an equation and how they reason about the expressed quantities. The assessment was adapted from the elementary project, Measure Up, and administered to Grade 5 and Grade 12 students. Findings from this research can add to the understanding of a quantitative reasoning trajectory.
The Curriculum Research & Development Group has developed A Modeling Approach to Algebra, a curri... more The Curriculum Research & Development Group has developed A Modeling Approach to Algebra, a curriculum created to support ninth-grade students' effort to learn Algebra I. Funded by a contract with the Hawai'i State Department of Education, materials were developed to support struggling learners by emphasizing modeling mathematical content and practice as described in the Common Core Curriculum Standards for Mathematics. In this paper we discuss the curriculum research and development from a design research perspective.
Children’s everyday measurement experiences serve as the basis for developing mathematical proper... more Children’s everyday measurement experiences serve as the basis for developing mathematical properties about number. In the Measure Up program, this context is applied to first develop foundational properties about mathematical relationships, and
later to place value and number magnitude. The mathematical concepts are introduced through learning activities in a measurement context. Measuring activities with nonnumeric quantities are designed to embody the magnitude associated with the place value. We argue that this approach develops understanding of the structure of multidigit numbers. This curricular approach contributes to the discourse laying
foundational ideas about number in the primary mathematics curriculum. In this paper we describe how number structure is developed from measurement contexts using everyday experiences to define unit and number relationships in different bases. We share student works and discuss how these give evidence for this curricular approach.
Uploads
Papers by Linda Venenciano
later to place value and number magnitude. The mathematical concepts are introduced through learning activities in a measurement context. Measuring activities with nonnumeric quantities are designed to embody the magnitude associated with the place value. We argue that this approach develops understanding of the structure of multidigit numbers. This curricular approach contributes to the discourse laying
foundational ideas about number in the primary mathematics curriculum. In this paper we describe how number structure is developed from measurement contexts using everyday experiences to define unit and number relationships in different bases. We share student works and discuss how these give evidence for this curricular approach.
later to place value and number magnitude. The mathematical concepts are introduced through learning activities in a measurement context. Measuring activities with nonnumeric quantities are designed to embody the magnitude associated with the place value. We argue that this approach develops understanding of the structure of multidigit numbers. This curricular approach contributes to the discourse laying
foundational ideas about number in the primary mathematics curriculum. In this paper we describe how number structure is developed from measurement contexts using everyday experiences to define unit and number relationships in different bases. We share student works and discuss how these give evidence for this curricular approach.