This study analyzes the mathematical knowledge to teach early algebra exhibited by pre-service early childhood education teachers, from the perspective of the Mathematical Knowledge for Teaching (MKT) model. The research adopts a mixed exploratory-descriptive methodological approach, based on the application of the MKT-early algebra questionnaire…

The United States has relinquished its mathematical prowess enjoyed in the 20th century with trending declines in performance on international and national measures and must make a concerted effort to regain this standing in the 21st century. Success in mathematics education also is important for individual citizens because it gives them college…

Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The qualitative study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about parity arguments for sums of evens and odds, as well as underlying…

This paper is part of broader research being conducted in the area of algebraic thinking in primary education. Our general research objective was to identify and describe generalization of a 2nd grade student (aged 7-8). Specifically, we focused on the transition from arithmetic to algebraic generalization. The notion of structure and its…

This paper is a part of a larger research study that we are conducting to develop a framework consisting of the data-driven best practices around teaching and learning algebra in K-12 classrooms. The purpose of this paper is to develop a usable definition for algebra interventions for the second stage of screening within the larger study, which…

This study describes how 24 third graders (8-9 years old) relate and represent the relationships between variables when working with a functional thinking problem. This aspect contributes to providing insights about how elementary school students attend properties and relationships between covarying quantities rather than isolated computations.…

A theoretical model describing young students' (Grade 3) arithmetic-algebraic structure sense was formulated and validated empirically (n = 130), hypothesizing that young students' arithmetic-algebraic structure sense consists of five distinct but correlated factors; structure in numerical equivalence and word-problem modeling, structure in…

In this study, it was aimed to investigate 4-to-6-year-old children's reasoning skills appearing in pattern tasks. 55 children studying in the classes of four different pre-school classes participated in the study. A classroom teaching experiment was conducted to examine the development of children's reasoning skills in pattern tasks. Both…

Given the relevance of graphs of functions, we consider their inclusion in primary education from the functional approach to early algebra. The purpose of this article is to shed some light on the students' production and reading of graphs when they solved generalization problems from a functional thinking approach. We aim to explore how 3rd and…

We share results from a one-year early algebra classroom intervention. One kindergarten, one first-grade, and one second-grade classroom participated in the intervention and three classrooms of the same grade levels served as control sites. The intervention addressed the structure of even and odd numbers, mathematical equivalence and equations,…

We conducted a randomized control trial assessing the effects of two variants of word-problem intervention with third graders (n = 304) experiencing mathematics difficulty. Students were assigned to a business-as-usual condition (BaU) or one of two variants of word-problem intervention. One variant included a pre-algebraic reasoning component…

Understanding how young learners come to construct viable mathematical arguments about general claims is a critical objective in early algebra research. The study reported here characterizes empirically developed progressions in Grades K-1 students' thinking about arguments concerning sums of evens and odds. Data are drawn from classroom lessons…

This paper explores Year 3 Irish students' problem-solving strategies when responding to a skyscraper growing pattern problem. Students' strategies reveal their understandings of multiplicative thinking, pattern, and algebraic reasoning. The version of the growing pattern lesson was that a 'teaching through problem solving' approach was taken,…

Relational thinking and dealing with variables are two essential aspects of algebraic thinking. Relational thinking means viewing mathematical expressions and equations as a whole rather than as individual computing processes. It is characterized by using relationships between mathematical objects, and refers to the relations of equality and…

In this investigation, the extent to which differences were present in the mathematics achievement by the ethnicity/race of Grade 3 students in Texas were analyzed. Data obtained from the Texas Education Agency Public Education Information Management System for all Texas Grade 3 students who took the State of Texas Assessment of Academic Readiness…