What Early Algebra Knowledge Persists 1 Year After an Elementary Grades Intervention?

Abstract

This research focuses on the retention of students’ algebraic understandings 1 year following a 3-year early algebra intervention. Participants included 1,455 Grade 6 students who had taken part in a cluster randomized trial in Grades 3–5. The results show that, as was the case at the end of Grades 3, 4, and 5, treatment students significantly outperformed control students at the end of Grade 6 on a written assessment of algebraic understanding. However, treatment students experienced a significant decline and control students a significant increase in performance relative to their respective performance at the end of Grade 5. An item-by-item analysis performed within condition revealed the areas in which students in the two groups experienced a change in performance.

An analysis of teacher knowledge for teaching functional thinking to elementary school students

“…Note that students’ functional thinking needs to be continuously supported. Research has shown that even students who had engaged in an effective intervention program concerning early algebra across Grades 3–5 had difficulties maintaining their learning—for example, in representing functional relationships (Stephens et al, 2021). We agree with the claim by Blanton et al (2019), “[P]art of the answer to how we might further increase student performance lies in better understanding how to support elementary teachers” (p. 1963).…”

Functional Thinking: A Study with 10th-Grade Students

“…Solving problems or demonstrating the veracity of a conjecture is impossible to accomplish without the use of mathematical reasoning. In both, solving problems and demonstrating conjectures are ways of developing mathematical reasoning [18][19][20][21]. The connections between different contents, the communication and representations used by the students are the basis of the developed mathematical reasoning, leading to decision-making in the learning process of each student.…”

Cognitive apprehension in visual pattern generalization problems / Aprehensión cognitiva en problemas de generalización de patrones visuales

“…En esta línea de investigación se considera que el pensamiento algebraico puede comenzar a desarrollarse en los primeros años de primaria (Cai & Knuth, 2011;Carpenter, Franke, & Levi, 2003;Godino, Aké, Gonzato, & Wilhelmi, 2014;Kaput & Blanton, 2001). Diversos estudios demuestran que los niños son capaces de identificar relaciones entre cantidades, estudiar el cambio y generalizar patrones antes de ser introducidos en el álgebra formal (Cañadas, Brizuela, & Blanton, 2016;Cooper & Warren, 2011;Radford, 2014;Rivera & Becker, 2011;Stephens, Ellis, Blanton, & Brizuela, 2017;Vergel, 2015). Uno de los ámbitos en los que se ha estudiado el desarrollo del pensamiento algebraico temprano es el de la generalización de patrones numéricos o visuales (Kieran, Pang, Schifter, & Ng, 2016).…”

“…This line of research considers that algebraic thinking can begin to develop in the first years of primary education (Cai & Knuth, 2011;Carpenter, Franke, & Levi, 2003;Godino, Aké, Gonzato, & Wilhelmi, 2014;Kaput & Blanton, 2001). Several studies show that children are able to identify relationships between quantities, study change and generalize patterns before being introduced to formal algebra (Cañadas, Brizuela, & Blanton, 2016;Cooper & Warren, 2011;Radford, 2014;Rivera & Becker, 2011;Stephens, Ellis, Blanton, & Brizuela, 2017;Vergel, 2015).…”