Developing a Learning Progression for Curriculum, Instruction, and Student Learning: An Example from Mathematics Education

Forty Years of Mathematics Education: 1980-2019

“…The mathematics education studies in WoS database were first published at early 1980s and despite the change in the rate of growth, the number of publications continued to increase in each period. According to keyword analysis, there were a great variety of studies in mathematics education to determine standards and principles of teaching and learning mathematics such as reform movements (Gravemeijer et al, 2016;Lundin, 2012;Sengupta-Irving, Redman, & Enyedy, 2013), curriculum (Fonger et al, 2018;Fouze & Amit, 2017;Pepin et al, 2017;Voigt, Fredriksen, & Rasmussen, 2020), educational policy (Dalby & Noyes, 2018;Lin, Wang, & Chang, 2018;Nortvedt & Buchholtz, 2018), equity (Jurdak, 2011(Jurdak, , 2014Nortvedt & Buchholtz, 2018;Tan & Thorius, 2019), assessment (Beumann & Wegner, 2018;Kim & Cho, 2015;Nortvedt & Buchholtz, 2018;Veldhuis & van den Heuvel-Panhuizen, 2014;Veldhuis et al, 2013), to evaluate the cognitive and affective skills such as problem solving (Boonen et al, 2016;Verschaffel et al, 2020), achievement (Ciftci, 2015;Veldhuis & van den Heuvel-Panhuizen, 2020), motivation (Schukajlow, Rakoczy, & Pekrun, 2017), to learn more about and support mathematics teachers such as professional development (Sztajn et al, 2007;Williams & Ryan, 2020), teacher education (Buchholtz, 2017;Healy & Ferreira dos Santos, 2014;Tatto & Senk, 2011), teacher knowledge (Koponen et al, 2017;Olfos & Rodríguez, 2019;Scheiner et al, 2019), teacher beliefs…”

Does Early Algebra Matter? The Effectiveness of an Early Algebra Intervention in Grades 3 to 5

“…In designing our intervention, we were interested in the occurrence of these practices in two of Kaput’s (2008, p. 11) three content strands (“the study of structures and systems abstracted from computations and relations” and the “study of functions, relations, and joint variation”) because of their close alignment with empirical research on children’s algebraic thinking. As reported elsewhere (Fonger et al, 2018), we organized key early algebraic concepts and practices relative to these strands under the “Big Ideas” (Shin, Stevens, Short, & Krajcik, 2009) of generalized arithmetic; equivalence, expressions, equations, and inequalities ; and functional thinking (see Blanton, Brizuela et al, 2018, for an elaboration of these Big Ideas).…”

“…Using this conceptual approach to algebra organized around essential algebraic thinking practices within content-based Big Ideas, we drew from learning progressions research (e.g., Battista, 2004; Clements & Sarama, 2004; Maloney, Confrey, & Nguyen, 2011; Shin et al, 2009; Simon, 1995) to develop an early algebra learning progression for Grades 3 to 5 that includes the following four components (Clements & Sarama, 2004): (1) a curricular framework and associated learning goals that identify core algebraic concepts within the Big Ideas and that are organized around the four algebraic thinking practices, (2) a Grades 3 to 5 instructional sequence (referred to here as the intervention ) designed to address the learning goals, (3) validated assessments to measure student learning in response to the intervention, and (4) a specification of the increasingly sophisticated levels of algebraic thinking students exhibit about algebraic concepts and practices as they progress through the intervention (see Fonger et al, 2018, for an extensive treatment of the development of these components). Components 1 to 3 are the basis for the effectiveness study reported here.…”

A capital idea: exploring the relationship between human and social capital and student achievement in schools

“…Critical to achieving student improvement are coherent changes in instructional practices that are aligned across grade levels (Fonger et al , 2018). In schools, collaborative settings such as grade-level meetings, peer observations and team teaching offer the opportunity for such exchanges and sharing of tacit or craft knowledge (Horn and Little, 2010; Kennedy, 2002; Spillane et al , 2015).…”