Source: Journal of Mathematics Teacher Education, 20 (3):231–257 (2017)
(Reviewed by the Portal Team)
This study investigates the insights and challenges that prospective teachers experience when exploring early algebraic reasoning.
The participants were thirteen undergraduate prospective teachers (PSTs), who enrolled in a content course for PSTs at a mid-Atlantic University in the USA. Twelve were female and one was male. All participants had taken algebra in high school and reported that they had little to no exposure to early algebra in their elementary education.
The author structured the lessons according to an inquiry-oriented approach. He introduced new content by having students work in groups—three to four students per group—on activities that explored algebraic ideas at an early algebra level. Afterwards, the students participated in whole-class discussions, in which they, using a document camera, presented their thinking to the class.
Data were gathered in conjunction with a course assignment. The author conducted five small-group meetings with the participants to work on early algebra tasks in groups of twos and threes. The group-meetings included three tasks, which mirrored the themes of the lessons.
The findings indicate that when PSTs engage in early algebra experiences during their preparation for teaching, they may experience meaningful new insights but may also face conceptual challenges.
The author also argues that the results suggest that PSTs may benefit from developing informal ways to represent algebraic expressions and equations.
However, PSTs found it a conceptual challenge to identify the relationships contained in algebraic expressions. The participants had difficulty to distinguish between unknowns and variables, to bracket their knowledge of formal algebra and to represent subtraction from unknowns or variables.
The author argues that this study provided a new conceptualization of PSTs’ experiences with early algebra, in terms of a transition from formal algebra to early algebra, comparable to the transition that elementary students make from arithmetic to early algebra. The author argues that this conceptualization is based on the assumption that most PSTs have not had many experiences with early algebra in their own elementary education.