## Investigating the Improvement of Prospective Elementary Teachersâ€™ Number Sense in Reasoning about Fraction Magnitude

Source: *Journal of Mathematics Teacher Education, Volume 19,* p. 57-77 (2016)

(Reviewed by the Portal Team)

This study explored whether and how prospective teachers (PTs) fraction sense could improve in the setting of a Number and Operations course.

**Methods **

This study took place at a large, urban university in the southwestern USA.

The participants were students enrolled in a first mathematics content course for prospective elementary teachers, belonging to a four-course sequence.

They completed an English language version of the Number Sense Rating Scale. This scale was administered pre- and post-instruction. Furthermore, the authors interviewed seven of the participants.

The authors referred to their previous study, where they devised a local instruction theory for the development of number sense, which focused on whole number mental computation. They found that prospective elementary teachersâ€™ whole-number sense improved when instruction in a Number and Operations course was guided by local instruction theory.

Furthermore, the results from the interviews with seven participants provide evidence that their performance and flexibility in comparing fractions improved. The authors found that 6 of the 7 interview participants adopted at least two new valid strategies for comparing fractions.

Consequently, these findings can guide mathematics teacher educators how to support PTs to reason meaningfully and flexibly about fraction magnitude. The intervention that the authors have described suggests the inclusion of comparison tasks and placement tasks on the number line, as well as particular sequencing of these and other tasks; this instruction can result in improved reasoning in terms of flexibility and sophistication.

The authors conclude that preservice teachers will be better equipped to lead classrooms of students who make sense of mathematics if they themselves reason in ways that are less bound to standard algorithms.