### Abstract

A task-based written survey was administered to 69 pre-service teachers (PSTs) at a large Midwestern University in the USA to examine their recognition of examples/non-examples of ¼ presented in various forms of the area model, their perceived mathematical key points in identifying examples/non-examples, and their instructional decisions in selecting and sequencing examples/non-examples. An inductive content analysis showed that typical examples of ¼ did not distinguish different levels of PSTs’ content knowledge. However, in cases of unconventional examples, PSTs’ levels of content knowledge were easily discernible. Also, PSTs across different performance levels perceived equal partitioning as a key mathematical point and gave it primary consideration in sequencing examples, but they interpreted “equal parts” in many different ways, and only the high-performance group incorporated unconventional examples in making a sequence. In all performance levels, the inclusion of a non-example in making a sequence was scarce. Implications for improving the teaching of fraction concepts in teacher preparation programs are discussed.

Original language | English (US) |
---|---|

Journal | International Journal of Science and Mathematics Education |

DOIs | |

State | Accepted/In press - Jan 1 2020 |

Externally published | Yes |

### Fingerprint

### Keywords

- Examples and non-examples
- Fractional models
- Mathematical knowledge for teaching
- Noticing
- Teacher preparation

### ASJC Scopus subject areas

- Education
- Mathematics(all)