**Beliefs of Pre-Service Mathematics Teachers in China About Mathematical Problem Solving – Focusing on Open / Close-Ended Problems**

**Yixuan LIU and Yiming CAO**

#### School of Mathematical Sciences

Beijing Normal University

China

Published in The Mathematician Educator, 2023, Vol 4, No. 3, pp 179-191.

### Abstract

Teachers’ beliefs impact their practice in mathematics classrooms. This paper examines the beliefs of pre-service teachers in China related to teaching and learning mathematics, and open/close-ended problems during problem solving. Beliefs of 84 pre-service teachers in master’s degree programme in three universities in China were measured using an adaptation of the Teachers’ Beliefs on Their Practice (TBTP) instrument by Safrudiannur and Rott (2021). The results showed that beliefs of pre-service mathematics teachers in China differed for high ability and low ability classes. It appears that mathematical understanding is significantly less emphasised in open-ended problem solving than in close-ended problem solving, which raises concerns about potential risks. On the other hand, the close correlation between teacher beliefs about open-ended problem solving and the nature of mathematics may allow more affordance for pre-service teachers to put their own ideas into practice through open-ended problem solving.

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