A Study On The Components And Application Of Mathematical Process Ability On Children Aged 5～7

Through the methods of quantitative and qualitative research, this paper aimed to explore the components of mathematical process ability of 5-7 year-old children and the difficulties encountered by teachers when they tried to observe and evaluate children’s mathematical learning from the perspective of process ability and what they need to get over these difficulties.The study evaluated 200 5～7-year-old children’s behaviors in three mathematical activities named operation, space and statistics. First, exploratory factor analysis was conducted based on children’s performance in operation. The result showed that mathematical process ability consisted of four components called mathematical communication, mathematical representation, mathematical connection, mathematical reasoning and proof. From this result, we built a model with four components. Confirmatory factor analysis was conducted to examine the construction of the model based on children’s performance in statistics. The result showed that the model was well-formed and better than the five-element-model from America and the other two competing models.Second, exploratory factor analysis was conducted based on 5～6-year-old and 6～7-year-old children’s performance in operation. The result showed that 5～ 6-year-old and 6～7-year-old children’s mathematical process ability all consisted of four components called mathematical communication, mathematical representation, mathematical connection, mathematical reasoning and proof which showed that there was no age difference on mathematical process ability.Exploratory factor analysis was further conducted based on children’s performance in space. We found that children’s mathematical process ability in space consisted of three components called mathematical communication, mathematical representation, mathematical reasoning and proof. This result showed that there were different process ability components needed in different mathematical activities. So if we try to evaluate children’s process ability in mathematical activities, specificities of activities and sensitivities of tasks must be taken into account.The study investigated if it is necessary and feasible for teachers to observe and evaluate children’s mathematical learning and development from the perspective of process ability. The results indicated that teachers viewed abilities as footstones that will be along with children’s lifelong development and must be important evaluating indicators. But, there were difficulties when teachers tried to observe and evaluate children’s mathematical learning from the perspective of process ability. Such as, they didn’t know the importance of process ability, they couldn’t find some components of process ability, they didn’t know how to evaluate and use the result of evaluation to further guide their teaching.This study also investigated the reasons why these difficulties showed up. The results indicated that there was no knowledge about process ability learned by teachers during pre-service education. During post-training, more concerns were given to teachers’teaching behavior, but children’s learning behavior got less attention. Teachers paid more attentions to the function of identification of evaluation and kindergarten paid less attention to teachers’observation records, this leaded to the lack of awareness of informal assessment. Besides, there were pressures from parents and elementary school teachers when teachers tried to observe and evaluate children’s mathematical learning and development from the perspective of process ability.