This article focuses mainly on two key mathematical processes (representation, and reasoning and proof). Firstly, we observed how teachers learn these processes and subsequently identify what and how to assess learners on the same processes. Secondly, we reviewed one teacher’s attempt to facilitate the learning of the processes in his classroom. Two interrelated questions were pursued: ‘what are the teachers’ challenges in learning mathematical processes?’ and ‘in what ways are teachers’ approaches to learning mathematical processes influencing how they assess their learners on the same processes?’ A case study was undertaken involving 10 high school mathematics teachers who enrolled for an assessment module towards a Bachelor in Education Honours degree in mathematics education. We present an interpretive analysis of two sets of data. The first set consisted of the teachers’ written responses to a pattern searching activity. The second set consisted of a mathematical discourse on matchstick patterns in a Grade 9 class. The overall finding was that teachers rush through forms of representation and focus more on manipulation of numerical representations with a view to deriving symbolic representation. Subsequently, this unidirectional approach limits the scope of assessment of mathematical processes. Interventions with regard to the enhancement of these complex processes should involve teachers’ actual engagements in and reflections on similar learning.

中文翻译：

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教师学习和评估数学过程，重点是表象，推理和证明

本文主要关注两个关键的数学过程（表示，推理和证明）。首先，我们观察了教师如何学习这些过程，然后确定了在相同过程中评估学生的内容和方式。其次，我们回顾了一位老师为促进课堂学习过程所做的尝试。提出了两个相互关联的问题：“教师在学习数学过程中面临哪些挑战？” 以及“教师的学习数学过程的方式如何影响他们在相同过程中评估学习者的方式​​？” 进行了案例研究，涉及10位高中数学老师，他们参加了数学教育教育荣誉学士学位评估模块的注册。我们对两组数据进行了解释性分析。第一组包括教师对模式搜索活动的书面答复。第二组包括9年级的关于火柴棍图案的数学论述。总体发现是，教师匆忙研究了表示形式，并更多地关注数字表示的操纵，以期获得符号表示。随后，这种单向方法限制了数学过程的评估范围。有关加强这些复杂过程的干预措施应包括教师对类似学习的实际参与和反思。总体发现是，教师匆忙研究了表示形式，并更多地关注数字表示的操纵，以期获得符号表示。随后，这种单向方法限制了数学过程的评估范围。有关加强这些复杂过程的干预措施应包括教师对类似学习的实际参与和反思。总体发现是，教师匆忙研究了表示形式，并更多地关注数字表示的操纵，以期获得符号表示。随后，这种单向方法限制了数学过程的评估范围。有关加强这些复杂过程的干预措施应包括教师对类似学习的实际参与和反思。