Identifying Competency Demands in Mathematical Tasks: Recognising What Matters

Abstract

In more and more countries, the goal of mathematics education is to develop students' mathematical competence beyond procedural and conceptual knowledge. Thus, students need to engage in a rich variety of tasks comprising competencies such as communication, reasoning and problem solving. In addition, assessment tasks should be constructed to measure the particular aspects of mathematical competence to align assessment with curriculum. Teachers need to be able to recognise competency demand in the mathematical tasks they want to use for teaching and assessment purposes, which might prove difficult. The aim of this study was to analyse the outcome of five teachers' and prospective teachers' use of an item analysis tool. For each of 141 assessment tasks, the teachers and prospective teachers individually applied the tool to identify the competency demand of the task on a scale from 0 to 3 for each of six mathematical competencies. Overall, the analysis reveals high consistency in their analysis. However, the teachers and prospective teachers utilised a restricted range of the scale, rarely judging a task to demand a high level of competence. This indicates that the five teachers and prospective teachers can use the tool to identify which of the six competencies are at play in solving a task, but can only differentiate to a limited extent between tasks that demand a low level of competence and those that demand a high level. In conclusion, we propose that an item analysis tool could be useful to teachers and prospective teachers as a means of analysing and selecting appropriate tasks that enhance development of mathematical competencies.

Science Teacher Candidates’ Epistemological Beliefs and Critical Thinking Disposition

“…Students need to engage in a wide variety of activities, such as reasoning, communicating, connecting, modelling and problem-solving. Teachers should be able to identify their competence needs in activities they want to use in teaching or measuring in mathematical activities (Pettersen & Nortvedt, 2018). In this context, the targeted process skills must be reflected in an effective approach to the problem activities used for the development or measurement of ML.…”

“…In a study by Lestari, Juniati and Suwarsono (2017), the views of high school teachers towards ML, their habits in mathematics teaching, and their beliefs in integrating ML's mathematics into learning-teaching were examined. In the study conducted by Pettersen and Nortvedt (2018), teachers' and preservice teachers' competence needs in the activities were determined using an item analysis tool. Concerning competencies (communication, devising strategies, mathematization, representation, symbols and formalism, reasoning and argumentation), each of the teachers and pre-service teachers used a tool about mathematical efficiency and efficiency requirements of activities.…”

Checklist on question design for mathematical literacy

“…Teachers should be able to determine competency requirements in mathematical activities, which they want to use for teaching or measurement purposes (Pettersen & Nortvedt, 2018). In this context, targeted process skills should be reflected in an effective approach to the problem activities used for the development or measurement of ML.…”

“…Öğretmenler matematiksel etkinliklerde öğretim ya da ölçme amaçlı kullanmak istedikleri yeterlik ihtiyaçlarını belirleyebilmelidirler (Pettersen & Nortvedt, 2018). Bu bağlamda hedeflenen süreç becerileri MOY'nin gelişimi ya da ölçülmesi için kullanılan problem etkinliklerine etkili bir yaklaşım ile yansıtılmalıdır.…”

Assessment Strategies for Enhancing Students’ Mathematical Problem-solving Skills: A Review of Literature

“…Besides that, it was shown that with PAs, students developed their confidence to tackle complex mathematical problems (Novita et al, 2012). Other scholars (e.g., Pettersen, 2017) have also stressed a need for students to showcase their competencies like communicating mathematically, mathematical reasoning, and problem-solving. It has been stressed that mathematical problem-solving tasks should trigger higher-order thinking and reasoning among learners.…”