When an individual obtains and implements the skill of critically reflecting something, they will begin to understand their reality and will be redirected in the way they engage with the world (Mezirow, 1990). In education, being able to critically reflect on the day is essential to understand where mistakes occurred, whether a lesson was presented well, or in this case, whether a rubric set student’s up for success or failure. By reflecting on these things, educators will become self-aware therefore correcting flaws they may have revealed in reflection.
A rich mathematics activity was chosen, presented to a student in grade four and marked against a unique rubric to then determine a final grade. The purpose of this investigation was to demonstrate capacity to design and assess mathematical processes of problem solving, thinking, mathematical communication. This reflection will discuss the results from the critical reflection process and make recommendations for improvement and effectiveness.
This assessment task was sourced from the New Zealand Ministry of Education website (New Zealand Government, 2018). This website developed by the Government of New Zealand (2018) believe that tasks such as appendix 1, are designed to provide as engaging and rich learning experiences for the students. Fortunately, the task has directly reflected achievement standards found within the year 4 Australian Curriculum of Mathematics. This specific task linked directly with Australian Curriculum content descriptors stating ‘Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder’ , ‘Solve word problems by using number sentences involving multiplication or division where there is no remainder’ and ‘Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction’ (Australian Curriculum, Assessment and Reporting Authority, 2017).
A rich task is viewed as a problem where students are required to analyze, theorize and engage intellectually with the world around them (Grootenboer, 2009). The task at hand requires students to work out how many broken sparkles were given out within the next 500 customers at the Museum. This context immediately sparks connections between itself and the student as it relates to real life problems, encouraging higher levels of engagement. This became evident whilst the year 4 student was completing the assessment task. The student concentrated on solving the problem for the duration of time spent on completing the task. This may have been due to the task being viewed as interesting to the student. Alternate literature describes rich tasks as having the capability to incorporate varied opportunities to meet the needs of a diverse range of students (Aubusson, Burke, Schuck, Kearney, Frischknecht, 2014). The Government of New Zealand (2018) has also stated that this task in particular, is one that is able to flexibly cater for all learners within the classroom. It is agreed that with such literature as the task evidentially provides a variety of differentiation. The year 4 student undertook the task with the understanding to demonstrate his ability to utilize the appropriate multiplication and division strategies to solve the problem. Post completion of the task, questions were posed about what strategies the child had utilized and why. This forced the consideration that it is unlikely that all students would attempt to solve the problem utilizing the exact same strategies. And that all students are provided the opportunity to utilize what strategies they are most familiar with. Such tasks will allow students to both excel and/or assist students who are contemporarily struggling in obtaining a variety of multiplication and division strategies. This works cohesively with following criteria as it further assesses the appropriateness and effectiveness of strategies and number sentences.
In order to assess students on their performance with the activity, it was important that a rubric was created (Appendix 2). The creation of the rubric was done thoughtfully and in alignment with the rich math task’s Australian Curriculum content descriptors. Rubrics are an effective assessment tool used to convey effective feedback (Dannelle D. Stevens, 2013), ensure consistency in scoring and has the potential to promote learning (Anders & Gunilla, 2007). Appendix 2 shows a copy of the created rubric.
While engaging with the grade four student, the work was marked against the rubric, (Appendix 3). The student overall scored a B- for their work, holding an A, B, D and B in the rubrics criteria descriptors, (Appendix 4). When reflecting on the ‘D’ mark that the student scored, the question was asked as to whether or not the child was set up to fail for this criteria. Upon reflection, it came to attention that the student had not learnt partitioning as of then and would not until the following semester. From this recognition of a gap in the students’ knowledge, it was questioned as to whether partitioning was really a relevant and critical part of the task. An alternative to the criteria being specifically about partitioning would be to replace it with the updated rubric, see Appendix 5. The criteria now states ‘Uses a range of Mathematical concepts’, which sets up the participating students to succeed by using any concept such as multiplication, division or partitioning. A sound level only requires the use of one mathematical concept. The students work would score a ‘B’ in this new criteria.
When further reflecting on the rubric, the descriptors for the fourth column could have been written more thoughtfully. It would be recommended that it be modified to contain ‘use of basic mathematical concepts and strategies to resolve the same problem’ at a sound ‘C’ level.
Staff of the University of Exeter (2001) discuss that when reflecting, it is important to evaluate the good and the bad from an experience. Some aspects of the rubric were completed well, including the variations of the descriptions, the first two criteria and the alignment with the curriculum. While marking the students’ work, these aspects were clear and concise, contributing to the ease of effective and simple marking.
Obtaining a conceptual understanding of key mathematics principles when developing a task is essential. The Australian Curriculum (2018) views understanding, fluency, problem solving and reasoning as an integral part of mathematics content across all three strands displayed within its curriculum. The task provided in Appendix 1 has incorporated all aspects of the proficiency strands in the purpose to provide as an engaging, effective and rich assessment piece for students. However, the task was not able to cover each concept within the proficiency strands, as they are broad and cover a range of mathematical concepts. In relation to this specific task, the Australian Curriculum describes the 'understanding' proficiency strand, as students demonstrating their abilities to make connections between representation of numbers, partitioning and using appropriate language to communicate times (ACARA, 2018). The 'fluency' strand referrers to the student recalling multiplication tables to assist when solving the word problems (ACARA, 2018). 'Problem solving' is when students model and record authentic situations involving operations and formulating through their work (ACARA, 2018). Finally, 'Reasoning' is evident as the student derives strategies for unfamiliar multiplication and division tasks. All these principles were utilized as a checklist in the development of this assessment task in order to ensure it had incorporated key mathematical principles.
In the educational system, having an understanding on the importance of reflection of teaching and learning experiences within the classroom is crucial (Mezirow, 1990). It allows an educator to criticize and deepen the understanding of why specific aspects went well or poorly. This reflection has allowed the educators to do this exactly, and have reflected on how cohesive the alignment was between the Australian Curriculum, assessment task and rubric. This rich mathematics activity was scoured, developed and presented to a grade four student that was marked against a rubric to determine their achievement standard. The practical experience with the child had assisted immensely in highlighting the flaws and attributes contained within the task and how well it had reflected upon the achievement standards. This critical reflection has discussed the results of the practical experience with the student and posed recommendations for improvement within the task, and also reflected on the alignment between the rubric and task.