As teachers, we are entrusted to work with students of different ages, genders, cultures, experiences, learning styles, and learning experiences. For many years, these influencing variables have not played a role in what the mathematics learning experience looked like for each student. The lessons were taught in vacuums of segmentation where the only variable was the concept itself. For the majority of classrooms, mathematics learning was simplified to teaching concepts one way for everyone and having students fit into that conceptual framework. In a presentation excerpt entitled "Changing Education Paradigms", Sir Ken Robinson spoke of student creativity and how the pedagogical methods of years past are not effective anymore for the current and future education system. Sir Robinson is very clear that individuality in learning strengths and learning styles needs to be harnessed in order to fuel student creative thinking. As educators, we need to learn from students how they learn best and harness the schema and context of their understanding in order to facilitate students building connections, awareness, and new learnings of the world around them that is authentic, meaningful, and inveterate. This can only be accomplished through a student centred mathematics program that is open and receptive to using assessment for learning, as learning, and of learning to inform instructional strategies.
In discussing assessment, it is imperative to make distinctive the separation from evaluation. Assessment is the process and tools used to gather information about student learning for the purpose of illuminating thinking, reasoning, and/or misconceptions that will provide the information for descriptive feedback to support the student in meeting the learning intentions. Evaluation is the use of assessment data to make a judgement about student learning at the end of a course of study that will be reported as a level of performance based on ministry expectations.
Effectively individualizing the learning experience in mathematics uses diagnostic tools to gather information that will illuminate student learning on similar concepts from the previous year. Diagnostic assessment tools can also describe how a student learns, reasons, and communicates mathematically. Detailed information gathered can be used to better support differentiation of the learning experience through the use of appropriate accommodations (multiple entry points, parallel tasks, ELL support, contextual relevance problems) and scaffolding. As the learning progresses through the 3 Part Lesson, formative ongoing assessment continues to monitor student thinking and reasoning as they work in pairs or small groups to collaborate in solving problems. The tools chosen to monitor the learning will present information in order to provide descriptive feedback to broaden and deepen the learning experience. In checking in on student learning of new concepts, teachers can use instructional rubrics, checklists, and/or success criteria (a combination can work as well) that are clear to the students as to their performance in the learning categories. The students can also be part of writing these tools that will make the tool more meaningful when used for teacher assessment and student self assessment (reflection). Continuing with self assessment, reflection through well placed questions and prompts will model for and support students in thinking about their learning and how they are learning (metacognition). This is also part of the learning experience at the end of the 3 Part Lesson where students share the strategies and reasoning that encompass their solutions. This assessment as learning (some choices include Bansho, Math Congress, and Gallery Walk) is very powerful as it teaches students how to self assess and gauge their own learning building their responsibility and accountability. At the end of the lesson, the learning continues to be monitored using assessment of learning tools (performance task, independent problem solving, etc.) where the purpose of the assessment is to determine how effective the learning experience was in relation to the learning intentions (based on ministry expectations). This summative assessment will also be used to inform teaching as it will illustrate next steps that are needed in order to clarify any misconceptions or bridge gaps in learning leading into the next lesson.
Throughout the different forms of assessment (diagnostic, ongoing formative, and summative), the teacher needs to be selective in differentiating the tool used for assessment. We are aware how unique our learners are and the schema within which they function daily can present difficulties in performing via certain assessment tools. It is imperative that the teacher use their understanding of the learner to match the most effective assessment tool that will provide the necessary information to delineate the selection of teaching strategies that will guide the student in meeting the learning intentions (e.g., some students may not verbalize their thinking as well as writing or using illustrations/manipulatives/ICT while this may be the opposite for others).
Teacher's are excellent at capturing the learning opportunity as it surfaces, but assessment can be more effective when planned for from the beginning. Knowing the student through diagnostic assessment can better inform the selection of the assessment tool to check in on the learning. As well, knowing the learning intentions of the Unit and lessons also prompts building the summative assessment in order to keep students focused in meeting the learning intentions. This planning with the end in mind becomes an organic structure that is built for success by having checks built in that will help adapt the learning experience. When students reach the summative task, the scaffolded individualized learning experience will have prepared students for success. Assessment planed and embedded throughout the 3 Part Lesson will ensure a successful learning experience for students and teachers.
In wrapping up my thoughts on assessment in mathematics, I'd like to underscore the necessity to include parents into the classroom. It is imperative that parents and the community are aware of the mathematical learning environment. Students do not learn in isolation outside of the real world. The purpose of the learning experience is to support students making meaning of the world around them in a way that is authentic and individualized to their learning dynamic. We need to share the vision of mathematics with parents and foster a learning community beyond the classroom. Having the home aware of how their child as a learner will support parents continuing the learning in similar ways at home and supporting the problem solving model. We need to demonstrate how we use assessment to support developing skills in the 4 categories of the achievement chart and how they connect to the learning skills.
