- Students are asked to complete short, focused assessment tasks aimed at probing their knowledge and understanding of particular sets of concepts. Their responses provide a diagnostic tool, exposing thinking and comprehension of the subject matter. The tasks are easy for teachers to administer, and this approach does not pressure students to get the correct answer, yet the information that can be gained is invaluable to gauge the student's progress.
- The probing tasks provide a means for identifying the learning needs of particular students, particularly those deemed at risk of lagging behind the general cohort. Unlike general assessment, this approach provides information about a student's learning difficulties in a more in-depth and targeted manner, which enables teachers to better address the specific needs of the student.
- Students bring to the classroom their pre-existing knowledge, ideas and ways of understanding, and these factors influence their learning of new concepts and information. Teachers who are familiar with these preconceptions can tailor their teaching to address how students are already thinking, thereby facilitating learning and understanding. By drawing students' attention to their own misunderstandings and misconceptions, teachers can develop students' self-awareness of their own way thinking and transform mindsets that form barriers to learning.
- Misunderstandings about certain mathematical concepts are common across all grade levels. For example, it is not unusual for students to lack a conceptual understanding of the differing magnitudes of certain numbers, with many seeing 1 million as the halfway point to 1 billion. Adding fractions is another area of common misunderstanding, with many students adding both the numerators and denominators. Another example relates to decimal fractions, with many students writing a number like 5.5 as 5.05 or 2.35 as 2.3½. As students progress through school and more complex mathematics involving geometry and algebra is introduced, common misunderstandings also become even more complex in nature, but addressing any learning issues as early as possible goes a long way to reducing such problems in the long run.
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