It makes sense to start from where learners are, but where exactly 'are' learners, and what do you do if they are all in very different places?
If taken too seriously, the slogan ‘start from where learners are’ requires detailed knowledge of what learners have mastered, experienced, and seen go by previously [
See-Experience–Master].
Starting by assuming ideas learners have never seen before is probably ineffective. If you give them a test and then build only on what you know they have automated and internalised may result in lessons which go over old ground and so do not catch the imagination of learners.
Asking learners about a topic perhaps by asking them to write everything they know about it on a poster (and perhaps challenge them to include what they think was the "hardest" thing) can be a useful technique that will give you information without the fear factor of a formal test whilst allowing all your learners to engage in a positive activity at their current level of knowledge and understanding. It may be particularly useful if you ask learners to work in pairs for this activity so that they can remind each other of things they may have forgotten or even be introduced to new ideas they have not come across before.
Over time you build up a sense of what learners recall and have access to, without having to conduct detailed tests. Indeed, tests may not reveal what learners have access to, but only what they manage to do at a particular time. But it is all too easy to make unwarranted assumptions about what learners ‘cannot do’ based on what they do not do.
The Realistic Mathematics Project initiated by the Freudenthal Institute in the Netherlands takes the view that mathematical ideas are a response to phenomena, and are used to make sense of those phenomena. Sometimes those phenomena are based in the material world of learners’ experience (forming shadows, scaling human proportions up to giants and down to miniature people, comparing sizes of objects, etc.); sometimes they are based on experiences which learners have not actually had, but can imagine having [Imaging & Expressing]; sometimes they are based on mathematical phenomena such as patterns and structure within numbers and geometry.
No matter how carefully described, any governmental curriculum is likely to include overlaps (whether intentionally as part of spiral learning, or unintentionally due to differences between schools or between previous learner attainment). It is well worthwhile therefore to consult with colleagues teaching both younger and older learners about the concepts being taught and the ways in which those concepts have been or will be encountered. [Curricular Alignment]