My area of expertise is really in the preschool and lower primary. I am afraid I am not able to help you here at the current moment as I have been concentrating only on those age levels.

May I hazard a guess and suggest you approach your daughter’s school’s vice principal (both of whom are trained in maths) for support. The older VP is really very good with explaining the workings with maths. She also used to teach the upper levels.
I do feel for you which is why I work very hard to ensure children are well prepared in the lower levels so that they do not come to this state handicapped. If you have any specific question, I can try to find solutions from my friends on my end. That’s the best I can suggest for now.

Well, good news. It’s not just a concept. It’s something I have been doing for the past thirty yeas - teaching teachers and parents how to help their children with maths. I shall try to share some basic ideas that parents can try with their children. To start with, children should be given lots of experiences speaking about numbers and developing their own number sense. Number sense can only be developed when children have many opportunities to interact in their daily life experiences when they guess, compare, estimate and find ways to confirm their guesses about quantity or size. Parents need to be ready to give their children loads of chances to make mistakes and discover their own learning - it is most vital (IMPORTANT) not to expect perfection from the very beginning but to allow for guesses, trial and error so that the child dares to learn. When we "teach" we often squash children’s instincts to learn and experiment.

The big ideas about early maths is being able to match, sort, group, classify and compare similarities / differences between objects and numbers of items. Symbols like + (plus) - (minus) = (equal) and even numerals like 5 (five) are abstract concepts that need to be tied to concert concepts to help children make the transition from hands-on learning experiences to abstract symbolic representation of that concrete experience. The failure of adults in helping children achieve this transition is often one recurrent problems. The next is the issue is the embedding children into rigid processes. Eg that when you see the symbol + (plus) you add and when you see the symbol - (minus) you deduct. That is not always the action to take. Therefore helping children understand the concept behind adding and subtracting and translating English language statements (problem sums) into math language (number sentences) is extremely important. Most importantly, giving children a chance to enjoy and love maths is still the key to good math performance.

I believe that children should have a good foundation in math language and concepts in their preschool years. It is my mission to change how math is taught to our children between 3 and 12 (the specific of what math is, how children learn and how it should be taught.) Children often "under-perform" in maths because they are passive recipients of ready-made concepts. They are not guided to discover their own math understanding and acquire a personal "tool-kit" to deal with more complex problems. Children need to be given the opportunity to make math meaningful to themselves instead of learning by rote meaningless drills and activities. Peggy