Teaching a 4 year old maths
Im 18 years old and getting to grips with advanced mathematics (pre-university) and I have a younger brother of 4 years old (quite an age gap). I want to get him interested in learning (and away from the iPad/tv), especially through maths. He hasn't formally started school, but went to a nursery where they may have taught numerics but that's about it. I have printed worksheets such as "add one to this number" kind of thing but he fails to understand. I also don't know how to convey the idea of counting. Is there a certain protocol to teaching kids of such an age mathematics, however basic? Is he too young to spend at least 10-20 mins doing some maths with me, or should I let him turn 5 and progress from school?
My aim is for him to develop a passion for maths as I currently do, and not take the subject as a burden as many people do.
thanks (sorry if this is not to be discussed on this site)
Here is how I taught my children at this age:
First, I tried to count things with them, like steps if we were walking up and down steps together, or parked cars as we walked along the footpath.
I would make up "stories" about characters they liked (e.g. Thomas the tank engine), of the form "Say there are two trucks in the yard, and Thomas brings in one more; how many trucks are in the yard now?".
I made them "number snakes" (something I learned from Joe Silverman): draw a snake on piece of paper, and break up its body (just by drawing lines) into a three of our segments. In each segment put a (very small, to begin with) number. Now your brother has to add up the numbers to see what total number the snake wants to say. It helps to be a bit theatrical about the whole thing.
One thing to remember is that at this age, even if your brother knows how to count "1, 2, 3, 4, ...", if you ask him to find $3 + 1$ (directly, or via a story or number snake), it probably won't be obvious that this is the same as just counting on one step from 3. So be patient, make the questions very easy and interesting, and don't overdo it. If you really want to do this, it has to be something of a long term project. (In particular, 10-20 minutes of studying with you may not be feasiable; going for a 10 minute walk around the neighbourhood, and using that time to incidentally count cars, or trees, or cracks in the pavement, or tell counting stories, might be better.)
You might also find this MO question helpful. I like this answer in particular.
Kids that age don't learn too well from worksheets; they're too abstract and not engaging enough. There's a huge conceptual leap between "two marbles in one hand and three in the other" and "2+3=5" that's difficult to see when you're on the other end of it. At this stage I'd focus on 'concrete' counting and visual math, like Möbius strips and Platonic solids. If you want him to get interested in math, then the flashy attention grabbing stuff like that is probably your best bet.
Physical objects and comparisons. Take objects that there are plenty of that the child is interested, I will use building blocks as an example.
Place a pile of three blocks, one at a time, in front of the child. Count each block as you place it. Don't make complex shapes with them, make the focus on the counting, not the presentation.
Create a second pile of four blocks. Count out loud again as you place them. Emphasize the new number you're adding, FOUR.
Do this again for a third pile.
Then with the child, count the first pile but stop at the number before the last block in the pile. "One," point at a block. "Two," point at the second block, then without speaking point at the third block. You may have to prompt the child.
Once the child is able to identify the number of blocks in the group, and the next number in the sequence, you can start with moving blocks from one pile to another. At this point it's all about teaching via comparison, and giving them something to put their hands on.
Did this with both of my two boys who are now going in to (US) first and second grade and they are able to handle math on 3rd and 4th grade levels respectively and have no problem with common tasks such as determining how many more of something they need or how many minutes are left between one time and the next, etc.