*Collecting thoughts and ideas to foster mathematical learning and mathematical amusement. *

**B>0 (BE POSITIVE!)**You can keep a positive attitude towards mathematics, to help your kid. What does this mean? Imagine it is all about reading instead. Reading helps in real life on a daily basis, and it is necessary for most jobs. Being an extremely fast reader is not necessary though, although it can be nice to possess this ability. If you read slowly, then there is no need to say it (but if you say it, then you can add that you wish you could read a bit faster, and that you hope that your kid will be faster than you some day).**TAKE TIME TOGETHER:**It makes a huge difference if your kid can experience some easy mathematics with caring adults. If you think about reading, nobody is expected to learn on its own how to read. And the more reading becomes an activity made together, then the more it becomes pleasant. There is no daily amount of reading that is recommended by a doctor though, and you can also keep an eye on and respect the kid's daily preferences. Indeed, you would not consider reading just to be a medicine to be swallowed, so although you can try to insist a bit, then you would stop if your kid really wants to do something else. Keep in mind also the trick of changing person: maybe one kid prefers to read (for whatever uncomprehensible reasons) more with one parent or relative than with others.**PEN AND PAPER:**Experiencing sets and learning counting (or, later, learning the multiplication tables) does not require a lab. Everyday objects can help, for example the coins from your wallet. Of course be 100% sure that your kid only has material that is safe to be played with, or that not totally safe material is used only under strict surveillance at all times and with no exception. This being said, to help your children learn reading, you would buy some or many colorful books (according to your budget and your inclination). And at the end of the day there is no book that is the absolute best: your kid may favour a specific one, and that's the book you need. Of course, you would go for some variation if possible, but not really against your kid's will.

This being said, I now present some toys that you can buy (or lend, or share..) if you like them: your kid may like some of them, expecially if everything is kept playful (and if for example the kid decides how long or when to play). The opinions and recommendations are my own, and in general you should try to follow your kid's inclinations and your gut feeling as a parent. If nothing is imposed, then nothing can go really bad: a kid likes presents and colorful stuff, and the worse that it can get is that the toy is not appreciated (if this does not bother you with other kind of toys because it can be a matter of luck, then it should not bother you with mathematical toys as well). Most toys can be used for several kids, and can be sold or given away when not needed anymore. Last but not least you can consider some of these toys as cool presents for a birth or a birthday.

- Some variants only have three shapes, namely circle, triangle and square.
- Check the parents' recommendations of the toy, because it happens with some versions that a shape fits more than one hole. This is very inconvenient if the kid finds out.
- A variant of this game consists in placing the solids onto a frame rather than inside a box. To vary the toys I recommend the box (for puzzles on a frame animals and numbers are more interesting).

- I recommend a version having for example 8 fishes below the number 8: not only this gives a surprise effect, but it also helps associating a number to a set having that number of elements.
- My favourite is a version with the numbers from 0 to 9 instead, not only because these are precisely all the digits, but also because kids have an occasion to learn the number 0 (and they easily see that zero corresponds to nothing).

- Keep it simple with two pieces! Some puzzles have three or more pieces because they also show some dice with the corresponding number of dots, or hands displaying the correct amount of fingers. The dice cards are not bad, but it is better to put them away until the kid is at ease with associating numbers and sets. The hands cards are in my opinion ugly and unnecessary.
- The first game is associating numbers to sets. The second game is ordering the number puzzles by placing the displayed numbers in increasing order.
- I particularly liked a version in which the cards were quite small, perfect for the small hands of a kid.

- Anything is allowed to play with sets (strictly mathematically speaking, one is playing with multisets as soon as some elements are indistinguishable). The sets are distinguished by characterizing properties (the color, the kind of animal, and so on).
- If one plays with sets with few elements, then one can also practice numbers and counting.
- Be open to the toys that you find: if you like them (didactically and aesthetically), then you will be happy to play with your kid. And your kid may like them too. But if you don't believe in something, then of course nothing is strictly necessary. For example some parents like to have many small colorful bears and colorful cups for the counting/sorting game, and that's totally OK.

- You can count the numbers while going up. When your kid is confident enough with the number sequence, you can count numbers backwards by going downwards.
- You can experience additions and subtractions by letting your kid for example mount two steps or go down two steps. In the same way, you can make your kid discover even and odd numbers.
- I recommend starting with the number sticker (or the number card) zero placed on the floor in front of the first step.

- You can practice counting and explore equalities and inequalities with a weight scale with two plates and many small identical objects.
- I like a version where there are numbers as objects: they weigh proportionally to their value, and you have further identical objects weighing like the number 1. It is very easy to explore addition and subtraction (only the correct number on the plate will give balance).
- By having different sets of objects with appropriate weights, one could explore some easy equations. By having weights corresponding to the powers of 2 and 3 one could explore the numeral bases 2 and 3 (working with base 10 is possible but the numbers up to 20 show less variation in basis 10 w.r.t. basis 2 and 3).

This page is a long-term work-in-progress dedicated to learning material that can be used beyond school.

The recommendations are of mathematical and didactical nature.

The images are needed for the explanations (and the displayed products are advertised for free).

Do you have items to recommend? Please contact the author: antonella.perucca@uni.lu