Many young children demonstrate a curiosity and interest in counting, proportion, symmetry, shapes, and patterns. Whether or not they have been formally identified as gifted, these kids tend to enjoy enhancing their math skills with workbooks, math toys, and manipulatives.
Manipulatives may include household objects such as craft sticks, marbles, and beanbag animals, or small edibles such as crackers, cookies, or hard candies. One of my children loved to “do math” with her collection of tiny toy horses! Just be aware to watch closely if the child is quite young and you use anything that may be a choking hazard. In addition (sorry for the pun!), you can purchase ready made math toys such as a set of geometric solids, a bucket balance, and counting bears. Montessori stores sell a wonderful variety of toys designed for sorting by starting letter, purpose, etc.
Beginners can simply count out objects, and as they are ready, advance to addition, subtraction, multiplication and division. Let the child set the pace, and drop the subject as soon as their interest starts to wane. Kids can classify objects, and sort by color, size, shape, etc. You can also encourage them to build designs with tangrams and pattern blocks. Dominoes and dice games such as Yahtzee help with math skills too.
Some children are ready to use workbooks sooner than others. A basic level of fine motor skills and the ability to sit still and focus on a workbook page are required for any measure of success in using a workbook with a young child. My girls started to demand workbooks when they were just two. They had very well developed fine motor skills. My boys both had fine motor delays and neither one wanted to have much to do with workbooks before age four. That was fine with me; they just learned in a different way until they were ready for the writing.
There are two workbook sets which I recommend for gifted preschool and early elementary age children. The first is Mathematical Reasoning by the Bright Minds division of the Critical Thinking Company. These large, colorful workbooks present concepts in multiple ways. The preschool book has 234 pages, while the kindergarten level has 250 pages. The font in the early grades is big and easy to read. A handy table in the front of each book tells you what National Council of Teachers of Mathematics standard each lesson addresses. So a parent or teacher can tell at a glance that pages 7,18, and 31 deal with matching, while 17, 19, and 30 cover odd and even numbers. In the grade two book, the authors talk about their approach to learning mathematical operations. They outline four stages:
1.concrete – manipulation of objects
2.semi-concrete – pictures of objects
3.semi-abstract – tally marks
4.abstract – numerals
“This cycle of stages MUST be repeated each time a new situation is encountered. While each child progresses through the stages at different rates, they all go through them. It is important to let each child progress at a natural rate.” I am not convinced that gifted kids really do go through all these steps, as it appears at times that they make intuitive leaps which don't require all the usual intermediate
stages to be mastered. But I do like the emphasis on letting kids go forward as they are ready, whether it is faster or slower than the norm.
The other series I like is Singapore Math. The Singapore series has won much acclaim from homeschoolers around the world. Their first math workbooks are known as the Earlybird set. These are labeled for kindergarten students, but gifted kids can start them earlier. The books begin with a minimal amount of writing required, as students are asked to draw connecting lines, underline, and circle. Writing actual numerals is reserved for later, following the assumption that kids will be working their way through the books for a whole school year, and will become more proficient at writing as the months pass. Singapore workbooks are available in a US edition, so money problems utilize American currency. These also have reference charts in the front which relate particular lessons to mathematical concepts.