"Because I felt like it" isn't going to cut it here--I think a coherent answer is in order.
Anyone who has heard me give presentations on math during the past eight years knows that I line up behind the scholars and educators who believe that we are harming our children when we push them into formal academics at an early age: Dr. Raymond Moore, Dr. Peter Gray, the researchers behind
"Too Much Too Soon" (England) and Finnish educators are some of the more prominent ones. A quote from each of these follows:
- In addition to our basic research at Stanford and the University of Colorado Medical School, we analyzed over 8000 studies of children's senses, brain, cognition, socialization, etc., and are certain that no replicable evidence exists for rushing children into formal study at home or school before 8 or 10.
- It is generally a waste of time, and often harmful, to teach academic skills to children who have not yet developed the requisite motivational and intellectual foundations. Children who haven’t acquired a reason to read or a sense of its value will have little motivation to learn the academic skills associated with reading and little understanding of those skills. Similarly, children who haven’t acquired an understanding of numbers and how they are useful may learn the procedure for, say, addition, but that procedure will have little or no meaning to them.
- There are several strands of evidence which all point towards the importance of play in young children’s development, and the value of an extended period of playful learning before the start of formal schooling. These arise from anthropological, psychological, neuroscientific and educational studies.... Early introduction of formal learning approaches to literacy does not improve children’s reading development, and may be damaging. By the age of 11 there was no difference in reading ability level between the two groups, but the children who started at 5 developed less positive attitudes to reading, and showed poorer text comprehension than those children who had started later.
- Finland has a history of producing the highest global test scores in the Western world, as well as a trophy case full of other recent No. 1 global rankings, including most literate nation.
In Finland, children don't receive formal academic training until the age of seven.... School hours are short and homework is generally light.
Unlike in the United States, where many schools are slashing recess, schoolchildren in Finland have a mandatory 15-minute outdoor free-play break every hour of every day. Fresh air, nature and regular physical activity breaks are considered engines of learning.
So, a math book for 4-year-olds? In light of the evidence, isn't that "Inconceivable!"? Not if two factors are present: high interest, and low stress. If you start with magical creatures who play around with math concepts, many children will want to try the activities out for themselves. The math in the book is open-ended, meaning that there are questions to think about and explore, but no answers are demanded. Children play with an activity in order to encourage vague thinking about the topic, which will allow them to do precise thinking about it down the road. But there is no pressure to do so--no consequences or punishments, and the rewards are intrinsic to what they themselves accomplish.
Here's a quote from the introduction of the book:
Math for young children is typically focused on solving arithmetic problems. But arithmetic is just one small part of the fascinating field of number theory, and number theory is just a small area of the vast subject of mathematics. Introducing children to the more interesting parts of math at an early age expands the scope of what they have to think about in quiet moments, which is when learning is internalized.
And thinking, not the accumulation of facts, is the goal of math education. In a day when calculators are everywhere, we must focus on the essence of mathematics: thinking through a complex scenario, pulling out the right facts, and applying logic to them. As G.K. Chesterson said, “It isn’t that they cannot see the solution. It is that they cannot see the problem.” Encouraging children to explore open-ended math questions can help them become creative and unintimidated when approaching new math topics. Unfortunately, as a society we have come to believe that cramming arithmetic facts into children’s heads at ever-younger ages leads to success in math. It may indeed lead to higher test scores in the short term, but “memorize-test-forget” takes the place of true understanding and internalization of useful and useable knowledge.
So let’s get rid of math “tunnel vision” and replace it with a focus on nurturing broad and flexible thinking skills. The math facts will then grow naturally out of the logic and number sense that the child has acquired, and the tests will take care of themselves.
When children grow interested in a topic, and learn it because they choose to do so, it isn't "schoolwork" or even "academics." It is simply play. It will look different as they grow--play for my 23-year-old looks like reading, writing, and creating art at a university--and some forms of play may be discarded (I hope the 4-year-old doesn't ever need the skills he built up today during the 30 minutes he spent fighting invisible ninjas). And though I wouldn't dream of interrupting the ninja battle, there ARE 23.5 other hours during the day when I can say, "Do you want to read a story and play a game with Mommy?"
Why do I think that's important? Because of this, which I'll repeat: Introducing children to the more interesting parts of math at an early age expands the scope of what they have to think about in quiet moments, which is when learning is internalized. I hope that my children will continue through their lives to have a love of play, which started when they were born and wasn't unnaturally interrupted at age five by seven hours per day of kindergarten attendance.