Having your children keep a garden journal is great for language, science, math, and fun! You can use anything for the journal itself. I like the art notebooks that are sold in craft stores. They are thick and sturdy and the unlined pages lend to drawing, keeping photos, etc. Spiral binding makes it easy to use.
When your child plants something, (s)he can start a record in the journal, keeping jots of what was planted (maybe paste in the empty seed packet or a picture of the plant from a garden magazine, or have your child draw it.) Make note of the date planted, the date sprouted, when it was transplanted, fertilized, appearance of blooms, harvest dates, observations. Making a growth chart is fun and great for math. You may also want to record where you got the seeds/plants and how much they cost.
As for general notes, your child can make a monthly weather graph. Have your child paste in seed packets, photos, or drawings of plants. You can record recipes for the types of produce you grow. Have your child draw a garden plan in the book when you're getting started. You can add a wish list for future gardening, pressed blooms, inspirational notes/quotes on gardening, and gardening websites you like.
Let your child make the garden journal his/her own, but also help him/her to keep it neat and organized.
Keeping a gardening journal each year will improve your gardening, because it allows you to look back and see what worked and what didn't, how the weather affected things and what typical weather seems to be for your area. It is also a great way to bring in extra math, science, language, and even art into your child's gardening endeavors!