Pinpointing the issue at hand is of foremost importance. Is it the curriculum, is it boredom or is it simply pushing the parental boundaries? Ask your child why she is acting as she is. This may take some time, as she may not initially understand why herself. It is your job to ask the necessary questions.
Talk with your child and make sure your tone is not accusing. Ask if he is having trouble with the schoolwork or understanding a certain problem. Ask if there is a problem understanding your instruction and be willing to hear that it may be your fault. Asking your child if the work is boring will almost always result in a "yes," so instead ask if there is anything he can think of that would make his work more interesting or fun. Often engaging him in his work can turn the day around completely.
Making a few simple changes can also turn a child from defiant to calm and even cheery. Touch can make a lot of difference, a simple hand to the shoulder shows that you are there to support her. Keeping a calm voice also goes a long way. Too often, it is easy for parents to expect more from their own child, which can turn into tension and a louder tone of voice.
It isn't always rebellion, sometimes the attitude it is a cry out for change. When a child is just plain challenging authority, a different direction must be taken. The Family Education website says that "parents sometimes contribute to a defiant child's rebellion by getting the child involved in too many activities."
Everyone has a different learning style and that means that a parent's style may be different from the child's. Thus, a visual child may not react well when taught verbally, at least not all of the time. This means a child with a literal learning style may not understand lessons that use innuendo or visual pictures, while an auditory child may not pay any attention to visual diagrams. What is seemingly defiant behavior is merely a child not able to achieve a task because of the way it is presented to her.
Occasionally a child is introduced to homeschooling after having been pulled from a public school due to issues he was having. When this is the case, it is important to give the child a cooling-off period, a time to adjust to the new way things will be done. There may at first be defiance, with the child trying to control things, but patience and involvement should be introduced.
Allowing a child to make minor decisions in daily schoolwork gives a child a sense of control. When a child is involved, she feels empowered and is more likely to stay on task. Understand your child and make necessary adjustments. An active boy might need to do his spelling while walking in circles, while a tactile or visual girl may need to have math manipulatives in order to master a problem. Choose battles worth fighting, but allow for flexibility and things are likely to go smoother.