The key approach to Montessori is flexibility based on the needs, knowledge and interests of the child. Even the order of activities can vary depending on your child. Lessons and activities can be adapted for individual needs of children. Montessori takes into account that every child is unique and learns in different ways. Montessori lessons and equipment are adaptable for individual teaching.
Sometimes a child will be introduced to the pink tower but is able to use it quickly and easily without any or much instruction. The child has passed this sensitive period and doing the activity won't have much benefit. It's best to move on to other activities instead of forcing the child to do it a certain way. When the child is bored with an activity it can be a sign that it's best to move on.
On the other hand, children who have difficulty with the pink tower can be introduced to every other cube. Doing five cubes with bigger differences in size is a great way to help your child succeed.
Children can go through activities very quickly if they know the underlying principle. This isn't a bad thing, but something we have to be aware of as we tailor the activities and environment for each child.
Reading is another example of a skill that can be tailored to a specific child and their development. A lot of reading becomes 'intuitive' with practice. It becomes a word recognition task based on memory. It's very important to expose children to many examples so they can memorize the rules and exceptions. Repeating words and practice helps with this type of reading. Reading software or text-based computer games can helpful for children as they learn to read.
We adapt the lessons for each child at their particular level, not always going through a firmly set sequence. The sequence is only a guide. The order for the equipment can be modified depending on the interests and abilities of the child.
Keeping this in mind, we can integrate other curricula, techniques and manipulatives into a Montessori approach, everything from programming to adaptations for specific native languages.
Children sometimes may not be interested in math or a specific part of math. Montessori math has lovely beads and hands-on equipment that make it very appealing. An example of this is the golden bead material. It's is very attractive and you can teach the four operations of math with it, base 10 (decimal system), counting and numeral recognition. The Montessori math equipment can be adapted especiallly for visual learners.
The Montessori environment is prepared and regulated to allow for growth. We can't always predict which way a child grows or when this growth will occur. The principle is to guide development from concrete to abstract, following the lead of the interest and ability of the students.