In a Montessori classroom, the main interaction is between the child and the materials, not the teacher and the children. At first, the teacher demonstrates to the children the proper use of each set of materials. Then, the child can take the materials out, place them on a mat, and use them as the teacher taught her. When she is finished, she puts it away before starting another project. The emphasis is on self-directed learning. Once the teacher has demonstrated the use of the materials, children work on them individually or in small groups. With this level of individualized instruction, children with learning delays or who are gifted often do well in a Montessori classroom. The materials used in a Montessori classroom are built around three areas. 1) Practical life skills (folding shirts, tying shoelaces); 2) Sensory (handling geometric shapes, putting blocks into the right holes) and; 3) Language and mathematics (handling sandpaper letters and numbers, counting beads on a long chain). As you can imagine, children learn a great deal with this curriculum - numbers, letters, adding, subtracting, practical life skills, information and more. The Montessori classroom is usually very bright, warm and inviting. There are usually several learning centers where children can explore via hands-on, tactile materials.
Most volumes begin with an explanation of basic arithmetic operations namely: addition, subtraction, multiplication, and division. Reference tables are supplied to provide clues for quick mental arithmetic and mastery of math facts. When ready to be tested, the student can select a drill, which has 10 questions and are selected from a database of number pairs for calculation. The Basic Level volumes use simple single digit numbers and the interactive math software at the Advanced Level uses mostly double digit numbers for math practice problems. Each drill is then scored and timed with the results saved. With the test records, students can follow their own progress and adults who may be supervising can monitor progress and assess if there are any learning issues that require intervention. Moreover, some math software programs are available also in different languages such as Spanish and French. There are also those with a Learning Management System (LMS) that automatically tracks students test scores and provides the teacher with a database to sort and print as needed.
Here, there is no pre-planned curriculum that kids follow. Since teachers are following the children`s lead, what kids learn from year to year and between the morning and afternoon sessions may be different. Children work at their own pace, learning through play. The interaction is between the children as opposed to between the children and the materials (as with Montessori). At no prescribed points are children expected to learn any particular skill. In fact, specific learning through teaching is frowned upon. This explains why my daughter didn`t have a "unit" on shapes - This just wasn`t done in a progressive school. Social interaction between children is very important in a progressive classroom. There is much talk about "community." Separation between child and parent is seen as a major developmental step and a lot of time and energy is spent on this. The atmosphere is informal. Kids often call teachers by their first names and you would never find uniforms in such programs. The school is usually more relaxed about when a child should be toilet trained.