This was prompted by a discussion at the Ambleside Year 0 group, where Phyllis and Kathy were talking about MEP, the free math program, being a spiral, and Charlotte Mason's defense of the use of a mastery program for teaching math. Phyllis suggested she'd like to at one point study CM's sayings on this, and we also have to be cautious because her idea of mastery may or may not be in total harmony with that understood today by the term. She points to MEP being a CM friendly program in the use of manipulatives and the way lessons are presented.
I'm going to write about mastery versus spiral from Engelmann's point of view, and present the argument that a homeschooling setting is ideal to make our teachings guided by mastery of skills, (even if we are using a program originally designed as a spiral). When we use a program and resources as an aid and are not constrained to follow anything by the letter, such as in a classroom setting, and when combined with a precise knowledge of our children skills (if wholesome or still being formed), this will help us avoid skipping too fast from lesson to lesson without the children fully understanding and mastering of the skills previously presented. Knowing this difference between mastery and spiral will also help us when buying programs or when putting together resources.
I don't intend to give a thorough analysis of CM at this time, I may make some conjectures but take them with pins and feel free to rebuke or add information that may prove or disprove my reflections on the matter.
Allow me to start by quoting Engelmann:
When students are taught to mastery, they become smarter, acquire information faster, and develop efficient strategies for learning. Teachers must have an understanding of what mastery is and how to achieve it in their students. However, teachers cannot teach to mastery without referencing the performance of their students. In addition, teachers cannot teach to mastery without a program design that supports the approach.We have to remember he is writing to a teacher/students audience. In a classroom setting, the program the teachers are mandated to follow makes all the impact. We, at home, are free to implement what we have in the way that best fits our family needs and our principles.
Englemann proceeds to give us five reasons for the benefits of a mastery program. Then he exposes the deficiency of the spiral as follows:
Most programs do not require teaching to mastery. Teaching to mastery is a foreign practice to many experienced teachers because most programs do not require mastery. Instead of providing continuous skill development, these programs present topical or thematic units. Students will work on a particular unit for a few days and then it will be replaced by another unit that is not closely related to the first and that does not require application of the same skills and knowledge. This design, referred to as a “spiral curriculum,” is more comfortable for the program designers, teacher, and students; however, it is inferior for teaching skills and knowledge.
It is comfortable for the designers because the design does not have to be careful. The designers do not have to document that everything that is presented is “teachable”; the amount of new learning does not have to be carefully measured. The amount of time required for a “lesson” does not have to correspond precisely to a period, because the design assumes that different teachers will take different amounts of time to get through a particular “lesson” and “unit.” The amount of new material is not controlled. The expectations for student performance is low because teachers understand that students will not actually master the material. They will simply be exposed.
If the systematic program is like a stairway, the spiral curriculum is like a series of random platforms suspended on different levels. Students are mysteriously transported from one platform to another, where they remain for a few days as they are exposed to information that is not greatly prioritized. Mastery is impractical with a spiral curriculum design because many students lack the background knowledge they need to stand on a particular “platform.” The poor design relieves the program designer of assuring that earlier-taught skills and knowledge are mastered and used. The poor design also relieves students of the responsibility of learning to mastery and it relieves the teacher of teaching to mastery. It therefore promotes poor teaching and poor learning.Reading the first paragraph of this quote, one can easily infer that if this is the premise of a spiral, it wouldn't have been Miss Mason's choice. She criticized the practice of some teachers lecturing about inconexed topics, and called that 'the art of fragmentation', and a spiral program can easily lead to lessons that fit that description.
In summary, a program that teaches to mastery is like a stairway. Mastery is the guarantee that students are able to reach each stair without falling.
I believe that homeschooling parents have a way with knowing if the children grasped a concept, skill, or if they haven't mastered it yet. We don't have to move on, we don't have to present results to the principal, district, etc. We don't have to follow the approved program to teach any given subject. We can, in other words, benefit from any materials, free programs, or what we have and base our learning experience in the mastery of skills. We also know when we have to wait for more maturity, and we are constantly revising and being sure the foundation is being built.
That's what I like about living math more and more, we don't need to follow and finish any text book. Many programs repeat the lessons across the different 'grade levels', many don't present them for enough time, and there are many key mathematical points such as place value that need to be mastered to move on to other aspects such as multiplication, etc. If we provide the children with a rich mathematical experience they will be climbing the mastery ladder with confidence.