Mastery Over Time:

MASTERY OVER TIME: EFFECTIVE LEARNING FOR ALL!

OCTOBER 3, FEBRUARY 3, OR JUNE 3???

* One student masters graphing equations on October 3rd, just one month into the school year.

* Another student initially struggles, but masters graphing equations on February 3rd, midway through the school year.

* A third student took a bit longer and graphing equations didn't "click" for them until June 3rd, at the end of the school year.

Is the student who masters the concept sooner “smarter” than the others?

Should the student who learned the concept faster get a better grade?

When, in the course of educational evolution, did fast learning become a priority?

What systems of teaching/grading shut out students who take longer to learn from being able to access the curriculum? Are there systems of teaching that honor student variability in learning times?

Should a teacher or a grading system regard the student who shows mastery on the initial test differently from the student who shows mastery on another test two weeks later? After all, what is two weeks (or a month, or two, or three) in the grand scheme of one's educational career?

Traditionally, units in math class are wrapped up in nice, neat, tidy three week packages. A class first spends two weeks learning the concepts. Throughout the unit, assigned homework provides students with opportunities to rigorously practice those concepts. Towards the end of the unit, there are a few days of reviewing. Lastly, students are tested for mastery of those concepts. Afterwards, the class moves onto the next set of concepts for the next three weeks… Then it’s lather, rinse, repeat. The class does not typically revisit concepts until a midterm or final exam. It's about teaching a topic and then moving on.

There are several problems with this model of learning. First, students do not all learn at the same pace. A nice, neat, tidy three week package may be a workable timetable for some students, but for others, it will take prolonged, repeated exposure before they “get it.” Second, when concepts are taught as distinct, separate topics, students often do not see the connections and relationships between those concepts. Lastly, when each set of concepts is covered only one time during the year, students often go through a cycle of learning and then forgetting. They learn the concepts in the midst of the chapter, but that supposed “mastery” is lost a few weeks after the unit because there is no further practice/utilization of that concept.

We don't always recognize this, but students are human beings, not robots. Shocking, isn't it? You can’t spend three weeks programming students on a concept and then expect them to be proficient in that concept for the rest of the year without any further use or practice of the concept. Enter the learning model of “mastery over time”... Mastery over times gives students the time necessary to learn, the time for the prolonged practice necessary to learn, and the time for multiple opportunities to demonstrate mastery.

Here are the salient features of mastery over time that we employ in AMS 8th grade math:

* The curriculum "spirals": On each practice assignment, 4 out of 6 problems are review problems. Only two problems on each assignment cover the current topic. Consequently, students get many, many opportunities throughout the school year to work on concepts from throughout the course. It’s not a model of teaching a concept and then immediately moving on because the unit is over. Students learn that they are accountable for learned concepts through the end of the year. In fact, it is far more important to us that a student be proficient in concepts at the end of the year rather than midyear.

* Monthly Mastery Check-Ins: Our goal is that students will have enduring mastery of concepts that they have learned throughout the year. We're trying to avoid situations where students learn, cram, and then forget by the next unit. Our monthly Mastery Check-Ins aim to communicate to students that they are being held accountable for the material they learn not only during the chapter, but for the duration of the year. To help facilitate this, we have a monthly Mastery Check-In. The Mastery Check-Ins are always cumulative, they cover content from throughout the year. Since the practice regularly covers topics from throughout the year, students will always have regular opportunities to work on all the concepts they are responsible for. Thus, students should theoretically always be in practice and also be prepared for a Mastery Check-In. Students shouldn't necessarily need to do any extra studying for Mastery Check-Ins outside of their normal practice assignments. Now, if there are problems on practice that students don't understand, they definitely need to get those figured out. Hopefully, doing the online corrections will enable students to address any difficulties that they are having on the practice problem.

* Multiple opportunities to show mastery: On our Monthly Mastery Check-Ins, 4 out of 6 problems cover concepts from earlier in the year. Only two problems on the Mastery Check-In cover the current chapter. This ratio of problems mirror the practice assignments that students do each night. Because two-thirds of Mastery Check-In problems are from previous chapters, each concept/standard will appear on a Mastery Check-In three to five times during the school year. Students are not “let off the hook” if they fail to show mastery on a concept during a particular Mastery Check-In. Students will see the concept again and again - on practice, on subsequent Mastery Check-Ins, and on Fix-Its. This system builds in multiple opportunities for students to demonstrate mastery of each standard. It's not a situation of "one and done."

* The goal is mastery… Period: Our ultimate goal is enduring student mastery of all standards and concepts. It doesn’t matter to us at all when a student achieves that mastery. Whether it takes three weeks, three months, or until the end of the school year, this system is designed to support all students achieving mastery in all standards. For those who learn faster, the regular practice will help with retention. For those who take a longer time, each repeated exposure will allow them to take small incremental steps towards mastery. This system of learning over time honors all learners, regardless of speed of learning. Our ultimate objective in helping students achieve mastery of math standards is to produce students who can think critically and problem solve.

In this video clip below, two math teachers describe their department’s focus on student mastery of skills and knowledge over time. They have developed a curriculum that creates multiple opportunities for students to learn and review key concepts. Admittedly, these two teachers may not be the most dynamic speakers, but their philosophies and practices are very much in line with ours. Take a gander and learn more about mastery over time.