Mastery (Part 1)

Mastery

The mastery approach allows students to work through material at their own pace.

Students will learn a concept/topic then when they are ready, they take an assessment on that concept.  If they earn 80% or above on that concept, they move on to the next concept and repeat.  If they scored less than 80% on the assessment, they need to go back and relearn the material and try the assessment again.  Homework is not part of the grade, and students view it as a tool to learn the concepts.  There are a couple of types of mastery.  The first is true mastery, and the second is practical mastery.

True Mastery

True mastery is the same as what is described above.  Students are given as much time as they need to get through the material.   A few students may only need half a year to get through a full year long course then they can either move on to the next math class or take an elective.  Most students will finish the year long course in a year while a few students may need to 1.5 years to mastery all the concepts in a course.  With true mastery it is easy for a math teacher to have several math “classes” throughout the day, but within each math “class” they have students in Algebra 1, Geometry, Algebra 2, and maybe even Pre-Calculus.   There is no need to have separate homogeneous classes since students are all working at their own pace.  Students just need a place to work on mathematics, and a teacher who can help them when they have questions, need an assessment, or need an assessment graded.  The Algebros (led by Spencer Bean spencer.bean@eu.dodea.edu , Michael Brust michael.brust@eu.dodea.edu , Timothy Kelly tim.kelly@eu.dodea.edu , and Corey Sullivan corey.sullivan@eu.dodea.edu , who all teach in different US Department of Defense schools in Germany) for the most part use this approach.  Their web site is http://www.flippedmath.com/.  One difference from true mastery that the Algebros implement is that students who do not complete a yearlong course by the end of the year are required to attend summer school to get caught up.

Practical Mastery

Practical mastery is what the Byron High School mathematics department use and what a lot of schools use.  The true mastery does not work for a lot of schools because of either required seat time and/or limitations of the individual school’s master schedule (See note below for more details on why true mastery does not work in most schools).  

With practical mastery there is a set test date by which all students must take the unit test.  This is beneficial for most students since they are more motivated to get concepts completed when there is a deadline.  We give our students a recommended schedule they should follow for when they should be taking each mastery quiz for the unit.  Students who get behind sometimes need extra motivation while others need extra help from the teacher or just more time on particular topics.

Flipped Learning and Mastery (True Mastery or Practical Mastery) work well together.  Flipped Mastery starts with students watching the video and taking notes on a concept followed by practicing problems.  Once they feel confident they know the material from doing a self-check they take a mastery quiz.  Depending on how the students do on the mastery quiz they will either move onto the next section or go back and relearn the material.

Visti troyfaulkner.com  and select Mastery Learning for for more information.

Solving Absolute Value Equations and Inequalities from a Graphical and Algebraic Point of View.

Solving Absolute Value Equations and Inequalities from a Graphical and Algebraic Point of View.

I have struggled with helping my students understand how to solve absolute value equations and inequalities with only one variable like |2x – 8| = 4, |2x – 8| > 4, or |2x – 8| < 4.  Some of my students in the past have understood it while others have not.  Most of the time they forget or do not understand to solve half the problem.  The will solve the 2x – 8 = 4 or    2x – 8 > 4 but not the other halves of those two problems or they do not understand when to use a compound inequalities versus two separate inequalities separated by an “or” statement. 

I started my lesson from scratch and approached the material from a graphical and algebraic point of view.  You can access my video lesson at    https://youtu.be/oSmeu3cwsfY

Below is an overview of the approach I took with more details in the video. https://youtu.be/oSmeu3cwsfY

Solve |2x – 8| = 4 by graphing

 Use the above picture and solutions to help students see the solutions for |2x – 8| > 4, and |2x – 8| < 4. 

 I follow this with the details of how the algebraic method ties into the graphical and how to get the solutions algebraically.

 

 

 

 Tying in more than one perspective in our lessons will help students better understand and make more connections with the mathematical concepts we are trying to help them learn.  It is not easy to make many of these connections.  It takes lot of time to think and reflection plus time to design an effective lesson but it is well worth it since it helps our students learn. 

The Power of "C" for Correct.

I have my students do “Check for Understanding” worksheets at the beginning of my flipped class.  These worksheets are typically 3 to 5 questions covering the basics of the lesson they watched before class.  Having students complete these problems provides many interactions between the students and me to make sure they do understand the material.  If they do not understand then I can work with them and help them learn the material.   For students who are shy or quiet these worksheets provide opportunities to really know what they understand.  

Students are expected to complete these problems and have me check their work before starting their normal assignment.  I am surprised at the power of me putting a “C” for correct on their problems even for my juniors and seniors in high school.  Many students won’t start their daily assignments until they have a “C” on each problem of their “Check for Understanding” worksheet even if I tell them that their problems are all correct.  They want that “C” on every problem. (see image)

Last spring I had some students whose goal was to get the “Big C” which was one big “C” on the whole page indicating that all the problems were correct.  (see image)

 

 

I surprised one of my students who often get the “Big C”.  One day I did not give him his normal “Big C”, I supersized it by taping eight more pieces of paper around his page making it a 3 by 3 big page then I put one “Mega C” on it.  (see image)  He loved it and took it home.  The “Mega C” has been hanging on his parents refrigerator for months.

Some of my students from this last fall heard about that students “Mega C”.  They decided that they wanted to beat that students “Mega C”.  So everyday they would do their “Check for Understanding” worksheets and they wanted me to check their work and answers but they did not allow me to put any “C’s” on their pages.  They had a plan to make a supersized “Mega C”.  At the end of the semester they taped all their worksheets together into a 12 by 12 page and had me paint one huge “C” on it.

 

I am surprised that something as simple as putting a “C” for correct on a problem for a student will motivate them to work hard.  Even a this simple “C” motivates my juniors and seniors to go above and beyond what is expected.  Look for ways you can motivate your students to succeed as you check for understanding or learning of your content.