Learning Mathematics Through Achievement Learning Based Model

07 Apr

What is an Achievement Learning Based Model in Mathematics?  This is a developmental model where the student has mastery of one topic before moving onto the next topic.  In using this model, one would first need to identify your academic goals.  For most educational institutions, the academic goals is that the student learn and maintain that learning.  Currently, most school systems use a model of a set of curriculum standards, currently the Common Core standards in much of the United States for Mathematics, and students are exposed to a classroom with objectives to teach these concepts that lead to the understanding and mastery of the standards.  Students start in Kindergarten and each school year is generally broken into 4 quarters where teachers are given a pacing guide so that they can get through all the objectives needed to FINISH the standards for each grade level.  Students are given classroom assessments along the way, including possibly quarterly benchmark tests and in later grades some type of End of Year test that measures the mastery of the standards for students.

The teachers are generally not allowed much freedom in deviating from this pacing guide and required topics that they must get through since these are all prerequisites for the knowledge base students will build on during the following year.  In the early elementary years, United States students actually do fairly well overall keeping up with the pace, although, there has been much controversy over the Common Core Standards for many different reasons including political reasons, lack of testing, and pedagogical methodology.  At some point, however, students (probably almost all students at one time or another) will come across a concept, unit, or topic either in elementary school, middle school, or high school where they will get confused.  There is no time built in for teachers to realize that the class is “lost” and they need to spend longer on a specific topic.  There isn’t even the flexibility for teachers to “speed up” when topics are easy so that they can slow down later when needed.  I have seen teachers finish a unit early and just give students “free time” since they were off their pacing guide.  Teachers are not being taught about “reading” students for understanding and “how to adjust” their lessons based on individual class feedback when taking methods classes because this isn’t even allowed anymore.  Teaching is no longer an art that allows for creativity and talent and therefore all the good teachers are leaving the profession in droves.

Let’s pretend for a minute that we care about student learning as our main goal.  If we consider an Achievement Learning Based Model, we can put student achievement before our need for control, before our need for cattle car education, before our need for convenience.  An Achievement Learning Model would require more work but in the age of technology, it is so very doable.  Many schools are considering a flipped curriculum these days.  A flipped curriculum if done correctly works like this:  lessons for each unit are taped, students watch the tapes for homework and then when they come to class, they spend classtime doing active learning with a teacher available for help.  Note, this is not time when the teacher sits and grades papers or takes time off, the teacher is actively participating with the students but it allows them time to have someone help with the active learning part, working problems rather than the static part of learning, watching the lesson.

Here is how the Achievement Learning Model can be added into the flipped curriculum model.  Let’s say that you have a group of high school freshmen who are taking Common Core Math 1 or Algebra 1 (we will just refer to to it as CCM1 here.)  Students will get a goal sheet of the units they need to cover, homework needed to turn in, and assessments they need to complete.  Students will watch the lesson at home.  The next day they come into the classroom and they work on problems assigned to them.  They start with easy problems and get problems that get more difficult as they are successful.  Once they are getting enough problems correct, they move onto to the second unit.  For some students this might be one day, for other students it might take longer.  When it gets close to quiz time, the student takes a practice quiz and self corrects the quiz.  The goal is that they don’t take an assessment until they are having success with their homework and practice quizzes.  If they did well (show mastery), they take their quiz, if not, they work more problems, get more help.  Each student works at his or her own pace.  However, the teacher does oversee the pace of each student and certain requirements are placed on students who are not putting in the effort (which is different from those struggling with the content).  At school, there are after school hours in place for students to come in and continue the same “work” they would do in class.  Every student will be successful since they don’t move on until they have shown success.  The goal is 4 years of math so students “take” math every semester, where a student ends up in their knowledge base will be different for every student.   At the end of CCM1, some will have finished the course and be ready to take the final exam.  If any finish early, they will be helpers to the remaining students!  What a great way to reinforce their knowledge.  If a student does not finish, they can continue in CCM1 the next year until it is complete and move into the CCM2 whenever they finish and start there.

Bright students may have a schedule that looks like this:

Block scheduling:  (just a sample)

First Semester        Second Semester

CCM 1                            CCM2

CCM3                             Precalculus

Calc AB                         Calc BC

AP Stat                          CCM – helper



A slower student might look like this:

First Semester           Second Semester

CCM1                               CCM1

CCM1                               CCM2

CCM2                               CCM2

CCM2                               CCM3

CCM3                               CCM3


Each student takes math every semester, each student has mastery but they get to do things at the pace they need and they will know far more mathematics than our current model where many get D’s and forget what they have learned.   This model needs the following to be successful:

1.  A good teacher who is excellent at explaining the content on the videos is easy to follow steps and includes problems for the students to “practice” while watching the video that shows that the student watched and paid attention to the video.

2.  A good curriculum writer who can create good practice problems so that students can have sufficient practice until they reach mastery with problems starting easy and getting more difficult and have practice quizzes and tests for students to take so that they know when they are ready for the real exam and ready to move forward.

3.  Teacher education where teachers are taught how to manage this new type of classroom, facilitate appropriate groupings among students working on the same topics, “read” students so they know who knows what and who is confused, be able to delegate helper students from within the class to students who need help, to be able to provide the best use of their time during the regular “workshop” settings of daily education.

4.  Test to see at what age students would be mature enough to handle “self” learning, although it will be new and a great skill that students will be learning so it is expected that students will have a normal adjustment period despite maturity issues.


Written by:


Lynne Gregorio, Ph.D.


Tags: , , , , , , , , , , , , , ,

Leave a Reply