Common Core Math Example

Common Core Math: Trying to Make Sense of It

By Ruth Kaercher,  Math Department, Libertas Christian School

Common Core is a reality in our Michigan schools.  So, what is the big deal with Common Core math?  What are the standards?  Should we as a Christian school embrace them?  Will our students be able to compete with students of public schools if we opt not to go by the standards?  Will our children do well on standardized testing if we use curriculum that does not support Common Core math?

These are weighty questions that do need answers.  After doing much research on the topic, I would like to give a summary of what I found to be true.  Much of my research is taken from the website, truthinamericaneducation.com.  Many articles are posted on this website by credentialed education specialists, teachers, and college professors. This is a summary of what I found.  I would encourage anyone who has questions to look into this matter himself.

First, how are the standards of Common Core math different from traditional math?  In trying to compete in a global market, government officials and educational specialists worked together to try to form a set of standards that they believed would help our children achieve at the level of many progressive countries.  Many students in the US score below their global counterparts in standardized testing.  So, they developed a list of standards that all schools should follow in order to help their students gain a better understanding of math concepts and functions.  Common Core is not a curriculum; it is merely a set of standards.

This sounds great on paper.  However, upon examining these standards many are worried about the long-term effects if implemented by schools across the US.  Here are some of the concerns:

  • From the youngest ages, Common Core seeks for students to have a conceptual understanding of numbers.  This comes, however, before a mastery of basic skills has been met.  This leads to delays in students being able to compute answers correctly.  Math becomes complicated in their minds and makes no sense. 
  • An “inquiry” model of learning is used to teach math in the elementary grades.  It is “student-centered” as teachers facilitate math discussions.  The goal is that students “discover” how math works without being told how to do it by the teachers.  This leads to frustration for many students as the “blind are leading the blind”.
  • There is a de-emphasis on math skills and memorization.  This leads to many students graduating from elementary school without having memorized their facts tables.  They become calculator dependent and poor math students at the upper levels.
  • At the youngest level, very cumbersome methods of solving math are used.  Instead of teaching straight-forward addition, subtraction, multiplication, and division, they are taught long, difficult methods of solving simple problems.  Parents and students alike spend hours at night trying to decipher “how” to do math when simple methods abound.
  • Because of the emphasis of conceptual math, students are delayed in using traditional methods of solving math problems.  So, two and three digit addition and subtraction is not introduced until 4th grade, two and three digit multiplication in 5th, and long division in 6th grade.  This is two years behind the standards of most progressive countries.  In the long run, this delays the upper level math of Algebra, Geometry, and Algebra 2 by two years as well for the average student.
  • There is an emphasis on being able to write explanations of how math is solved.  This takes the emphasis from actually solving math problems to trying to explain how a math problem would be solved.  And many times, students must do both on their assignments at the elementary level.  Therefore, the problem sets are small, students do not do enough practice solving basic math problems, and students have high levels of frustration trying to put into words something that their mind cannot fully grasp yet.

In looking at all these points, one overarching problem emerges: students are being asked to do math in a way that they are not developmentally and cognitively ready to do.  This leads to student and parent frustration, low success rates, poor basic math skills, and little interest in higher levels of math.  Students who previously had A’s in math are now struggling to receive C’s.  The testimony of this is overwhelming on the internet. 

Based on this research, what is the response of Libertas Christian Schools in its math department?  First, we establish that we want to serve our students in a way that is developmentally correct.  The classical approach to education recognizes that at the elementary level (K-6), students absorb basic skills and facts easily.  This is a time to really drill into them what they need to know.  Many times we can give brief, concise explanations of “how” the methods of addition, subtraction, multiplication, division, fractions, percents, and decimals (among others) work without burdening students to have to repeat those conceptual understandings.  Most students will have “aha” moments in upper level math when all their elementary math begins to come together.

At the middle school and high school level, once the basic math skills are learned, we then attempt to pull all these concepts together and teach more abstract ideas in Algebra 1 and 2, Geometry, PreCalculus and Calculus.  We have more of an emphasis on word problems which apply concepts we learn.  We ask students to give verbal explanations of what they do (generally at the board demonstrating to the class “how” to do a problem).  We teach and test them at a developmentally appropriate level.  This also follows the classical model of education that at these levels students can speak, read, and write about the subject matter in a logical way.

Below is a summary of some changes we are currently working on:

  • We are developing a clear, logical, and age-appropriate scope and sequence for our math in grades K-12.  Teachers will know what new content is to be mastered each year and which concepts are reviewed from previous years.
  • An emphasis will be placed on mastery of basic skills at the elementary level.  The new curriculum we will be using contains lots of review practice so that students will naturally master the content as well as a progressive standard of learning.
  • All basic math skills will be mastered by the end of 6th grade.  In 7th grade, all students will take PreAlgebra which includes basic Algebra, Geometry, and Consumer Math ideas.  Review of basic math skills will also continue and be perfected.
  • Algebra 1 will be offered in 8th grade and upper level math classes will be offered through 12th grade Calculus for those interested in continuing with upper level, college-prep courses.
  • In Algebra 1, we will continue to review basic skills to make sure they are mastered.
  • In 10th and 11th grades, we will incorporate ACT (or similar) math practice so that our students can be competitive on college-entrance exams.  Because our students will not be using Common Core math, we need to make sure that our students can understand unfamiliar wording in testing situations.
  • In upper level math classes, students will be expected to explain math problems to the class showing that they are competent not only to “do” math but also to explain and teach math skills to others.

I would like to end with a quote taken from Wisdom and Eloquence: A paradigm for classical learning by Littlejohn and Evans. 

It is especially critical that from the earliest years basic arithmetic be taught in an incremental and cumulative manner and that students be allowed sufficient interaction with the material to achieve mastery.  More than any other discipline, math is a cumulative exercise, building year by year.  Students who have a “bad” year in math are likely to suffer for years as a result, and a mastery focus in the curriculum can help to ensure that students are not penalized because the school has low standards or inexact goals for student success.  This means beginning with the simplest principles and sticking with them until they are thoroughly apprehended before moving to more complex principles. . . As with reading, writing, and spelling skills, we are seeking automaticity.  The basic skills should be second nature to our students so they are not hindered in tackling more complex computations by lack of facility in the basics.

In conclusion, our goal is to develop a thorough, well-thought out math program which insures that our students are well-prepared to be critical thinkers in this world of ambiguity and well-prepared for future careers in math, science, and technology.   We are currently working on this scope-and-sequence in math and hope to implement it in the school year 2015-16.  Furthermore, we feel that the standards of the Common Core are not developmentally correct.  By implementing the above program using classical models of education, we feel that by the end of a student’s final year of high school, he or she will be above and beyond the standards of the Common Core.  May God bless and guide us in our endeavor to prepare our students for the future.

We encourage our parents to research this topic for themselves.  We would refer those interested in more information to the Facebook page of “Missouri moms against common core” or the website, truthinamericaneducation.com.  Also here is a link to a YouTube video by Terrence Moore speaking at Hillsdale College entitled, “Story Killers: How Common Core Destroys Minds and Souls.”

Link: https://www.youtube.com/watch?v=xCoOv_DwaAk