Many students find when they get to their freshman year in college that they are not prepared for college math or writing, and they need to take remedial courses. Remedial courses, which have to be paid for affect students chances of graduating college in four years. On the other end of the spectrum are those students who were advanced in high school mathematics, and scored a level 3 or above on the Calculus AB exam. They found that if they skipped Calculus I (they had received college credit) in their first semester in college they were struggling with Calculus II.
What causes such a gap? College math focuses on theory (such as Calculus II)- an approach to learning the abstract nature of math that is not often addressed in high school. Once upon a time, there was a focus on deductive and inductive reasoning addressed in geometry (as proofs) and pre–Calculus (as converging series) courses. Logic, the basis of deductive reasoning, was taught as an integral part of the high school Algebra and Geometry curricula. Sadly, the study of logic was omitted from the Common Core mathematics standards. Adding to the confusion of when to teach deductive reasoning was the Common Core implementation of rigid motion proofs to prove congruence. Sounds like a foreign language!
All of the above addresses the abstract nature of mathematics that is rarely addressed in high school math courses. But let’s take the idea of achievement down a few notches, and look at the student who just passes the math assessments with sixty-five percent. Sixty-five percent is considered on the standards scores (the grade 3-8 state assessments) a low level 3. Eighty-four percent is a high level 3 score. Level 4 on the assessments is considered 85% to 100% (mastery of math).
In many cases, students who just barely pass the state assessments in grades 3-8 with a score of a low level three (65%) are not really prepared to master Algebra. In fact, many schools today only require students to pass the Algebra state assessment. The schools then require students to get a passing grade for geometry and trigonometry, but not necessarily pass the state assessments for geometry and trigonometry. Schools only require students to take and pass three years of mathematics, thus relieving a good percentage of the student population from a tortuous fourth year of math.
To be successful in the high school math courses (Algebra, Geometry Trigonometry and perhaps Pre-calculus), students must score on the mastery level for Algebra. For those students who repeatedly score a level 2 on the grades 3-8 math assessments, with no individual intervention for remediation, their inadequacy with math skills and concepts are carried forward; and many just achieve passing (65%) only after a grueling two years of Algebra.
Vigilance is important in keeping on top of your child’s math education along the whole spectrum. A child who scores a level 2 on the state math assessments in grades 3-8 is not likely to blossom in algebra in high school. A child who achieves a passing score of 3 on an AP Calculus AB exam is not guaranteed an easy transition to college-level math. Just passing is not a cause for celebration, it is a false indicator for success in college.
Assessments are useful in identifying what a child knows and what needs to be studied for mastery in a subject. End of the year assessments are key in identifying those math concepts and skills that have been mastered and those that are deficient. High school math assessments like the math Regents exams are available for all students to review. Students need to reflect on their achievement and make a remediation plan to move to the next level, whether middle school, high school, or college.
A student who scores 100% does not guarantee that he/she knows 100% of the math curricula. It could reflect only the concepts and skills that were on the state assessments. How many times did you, as a student, study for a test and then realize that the test was not comprehensive?