The Cumulative Nature of Math and Why it Matters

Math is a subject that a lot of students struggle with. Sometimes just the look of a problem can make them think it is too difficult before they have even tried. Plus, the fact that answers tend to be right or wrong with no middle ground can be frustrating. Students who did well in math in lower grades may find that in upper grades they are not doing as well.

What many people fail to realize is that math is a cumulative subject. Concepts build on one another. Understanding the basics is a key building block for future success. When students do not have a strong foundational knowledge, more advanced concepts are harder to make sense of. For instance, students must understand addition before moving on to multiplication, which is repeated addition (at least when it comes to whole numbers).

Memorization is Not Enough

A lot of students skate by because they are good at memorization. But that does not mean they truly understand the concept. They can recite multiplication facts and formulas, but do they understand that 3×4 equals 12 because you are adding together 4+4+4? They know that PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction, but do they know how to correctly apply that when presented with a problem?

It is hard to apply concepts to a wide range of problems when students do not actually comprehend what they are doing or why it works. They need to know which operation or formula to use and why.

A Rush to Move Ahead

Teachers also have limited time to cover a lot of information. If most students seem to get a concept, they move ahead. But if a student starts to fall behind and does not have a solid grasp on the material being covered, the next topic will likely be more difficult because they don’t understand the basics. Slowly this gap widens, and math becomes more and more challenging and confusing.

Continuous practice and reinforcement of skills are important. Moving on too quickly only causes more issues. For instance, a student who barely passed pre-algebra is more likely to struggle in algebra I because they are missing some of the fundamental building blocks needed to be successful. Advanced courses are an extension of concepts that were learned previously.

Closing the Gaps

Recognizing where there is a disconnect and what material students don’t thoroughly understand is essential for helping them to be more successful in the future. The switch to remote learning has made some parents more aware of some math skills that their child may be lacking as students had to work more independently. It requires a lot of practice and reinforcement to master one concept before moving on to the next.

Crafting Scholars emphasizes the importance of developing a strong cumulative understanding of math and is aware of how gaps in knowledge can create problems later on. That is why we offer a math diagnostic test to identify each student’s strengths and weaknesses. We are able to see what concepts they still have to work on. Then we use that data to create a customized learning plan to help them master the fundamentals they need before moving to the next level.

If you are concerned that your student is missing key skills and may not be as prepared as they should be for next year, contact us to schedule diagnostic testing and personalized tutoring. We support students in boosting their academic performance and developing the knowledge they need for higher level courses.