One of the most common frustrations heard from secondary math teachers:
HE SHOULD ALREADY KNOW THIS! HOW CAN I TEACH HIM IF HE DOESN'T HAVE HIS BASIC SKILLS?!?!
In a typical math classroom, all students learn the same thing on the same day. This makes practical sense - it allows for standards to be covered in a timely manner; teachers only need to create one lesson a day. It is very difficult for teachers to manage small groups or individualized lessons.
This type of lesson planning is effective for 80% - 85% of students.
But what happens to the other 15% -20%, who are lacking the significant skills necessary to understand the new lesson?
They sit there BORED, DISENGAGED, CREATING DISTRACTIONS.
Many math teachers (secondary or otherwise) do not know how to help students who are missing major pieces of their math education. Students are sent to tutorials where teachers walk them through the current topic, often holding their hand through each step. Students white-knuckle through, memorizing just enough steps to pass with little understanding of the concepts behind them. They are alcoholics clinging to sobriety, desperate to get through one problem, one quiz, one day at a time. Tutorials are the equivalent of removing liquor from the home. It only pacifies the immediate and does nothing for intervention.
We must address the root of the problem by discovering students' specific weaknesses and methodically addressing each gap. Picture math like a Jenga game, with each block representing a major skill.
This math tower begins to build in preschool, as students learn basic counting principles, addition, subtraction, grouping, and measurement. The foundation of their tower is in number sense, basic fact retrieval, computation skills, and an understanding of fractions and decimals.
As students continue through their K-8 math education, their tower becomes enormously tall and complex, but most students are missing at least a few blocks. The lower on the tower these missing pieces are, the more a student will struggle. We continue to add new blocks but do nothing to replace the missing pieces. Tutoring only on the current skills aids the student in adding more blocks to the top. While the tower gets taller, it also gets weaker.
It is no wonder that by the time a student reaches Algebra I, his tower has already crumbled.
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