According to the National Center for Education Statistics, the United States is in the bottom 15% for math proficiency. But here’s the reason why.
When students were asked surface level questions like “What is the value of x?” or “What is the slope of the graph?”, they could easily answer. But when the test questions pushed deeper with questions like “What does that slope represent in context to the problem?” students were UNABLE to answer.
This means that students are pushed to find the answer, but not to know WHY that answer works or HOW it connects to other pieces. The critical thinking is something our students LACK.
If we truly want our students to succeed, we need to stop pushing for the answer, and start pushing for the “But, why?”
The first thing I teach my students is the idea that x represents the unknown number that maintains balance between the two sides. I love using the analogy of a seesaw, scales, or a barbell! That starts the beginning processes of truly understanding the idea of solving for the value of x.
Once that baseline is engrained that both sides are balanced, then comes the idea of actually finding that missing value.
That sets students up to fall into the “procedure” category rather than the “comprehension” category. Later on, when you follow my steps, inverse operations will become a natural step for students because they truly understand WHY it helps find the value of x.
For the equations x+5=8, push the question “What number plus 5 makes 8?”
If your students struggle with number sense, provide number lines, 100 charts, and multiplication charts. Provide students the tools THEY NEED, rather than skip to inverse operations.
When students are given a set of problems (like in the activities below) I have them write out or say the equation as a sentence. This trains their brain to read the equation correctly.
Using this “Intuition Method”, I have found division to be the most challenging one. Similar to subtraction, commutative property does not work. Push students to think critically about the problems when they come across ones that involve subtraction or division.
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