Algebra Teachers - If Your Students Can't Verbalize It, They Haven't Learned It

If you believe everything you read about trends in education, then you most likely believe the skill level and effectiveness of today's teachers to be much lower than "when we were in school.
" In reality, this is far from true. At the time I was learning to become a teacher back in the late 60's, I was attending the #2 rated education school in the nation; and yet, my initial training in the art and science of teaching was minimal compared to the instruction given to our teachers today.
In addition, we now have factual research data as to how the brains learns instead of the educated guesses of the past.

Does this mean that math teachers today are doing the best that they can? We all know there is always room for improvement, and one technique that improves learning possibly more than any other is to have students verbalizing their understanding--both in school and at home. There are two major reasons why having students read, do homework, review, and study for tests OUT LOUD is so effective and, thus, so important: (1) Speaking out loud immediately adds hearing to the senses being utilized for learning. The brain will learn faster as the number of senses used to input information increases.

This fact also explains why the use of individual white boards is so beneficial--it adds the touch or the kinesthetic aspect to learning.
If your students are seeing, hearing, and doing/touching what you are teaching, learning is almost guaranteed.
Students have to work hard to fail! Sadly, there are a few who do.

(2) Information--definitions, processes, applications, etc.

--cannot be verbalized if learning has not occurred.

If they can't explain it, they don't know it! On of the best examples of this idea can be demonstrated by asking Algebra students what it means to solve an equation.

First and foremost, they don't give the answer as a complete sentence. This immediately limits the learning.

Students need to give complete answers that begin with "To solve an equation means.

.

." Invariably, students will say, "to find the answer.
" We then respond, "What's an answer?" They say, "It's what works.
" We say, "What does it mean to say it works.
" And they come full circle to "It's the answer.
" It takes skilled questioning to get students to the point of saying that an "answer" or "solution" makes the equation TRUE.

Then they need to practice the entire definition/explanation: To solve an equation means to find value(s) of the variable(s) that make the equation true.
To thoroughly ingrain this concept takes many, many out loud repetitions.

The previous non-definitions need to be "un-learned"--replaced with the correct definition.
In class, these repetitions can be done in different ways: 1) "Turn to your partner and take turns explaining what it means to solve an equation." As you walk around the room, be listening for complete sentences.
2) Every 5 to 10 minutes, stop and call on someone to give the definition.

Do this many days in a row, then a couple times a week.

Occasionally return to this definition until you KNOW that every student can say it correctly and understands it.

3) Occasionally ask students to write the definition on their white board and show it to you.
4) Have students write the definition on a piece of paper (with their name) and hand it to you as their "ticket out.

" Note: #1 and #2 are for learning and #3 and #4 are checks for understanding. This same out loud verbalizing process needs to be done for every new concept, definition, process, and application. We math teachers have a very bad--even arrogant--attitude that we did such an excellent job of explanation that, of course, our students understand; but we seldom put that to the test by asking them to verbalize OUT LOUD what we just taught. We generally don't find out until the quiz or test that, NO, they didn't really get that concept.
Never ASSUME they understand. Ask them to demonstrate their understanding.
If they can't verbalize it, they haven't learned it!