- Joy of mathematics
- The teacher’s task is to see what they can do to help the student be successful.
Henry Borenson, Ph.D. (doctorate in educational administration), an educator for many years, and an educational entrepreneur for nearly 20 years.
He invented Hands-On Equations® to help teach algebraic concepts to students because he felt the traditional method just wasn’t working with his students.
Today Borenson’s network of teacher-practitioners and presenters that blankets the country year-round with his program designed to help motivate teachers to make learning algebra fun for students.
The kinesthetic approach built makes it engaging and effective for students—and establishes a sense of self-confidence and motivation, where fear and anxiety had once stifled a student’s progress.
I reflected upon the pleasure of teaching and the joy of mathematics and I decided that I would become a high school mathematics teacher.
The way much of mathematics, and algebra in particular, is taught at the high school level is so theoretical and abstract, it involves memorization, and students are taught a series of steps to follow, and they’re told if they follow these steps, they’ll arrive at the right answer.
But these set rules, and the symbols upon which they operate, have as much meaning to the kids as Greek or Chinese symbols would have.
The process of getting the “right” answer, as traditionally taught, is often devoid of meaning.
Instead of using symbols and set rules to memorize, he gives the students a concrete representation of the algebraic symbols and algebraic processes.
The symbols are represented by game pieces. The algebraic processes are represented by physical actions upon these pieces. In other words, we have a counterpart for what’s done on the blackboard, and it’s done physically.
As the equations are solved, the child can see what he’s doing, can actually move the pieces, so he’s now using his whole brain, and not just part of it to solve the problem mentally. It turns out that doing algebraic equations this way, even though many of these equations would not normally be presented until the ninth grade, is in fact easier than much of the curriculum we have in the elementary schools.
So, a fourth grader can really be very successful in learning algebraic concepts presented this way, more so, for instance than in learning to divide fractions or do long division.
The teachers can see that the students can learn something that would normally take older students a week or several weeks to learn through traditional teaching methods.
Of course, it would be helpful if these concepts were reinforced over the ensuing years prior to taking a formal course in algebra. But even if they are not, the concepts have been learned at a deep intuitive and kinesthetic level.
It’s the challenge to solve the mystery, to play with the pieces, to use whatever strategy they would like to try, until the answer is obtained, and that’s self-motivation.
Because algebra has traditionally been talked about as being difficult, the students build up a great deal of anxiety about finally taking algebra in ninth grade. But we can turn this situation around.
We touch upon “Piagetian learning” in our seminars for teachers, so they’re aware of what makes HOE so effective.
If you were to try to teach Chinese to a high school student, she would have a lot of hard work to do to learn the language: There are the unique sounds, the Chinese characters, the words, the grammar.
An environment provides a very powerful arena for learning.
The “natural algebraic learning environment” that we present to students makes it possible for them to succeed in their work, especially since they can use so many of their senses in their work.
Learning algebraic concepts through the traditional abstract methods, on the other hand, is very difficult for most students. They try to memorize as best they can, but without understanding, they can only go so far.
The professional educators present are able to witness first hand the student thinking that is used to solve the problems, and they recognize that thinking as valid and on target.
We have a number of objectives for the seminar:
One is for the teachers to understand the concept of the teacher as a coach, or facilitator.
Many teachers still think that the role of the teacher is to stand in front of the room and lecture for 50 minutes, that this is how knowledge is obtained by the student.
Many teachers have difficulty with the student putting up the “wrong” answer, and they’ll immediately “correct” it, rather than talk the student through the process of thinking about how he got the answer, and how he can adjust his thinking to achieve another more desirable answer.
We’d like teachers to encourage students, to let them interact with each other.
The teachers take cognizance of the dramatic change in self-perception of their ability to teach these concepts that has taken place within the span of a few short hours.
This change in teacher attitude is dramatic and consistent. Any participant attending a program is able to witness this transformation in teacher self-perception of their ability to teach algebraic concepts using HOE vs. the traditional methods.
It is important and essential for teachers to realize that it is up to us, the educators, to develop the techniques and the means by which the students can learn.
“If you really want the students to learn, you will do whatever is necessary. You will find new methods, or you will change your approach in the middle of the lesson, so that they will learn.”
It is up to us, the educators, to develop the techniques and the means by which the student can learn.
It is not satisfactory for teachers to simply say, “Well, they don’t have the ability, they can’t cut it,” or “I can’t do anything about that, the curriculum is set.”
The teacher’s task is to see what they can do to help the student be successful.
Unfortunately, very often, teachers want to stump the students, like a game, rather than to ensure their growth or to help them discover what they can do. That should be our goal.