Our focus is to
offer affordable tutoring for the most essential
math class your student will ever take.
Why not just teach steps?
Students take information from the world using all
their senses. Why should learning algebra be much
Let's look at how athletes learn to play sports.
Imagine taking a child to watch a professional baseball
player for 50 minutes a day and then be expected to win
a game. It seems ridiculous, because, in order to play
the sport, the player must feel the bat and gloves in
their hands. They must run the bases to determine how
long it will take. They need to imagine hitting the ball
into the outfield. No matter how much you watch the
pros, until you get your whole body involved, there is no
way to really excel at the sport.
This is not much different than a student watching a
teacher for 50 minutes and then be expected to do their
homework perfectly. Truly understanding algebra involves
more than just memorizing steps. In order to best reach
this level of understanding, our teaching methods
involve the use of moving and placing algebra tiles in
order for students to feel and see what is really
happening in a problem and therefore be able to predict
a reasonable outcome.
Doesnít this make the student dependent on the
Students move away from using tiles at their own
pace. Typically, students follow the following learning
Concrete > Representation > Abstract
The concrete stage involves actually moving and
touching the tiles by the students. The students use the
visual aid in order to form number sense and develop
special understanding of the different types of numbers
and unknowns. If compared to elementary arithmetic,
students use cubes, beans, stuffed animals or chips to
add or subtract.
The representation stage is the intermediate point.
Students quickly tire of moving the tiles and start to
draw the different forms instead. When compared to
arithmetic, this is the equivalent of students counting
on figures or creating tick marks when adding. The
students find this method quicker than taking out the
The final stage is the abstract stage. In my opinion, it
is best to allow the students to determine when they are
ready for the abstract stage themselves. They will move
away from the pictures and use the traditional symbolic
representations of variables, unknowns and numbers.
Again, if compared to arithmetic, students use the Arabic
numbers (1,2,3,4,5,? to symbolically represent a
quantity instead of showing tick marks on a page.
Of course, every student learns in their own way. Some
students skip the representation stage and go directly
to the abstract. Others might never move away from the
representation stage. What is important is to keep the
sense of alternate methods of solving problems so
students donít feel trapped into having to rely on
only their memory to solve a problem. Students can
always revert back to the concrete stage or
representation stage in order to solve a more demanding
question. These alternatives foster problem-solving
techniques and lessons for everyday life. Basically, use
what you know to get through unknown territory.
What if my student doesnít want to learn this
No problem. Although we encourage students to give
conceptual learning a try, Aplusalgebra.com teaches
skills using various methods. Each skill can be
presented in a variety of ways. Encourage your student
to view the various methods so they can pick the lessons
that are best for them.