What Makes Algebra So Difficult For Kids To Understand And Challenging for Teachers To Teach?

At first glance this seems to be another Chicken or the Egg situation. Are kids not understanding because Algebra is a subject that is difficult to teach or is Algebra difficult to teach because kids have so much trouble understanding it? In reality, there is some truth to both of these issues; and, theoretically, solving one will solve the other as well. So, exactly what is it that makes Algebra so unique?

Algebra is like a giant question mark in the brain of every freshman who walks into the classroom. These 14- and 15-year old students enter the classroom having absolutely no expectations of what they are going to be learning; and teaching Algebra successfully is one of the greatest educational challenges existing today.

Students in elementary school know just exactly what math was covered in each grade and what is coming next year. Addition, subtraction, multiplication,... They know. In high school, at the end of Geometry, Trigonometry, and Calculus, students can explain to you what the course was about. But Algebra is a different kind of animal. Too often Algebra teachers assume their students know what Algebra is, so Day One of school is Section One of Chapter One in the textbook and off they go on their unknown journey. Sadly, many students are as clueless at the end of the school year as they where at the beginning as to what they have been studying. Some students can tell you they solved(?) equations, they factored something, and they graphed things. Some students can actually be good at Algebra skills, but still have no idea why they were doing any of it. That's very sad.

The numerical skills required in Algebra (the HOW) are really pretty basic. It is the understanding of the WHY and WHEN that students don't get. But is this a student issue or a teacher issue?

Students issues to consider:

(1) knowledge of multiplication facts is the #1 indicator of success in Algebra, yet many students enter Algebra with weak multiplication skills,

(2) most students are lacking the ingrained sense of "I am smart enough" that they possessed when learning language,

(3) many students have lost the persistence they demonstrated when learning to walk, talk, and read,

(4) most students lack a pre-school math foundation similar to what parents provide for language skills,

(5) unlike all previous math courses in which only 25% of the material is new (never seen before), the amount of new material being covered in Algebra is approximately 75% of the course which seems to be too much for them to absorb,

(6) the pace required to cover so much new material seems too fast for students to absorb, and

(7) many Algebra students see no practical application to their lives, so they view it as unnecessary to learn. Have I missed any student issues? Probably, but you get the point.

Teacher issues to consider:

(1) the assumption that students already know what Algebra is is incorrect,

(2) teachers sometimes don't recognize that the problem is weak basic skills until the damage is done,

(3) the large amount of new material to be covered does not allow for proper processing but teachers do not have a choice about removing some of the subject matter,

(4) some teachers are weak at task analysis, (5) a few teachers have trouble explaining a topic several ways to deal with the different ways students learn, and

(6) No Child Left Behind has caused immeasurable harm to mathematics education and the learning environment. Again, you get my point even If I missed something.

In spite of all the issues I just listed, it should be noted that this "problem" has existed literally forever. The failure rate was 50% when I started teaching in 1972 and it still is. Many attempts have been made over the years to solve these issues. Nothing has been successful. So the answer to the initial question is: we don't know. If we knew, the issues would get solved.

Shirley Slick, "The Slick Tips Lady," is a retired high school math teacher and tutor with degrees in Mathematics and Psychology and additional training in brain-based learning/teaching. Her goals: (1) to help parents help their children with math, (2) to help eliminate the horrendous Algebra failure rate, and (3) to inform the general public about problematic issues related to the field of education. For your free copy of "10 Slick Tips for Improving Your Child's Study Habits," visit her website at http://myslicktips.com/

What Makes Algebra So Difficult For Kids To Understand And Challenging for Teachers To Teach?

At first glance this seems to be another Chicken or the Egg situation. Are kids not understanding because Algebra is a subject that is difficult to teach or is Algebra difficult to teach because kids have so much trouble understanding it? In reality, there is some truth to both of these issues; and, theoretically, solving one will solve the other as well. So, exactly what is it that makes Algebra so unique?

Algebra is like a giant question mark in the brain of every freshman who walks into the classroom. These 14- and 15-year old students enter the classroom having absolutely no expectations of what they are going to be learning; and teaching Algebra successfully is one of the greatest educational challenges existing today.

Students in elementary school know just exactly what math was covered in each grade and what is coming next year. Addition, subtraction, multiplication,... They know. In high school, at the end of Geometry, Trigonometry, and Calculus, students can explain to you what the course was about. But Algebra is a different kind of animal. Too often Algebra teachers assume their students know what Algebra is, so Day One of school is Section One of Chapter One in the textbook and off they go on their unknown journey. Sadly, many students are as clueless at the end of the school year as they where at the beginning as to what they have been studying. Some students can tell you they solved(?) equations, they factored something, and they graphed things. Some students can actually be good at Algebra skills, but still have no idea why they were doing any of it. That's very sad.

The numerical skills required in Algebra (the HOW) are really pretty basic. It is the understanding of the WHY and WHEN that students don't get. But is this a student issue or a teacher issue?

Students issues to consider:

(1) knowledge of multiplication facts is the #1 indicator of success in Algebra, yet many students enter Algebra with weak multiplication skills,

(2) most students are lacking the ingrained sense of "I am smart enough" that they possessed when learning language,

(3) many students have lost the persistence they demonstrated when learning to walk, talk, and read,

(4) most students lack a pre-school math foundation similar to what parents provide for language skills,

(5) unlike all previous math courses in which only 25% of the material is new (never seen before), the amount of new material being covered in Algebra is approximately 75% of the course which seems to be too much for them to absorb,

(6) the pace required to cover so much new material seems too fast for students to absorb, and

(7) many Algebra students see no practical application to their lives, so they view it as unnecessary to learn. Have I missed any student issues? Probably, but you get the point.

Teacher issues to consider:

(1) the assumption that students already know what Algebra is is incorrect,

(2) teachers sometimes don't recognize that the problem is weak basic skills until the damage is done,

(3) the large amount of new material to be covered does not allow for proper processing but teachers do not have a choice about removing some of the subject matter,

(4) some teachers are weak at task analysis, (5) a few teachers have trouble explaining a topic several ways to deal with the different ways students learn, and

(6) No Child Left Behind has caused immeasurable harm to mathematics education and the learning environment. Again, you get my point even If I missed something.

In spite of all the issues I just listed, it should be noted that this "problem" has existed literally forever. The failure rate was 50% when I started teaching in 1972 and it still is. Many attempts have been made over the years to solve these issues. Nothing has been successful. So the answer to the initial question is: we don't know. If we knew, the issues would get solved.

Math Teachers - Cautions With Vocabulary! Your Mental Images May Not Match - Never Assume They Know!

In my early days of teaching--a long time ago--I treated math vocabulary just the same way vocabulary has always be treated in English class. I gave definition and spelling quizzes. The complaints were loud and frequent: "This isn't English class." My favorite was: "What does this have to do with math?" In spite of the complaints, my students knew how to PROPERLY pronounce and spell "commutative," and they had a good understanding of the definition. With all of the time pressures of No Child Left Behind, I, like so many other teachers, was forced to let go of this focus on definitions and spelling. Students went right back to spelling and pronouncing commutative as "communitive" and their understanding of the meaning went right out the window. Commuting to work and back is hardly the same thing as communing with nature, but they never got the concept of the importance of pronunciation, spelling, and definitions.

I recently read a teacher's blog by David Ginsburg in which he was making the point that we math teachers need to work harder on language fluency--especially when we are using terms that have very different meanings in our mathematics class than they have in everyday life. His focus is on elementary school; and my favorite of his examples deals with the word "borrow" in subtraction. Why should we say borrow when it is never going to be returned as the everyday meaning of borrow implies?

The very same issues happen in upper level math. In Algebra, factoring is an extremely important concept. Our students are frequently given instructions like: Factor x^2 - 3x - 28

I know from many years of both teaching and tutoring Algebra that even when students can actually correctly factor this expression, they cannot tell you in words what it actually means "to factor." Similar to Pavlov's dogs salivating to the sound of a bell, many of our students know that when they see the word factor beside a trinomial like x^2 - 3x - 28 they are supposed to write (x - 7)(x + 4). But what does the word "factor" actually mean to them?

They are familiar with this use of the term: (1) washing hands is an important factor in slowing the spread of disease, or (2) teens' failure to use protected sex is a major factor in teen pregnancies. To our students, "factor" implies a reason or a cause. What does that have to do with x^2 - 3x - 28?

Note: In mathematics, to factor means to re-write as multiplication. x^2 - 3x - 28 becomes (x - 7)(x + 4) when written as a multiplication problem.

Another example from Algebra involves another extremely important concept: Solve. We know what it means to solve a puzzle or to solve ones own troubles. How does "put it together," as with a puzzle apply to: Solve the equation x^2 - 3x = 28? Find your own answers sort of applies, but what is an answer to an equation? How do we know when we have an answer to an equation? We simply do not do a good enough job of drilling in the concept that an answer "makes the equation TRUE." We say it once or twice and from then on ASSUME they understand.

In Geometry, we start using protractors to measures angles in degrees. Does that have anything to do with temperature? Are you certain that all of your students are picturing in their minds the same thing for one degree that you are, or do you just assume they are?

On of my biggest frustrations with missing understanding is with the use of the word "value" with respect to fractions. We say that reducing a fraction does not change its "value" or we tell our students to compare 3/4 and 1/2 as if fractions themselves have "value." THEY DO NOT HAVE VALUE--YET. We cannot compare 3/4 and 1/2 until we know 3/4 "of what" and 1/2 "of what." I can almost guarantee you that 3/4 of the money in my pocket is LESS than 1/2 of the money in your pocket. We do not stress enough to our students that to know if 3/4 > 1/2, we must first know that they deal with THE SAME THING. Even on a number line, the reason that 3/4 > 1/2 is because BOTH are fractions of THE SAME UNIT. However, 3/4 of an inch and 1/2 of a foot CANNOT be written 3/4 > 1/2!

I strongly suspect that if you asked Algebra students, "Is 3/4 always greater than 1/2?" the vast majority, if not all, would say "yes." Homework instructions never say "compare these two fractions from a number line" or "assuming these fractions are of the same item, compare things fractions."

We math teachers must be constantly checking for understanding about what students are picturing with terms and definitions. Be honest with them about the possibilities for misunderstanding. If we don't catch these early, the misunderstanding can become practiced and learned and become almost impossible to repair.

Never ASSUME they are picturing what you are. Never ASSUME they know what you think they know. ALWAYS VERIFY!