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Where The Common Algebra Mistakes Really Come From

Algebra for high school students (and, sometimes, middle school students) is hard enough. Throw in a constant repeat of common Algebra mistakes and it’s a huge blow to a student’s confidence in math.

This blog post will go over these top three common mistakes in Algebra:

1. Low Prerequisite Knowledge
1. Lack of Calculator Experience
1. Improper Note-Taking Skills

I’m a high school math teacher and I’m sharing the mistakes I’ve seen over the years.

As a bonus, I’m also shining a light on how your child can avoid these mistakes.

Let’s jump in.

Low Prerequisite Knowledge

Understand this: Common mistakes in Algebra class are rarely because of the actual Algebra material.

Most students struggle because they lack the foundational skills from the lower level math classes, which are usually taught in middle school.

For example, students will see fractions in Algebra. That’s a given. We use fractions to graph slopes for linear equations and other things.

But some students lack the skills to correctly multiply/divide and add/subtract fractions and decimals. That’s were a lot of mistakes come from.

Algebra teachers often don’t have time to reteach prerequisite material. Some teachers will go over it, but students on a shaky foundation need more time and repetition to become more proficient in those basic skills.

The first 3 units taught in Algebra are typically based on slight expansion of concepts students have seen before. For example, students should walk in knowing how to solve for x and how to find coordinate points on a graph.

Small mistakes are BIG in Algebra I.

A lot of the incorrect responses I see are from a student not marking a number negative when it should have been negative.

Sometimes, these foundational skills were just forgotten over the summer and a condensed review is all the student needs to get back on track.

For others, it’s a larger gap. Here’s what those students can do:

• Ask your teacher for additional work to drill and become fluent in those weaker math concepts. For my students, I offer online work so students can have instant feedback or sometimes I give paper assignments for extra credit.
• Seek out additional teaching resources, like Khan Academy and Illustrative Mathematics Also, practice with brain teasers and math word problems.
• Find a study buddy. Review assignments or additional work over the phone or online with a friend, a tutor, or in self-paced learning programs, like USATestprep.

A Quick Note About Critical Thinking

Critical thinking (also referred to as problem solving or logic) is worth a mention here.

Students should be able to use the information and knowledge they already have to try to solve problems. And I’ve noticed that is also a lacking prerequisite skill.

To an extent, critical thinking experience starts as early as kindergarten.

The writers of Dora The Explorer said in an interview that they created the show to teach their own children how to solve problems. And if you actually watch the show, with almost every step Dora takes, it requires her to solve some sort of problem.

Problem solving skills start early and should be building on itself as the student gets older. It should build to the point where students have the willing mind to face a challenge without automatically saying, “I don’t know how to do this.”

One way to improve this skill is to intentionally approach more unfamiliar problems and study their solutions. Even if the student gets the problem wrong, the regular practice is building their mind and their thinking ability.

I find that a lot of students just don’t want to get the problem wrong so they don’t even try (which is wrong, in and of itself).

As a teacher, I can do my best to teach students in the formats that they will see for standardized testing. But there’s always a chance the material won’t be exactly the same. And in the real world, it’s definitely not going to be that way at all.

Critical thinking is a perishable skill.

While you child may have developed some of it in their younger years, it can be lost. Students lose it through teachers who don’t develop it, through too much dependence on technology, and through other means.

Lack of Graphing Calculator Experience

At least 90 percent of all the new Algebra students I have taught are not familiar with their calculator. And that can become a bigger problem than it seems.

Calculator skills will walk with students through their high school career all the way up to college math. But those advanced classes aren’t teaching how to use the graphing calculator.

Those teachers and college professors expect their students to already know.

And where are students expected to learn it?

Algebra I class.

Algebra students need a calculator from Day 1.

I hit the ground running, teaching how to use the calculator to solve equations, factor quadratics, graph functions, and more. Students need every bit of that time in order to be ready for end-of-year standardized testing.

We teachers want to make absolute sure that our students are really comfortable using the calculator.

Schools typically have class sets of graphing calculators passed out at the beginning of class and collected after class is done.

But your child really need to have their own calculator.

Some (brave) teachers may allow their students take class calculators home. But usually not.

A class set calculator is luck of the draw, too. We deal a lot with low battery, functionality issues, and then of course, students can’t use outside of class.

New Algebra students need either a scientific calculator, like the TI-36 or TI-30, or a graphing calculator, like the TI-84 plus. I see a few students with the TI-Nspire. It’s a high-end graphing calculator, typically used in Advanced Placement, or AP classes. Not necessary for Algebra, but a nice investment.

Whichever calculator you choose, make sure it’s on the approved list for your state’s standardized testing.

Some state tests allow students to use the online graphing calculator Desmos. That’s an option and also takes some time to learn how to make the most out of it.

Whatever calculator you get, make sure your student knows how to use it or pays close attention to their teacher when it’s taught.

Improper Note-Taking Skills

Research proves that note-taking strategies increase learning, so it’s important your student does it right to avoid common mistakes in Algebra.

Nowadays, most of us favor the tactile, or kinesthetic, learning style and that’s the value in improving note-taking. It’s like muscle memory. It helps embed the information in the mind.

An example would be being able to write the quadratic formula.

The common mistake in note-taking is just not taking notes.

I also don’t see many students saving their notes. It’s important for new Algebra students to write complete notes. I see a lot of students skipping steps in their notes.

Now, math teachers are going to write out every step.

Some students just write the answer and think they don’t need to put every step in their notes — either because:

• Students think they understand the concept enough or
• Students just don’t want to write a lot.

But students need detailed notes to refer back to when they are studying and the teacher isn’t there.

On the other end of the spectrum, I find some students write EVERYTHING I write on the board.

Students need to know what is important. Not everything is for notes.

Some of what I write on the board is for in-class learning so students can concentrate on grasping the material. Writing every single thing interferes with understanding and time management. Those students are the ones often telling me to slow down during lecture. Those students can also run out of time and miss out on the material they really need.

So, what does note-taking look like in Algebra class?

At a basic level, students need to know the key rules and formulas, examples of the standard way to solve the problem, and variations of the problem.

Teachers also often tell the class when something is important enough for students need to write it down.

Types of Note-Taking

Some teachers encourage Guided Note-Taking, where lecture notes are almost completely filled out except for certain blanks. Students fill in the blanks with a key words or phrases from the lecture.

The Graphic Organizer is a way to visually compare and contrast multiple concepts. This method can look different every time. A Foldable is a very common graphic organizer where students make a series of folds to create flip strips to help remember information.

The Double Bubble Map (not be confused with a Venn diagram) guides students in mapping out concepts and sub-concepts.

Quick-write is the traditional note-taking where the student is writing the definitions, examples, formulas, etc. Examples are great for the student to refer back to during their daily review time.

And there are many more ways to take notes than those.

In the virtual learning environment, students can expect more summary sheets, notes, and documents already prepared. A lot of the lesson will be self-paced for the student to watch a recorded video lesson and read supported materials.

But the suggested note-taking strategies still apply. Students still need to be physically taking notes.

No student will want to re-watch and sift through the 1 hour of recorded teaching every day just to find whatever they need.

Note-taking makes for organized information. Without it, it also takes away the kinesthetic advantage in learning. Virtual learning can make it tempting to just mindlessly watch a lecture and read through what someone else wrote or typed out. But students need that writing element. Many students are that type of learner, especially with advances in technology pulling us to tap on handheld devices.

Final Thoughts

New students need to practice to the point where they aren’t making many of the common Algebra mistakes.

The idea is doing over and over again. It’s tiring but it needs to be done.

I suggest 15-20 minutes of study a day in a student’s math course outside of school to practice how to become an individualized math learner and increase fluency.

It’s like playing an instrument or a sport. All the top athletes practice outside the official practices and you can do that with math or any other subject and become better at it because of it.

Algebra class is often portrayed as difficult in the media. And your child knows it and likely believes it.

I can usually tell how new students feel about the subject when they first walk in my classroom.

Here’s what I try to drive home:

I tell my students that all they have to do is do the work, take notes, try your best to ask questions, and allow their parent or guardian get involved in their learning.

Success comes from doing the work – that’s in Algebra class and in life, really.

For Algebra, the work doesn’t have to be done right. The teacher can help you learn how to do it right. But the student needs to make the first step.

Go with the flow of your student’s teacher.

Your teacher wants you to be successful in Algebra class.