What Do We Do About Kids Behind in Math?

A MiddleWeb Blog

I teach Algebra I to 10th graders. This happened recently.

I put this problem on the board to illustrate the concept of distribution:

3(x + 1/4) (distribute the 3)

I then wrote the following:

3x + 3/4

I immediately heard a chorus of “Where did the 3/4 come from?” So off to the side I showed them that 3 multiplied by 1/4 is 3/4. They were satisfied on that count, but now distributing had been forgotten.

This exact scenario happens in every lesson, every day. (In the example above the issue was not knowing how to multiply three by a fraction, but even if it had been three multiplied by six, at least a few students still would have been confused).

It’s not that I mind explaining, I don’t. But they are having a hard time learning new material because they haven’t mastered old concepts. Students understand higher levels of math much better when they can build on the concepts they have already mastered.

These unmastered foundational skills keep students stuck in no man’s land; they don’t understand past concepts and they are not learning new ones either.

Obviously, this is having an impact on their learning, but there is also an emotional toll. I see how dejected they are when they don’t know how to start a problem or can’t follow along with what’s happening. It’s easy to see why they become disengaged. I understand why some students feel the need to resort to Googling the answer or use Photomath; they don’t feel like they have any other options.

Why so many unmastered concepts?

First of all, this should never become a blame game. I know these students have been taught these concepts; I know their previous teachers and they did the right things. So why haven’t the students mastered the concepts?

Well, some students moved from one school to another; some students were very sick for periods of time; other students were dealing with family issues. Obviously Covid-19 has had an impact, but if I am being honest, this is not a new problem.

Sometimes confidence can be the problem. I’ve had personal experience with this. In 6th grade, almost overnight, I couldn’t see the board. I was in advanced math class and on the math team. In the time it took me to get glasses I was a whole unit behind. I should have told the teacher I couldn’t see the board, but I was too shy to do that. It wrecked my confidence and left me with a lot of gaps.

Sometimes it’s just a matter of individual differences. It’s a fact that some students take longer to master concepts. There is nothing wrong with that. Once they “get it” they can be as proficient as any other student. But it does require us to individualize our teaching to take these differences into account.

Whatever the cause, what do we do?

Whatever the source of the problem, I’m still left with the need to help students master unlearned concepts while simultaneously teaching them new and more advanced concepts. In short, I need a systematic, effective way to teach all the Algebra I standards and help students with those concepts and skills they didn’t master the first time, addressing the gaps that are hindering their mastery of current standards.

I will be honest. I haven’t found the magic formula yet. In fact, I was becoming a little discouraged – until I read Sean Cavanagh’s article, Low Performers Found Unready to Take Algebra, which said you can’t expect to make up several years of math in a year or two.

As state and school leaders across the country push to have more students take algebra in 8th grade, a new study argues that middle schoolers struggling the most in math are being enrolled in that course despite being woefully unprepared.” – Education Week (September 2008)

The same article (written in 2008) said that some students who were taking Algebra I had the math skill levels of 2nd or 3rd graders. How that compares to 2021, I’m not sure, but other reading and my own experience suggest this problem of students falling further and further behind still persist.

Just realizing it’s not all my fault helped immensely, and it also let me shift gears and think logically about what I could do. Over the course of several weeks, I came up with the following goals.

My Goals:

Teach current standards so that students don’t get further behind.

Ensure that students have the math automaticity they need to be successful. (For example: know multiplication tables to 12, add/subtract and multiply/divide fractions, combine like terms, do one step equations, combine positive and negative numbers, understand distribution and how to do it.)

Give attention and thought to students who aren’t struggling and strive to help them advance.

Support all my students and help them enjoy math wherever they are on the learning spectrum.

So those are the goals. The challenge is implementing them in a 55-minute class period that feels like 45 minutes.

Plan to Accomplish My Goals:

This is my plan for the 2nd semester to help me achieve the goals above.

1.) Multiplication matrix (keep it posted at all times and make a laminated copy for students). Students need to know their multiplication facts.
2.) Remediate foundational math skills. Aim for slow, steady and measurable growth (for example, 80% of the students have mastered combining like terms). I will measure it with quick formative assessments that will be easy for me to grade.

3.) Purposefully embed concepts where I can tie in current standards (for example, when we study systems of equations, I can review graphing lines, combining like terms, etc.).

4.) When we have a few minutes in class, give students yellow paper (I’m going to use yellow because that’s what I have the most of) with problems that help them practice basic math skills. Yellow paper will signal NO CALCULATOR allowed.

Final Thoughts

I am going to have to remind myself to be realistic about what can be accomplished in one period: if we spend too much time on past concepts, I won’t have the time I need to spend on current standards.We’ll have to be satisfied with slow, incremental growth; I have no choice but to work with the time I have.

When students are working below grade level, nothing is easy for them and they need to be allowed to celebrate their victories. Just because they are behind right now doesn’t mean they can’t get caught up or make progress.

Above all, I want students to find something in math that they are good at and can enjoy! I will make that a priority every day.

If you have any suggestions about how to help students who are struggling with foundational concepts while taking Algebra I or II, please share them with me!

Michelle Russell

Michelle Russell (@michel1erussel1) is a math teacher at Florence (AL) High School. She began her career as a student teacher in middle school and has taught students from 7th to 12th grade. For the past 13 years, she's taught high school math, including Algebra IB, Algebraic Connections, Pre-Calculus, AP Statistics, Algebra with Finance, and Algebra 2 with Trigonometry. In her free time, she enjoys reading books about math education and following other teachers on Twitter.

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