Filling Foundational Gaps and Preparing Students for Algebraic Concepts
Each year as a new group of bright-eyed, bushy-tailed students file into our math classrooms, we see their math ability reflected in their degree of eye contact. The ones who are confident and get good grades (the school’s form of success) are eager to impress you on that first day and keep good eye contact. The ones who haven’t made good grades (the school’s form of failure) will typically avoid eye contact, which conveys their fear that you will ask them a question.
In most cases, students who come to us with missing foundational skills are below grade level. For years they have been stuck in the vicious cycle of not understanding a concept, starting a new one that builds upon the last, and then falling further behind. As a result, these missing proficiencies create a variety of skill levels in a single classroom. So how do we begin the change this?
Time. One problem plaguing teachers is that there is never enough time to plan lessons, to individualize instruction, or to help students who are missing foundational skills. It is also difficult to keep up with the ever-changing demands of education, shifting curricula, budget cuts, and professional development requirements. Could I continue? Yes, of course, but instead let’s focus on what we can fix, or at least start filling in.
I challenge you (with the use of your teacher superpowers) to find time to help students fill in those foundational skills.
Start tutoring before or after school. I know this is easier said than done, but chances are that you come in early or stay after school at least two or three times a week. (If you don’t, I would LOVE to know your secret!)
- Take one hour out of that time and devote it to students who need additional assistance.
- If you can’t find an hour, find someone who can; the year I was pregnant and so incredibly sick, I found people in the community who were willing to come in and tutor my students. You know what they say, it takes a village! I tutored after school for an hour each Wednesday.
- If your school does not have a program for later bus runs for students participating in afterschool activities, then parent pick-up is necessary. But again, there are ways around it.
- Have the students carpool, pair up with another math teacher where you teach the first hour and they teach the second, or ask that that teacher who always stays late if those one or two students can have a study hall with them until a parent can come (and don’t forget to bring that teacher coffee, muffins, or buy their lunch once or twice for helping out).
Use your schedule to your advantage. If there is time during your students’ lunch period, have them come back to your class for help one to two days per week. Often, working with students in a small group setting helps close the gap faster.
Host a Saturday Academy where community volunteers tutor the students. If you teach an in-class resource class, differentiate. Use your co-teacher to teach one group while you teach the other.
The bottom line is to be creative—isn’t that one of our best qualities as teachers?
As foundational skills are built, students will be better prepared for learning algebra, the gateway math to higher learning. This is the time in a student’s math career when they begin the transition from concrete mathematical concepts to abstract concepts. They will begin to develop higher-level reasoning skills that will be used in advanced math courses throughout high school and college. Starting algebra with a strong foundational base will be vital to their success.
Conceptually, students will need to have a core foundation and understanding of their multiplication facts, fractions, integers, and how to solve one-step equations. But not all of what they will need is content based. I feel very strongly that a large part of a student’s math ability is confidence and perseverance. If a student believes they can be successful, they will. This may come after multiple failed attempts, but eventually they will succeed.
Math is like a sport—you cannot succeed unless you practice. Are practicing math problems fun? No, but neither is running sprints to prepare for basketball season. But is it necessary for one’s success? Yes! Many students have a hard time learning how to study for math because it does not involve traditional study methods such as flash cards or rereading notes. To successfully study for math, students should practice problems and check their answers. I always add the last part about checking answers because if you don’t know if you are getting the problem correct, it’s like shooting free-throws blindfolded and hoping you make the shot.
If this were a perfect world, then each year all of our students would arrive at our classroom doors on grade level and eager to learn. But since we are drenched in reality we must find ways to fill in the foundational skill gaps that students have and help prepare them to enter in to the gateway to higher-level math—algebra.
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