Using Graphic Organizers in Math to Increase Independence
As a special education teacher I am given the challenge to support those with some of the greatest obstacles to learning. This year, I am working with a class of students who range in mathematical abilities from about a 1st grade level all the way to high 6th grade/low 7th grade level. Some of these students also have behavioral and emotional needs that may impinge on their ability to achieve in the classroom. While my students come in grade levels behind their peers, I also feel strongly that I would be doing them a disservice by not exposing them to grade level standards.
I admit that I am rather idealistic at the start of each year. While I knew these students through professional conversation with colleagues, I definitely did not comprehend the depth of their needs and what new strategies I may need to use to support them until I was a few weeks in. I would leave class feeling highly triumphant, because the students were really demonstrating mastery of a new skill or concept – only to feel defeated beyond measure the next day, when they would get over half of their homework wrong, and not recall what we had “learned” the day before. I have always pushed my students to increase independence and use their resources – notes, reference sheets, multiplication charts, etc. – but this was not working for this particular group of students. I needed a new strategy for some of those mathematical skills that have so many steps embedded within.
Planning for Success
When I sat down to start preparing my lessons for adding and subtracting fractions with unlike denominators, I tried to prepare myself for the questions that the students would have, the steps they would get tripped up on, and how they used the embedded skills together. What I found, was I never really realized how many steps it actually takes to accomplish this task. For me it was always find a common denominator, change your fractions to be equivalent, then add and subtract your fractions – simplifying if needed. For most of my students, however, the task appeared much larger. This is how they see the steps, and the strategies they have now learned to answer them.
- Find a common denominator. How do I do that? What’s a denominator? What is a multiple? How do I find that? Then what?
- Make equivalent fractions. How do I do that? What does equivalent mean? How do I know what numbers to multiply by? Then what?
- Add or subtract the fractions. How do I do that? What do I do with the numerators and denominators? Then what?
- Simplifying Fractions. How do I do that? How do I reduce? What are common factors? What’s an improper fraction? How do I divide? What number goes in the house? What do I do with the remainder? How do I know when I’m done?
Then it dawned on me — a skill specific graphic organizer. They work so well for the students in ELA classes – why not try them in math?
Graphic Organizers for Adding Fractions
To be independent in this skill, they needed to have 3 things in their strategy bank– a graphic organizer to remember all of the steps, multiplication charts to find the least common multiples, and a factors chart from 1-100 to reduce their final answers. I created two different graphic organizers that addressed all of these questions – one highly scaffolded one for a student with an intellectual impairment, and another for my middle to higher ability students. The organizers have varied levels of prompt – but both of them provide a structured approach to the task, and are color-coded to provide further visual reminders.
It was really interesting to see the students transition – some did so independently, and others needed to be weaned off of the security they found in it towards independence. But what I found was that the entire class was eventually weaned off the use of these graphic organizers in solving the problems, in their own time.
(Link to less scaffolded organizer here)
Independence and Next Steps
The students have internalized the steps that are needed to solve. When they solve the problems without the graphic organizer, they often set it up in the exact same format as the graphic organizer is set up, because they can visualize what it is supposed to look like. If they get tripped up on a step, they know that they can fall back on the graphic organizer to support them. Rather than having to walk the students through every step, I can give them a prompt to use their graphic organizer, and they can usually figure out the rest independently, which affords me the ability to spend time elsewhere in the classroom. Graphic organizers have proved to be a highly effective tool for our classroom, and I have been able to incorporate them into different units – proportions, percent problems with tip, tax and discount, etc.
They came to me as a class of students who were almost entirely reliant on teacher support in solving problems. Given their extremely different ability levels, this dependency made classroom management nearly impossible. The use of differentiated graphic organizers when introducing skills with multiple steps has been transformational in bridging the gap towards independence.
My job as their teacher is to provide them with the appropriate supports to access the curriculum and meet the relevant math standards. My goal on how students access the curriculum is different for each one. The use of graphic organizers allows me to instill in all of them the ability to use their resources independently to solve problems. I hope that I will not only have provided them a way to engage the standards, but I will also have given them a sense of self-sufficiency to meet any problem.