1 Math for multiple intelligences
How a middle-school math teacher realized she was boring and jump-started her career — and her students.
When I started teaching middle school mathematics, I was motivated to find many different methods of presenting information and giving my students different learning experiences within the classroom. But as I continued teaching, I started lecturing more and creating varied learning experiences less, because it was easier to manage a classroom during a lecture and because preparation for class also took less time. After five years of teaching, I came to realize that I was boring! I needed either to regroup or to quit teaching.
I decided to regroup and give meaningful teaching one last try. Two years ago, I began the school year with renewed vision and determination to make learning relevant to my students through problem solving. I emphasized the need for the students to be problem-solvers and thinkers, not just memorizers. I further explained that my goal was to change the students’ preconceived ideas about math — I would present examples of how math was used in real-life situations and help the kids understand how mathematical concepts were related to one another. I told them that we would discover why the rules of math made sense. I even went as far to say that I would not teach the students any skills for which I could not show them a practical application.
Class morale and enthusiasm were high as I led the class through my first thematic unit. Students were engaged in learning and were beginning to overcome their fears of the dreaded "word problem." After about a month of my problem-solving teaching, I ran into some difficulty creating a problem that would teach the rules of exponents and fit into my unit. I approached the class honestly, explaining that the concept of exponents was important to their prealgebra foundation, but that I was struggling to find an application in this specific unit that would apply to real life.
As I proceeded to explain the rules of exponents and give examples, one, student, Michael, just couldn’t "get" it. I asked him to watch a few more examples to find the pattern I was teaching. That’s when Michael’s breakdown came. I ended up having to remove him from the class. As we conferenced privately about his breakdown, he said, "If you can’t show me how it can be used in real life, I don’t see why I have to learn it." Knowing that Michael was not a misbehaver and that he had struggled greatly the year before in math, I realized that I had failed to fulfill my promise to make learning relevant. Michael’s inability to grasp a fairly simple concept reinforced my thinking that I needed to continue using a problem-solving approach to help motivate my students to learn.
As the year progressed, I felt that the students were consistently more motivated. I was able to grab their attention through the topics studied throughout the year’s themes. They seemed to be more invested in their own learning processes — taking responsibility for solving problems individually or in groups. While this process of learning math is more challenging for my students, they have risen to the challenge and impressed me with the development of their knowledge and reasoning skills.
When I sat down two years ago to re-evaluate my teaching, I realized that I needed to make four major changes:
- I needed to make sure I was getting through the math content effectively. How could I encourage mastery of the content each day?
- I needed to show the students how math applied to their lives. How could I teach them the required skills while showing them when it could be used?
- I wanted the students to become more independent learners and thinkers. How could they start to see connections between information and manipulate between mathematical patterns and concepts on their own?
- I wanted to use different learning styles to interpret and analyze information within each unit and lecture no more than about two times a week. How could I provide learning experiences that used the student’s strengths to interpret and analyze the mathematical information I had given them to determine an answer?
Each of these questions launched me into making major changes in the way I approached my teaching to make it more meaningful for the students, as well as for myself. The math content was the fundamental part of teaching, so I created a curriculum map that included each of the state and district standards. I also highlighted the skills that tend to be used most frequently and skills that the students had usually not mastered; these skills I decided to revisit and review throughout the year’s units. With the skills mapped out, I grouped them into the units that I would teach through the course of the year.
Next, I analyzed how to use math problems that would apply directly to the skills I needed the students to learn. I found several "word problem" ideas through textbooks, websites, and other resources. I found that the more word problems I worked through and incorporated into my lessons, the more ideas I had for creating additional word problems that would also support the skills I was teaching on a daily basis. These ideas sparked my change to thematic planning — the process of teaching an entire group of lessons based on a specific theme. I felt that this attention to real life connections to math would help the students be more motivated to learn and master the skills. (See my article "Grouping Skills for Mastery.")
Third, I addressed the desire to help the kids become independent thinkers and learners. I knew the students needed daily opportunities to practice thinking and learning on their own. To encourage independence, I planned to use questioning techniques to help students see connections between mathematical concepts. My questioning techniques emphasized reasoning through the content, not just getting the "right" answer. For example, after looking at three types of problems and their answers, what pattern could be used to consistently find the answers given? The pattern illustrated was the concept I intended the students to learn. This focus on reasoning took the attention of the lesson off my lecturing and put the expectation on the students to come up with solutions on their own and in small groups. (See my article "Making Small Groups Work.")
Finally, I decided to provide different types of learning experiences for the students to discover meaning in the content. By some estimates, only 20 percent of adults are auditory learners, and even fewer kids fit into this category. I needed to stop lecturing all the time! Instead, I thought that individual and group work would provide the flexibility within the lessons to lead the students to skill mastery. I incorporated lessons that supported many of the multiple intelligences and then allowed the students to decide which activities they wanted to try in order to learn the desired skills.
For example, in teaching addition of integers, individual students (or groups) could choose to illustrate, model with algebra tiles, or make a numerical example of adding two integers. Students still had to show their competency in a particular skill, but in one of various ways that supported their different learning styles. To complement the lessons, I created rubrics that supported different learning styles and questioning to assess student learning as I moved from group to group, holding students accountable for their own learning. (See my article "Assessing the Learning Process.")
And the students responded!
When I set up these new standards for my eighth grade math classes, I talked to my students, emphasizing the need for them to become problem solvers and thinkers, not just memorizers. We thought about how we tended to solve problems outside of school. Many students talked about how they would ask friends and family for advice or share their experiences to figure out how to solve a particular problem. They agreed with me that problem solving should be the focus of our attention in the classroom, not just included as a few problems on a homework assignment. Spending quality classroom time on problem solving supported my desire to present math in a way that not only made sense to the students but also demonstrated its application in everyday life, and the students were willing to work with me. It wasn’t always easy, but students like Michael helped keep me on track, reminding me to keep my promise to make math relevant.
For the past two years, I have felt that my students are more prepared by the end of the year for the next level of math. They can better determine which mathematical information is useful and not useful for solving problems, make connections among useful information, and communicate knowledge gained through problem solving than in my previous years of teaching. Just when I thought I was hitting a dead end in teaching, I realized the greater potential of motivating and challenging my students. And the effects of these changes have made all the difference in enjoying meaningful teaching.
- Next: Making small groups work