Chapter 3: Knowing and Understanding Students as Learners
The differentiated math classroom is learner-centered and attempts to tap into individual student strengths and styles since each student’s background is different. This chapter reviews the importance of learning styles, individual characteristics, and brain function in the learning of math.
The authors begin by sharing an example of a “line design” lesson that is used by sixth-grade teachers. The lesson is designed to reveal student characteristics like math disposition, work habits and learning styles. The lesson involves minilessons that lead to a product. First, they learn how to create paper and pencil drawings, using straight lines (but giving the illusion of curved lines.) Then they create their own designs and stitch them onto cardboard (I used to do an activity like this years ago, and I found this example in my closet - I never throw things away!)
The authors explain that this project can be completed by all students, but the resulting product will demonstrate the range of learners, as well as the way in which they approach math work.
As students work on this project, the teachers observe to see how students work, types of interactions between students, how students deal with making mistakes, how well they use their time, who is motivated, who is resistant, quality of work, and so on. The project helps students to learn a bit about themselves as learners and helps them to understand that they need to be responsible for their own learning.
The authors reference Caine and Caine (1992) and Jensen (1998) to point out that teachers need to be aware of the following facts about the way the brain operates: 1) “brain functions are significantly affected by social relationships and emotional responses; 2) the brain responds with positive intensity to appropriate challenge but shuts down when threatened; and 3) like fingerprints and DNA, the subtle organizational working of each and every individual brain are different.”
In order to be ready to adapt lessons and to plan effectively for the entire class, it is important to know the characteristics of students - their interests, cognitive attributes, emotional/social characteristics, intellectual needs and learning styles. The authors reference the Addressing Accessibility in Mathematics project that proposes that a teacher select three students who are representative of the range of learners in the room and create a “focal student” profile of those three students, showing their strengths and weakness in the following areas: conceptual, language, visual-spatial, organization, memory and attention. The thought is that by being sure to address the needs of those 3 learners when planning lessons, the needs of most other students will be addressed as well.
Students’ dispositions in math are important as well – are they quiet, withdrawn, outspoken, motivated (and by what), eager to think and learn, or are they discouraged?
The authors take a good deal of time to discuss learning styles (visual, auditory, kinesthetic), as well as four typical styles that have common threads.
They also reference the styles set forth by the Human Dynamics program by Dr. Sandra Seagal, and Gardner’s Multiple Intelligences. All of these are important to consider as teachers are working to create the differentiated classroom.
There is, again, quite a lot to think about here. I will have much larger classes this year, with a greater range of interests, strengths, and needs, I'm sure. Much that is offered in the chapter will be very helpful!