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The Differentiated Math Classroom: Chapter 8 - The Teacher: Knowing and Sharing the Self

Part II: The Glue: Holding It All Together
Chapter 8: The Teacher: Knowing and Sharing the Self

Chapter 8 focuses on why teachers need to know themselves, as well as know the strategies for metacognitive work. In knowing ourselves as teachers, the authors emphasize that we must truly know our own biases and beliefs, as these could “…have the potential to sabotage the good intentions of a differentiating mathematics teacher.” The authors state that teachers need to examine their own teaching and learning styles, multiple intelligences, talents and strengths, and thinking dispositions. The authors suggest that one way for teachers to learn more about themselves is to write their own math autobiographies, as was suggested for students in an earlier chapter.

The authors point out that it is somewhat true that teachers teach the way they were taught, which may or may not be the best method for the next generation of students. It is important that teachers examine the way that they teach, in order to determine whether or not they are teaching the way they were taught.

An important factor for teachers to consider is their Gregorc Mind Styles (work of Dr. Anthony Gregorc, 1982). His Mind Styles represent four possible extreme combinations for perceiving and ordering information. According to Gregorc, everyone “...has a natural, inherent predilection toward one or two of the combinations.”
The combinations (and when I read these I was reminded of a past principal being good-naturedly irritated with a colleague because he was so “abstract random!”) are:
1) Concrete and Sequential  (perceive concretely and order sequentially)
2) Concrete and Random
3) Abstract and Random
4) Abstract and Sequential

The perceiving of information ranges from concrete (using the five senses) to abstract (naturally intuitive ways), and the ordering of information ranges from sequential (step-by-step linear approach) to random (chunking information in no particular order). Referring to a 1998 ASCD publication by Pat Guild and Stephen Garger, the authors summarize each of these styles in regards to teaching:
1) Concrete Sequential teachers are practical, hands-on teachers who manage highly structured logical classrooms. They expect students to be on-task and thorough in their work. Their classrooms are predictable, realistic, and secure for students.
2) Concrete Random teachers are practical and realistic, but are also original, spontaneous, and creative. Students are encouraged to make choices, be active, and think for themselves. This type of teacher is comfortable with change, a busy environment, and a variety of methods.
3) Abstract Random teachers are enthusiastic and sensitive, and design child-centered classroom experiences. They expect students to cooperate and share. This type of teacher is spontaneous and responsive to students’ needs and interests, but also strives to increase their own understanding of content.
4) Abstract Sequential teachers provide rich but structured environments, and encourage students to be analytical and evaluative. They expect students to develop good work habits and to provide evidence to support their conclusions. This teacher pushes for greater understanding.

Which type of mind style are you? Once you have identified that, the authors believe you can develop differentiation strategies that are comfortable for you and for the other mind styles of the students. The authors mention that a concrete sequential teacher (like me) can have highly structured centers, but that the activities in the centers can meet the learners styles by being open-ended and creative. They also suggest that menu and tiered activities, as discussed in chapter 7, can be differentiated to meet all teaching and learning styles.

In addition to analyzing their mind styles, teachers need to examine their intelligences using Howard Gardner’s Multiple Intelligence Theory (verbal/linguistic, logical/mathematical, visual/spatial, bodily/kinesthetic, musical, interpersonal, intrapersonal).  The authors suggest placing  teacher strengths and natural styles at the center of the planning process. Then, teachers can visualize the four learning styles as surrounding that center, and think about a particular student in each style. Planning to meet the needs of those particular students will help the teacher to meet the needs of most students.

Bottom line - teachers need to know themselves in order to most effectively teach their students.

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