8: Forms of Thinking
- Page ID
- 10373
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)A few years ago one of us (Kelvin) had the privilege of co-teaching with an experienced first grade teacher, Carolyn Eaton. As part of a research project, Ms Eaton allowed some of her reading lessons to be observed. Here is what Kelvin saw when Ms Eaton was having a conference with Joey. They are reading a book "together", except that Ms Eaton wants Joey to do as much reading as possible himself. Joey's comments are capitalized, and Ms Eaton's are in lowercase.
JOEY: FIRST YOU READ-THEN ME. THIS IS WHAT YOU HAVE TO DO. I READ AFTER YOU, OK?
Ms Eaton: OK. [Ms Eaton begins.] "In the great green room there was a telephone, a red balloon, and a picture of..." Are you going to read, or what?
YES.
"In the great green room there was..." Are you ready yet? Ready to read?
OK. "IN THE GREAT GREEN ROOM. . . "
"...there was..."
"THERE WAS A..." [pauses, looking at Ms Eaton rather than at the words]
"...a telephone..."
YES, THAT'S IT, A TELEPHONE! "IN THE GREAT GREEN ROOM THERE WAS A TELEPHONE, A RED BALLOON..."
"and a picture of..."
"AND A PICTURE OF" [pauses, staring at the wall]. .A COW JUMPING?"
"a cow jumping over the moon".
"OVER MOON" [smiles from both Joey and Ms Eaton].
Joey, what does this say? [She points to the word telephone.]
"THERE WAS A TELEPHONE".
How about here? [She points to next page, which reads "And there were three little bears, sitting on chairs".]
"THERE WERE BEARS, THREE BEARS, AND THEY SAT ON CHAIRS".
Can you read the whole book?
SURE!
OK, then you start this time.
[Joey looks at first page, alternately at the picture and at the words.]
"IN THE GREAT GREENROOM THERE WAS A TELEPHONE".
[Actual text: "In the great green room, there was a telephone",]
"AND THERE WAS A RED BALLOON",
[Actual text: "...and a red balloon",]
"AND A PICTURE OF THE COW JUMPING OVER THE MOON".
[Actual text: "...and a picture of the cow jumping over the moon".]
"AND THERE WERE..." THREE BEARS?... "LITTLE BEARS SITTING ON CHAIRS".
[Actual text: "And there were three little bears, sitting on chairs,..."]
Could you read this book with you eyes closed?
SURE; WANT TO SEE ME DO IT?!
Well, not right now; maybe another time. Could you read it without the pictures, just looking at the words? That's how I do best— when I see the words instead of the pictures.
[Joey pauses to consider this.] MAYBE, BUT NOT QUITE SO WELL.
Let's try it. [Ms Eaton proceeds to copy the words on a large sheet for Joey to "read" later.]
As Carolyn Eaton's behavior suggests, there are decisions to make "on the fly", even during the very act of teaching. Ms Eaton wonders when to challenge Joey, and when to support him. She also wonders when to pause and ask Joey to take stock of what he has read, and when to move him on ahead— when to consolidate a student's learning, and when to nudge the student forward. These are questions about instructional strategies which facilitate complex learning, either directly or indirectly. In this chapter we review as many strategies as space allows, in order to give a sense of the major instructional options and of their effects. We concentrate especially on two broad categories of instruction, which we call direct instruction and student-centered instruction. As we hope that you will see, each approach to teaching is useful for certain purposes. We begin, though, by looking at the ways students think, or at least how teachers would like students to think. What does it mean for students to think critically (astutely or logically)? Or to think creatively? Or to be skillful problem solvers? Forms of thinking lead to choices among instructional strategies.