V1: Double-Column  Addition  (C.  Kamii)

     Answer the following questions based on the video Double-

Column Addition.


   1.   Recall the five "theme standards" of the NCTM Stan-

        dards  2000  Draft:  problem  solving,  reasoning  and  proof,

        communication,  connections,  and  representations.   Cite

        specific  instances  from  the  video  which  illustrate  these

        themes.



   2.   On  page  6  of  Van  de  Walle  there  is  a  list  of  five  shifts

        in the environment of mathematics classrooms that

        were proposed in the Professional Standards of 1991.  What

        episodes  in  the  video  indicate  that  the  classroom  shown

        seems  to  be  moving  in  the  direction  suggested  by  these

        shifts?



   3.   On page 34 of Van de Walle there is a list of seven strate-

        gies  for  effective  teaching.  Which  of  these  strategies

        were employed in the video?  Support your answers with

        situations from the video.



   4.   What episodes from the video are related to our discussion

        of procedural vs.  conceptual understanding?



   5.   On page 32 of Van de Walle, there is a figure outlining five

        different representations of mathematical ideas.  Van

        de Walle encourages getting students to translate back and

        forth between the various representations to help students

        make mathematical connections, including connections be-

        tween procedural and conceptual understanding.  Which of

        the five representation modes occur in the video?  There

        are 20 possible translations between representation modes.

        Cite examples of 2 or three, if they were present.