Understanding student misconceptions in elementary is important for

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					ED 661 Understanding Student Thinking in Geometry and Measurement

October 21-22 Agenda

1-1:30      Syllabus for Course                                     Document camera
p.m.        Goals for 2 days                                        Handout – goals and agenda
            Agenda                                                  Syllabus
            Understanding student misconceptions in                 Goals Document for Document Camera
            elementary is important for laying the                  Rubric for grading
            foundation for future work. For example,
            interpreting geometry problems in which you
            need to make a sketch, finding areas of
            polygons without an understanding of the
            attributes of those polygons…
1:30-2:00   Discuss the Van Hiele levels.                           Big Ideas posted on chart paper as
             Discuss the reading in the Van de Walle 3-            participants share
                5 book.                                             Vandewalle book
             Use the “Big Ideas” and questions brought
                by the participants as part of their pre-
                class assignment. Share at tables first,
                then in large group
             At tables discuss your big ideas, then we
                will do a large group share
             Be sure to include:
            Difficulties that students have in geometry
                 1. Build student understanding in Geometry
                     as a basis for later work in mathematics.
                 2. Discuss reading in Van De Walle. (What
                     thoughts and questions did you have?)
                          a. The van Hiele Levels of Geometric
                              Thought
                                     i. Levels are hierarchal but
                                        you can be this at any
                                        time.
                                    ii. So dependent on spatial
                                        sense
                          b. Van de Walle defines geometry
                              and number sense etc. as intuition
                              and it is up to us as teachers to
                              give kids experiences to develop
                              this.
                 3. Has Geometry been pushed to the back
                     burner due to national standards etc.
                     Right now the trend is that if the
                     mathematical strand supports algebra,
                     then we should teach it.
                 4. Should build the attributes in geometry
                     before giving students the definition.
                 5. Elementary students are at level 0 and 1.
                 6. Coverage is a myth that people have been
                     sold….covering doesn’t necessarily mean
                   learning.
                7. Graphic on Pg. 209 will help teachers
                   understand that you can’t skip steps.

2:00-2:15   Brief Discussion of Triangle activity:               Triangles document
            Tables share what their students circled and their
            definitions of triangles.
            Large Group:
            Found that all levels of students have
            misconceptions of the attributes of a triangle.
            We will refocus on this in more depth as we
            experience van hiele’s levels during the day.

2:15-3:00      Van de Walle Activity 8.1 or 7.1 Shape           Black Line Masters-BLMs 20-26
                Sorts                                            www.ablongman.com/vandewalleseries
             Note: All BLMs for the book can be                 Chp. 8 - Pages 212-213 in vandewalle book 3-
                downloaded at The ones you need are on           5
                                                                 Chp. 7 - Pages 194 vandewalle book K-2
                the CD, too.
                Read through bullets one and two, do
                bullet three, read bullet four, and do bullet
                five.
            Discuss the question under the STOP sign.
            Keep track of the language used; read and
            discuss the “Assessment Note” on page 214.

3:00-3:15   Break

3:15-3:45      Activity 8.3(7.3) Geoboard Expansion             handouts, “Geoboard Shapes to Copy.”
               See also Kathy Richardson, page 50:              Geoboards and 5 rubber bands per board
                Creating Shapes on the Geoboard.                 Pg. 215 vdw3-5, pg. 197 vdwK-2
                                                                 Kathy Richardson Book
3:45-4:15      Activity 8.6 (7.6) Mystery Definition            Mystery Definition handout
                     Provide handout to see if they can         Pg. 224 vdw3-5, pg. 207 vdw K-2
                        figure out the rule
                     Individual think time
                     Pair/share
               Design your own and have others solve it.
                See Figure 8.14(7.14) on page 225 (206) as
                an example.
                See also Kathy Richardson, page 52:
                Sorting Shapes on the Geoboard.

4:15-4:45      Activity 8.7 Triangle Sort, page 225             (BLM 29). On web.
               Give directions orally; the directions in the
                book give too much information.
               Your task is to sort the entire collection
                into three groups so that no triangle
                belongs to two groups. When this is done
                and descriptions of the groupings have
                been written, students should then find a
                second criterion for creating three
                different groupings.
                Note: the graphic on page 225 is the same
                activity we did in “Geometry Camp” (page
                4).

4:45-5:00      Closure                                       Handout for Reflection
                Exit Question - Comments
Day 2          Response to questions                       Geom. Camp materials
8-8:30         Activities 8.8, 8.11, and 8.12 correlate to Vandewalle book
                activities from “Geometry Camp” (pages 6-
                8). Review these pages and relate to the
                reading in the Van de Walle book.
            Discuss the question under the STOP sign on
            page 231.

8:30-9:30      Read the Introduction to the Casebook on      Handouts of intro and case studies 1, 2, 5
                pages 1-3. Think about the Van Hiele
                Levels as you read.
                Chapter 1: Describing 2-D and 3-D
                Objects. Read the introduction and Cases
                1, 2, and 5.
9:00-9:30      Video clip, “Quick Images”, Chapter 1 in      Video from Examining Features and
                Examining Features of Shape                   Shapes
               See notes on pages 27-28 F.G. What            (BLMs on pages 35-37 F.G.)
                different ways do the children describe the   Printed Quick Images
                images? Think about the Van Hiele levels
                that are illustrated.

               “Quick Images” math activity:.
               Seeing things in different ways. Share the
                attributes that you kept in your mind in
                order to recreate the images.
               Children relied on 3-D, real-world objects
                to describe 2-D shapes, but they don’t
                necessarily make the distinction between
                two and three dimensions.
                     Some students were not limited by
                        the orientation of the objects.
9:30-       Discuss the Focus Questions: 1, 2, 3, and 4 Focus Questions Handout
10:15        (page 38 F.G.).
             Note: Questions 1 and 2 bring up two
             topics: the use of technical geometric
             vocabulary, and the different ways a 3-D
             object can be described by listing its 2-D
             components. Throughout this course, we
             will explore the difference between a
             mathematical definition and a description
             of an object, recognizing that correct
             vocabulary includes concepts and ideas to
             think about before definitions make sense.
            Small group discussion: Focus questions
             #1-4
             (Compare the language and results you
             observed when students completed Circle
             the Triangles to the children’s’ language
             and thinking in the cases.)

            Take turns recording your thoughts on
            paper to use during the whole group
            discussion.
            Again, keep in mind the Van Hiele Levels.
          Whole group discussion
          Discussion of the shape as a whole vs. the
            parts of the shape
          The way you are thinking affects the way
            you see an object or what you notice
            about it (some may think of the shapes as
            nets)
          Purpose of the activities: develop mental
            images of the figures and the means to
            communicate about them.
10:5-    Break
10:30
10:30-      Math Activity: “What’s in the Envelope?”      Envelope and shapes
11:00        (Groups of 3) Page 39 F.G.
             Can we put 2-D shapes into the envelope?
             Discuss the names of the shapes (briefly).
             Sort the shapes into categories of your
             choice.
             Possible extension: Sort as if you were at
             a specific Van Hiele level: for example, sort
             by Level 0 criteria (or choose a different
             level).
11:00-        Chapter 2: Developing Meaning for              Orange pattern bock and rectangular
11:30          Geometric Terms. Discussion of Cases 9,        prism
               10, 11. Focus Questions 1, 2, and 3 (page
               50 F.G.) go with these cases. Have an
               orange square pattern block and a
               rectangular prism for the Case 10
               discussion.
               Small groups-Discuss the Introduction as it
               relates to the Van Hiele Levels.
             Whole group (Discuss Focus Question #6,
               too.)
11:30-      Lunch
12:30
12:30-           View the video, “Angles in a Triangle”      Video clips
1:15              See notes on page 46 F.G.                   Focus Questions 1, 2, 4
                 Math Activity, “Angles and Angle
                  Measures”—page 51 F.G. Questions 1, 2,
                  4, and 5 are activities from Geometry
                  Camp. Decide how much of each of these
                  activities you need to do to refresh your
                  memory. I would actually suggest that you
                  redo all of the activities. Discuss all the
                  questions, including #3.

1:15-3:45         Teacher Presentations: 20 minutes each      Geometry manipulatives
Break             with a bit of time to spare                 Handouts for each team
inclusive       Marnie/Colleen           Oct. 22
                Cindy/Mary               Oct. 22
                Rachel/Laurie            Oct. 22
                Sandy/Annie              Oct. 22
                Pam/Samra                Oct. 22
                Sherry/Connie            Oct. 22
                Samantha/Doreen/Nancy    Oct. 22
3:45-4:00         Exit Question                               Handout
                  Homework assignment
                  1. Provide a document asking your
                      students what an angle is through
                      words and pictures.
                  2. Hold up 3 lengths of string and ask
                      them to write their estimated length
                      and how they came to the decision for
                      that length
                  3. Next group presentations.