Which Shape? Student Task Core Idea 4 Geometry and Measurement

Transcription

1 Which Shape? Student Task Core Idea 4 Geometry and Measurement Identify circles, triangles, and squares among a collection of shapes. Identify two attributes of all triangles. Recognize and use characteristics, properties, and relationships of two-dimensional geometric shapes. Describe and classify two-dimensional shapes according to their attributes and /or parts of their shapes.

2 Which Shape? 1. Put the letter C inside all circles. Put the letter S inside all the squares. Put the letter T inside all the triangles. 2. List 2 ways to describe all triangles

3 Mathematics Assessment Collaborative Performance Assessment Rubric Grade 2 Which Shape? Grade 2: MAC 2004 Performance Exam Points Section Points The core elements of the performance required by this task are: Describe and classify 2 and 3 dimensional shapes according to their attributes. Communicate thinking using words or pictures. Based on these credit for specific aspects of performance should be assigned as follows 1 Correctly identifies the 2 circles, 3 squares, and 3 triangles with no 3 additional incorrect identifications. Correctly identifies eight shapes with only 1extra identification. Correctly identifies six or seven shapes with no extras or errors. (2) Correctly identifies 4 or more shapes. Additional incorrect 3 identifications may occur. (1) 2 Correctly describes 2 attributes of triangles such as: 3 sides 3 corners straight sides 1x2 closed figure 2 Total Points 5

4 Looking at Student Work Which Shape? Student A is able to discriminate the shapes requested from many different shapes represented on the task page. This student is also able to name two attributes commonly given to identify triangles. Student B is able to do the same but gives straight sides as an attribute of a triangle. Student A Student B

5 Many students did not consider the square with a corner pointing to the bottom of the page as a square. It was especially difficult for many to identify the upper middle square. This is evidenced in the examples of Student C and Student D. Student C Student D

6 Approximately 20% of the students were able to list at least two attributes of all triangles but did not use them to identify the triangles on this page. Student E identifies the isosceles triangle but not the two right triangles while Student F names the bottom right triangle and not the other two. Student E Student F

7 20% of the students could correctly identify all eight shapes from the different twodimensional shapes on the page. However, when it came to naming attributes of all triangles, they described what the shape looked like rather than a characteristic that set it apart as a triangle. Student G says that all triangles have a point at the top. Student H knows that triangles look like roofs and slides. Student I sees triangles in blades of grass and vampire teeth. Student G Student H Student I

8 Student J exemplifies one of the just over 17% of students who filled in every shape with a letter to mark them as circles, squares, or triangles. Several of the papers in this group still listed one or two correct attributes for all triangles but the majority were only able to describe what triangles looked like as evidenced in this example. Student J Teacher Notes:

9 Frequency Distribution For Each Task Which Shape? Which Shape? Mean: 2.93, S.D.: Frequency Frequency Score Score: % < = 0.9% 16.3% 38.4% 65.3% 85.7% 100.0% % > = 100.0% 99.1% 83.7% 61.6% 34.7% 14.3% The maximum score available for this task is 5 points. The cut score for a level 3 response is 3 points. Most students (61.6%) could correctly identify at least 4 shapes and identify at least one attribute of a triangle. 14% of the students could correctly identify all eight shapes and give two attributes for all triangles. Just under 1% of the students scored a zero on this task. 100% of the students attempted the problem.

10 Which Shape? Points Understandings Misunderstandings 0 100% of the students attempted to solve this task. Of the 1% of all our students who scored a zero on this task, all filled in each shape at the top of the page as if they were only circles, 1-2 Some of these students were able to identify at least four shapes correctly. 3-4 Students scoring a three or a four were able to identify most but not all of the shapes on the task page. 5 14% of the students could identify the eight shapes correctly and give two attributes for all triangles triangles, or squares. Many of the students filled in all of the shapes at the top of the page with a C,S or T regardless of their shape. About 50% of these students gave descriptions of a triangle rather than attributes. Many students could list two attributes of all triangles but did not use this information to identify either one or both of the right triangles. Those students who did not identify all eight shapes correctly were most likely to not mark the squares of non-standard orientation. Based on teacher observations, this is what 2 nd graders seemed to know and be able to do: identify the triangles and the circles identify most of the shapes Areas of difficulty for second graders, these students struggled with: identifying the rotated squares giving specific attributes of all triangles they described instead looks like a roof quantifying the number of sides and corners on all triangles only filling in the circles, triangles, and squares at the top of the page and leaving the other shapes empty.

11 Questions for Reflection Which Shape? Look carefully at your student work. How many of your students: Identified all 8 shapes correctly Identified at least 6 shapes correctly Identified at least 4 shapes correctly Gave 2 correct attributes of all triangles Gave 1 correct attribute of all triangles Now look at your student work to notice some common error patterns or misconceptions. How many of your students: Identified an oval as a circle Did not identify the rotated square(s) Did not identify all three triangles Filled in all shapes with a C, S, or T Described all triangles as: looks like a How often do your students have the opportunity to sort objects in several ways? Are your students asked to sort objects by the numbers of sides? Number of corners? Which shapes can be made with toothpicks and which need to have yarn to complete? Do your students have the opportunity to see that some shapes can be sorted into several different classifications? What would you like to remember when you are teaching Geometry next year? What would you do differently? Teacher Notes:

12 Instructional Implications: More than half of the students were successful with this problem. Teachers felt, however, that students needed to be paying more attention to the attributes of the shapes and not to just what they looked like. Looking at the similarities and differences between shapes will lead to more efficient and more correct classification and definition of basic shapes. As young children work to define shapes, they first notice large obvious aspects of the shapes. It is through handling and examining objects that they develop ideas about shapes and become more aware of which properties or attributes are important and which are not. Is a square still a square if one of its corners is pointing toward the bottom of the page? What if it is rotated just slightly is it still a square? What if I rotate it just a bit more? Sorting a set of objects in several different ways focuses students attention on the various parts of shapes and helps them to define those salient attributes. As young children participate in hands-on work with geometric shapes, they will become more and more discriminating. They will be able to sort and describe by attributes such as the number of sides, the number of corners, the number of faces, the relationship of the lengths of the sides or whether the figure has straight or curvy lines. Opening up discussions around mistakes and misunderstandings can be springboards for new learning as well as for clarifying incomplete understandings. As you review your curriculum, check to make sure that it allows for the hands-on, exploratory opportunities our students need in order to become more discriminating mathematicians. Look at the examples your curriculum presents. Are shapes represented in various orientations? These incomplete understandings may be reinforced by limited examples. Resources: Math By All Means-Geometry Grade 2 (Confer), Understanding Geometry (K. Richardson), Navigating Through Geometry (NCTM Publication Pre-K 2 nd Grade. Teacher Notes: