Transcript Geo and Measurement_Module 11

ASSESSMENT AND CORRECTION
MATHEMATICS EDUCATION:
ECED 4251
Rosalind Duplechain, PhD
University of West Georgia
College of Education
Geometry and Measurement
Module 11
Basic Structure of PPt
• Lecture (slides 3-10)
– How the D&C Process works with Geometry and Measurement
– Geometric Thinking and Measurement
• Application (slide 11)
– See textbook for more examples of error patterns associated
with geometry and measurement.
• Other related ideas (slides12-13)
– What you should student know?
– Other ideas related to correction
• Homework - (See Course Calendar).
The D&C Process: Four Sub-processes
DIAGNOSE errors in pre-data
GOAL: Find out exactly what
student is doing to get problem
wrong so error can be corrected.
REFLECT on post-test score
GOAL: to determine next step.
CORRECT errors
GOAL: Use specified correction
steps to correct problems that
are wrong so student can be
successful.
EVALUATE correction strategy
GOAL: to determine if errors have been
corrected by administering a post-test.
Correcting Algorithm Errors…
Conceptual Only – Using manipulatives/drawings only, show Teacher Guided
and talk aloud while solving problem. Emphasize ideas related
to student’s error. Repeat until student can do alone.
Experiences
Intermediate – Using manipulatives/drawings, show and talk
Teacher Guided
Experiences
aloud while solving problem. Also, teach and show that the
algorithm is a step-by-step record of what is being done with
manipulatives. Emphasize ideas related to student’s error.
Repeat until student can do alone.
Procedural Only – Using only the algorithm, show and talk
aloud while solving problem. Emphasize ideas related to
student’s error. Repeat until student can do alone.
Independent Practice (procedural) –
Provide problems
for student to solve alone, using only the algorithms. Once
practice is completed, teacher checks work. If work earns
<85%, teacher repeats correction cycle beginning on either the
intermediate level or the procedural only level.
Teacher Guided
Experiences
Student-only practice
Teacher feedback
Geometric Thinking…
• Pierre and Dina van Hiele, a Dutch husband-and-wife team
of mathematicians investigated and described how children
develop an understanding of Euclidean forms for many
years.
• They concluded that children pass through five stages of geometric
understanding (Van de Walle et al., 2010, pp. 400 - 404), irrespective
of age (p. 404):
–
–
–
–
–
Stage 0: Visualization
Stage 1: Analysis
Stage 2: Informal Deduction
Stage 3: Deduction
Stage 4: Rigor
• “Most students in Pre-K through grade 8 will fall within the” first three
stages (p. 404).
– This suggests that Pre-K to 5, our certification range, would need to focus on the
first two stages: Stage 0 and Stage 1.
5
Geometric Thinking
• van Hiele – Levels of Geometric Thinking
– Level 0: Visualization
– Level 1: Analysis
– Level 2: Informal Deduction/Abstraction
– Level 3: Deduction
– Level 4: Rigor
• For specific information:
• See Van de Walle (2010), pp. 399-404
• Teaching and implications, pp. 404 - 433
• Google van Hiele or Geometric Thinking
Geometric Thinking…
• Level 0: Visualization (Van de Walle, 2007, pp. 413414)
– Recognize, sort, and classify shapes based on global
visual characteristics, appearances.
• “A square is a square because it looks like a square.”
• “If you turn a square and make a diamond, it’s not a
square anymore.”
– Because appearance is dominant at this level,
appearances can overpower properties of a shape.
Geometric Thinking
• Level 1: Analysis (Van de Walle, 2007, p. 414)
– Recognize, sort, and classify shapes based on
their properties (number of sides/faces and edges
and the size of angles).
• “A square is a square because it has four equal sides and
four equal angles.”
• “This is a right triangle because it has three sides and three
angles and one of those angles is a right angle.”
• Because an understanding of how properties of shapes relate
is lacking, each property is understood in isolation of other
properties.
– “A square is not a rectangle.”
Measurement
• Area - “The measure of a bounded region on
a plane or on the surface of a solid” (Webster
1996, p. 72).
– Bounded region = inside
• Perimeter - “The outer boundary of a figure
or area; circumference” (Webster, 1996, p.
1004).
– Outer boundary = outline
Unit Conversions of Measurement
• Some common measurement relationships:
– 1 Gallon = 4 quarts
– 1 Foot = 12 inches
– 1 Quart = 4 cups
– 1 Yard = 3 feet
Application
• Let’s apply what we’ve learned today about the
D&C Process to violations of algorithms, and in
particular to Geometry and Measurement.
–
–
–
–
Martha
Oliver
Denny
Margaret
What Should Student Know?
• Determining what a student should know about solving these types
of problems is very similar to analyzing student work for their errors.
• Work each problem on the pretest and compare student’s work
(step by step) and answer to your work (step by step) and answer.
– For any problem that is wrong, ask yourself:
• What exactly is student doing to get this work (step by step) and this
answer?
• Making this kind of comparison enables you to do two things:
– 1) Develop a checklist for these types of problems. Then you can use this
checklist to help you diagnose future errors with these types of problems.
– 2) Tells you exactly what the student is doing to get the problem wrong. Then
you can devise a strategy for correcting his/her error.
Other ideas related to correction
• For numerous activities that can be turned
into learning center activities or that can
be tweaked to fit into the correction
process discussed in this course, refer to
Van de Walle (2010), pp. 404-433.
– Level 0 Thinkers
– Level 1 Thinkers
– Level 2 Thinkers
Homework
• See Course Calendar.