Leveraging Formative Assessment & Technology
Using GeoGebra to Help Diagnose & Address
Mathematical Misconceptions
Dr. Pamela J. Buffington
Education Development Center
GeoGebra at Ithaca 7/26/10
“Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances student’s learning.”
NCTM Principles and Standards for School Mathematics, 2000
Abstract Visual
“A major problem for students who struggle with mathematics is weak understanding of the relationships between the abstract symbols of mathematics and the various visual representations.”
Hecht, Vagi, and Torgesen (2007)”
The Power of Convergence
Formative Assessment– Assessment Principle:
Assessment should support the learning of important mathematics and furnish useful information to both instructors and learners. (NCTM, 2000, p 22)
Interactive Technology– Technology Principle: Technology
is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances learning. (NCTM, 2000, p 24)
Formative assessment can provide critical information about existing conceptions / misconceptions
Technology can provide accurate, interactive, visual images of mathematical concepts and ideas
Instructors can provide a targeted instructional intervention for learners’ specific needs and remediate potential barriers to learning
Enrich Student Learning of Mathematics
Instructional technology enriches student learning of mathematics by: – improving their skills and concepts through
multiple representations; – enhanced visualization; – increased construction of mathematics meaning; – providing interactive examples that extend beyond
“real world” limitations;– individualized and customized diagnoses, remediation,
and evaluation.
(EdThoughts: What we know about mathematics teaching & learning, p. 66)
Key Resources
Diagnostic Assessment
Interactive Technologies
Resources
Research Brief around a Given Topic
Diagnostic Probe to Elicit Understanding and Misunderstandings
Instructional Materials:AppletSupporting ResourcesOverviewStudent Exploration
Typical Student Errors
Overgeneralizations: – Applying incorrect rules such as “multiplication
makes bigger”Conceptual Misunderstandings
– Viewing the equals sign as “place answer here”Common Errors (Procedural)
– Incorrect Decimal Placement when multiplying
Diagnostic Assessment Prompts
Diagnostic assessment prompts are designed to uncover understandings and misunderstandings and the results are used to inform instruction rather than make evaluative decisions.
Paper & Pencil, Moodle Quiz, Zoomerang, Google Form, Polls
Example from Research
Parenthesis and other bracketing symbols should provide a perceptual aid for unitizing...Some students ignore or overlook bracketing symbols, as in 4(n+5)=4n+5. Other students perhaps in response to the order of operations exhortation to do what‘s in parenthesis first, focus on parenthesis to the exclusion of the overall structure of the expression. And finally, the equation-solving advice to clear the parenthesis first may prompt many students to overlook the variable unit in their haste to eliminate grouping symbols.
(Algebraic Thinking)
Elicit Student Thinking
Is a(b+c) equivalent to a(b)+c ? Distributive Property Applet
Distributive Property: Area Model
Comparing Whole Number Products Applet
5 ( 9 )5 ( 5 + 4 )5 (5) + 5 (4 ) 25 + 20
Prerequisite Knowledge
Visual / Interactive Approach
Applet (2b)
Participant List 13-17Jing
Difference of Squares - Conceptually
1
Visual Representation
Difference of Squares – Tool for Thinking
2
Predict – Check - Generalize
Decimal Probe
Comparing Decimals
Learning Tools List # 4
Integer Operation: Walking the Number Line
Participant List
Formative Assessment: How long is the pencil?
Sample
Reading a Ruler
19d & 19e
Comparing Fractions
Interactive Resources
Accessible online at http://maine.edc.org/
For Additional Information Contact:Pam Buffington [email protected]