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 pbuffington@edc.org