studying learning through activity: a basis for a theory of task design martin a. simon new york...
TRANSCRIPT
Studying Learning through Activity: A basis for a Theory of Task DesignMartin A. Simon New York University
University of Maryland, Feb. 1, 2013
Collaborators
Ron Tzur, Luis Saldanha, Evan McClintock, Arnon Avitzur, Nicora Placa, Jessica Tybursky, Tad Watanabe, Gulseren Karagoz, Ismail Zembat, Karen Heinz, Margaret Kinzel, Peg Smith, Barbra Dougherty, Zaur Berkaliev
Omitted from this Talk
Discussion about the research approach upon which this is all based
Discussion of what we mean by “studying learning” in contrast to many other researchers.
See Simon et al, 2010
Fair game for Q&A
Problem
Many students do not develop deep understanding of mathematical concepts
Limits most students
Major issue of equityDisadvantagedLate bloomersSpecial education
IntroductionMultiple aspects of mathematics education (problem solving, conceptual understanding, communicating about mathematical ideas …)
Focus on the learning of mathematical concepts
How does one promote new mathematical concepts?
Limitations of problem solving approach (being the non-solver)
Lack of theory supporting building from concrete.
Approach to promoting concepts based on research on learning.
We Are All Piaget
Chess example (e.g., fork)
Learning through activity (reflective abstraction)
AbstractionAnticipationGoal directed activityReflection
The Road Less Traveled
IF learning through activity is a useful description of learning alternative to problem solving approach.
Possibility of designing to directly foster the process.
Promoting activity (raw material)Promoting reflection (processing the raw material)
Learning through Activity
Analyze the learning in chess example
Odd-Even Example
odd X odd = ?5x5=2519x21=39939x37=1443
Learning that it seems to be true
Mathematical understanding is not the result of an empirical learning process
RA not ELP (cont.)
Mathematical understanding is the result of reflective abstraction Knowing logical necessity Development of an anticipation Abstraction from one’s activity
Analyze following example:
Odd-even example:
Even ≡ everyone has a dance partner
Odd ≡ everyone has a dance partner except one person
RA not ELP (cont.)
Example with objects: 5x3
OOO OOO OOO OOO OOO
RA not ELP (cont.)
Example with objects: 5x3
O O O O O
OO OO OO OO OO
Similar activity with different numbers
Current Work
Contrast with important work on social interactive aspects of learning
Design experiments (teaching experiments) promoting concepts fractions and ratio
Begin with conjecture about design for learning through activity (next slide)
Develop concept-specific learning trajectories
Deepen understanding of learning through activity
Develop design principles
Conjecture about Design for Learning through
Activity 1. Assess student understanding
2. Articulate a learning goal (articulation of understanding)
3. Specify an activity or activity sequence that students currently have available
4. Design tasks that will engage students in the intended goal-directed activity AND lead to learned anticipation – reflection on activity (not deterministic)
Example from Research
Goal: recursive partitioning (part of concept)
Here is 1/3 of a unit, make 1/6 of a unit
Kylie repeats part 3 times and then cuts the first third into two parts
Repeats this process with 1/5 of a unit to make 1/10 of a unit
Recursive Partitioning (continued)
Given 1/3, asked to make 1/9
K: [Cuts the bar into 3 parts] One of those is one ninth.
R: How do you know
K: Because, um. How many times does three go into nine? ... Three times. And it's one third! So. Three times three is nine [indicates that since the bar is 1/3, there would be 3 of the 3 parts, therefore ninths
[continues this process on subsequent problems]
Analysis of Example
How do we explain the learning?
Planning this learning.
If the student gets stuck, we missed something.
Contrast with problem solving approach.
Potential Contribution to Instruction
Goal: Improved ability to engineer task sequences that foster particular understandings for a diverse set of students.
A Thought ExperimentNot atypical classroom scene
Competent teacher
Problem representing math to be learned
Students work in pairs – rich representations available
1or 2 pairs solve problems –most don’t
Class discussion – 1 pair presents solution
With teachers help others seem to understand solution
Who will more likely … ?
Difference in cognitive demands of generating a solution versus understanding a solution (apply to abstraction)
A Thought Experiment (cont)
Equity issuemore-advanced students work novel problems, less-advanced students struggle to follow explanations of solutions
Vision for Instruction What if 80% could produce the new abstraction?
Understand LTA design principles task sequences foster abstractions
(build up requisite experience)
Apply this in small groups (change in large group)
Potential Contribution to Curriculum Development
Provide strong conceptual framework for task development and sequencing
Thank you for your attention!
Q&A