Learning and Science
Mathematics cont.
Bluebook Anticipatory Set
 Learning and Mathematics cont.
 Discussions–Questioning Strategies
 Learning and Science
 Current Issue Journal Article for D2L

For Thursday: Quiz #1, Current Issue Journal
Article topic approval by Oct. 12th
Bluebook Anticipatory Set
Review all previous types of
assessment (strengths and weaknesses
in each charts) and describe how you
would create an assessment for Quiz
#1 (Chap. 1-6).
 How would you divide the 25 pts.?
 What kinds of questions would you use?
 How would you divide the chapters?
Justify your response…

Problem Solving in Mathematics

Problem Translation
• Linguistic and Factual knowledge

Problem Integration
• Schematic knowledge

Solution planning and monitoring
• Strategic knowledge

Solution Execution
• Procedural knowledge
Expert v. Novice Problem Solvers
Area
Experts
Novices
Translation &
Integration
(representing
problems)
Focus on structural features.
Search for context,
underlying principles and
relationships in problems.
Focus on surface
features. See
problems in isolated
pieces.
Planning
Plan carefully before
attempting a solution to
novel problems.
Plan briefly then
quick adopt and try
solutions.
Monitoring
Demonstrate well developed
metacognitive abilities;
abandon inefficient
strategies
Limited
metacognition;
persevere with
unproductive
strategies
Conservation of number
Questioning Strategies
Blooms Taxonomy
(1956)
Knowledge
Comprehension
Application
Analysis
Synthesis
Evaluation
Anderson & Krathwohl
(2001)
Remember
Understand
Apply
Analyze
Evaluate
Create
Science
“The whole of science is nothing more
than the refinement of everyday
thinking.”
Einstein
Science
Before we talk about learning
science, let’s take a few minutes to
think about our experiences with
science.
Here’s a little writing task. Write
your response to the following:
Science
1) Describe a scientific
misconception you held at one time.
2) What was the source of this
misconception?
3) How long did you hold this
misconception?
4) How did you come to a new
understanding?
Mental Representations are:
The symbol structures we construct
to encode our experiences, process
them, and store them (schema).
The symbolic links between the
external environment and our
internal mental world

Mental Representations
The representations we construct
in encoding our experiences have
profound effect on our behavior and
our learning.

Learning in Science
A traditional view of science
Learning in science is similar to
learning in other areas.
Learning in science also differs in
some important ways.
Conceptual Change Model
Learners enter science instruction with
many pre-existing misconceptions or
incomplete representations that can
conflict with the teacher’s teaching of
scientific concepts.

Goal of Conceptual Change
Learners must replace their
misconceptions with new conceptions

-that is, they must find new mental
models that explain observations (data)
better than the previous ones.
-Piaget called this accommodation
Science
In addition as part of the- Conceptual
Change Model
Students need to develop scientific
thinking skills, such as how to use
their conceptions to solve problems.
Steps Toward Conceptual Change
Changing misconceptions to more
accurate conceptions involves multiple
processes.
•Recognizing an Anomaly
•Discarding a Misconception
•Constructing a New Model
•Using a New Model
•Learning to Build & Use Scientific Knowledge
Stages in Conceptual Change
Conceptual change isn’t easy,
but does follow a predictable
course.
Stages in Conceptual Change
Initial discomfort
Attempts to explain away
Attempts to adjust observations
Doubt
Vacillation
FINALLY, conceptual change

Learning and Science
Mathematics cont.
Bluebook Anticipatory Set
 Learning and Mathematics cont.
 Discussions–Questioning Strategies
 Learning and Science
 Current Issue Journal Article for D2L

For Thursday: Quiz #1, Current Issue Journal
Article topic approval by Oct. 12th
Quiz #1
Chapters 1-6 in the text
 Table of Contents/Summaries
 PP Presentations (electronic syllabus)
 Assessment Item Analysis
 Multiple Items (some of each to
match different learning styles)
 No time limit

“It is better to ask some of the
questions than to know all the
answers.”
- James Thurber