How Do Students Learn? Let’s take a look and see.
Jan 06, 2018
How Do Students Learn?
Let’s take a look and see.
In a Balanced Mathematics Program
• Students become proficient with basic skills, develop conceptual understanding, and become adept at problem solving.
• All three areas are important and included—none is neglected nor de-emphasized.
- Skills without conceptual understanding are meaningless.
- Conceptual understanding without skills is inefficient.- Without problem solving, skills and conceptual
understanding have no utility.
• A rigorous, balanced program, requires that the students are competent in each area.
Me and My Brain
• Identify who will be your 3:00, 6:00, 9:00, and 12:00 date. (It can’t be an individual in your group because families don’t date.)
• Simple facts about the brains• Take 30 seconds to list everything you
remember about the brain.• Talk with your 3:00 date about what is on
your list. Add any additional information they have.
• Do the same thing with your 9:00 date.
Teaching Mathematics the Way the Brain Learns Best
The nature and structure of Mathematics is brain compatible. The brain is naturally predisposed to processes that facilitate and enhance the learning and understanding of Math. Math is not always taught effectively. The problem is, we don’t always teach in ways that use the brain’s most natural and strongest predispositions. The key is to teach the way the brain learns best. The process by which the brain learns can be described in the diagram on the following slide.
The Process by Which the Brain Learns
Pre-Dispositions for Learning• EMOTION affects learning.• The brain naturally seeks PATTERNS.• The brain naturally searches for UNDERSTANDING and
MEANING.• The brain naturally connects new learning to PRIOR
LEARNING or EXPERIENCE.• The brain naturally has a SENSE of NUMBER or quantity.• The brain is predisposed to REASON by predicting outcomes or
patterns.• PROBLEM SOLVING is a propensity of the brain.• The brain naturally adapts to and interprets ABSTRACTIONS.• The brain has a propensity of verbal or nonverbal
COMMUNICATION.• The brain naturally learns by OBSERVATION or MIMIC.• People have different PREFERENCES and ABILITIES for
learning.• The brain has NEEDS and LIMITATIONS for learning.
MATH CONCEPTS SHOULD BE REPRESENTED USING VARIOUS
MODELS OF LEVELS OF ABSTRACTION
LEVELS OF ABSTRACTION AS DIFFERENT CONNECTIONS
CONCRETE: Actual objects
SEMI-CONCRETE: Pictures of objects
SEMI-ABSTRACT: Countable marks
ABSTRACT: Symbol 3
CONNECT TO SEVERAL MODELS, PRIOR LEARNING
LEVELS OF ABSTRACTION AS DIFFERENT CONNECTIONS• Understand the MEANING of Operations.• Use THINKING STRATEGIES including
chunking, number structures, properties, and patterns, to retrieve the facts.
• Use REHEARSAL techniques and consolidating activities for retention and memory (see next slide):a. short, frequent episodesb. novel, fun approachesc. spiral chunks of learning in practice episodes
• EMOTION can enhance or impede learning and memory function. Success is vital.
• Connect new learning to PRIOR LEARNING for understanding.
Effect of Rehearsal
Think-Pair Share
• With a partner in your group discuss how you currently incorporate rehearsal into your instruction.
• With the same partner discuss what you can do to better incorporate rehearsal into your instruction.
Primacy/Recency Effect
The brain learns best the first part, next best the last, and learns least the part just past the middle. The brain is attracted to boundaries and lines.
Processing New Information• Write the numbers 1-10 on a piece of paper as shown
below.1.2.3. : :
• You will have 12 seconds to look at the list of 10 words on the next slide.
• When the words disappear, write as many of the 10 words as you remember on your paper.
• Write each word by the number that represents its position on the list, i.e., the first word on line one, etc.
KEF
LAK
MIL
NIR
VEK
LUN
NEM
BEB
SAR
FIF
1. _______
2. _______
3. _______
4. _______
5. _______
6. _______
7. _______
8. _______
9. _______
10. ______
Retention During a Learning Episode
Retention During a Learning Episode
Retention in a 40-Minute Learning Episode
Retention in an 80-Minute Learning Episode
Retention in a 20-Minute Learning Episode
AVERAGE PRIME AND DOWN-TIMES IN LEARNING EPISODES
Retention in Two 20-Minute Learning Episodes
Approximate Ratio of Prime-Times to Down-Time During Lesson Episode
Approximate Ratio of Prime-Times to Down-Time During Lesson Episode
The Learning Pyramid
Teach Others/Immediate Use of Learning
Practice by Doing
Discussion Group
Demonstration
Audio-Visual
Reading
Lecture
The learning pyramid shows the average percentage of retention of material after 24 hours for each of these instructional methods.
AverageRetention Rateafter 24 Hours
5%
10%
20%
30%
50%
75%
90%