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%