Brain Compatible Strategies Boomerang Brain Compatible Strategies Boomerang Teachers spend on...

Brain Compatible Strategies

Boomerang

Teachers spend on average a total of 26 school days of a year

trying to quiet students down.

Boomerang

WhistleMusic

SingingMusic Instrument

Hear My VoiceClapping

Processing Questions

• What

• So What

• Now What

ACTIVITYSPORTS

Football

_____________

Baseball

_______________

Hockey

_____________

Basketball

____________

ACTIVITYSPORTS

Football

Giants

_____________

Baseball

Yankees

_______________

Hockey

Rangers

Islanders

_____________

Basketball

Knicks

____________

Make an Make an AppointmentAppointment

Draw a clock face. Write 3, 6, 9, and 12.

Draw lines outward from each number. Make an appointment with four different, new people in the room.

But we want different results.

Change is difficult.

We want to bring the joy and passion back into the classroom.

Discussion QuestionThink-Pair-Share

• Find one person you do not know and be ready to report the following to the large group in 5 minutes:– Other person’s name– Other person’s teaching experience– Other person’s neuroscience strategies already in

Building a Group Ladder

Start any activity or discussion by having everyone write down a response, alone. Next

have them share with one other person, pairs. After that they share in a small group and finally in the large group you will have

created a level of comfort for most students in the group. By using this ladder you will never face a room of blank stares when you hope

for a response.

Mathgician

I promised answers.Understand math and have fun?

Accessible for all students without sacrificing rigor?

How?Instruction informed by brain-based learning research

will develop students’ visual understanding into symbolic math competency.

Students’ develop a rich and rigorous conceptual understanding… for continued math

achievement.

Magic Square

Have the students create a Magic Square by placing the numerals 1, 2 , 3, 4, 5, 6, 7, 8, and 9 in three columns of three.

Have them arrange the numbers so that when you add them vertically, horizontally, and diagonally, the answer will continue to be 15.

Magic SquarePlace the numerals 1, 2 , 3, 4, 5, 6, 7, 8, and 9 in three columns of three so that when you add them vertically, horizontally, and diagonally, the answer will continue to be 15.

Magic Square

Place the numerals 1, 2 , 3, 4, 5, 6, 7, 8, and 9 in three columns of three so that when you add them vertically, horizontally, and diagonally, the answer will continue to be 15.

Magic SquarePlace the numerals 1, 2 , 3, 4, 5, 6, 7, 8, and 9 in three columns of three so that when you add them vertically, horizontally, and diagonally, the answer will continue to be 15.

•Increases student achievement by 22%

•Cues, questions and advance organizers help students use what they already know about a topic to enhance further learning.

•These tools should be analytical, focus on what is important, are most effective before a learning experience.

Cues, Questions, and Advance Organizers

CONNECTING TO PAST LEARNINGS

InterviewsShort StoryGraphic OrganizersMural or Collage

CONNECTING TO PAST LEARNINGS

Music Activity

Models

Student Ideas

Quotes

Are you running out of wall space to hang posters? I bought a 10 ft. section of 1/2 inch PVC pipe and four ninety

degree corners at my hardware store. I then cut the pipe into equal lengths

and put it together using the four corners. I hung it form my ceiling with

a swivel and string. Then I attached four posters I had made on my

computer relating to operations of integers. Now my kids can look at the

rules for adding, subtracting, multiplying, and dividing integers at a

glance.

Research QualityGrade Level of

EvaluationExamples

A 1 High quality experimental study, blind comparison, reference standard, appropriate population

Low quality experiment

High quality observational study, population is specified and appropriate, referenced standard, not blind

C 4 Low quality observational study, evaluations were completed without sensitivity

D 5 Expert opinion

Khan, Riet, Kleinjen, 2001, Undertaking Systematic Reviews of Research on Effectiveness

OUTCOMES% of Participants who Demonstrate Knowledge, Demonstrate

New Skills in a Training Setting, and Use New Skills in the Classroom

TRAINING

COMPONENTS

Knowledge SkillDemonstration

Use in theClassroom

Theory and Discussion

10% 5% 0%

..+Demonstration in Training

30% 20% 0%

…+ Practice & Feedback in

Training

60% 60% 5%

…+ Coaching in Classroom

95% 95% 95%

Joyce and Showers, 2002

Coaching Impact

RESPECT

ATTITUDE

BEHAVIORS/MANNERISM

KNOWLEDGE/SKILLS

SMART MODEL

Physician’s Creed:

First, Do No Harm

Educator’s Creed:

Above all, do nothing to

diminish hope

Wisdom from Dr. Bill…

• If your students like you, there is nothing they won’t do for you.

• If your students don’t like you, there is nothing they won’t do to you.

TRUST ACTIVITIES

Grapho

Remote Control Math

Dicated Math

• Student populations do not look or act like they did 50 years ago or even 20 years ago.

• Educators and parents need to let go of what worked 10 years ago.

Diverse Subpopulations of LearnersCity White African

AmericanLatino/ Hispanic

Asian Other

Los Angeles

8.9 11.2 73.3 3.8 2.8

Atlanta 8.37 85.98 4.1 0.59 0.96

St. Louis 14.1 81.8 2.3 1.7 0.3

Philadelphia

13.3 64.4 15.8 5.6 0.3

Detroit 3.0 90.73 5.1 0.8 0.3

Chicago 8.1 48.6 37.6 3.2 2.5

Oakland 6.3 40.0 33.2 16.3 4.2

Cleveland 16.7 70.3 10.4 0.3 2.0

New York City

14.3 33.1 39.0 13.5 0.0

Dallas 5.1 29.7 64.1 0.9 0.2

2005-2006 Enrollment Demographic Information gathered from district websites.

The Achievement Gaps Continues…Comparison of CST Math Achievement Over Time By Demographic Groups

Year and Grade

All Students

Econ Disadv (55%)

Parent no college(35%)

EL (20%)

African Am. (7%)

Latino(46%)

Students from traditionally underserved demographic population continue to under-achieve over the past 7 years.

Data from star.cde.ca.gov

2007 TIMSS DATA2007 TIMSS DATA

• The Trends in International Mathematics and Science Study (TIMSS) measures mathematical content domains including number-sense, geometrical shapes, measurement, algebraic skills, and data displays in both 4th and 8th grades. There were 36 countries participating in grade 4, and 47 countries participating in grade 8. Key findings include:

In 2007, U.S. 4th graders (529) and 8th graders (508) were higher than the TIMSS average of 500.

Compared to 1995, the average math score for U.S. 4th graders (511) and 8th graders (492) was higher.

In 2007, 10% of 4th graders and 6% of 8th graders scored at or above the advanced international benchmarks for mathematics.

At grade 8, there were no measureable differences between U.S. males and females, though at grade 4, there was a 6 point male advantage.

2007 TIMSS DATA 42007 TIMSS DATA 4thth Grade GradeCountry Average Score International Average 500Hong Kong 607Singapore 599Chinese Taipei 576Japan 568Kazakhstan 549Russian Federation 544England 541Latvia 537Netherlands 535Lithuania 530UNITED STATES 529Germany 525Denmark 523Australia 516Hungary 510Italy 507Austria 505Sweden 503

Slovenia 502

Armenia 500

Slovak Republic 496

Scotland 494

New Zealand 492

2007 TIMSS DATA 82007 TIMSS DATA 8thth Grade GradeCountry Average Score

International Average 466Chinese Tapai 598Korea 597

Singapore 593Hong Kong 572Japan 570Hungary 517England 513Russian Federation 512*UNITED STATES 508 Lithuania 506Czech Republic 504Slovenia 501Armenia 499Australia 496Sweden 491Malta 488Scotland 487 Serbia 486Italy 480Malaysia 474Norway 469Cyprus 465Bulgaria 464Israel 463Ukraine 462

PISA DATA: 15 yr. oldsPISA DATA: 15 yr. olds(Program for International Student (Program for International Student

Assessment)Assessment)

A test of mathematical literacy for 15 year old students which focuses upon the direct application of mathematical principles. The test is administered every three years, with 57 countries participating in 2006. The test was not designed to measure curricular outcomes, but rather to assess mathematics within a real world context.

In 2006, the average U.S. score in mathematics literacy was 474, lower than the international average score of 498.

Among the 57 countries in the sample, the U.S. was outperformed by 31 countries in math and 22 countries in science (m = 489).

There was no measureable change in either the U.S. mathematics literacy score from 2003 to 2006, or the U.S. position compared to the international average.

PISA DATA: 15 yr. oldsPISA DATA: 15 yr. oldsCountry Average ScoreInternational Average 498

Chinese-Taipai 549Finland 548Hong Kong-China 547Korea 547Netherlands 531Switzerland 530Canada 527Macao-China 525Liechtenstein 525Japan 523New Zealand 522Belgium 520Australia 520Estonia 515Denmark 513Czech Republic 510Iceland 506Austria 505Slovenia 504

PISA DATA: 15 yr. oldsPISA DATA: 15 yr. olds

Country Average ScoreInternational Average 498

Germany 504Sweden 502Ireland 501France 496United Kingdom 495Poland 495Slovak Republic 492Hungary 491

Luxembourg 490

Norway 490

Lithuania 486

Latvia 486

Spain 480

Russian Federation 476

UNITED STATES 474

PISA TragedyPISA TragedyNational Science Board (2004)

Enrollment in science and engineering programs is expanding ten times faster in China than in the United States.

Approximately two-thirds of Chinese undergraduate students earn math, science, or engineering degrees compared to just one-third of United States undergraduate students.

Science and engineering graduate programs have seen a 10 percent decline in the enrollment of U.S. students over the past decade, while enrollment of foreign graduate students has increased by 35 percent.

Approximately 5.7 percent of 24 year-olds in the United States have a science or engineering degree, which is half that of Taiwan (11.1 percent), South Korea (10.9 percent), and the United Kingdom (10.7 percent). (Sivy, et al., 2004)

Given the global demand for high tech workers, there is a greater exportation of jobs overseas due to a combination of cheaper wages, as well as a better educated workforce in mathematics and science.

No Child Left Behind does not emphasize Science in the curriculum. Therefore, the No Child Left Behind does not emphasize Science in the curriculum. Therefore, the applicational possibilities of mathematics often overlooked!applicational possibilities of mathematics often overlooked!

4 Reasons for U.S Decline4 Reasons for U.S Decline

1. The language of math matters! Building number connections centered around a base-10 principle is crucial in the development of mathematical efficiency when problem solving.

2. Dry and boring material. Mathematical skill building needs to be FUN, and therefore needs to be presented in the format of games and activities.

3. Too much focus on the answers. In order to become facilitators of mathematical knowledge, students should practice multiple methods of problem solving from both a visual-spatial and verbal approach.

4. Time on task. Most elementary math instruction occurs in the afternoon, just 45 minutes per day.

Percent of First Year College Students in 2-year and 4-year Institutions Requiring Remediation

Those who require remediation in college often fail to earn a degree

Many High School Graduates Report Gaps in Their Preparation

Impact of When Algebra is Taken

Problem SolvingProblem Solving

What’s the problem with problem solving?

Basic computation: 80%-90% accuracy

Comprehension:Comprehension:33% accuracy33% accuracy

Optimizing the Optimizing the Problem Solving ProcessProblem Solving Process

• ProcessingProcessing by encouraging students to restate the problem and state their solution plan.

• Vocabulary developmentVocabulary development for consistent and clear verbal and written communication.

• Effective questioningEffective questioning to foster independent, creative thinking and curiosity.

• Equitable practicesEquitable practices to ensure student engagement and to foster resourcefulness, independence, interdependence, and confidence.

Sample 8th grade problem I373

- 194a) 179b) 189

c) 221d) 289

94% correct

Sample 8th grade problem IIIIf John drives his car at an average speed of 50 miles per hour, how long will it take him to drive 275 miles?

a) 5 hours, 5 minutesb) 5 hours, 25 minutesc) 5 hours, 30 minutesd) 2 hours, 5 minutes

32% correct

Problem Solving Computational and Procedural Skills

Conceptual Understanding

“Where” the math works “How” the math works

“Why” the math works

Balance Defined

Memorization Procedureswithout connections to understanding, meaning or concepts

Procedureswith connections to understanding, meaning or concepts

Doing math

Cognitive Demand Spectrum

Tasks that require memorized procedures in routine ways

Tasks that require engagement with concepts, and stimulate students to make connections to meaning, representation, and other mathematical ideas

Smith, Stein, et al.

Enhancing Math Skills

• In both algebra and geometry, use different steps and the same colors to do the same steps in each problem. Alternatively, students can use different colored highlighters to identify the steps of problems.

• In word problems, box or highlight the words indicating the operation, underline the words indicating what the problem is looking for, and circle all numbers, whether in digits or in words. This will help the child translate the words into math.

• 24. You can make this game yourself by taking square cards on which you put 4 numbers. The students are to make 24 by adding and subtracting all the number, and there may be more than one way to achieve the goal. More advanced students may have double-digit numbers and may use multiplication and division and division. Students in algebra can use the number as exponents.

• PEMDAS. This exercise teaches students the importance of order of operations and is for middle school students. The numbers are place horizontally and the student is to use the order of operations without changing the positions of the numbers to make a true statement. You can use problems from the text by removing the operational signs.

PEMDAS.

3 8 10 6 5

PEMDAS.

(3+8) = (10+6-5)

(3+8-10) = (6-5)

PEMDAS.

(3+8-10) = (6-5)

School Statistics.

Graphing

Human Graphs

Measurement

Length

Volume

Weight

Cinquains

• a short, simple poem.

• It is a creative outlet for reflecting on the meaning of a concept of information just learned.

Why use CINQUAINS in the classroom

• Synthesizes information for greater understanding

• An evaluation tool as an alternative to a regular assignment or quiz

• Creative expression—get students involved more

Guidelines

• The first line is a one word title (usually a noun).• The second line is a two word description of the topic

(usually two adjectives).• Line three is three words expressing action of the

topic (usually three “ing”• words).• The fourth line is a four word phrase showing feeling

for the topic.• The fifth line (last line) is a one word synonym that

restates the essence of the• topic.

6th Grade Cinquain

Integer

Positive, Negative

Opposing, Counting, Numbering

Whole and its opposite

Signed

7th Grade Cinquain

Central Number

Summing, Averaging, Middle

Sum divided by count

Statistic

Algebra 1 Cinquain

Steepness, direction

Rising before running

Measures rate of change

Write your own Cinquain….

• Polygon

• Probability

• Circle

• Inequality

Prior Knowledge Shout Out

Assessing Your Current Knowledge Of How We Learn Mathematics

1. The brain comprehends numerals first as words, then as quantities.

2. Learning to multiply, like learning spoken language, is a natural ability.

3. It is easier to tell which is the greater of two larger numbers than of two smaller numbers.

4. Practicing mathematics procedures makes perfect.

5. Using technology for routine calculations leads to greater understanding and achievement in mathematics.

6. Symbolic number operations are strongly linked to the brain's language areas.

Is the statement generally True or False?

Each Brain is Unique

• We are products of genetics and experience

• The brain works better when facts and skills are embedded in real experiences

Multiple Learning Styles

HOW DO INDIVIDUALS PROCESS INFORMATION?

SIGHT - 75%

HEARING - 13%

TOUCH- 6%

TASTE - 3%

SMELL - 3%

Information Flow

• Eyes 10,000,000

Sensory System

TotalBandwith

(Bits/sec)

ConsciousBandwith

(Bits/sec)

• Ears 100,000

• Skin 1,000,000

• Taste 1,000

• Smell 100,000

Mind Map Guidelines

• Start in the center of the paper with an image or symbol.

• Make the branches closest to the center thicker, and make the attached branches farther from the center thinner.

• Each line must be connected, starting from the central image.

• Organize like things together on connected branches.

• Use at least 3 colors.• Use colors as your own special code to show

people, topics, themes or dates, to make the Mind Map more beautiful.

• Include symbols and pictures whenever possible.

• Develop your own personal style of Mind Mapping. Your Mind Maps should be unique.

HandshakeHandshake Handshake

Brain Compatible StrategiesHandshake – Handshake – Handshake

This activity can be used in many ways from introductions to reviewing content. Facing

each other pairs shake hands while repeating their life history, recent content, or content anticipated. It is not intended as a listening

activity as both people are talking at the same time. If they cannot think of what to say next

they repeat “hallelujah” over and over until the brain engages once again.

Thinking Outside the Box

Turn the Roman numeral IX into 6 by making only one line.

IX IX invert it XI top half is VI

I X 6 = 6

How many squares are there in the figure below?

Thinking Outside the Box

4 X 4 = 16 4 across and 4 down

Four more, 4 by 4 interior squares

4 X 4 = 16 + 4 = 20

4 X 4 = 16 + 4 = 20 + 2 = 22

Two more 4 by 4, vertical middle squares

Two more 4 by 4, horizontal middle squares

4 X 4 = 16 + 4 = 20 + 2 = 22 + 2 = 24

One more 4 by 4, middle square

4 X 4 = 16 + 4 = 20 + 2 = 22 + 2 = 24 + 1 = 25

3 by 3 squares

3 by 3

Four more, 3 by 3 squares

4 X 4 = 16 + 4 = 20 + 2 = 22 + 2 = 24 + 1 = 25 + 4 = 29 3 by 3

One more large square

4 X 4 = 16 + 4 = 20 + 2 = 22 + 2 = 24 + 1 = 25 + 4 = 29 + 1 = 30

What is Brain Based Learning?

• Taking what we know about the brain, about development and about learning and combining those factors in intelligent ways to connect and excite students’ desire to learn.

• Combining emotional, factual and skill knowledge into a cognitive tool.

Brain Basics

Parts of the Brain

Brain Functions

Brain Processing

• Frontal lobe - Cortex– Creativity - Judgment - Optimism - Context– Planning - Problem solving - Pattern making

• Upper temporal lobe - Wernicke’s Area– Comprehension - Relevancy - Link to past (experience) - Hearing - Memory

- Meaning• Lower frontal lobe - Cortex

– Speaking/language - Broca’s area• Occipital lobe - Spatial order

– Visual processing - Patterns - Discovery• Parietal lobe

– Motor - Primary Sensory Area - Insights - Language functions• Cerebellum

– Motor/motion - Novelty learning - cognition - balance - posture

Musical Activity

Choice (content, process, resource, environment)

Relevance (personal, in context)

Feedback (as immediate as possible)

Engagement (emotionally, physically, verbally)

“How Are You Today?”(choose one of these)

Passionate Very BlessedAmazing Nearly IllegalSlightly Irregular AwesomeExcellent Beautiful It’s a Long Story Highly

Underrated

Increase Student Motivation

Working in cooperative groups; encouraging teamwork

Providing challenging, exciting, and relevant curriculum

Extrinsically from rewards (or punishments) such as grades, promotion, jobs and opportunities

Providing an environment to develop ownership for learning

Teachers and Students Working Together!

• Intrinsic student motivation is powerful!

•Extrinsic motivations are less powerful in student learning

Differentiation by InterestMath

Sequence of Numbers –Real Number System Choice Board

Write a poem about the number groups or sequence of numbers

Sing a song/rap about the groups or sequence of numbers

Draw a picture that represents the grouping of numbers

Explain and describe the problem generated from a geometric representation of an irrational number using the Pythagorean Theorem

Construct a number line with only decimals and fractions with different denominators

Web search and report- if it’s not a Real Number, what is it?...how do we sequence non Real numbers

Write a paragraph about the importance of understanding the ordering of numbers in elation to Money/Finances and what number groups are associated with money

Emotion and Learning:Implications for Mathematics

Instruction

Emotion and Education

Emotion drives attention, which drives learning, memory and problem solving and almost everything else we do…by not exploring the role that emotion plays in learning and memory, our profession has fallen decades behind in devising useful instructional procedures that incorporate and enhance emotion. (Sylwester, 1998)

Mathematics Education Slope

• Standard 1: The student must be able to calculate the slope of a line that passes through any two points on the coordinate plane.

• Standard 2: The student must differentiate between positive/negative slope.

• Standard 3: The student must understand the meaning of slope in application problems.

Mathematics EducationSlope: Standard Approach

• Algebraically define slope

• Calculate slope for several pairs of points

• Describe positive and negative slope

Mathematics EducationSlope: Standard Approach

122211 ),(),(

yymasdefinedisslopeyxandyxFor

488,3,4,2

righttoleftfromfallslinem

horizontalislinem

righttoleftfromriseslinem

Mathematics EducationSlope: Emotional Approach

Year Blue Book Value1997 $21,0651998 $18,0251999 $16,2402000 $14,4602001 $12,7052002 $11,0002003 $9,2502004 $7,600

Subaru Outback DepreciationSource: www.kellybluebook.com

$5,000

$10,000

$15,000

$20,000

$25,000

1997 1999 2001 2003

122211 ),(),(

yymasdefinedisslopeyxandyxFor

488,3,4,2

righttoleftfromfallslinem

horizontalislinem

righttoleftfromriseslinem

• Interpretation: Depreciation of -1,923.57 $ per year• Follow Up:

– Which cars might have higher/lower rates of depreciation? Why?

– Do any cars have a positive appreciation? Why?

– Will depreciation always be linear? Why?

27.195320041997

600,7065,21

Mathematics EducationLines: Emotional Approach

The price of cable television has rapidly increased in the recent past. Mathematically model this trend and use your model to make several predictions regarding the future pricing of cable television.

Average Cable TV PricesSource: Paul Kagan Associates, Inc

1994 21.62

1995 23.07

1996 24.41

1997 26.48

1998 27.81

1999 28.92

Cable TV Costsy = 1.5083x + 15.581

R2 = 0.9938

4 5 6 7 8 9

Cable TV has steadily raised about $1.51 per year. A linear model was used because when a steady increase of something is used it is a viable way to predict the future. The linear model for this particular problem was y = 1.508x +15.581. The model tells us that the increase each year is about $1.51 and in 1990 the cost was about $15.58. If you plug in “x” … you can predict the cost … in the year 2010 the cost will be about $45.74.

(Student Response)

Mathematics EducationQuadratics: World Population

World population has been increasing rapidly in the last century. Accurately predicting world population is important from an economic, political and social standpoint.

World Population

(source: www.xist.org)

Year Pop (Billions)

1950 2.555

1955 2.780

1960 3.039

1965 3.346

1970 3.708

1975 4.088

1980 4.457

1985 4.855

1990 5.284

1995 5.691

World Population y = 0.0004x2 + 0.0526x + 2.5113

R2 = 0.9993

0 10 20 30 40 50

Year (1950=0)

I think the quadratic … (y = ax^2 +bx+c) better illustrates the world population. The past chart shows that the population [rate] rises nearly a full billion every 10 years. The quadratic form follows this pattern more closely. Notice that more of the points line up with the quadratic’s solution.

(Student Response)

Having an accurate count of future population makes it possible to make predictions for what social needs must be met in the future. It tells us how many people will be living in a voting district or estimated population of a city. It can tell us how much money we will need for social program like welfare, or how big to build roads leading to growing rural areas. With a linear growth model we will not have accurate numbers for determining social, political and economic needs. (Student Response)

Movement

• Physical activity helps oxygenate the blood, which in turn oxygenates the brain.

• Sensorimotor skills and practice encourage muscle memory.

• Muscle memory can tie to academics.

Problem-solving is promoted through individual and group physical activities.

Partners

Visual Representations are excellent for teaching math

Concrete to Representational to Abstract(CRA)

Three stages of learning

C = Learning through concrete hands-on manipulative objects

R = Learning through pictorial forms of the math skill

A = Learning through work with abstract (Arabic) notation

CRA Strategy

Fractions with popsicle sticks and how they translate into

adding and subtracting fractions

Small Manipulative Modeling Tips

Use transparent manipulative objects on an overhead projector

Apply magnetic adhesive to a teacher set of manipulative objects to use on magnetic white boards

Develop large posterboard renditions of the manipulative objects to use on table tops or walls

Use an evaluated table with an angled stand that can support manipulatives securely

Provide students with their own set of manipulatives as you modeled

Virtual Manipulatives

Virtual Library of Mathematics Manipulatives

http://nlvm.usu.edu/

Parallel Lines Cut by a Transversal

• Kinesthetic: Walk It Tape the diagram below on the floor with masking tape. Two players stand in assigned angles. As a team, they have to tell what they are called (ie: vertical angles) and their relationships (ie: congruent). Use all angle combinations, even if there is not a name or relationship. (ie: 2 and 7)

Circumference and Diameter of a Circle

Create enough space for all students to form a circle.

Have one student walk heel to toe around the entire circle making sure to count his steps and finish at the same spot where he started.

At the original starting point have the same student turn toward the circle and walk a straight line from one side of the circle to the other, heel to toe and counting all of his steps.

That student has just marked both the circumference and diameter of a circle. The relationship is pi. The general equation is the circumference of a circle is a bit more than three times the diameter of the same circle (pi=3.141).

Doing this kinesthetically could produce and inexact results but will be close enough to teach the concept.

Triangle

Have five students stand side by side, each about five feet apart.

Ask the student to the immediate left and right of center to take three steps forward.

Ask students on the outside to take six steps forward. The group has now formed a triangle.

ArabicComprehension

VerbalComprehension

[EIGHT]

MagnitudeComparison

5 < 8?

Prepare & ExecuteResponse

[right]

Identification Comparison Response Notation effect Distance effect Response-side effect(arabic vs. verbal) (close vs. far) (left vs. right)

(S. Dehaene, J. Cognitive Neuroscience, 8(1), p49, 1996)

Mapping Cognitive Functions onto Neural Structures

Dehaene & Cohen 1995

Comparison

The Neural Machinery of The Neural Machinery of MathematicsMathematics

EXECUTIVEDYSFUNCTION

• Selective Attention

• Planning Skills

BRAIN REGION

• Anterior Cingulate/• Subcortical

structures

• Dorsal-lateral PFC

MATH SKILL

• Procedure/algorithm knowledge impaired

• Poor attention to math operational signs

• Place value mis-aligned

• Poor estimation• Selection of math process

impaired• Difficulty determining

salient information in word problems

• Organization Skills

• Self-Monitoring

BRAIN REGION

• Dorsal-lateral PFC

MATH SKILL

• Inconsistent lining up math equations

• Frequent erasers• Difficulty setting up

problems

• Limited double-checking of work

• Unaware of plausibility to a response.

• Inability to transcode operations such as (4X9) = (4X10) – 4

• Retrieval Fluency

BRAIN REGION

• Orbital frontal PFC• Anterior Cingulate• Dorsolateral PFC(dictated by strategy

and effort)

MATH SKILL

• Slower retrieval of learned facts

• Accuracy of recall of learned facts is inconsistent

Working Memory In The BrainWorking Memory In The Brain

Working Memory System

• Phonological Loop

• Visual-Spatial Sketchpad

• Central Executive System

Mathematical Skill

• Retrieval of math facts

• Writing dictated numbers

• Mental math

• Magnitude comparisons

• Geometric Proofs

• Inhibiting distracting thoughts

• Modulating anxiety

• Regulating emotional distress.

Executive Functioning Skills: (frontal lobes)

Executive control mechanisms are a set of directive processes such as planning, self-monitoring, organizing, and allocating attention resources to effectively execute a goal directed task.

Executive functioning dictates “what to do when”, a critical process in solving word problems.

Executive functioning allows students to choose an appropriate algorithm when problem solving.

Executive Functioning Skills:

Dorsal-lateral cortex - helps to organize a behavioral response to solve complex problem solving tasks.

Orbitofrontal cortex - rich interconnections with limbic regions and helps modulate affective problem solving, judgement.

Anterior cingulate cortex - allocates attention resources and modulates motivation.

Discovery Neurogenesis

The discovery thatthe human brain cangrow new brain cells.

What downregulates neurogenesis:• Acute and chronic stress• Lack of physical activity• Poor nutrition

What enhances neurogenesis:• Low stress• 30-90 min./day of physical activity• Quality nutrition/Novelty

Neurogenesis:Neurogenesis: If you’re not enhancing it,

you’re working against yourself.

Runner Bingo

Discovery - Allostasis

“Allo” ….meaning “adjusted”

“Stasis” … meaning “stability”literally…

“a new stable baseline”

Breathing

Your Most Powerful Tool

Laughter!Physiological Effects –

Increases oxygen in the brain

Produces endorphins which boosts learning

Psychological Effects –

Bonding occurs when laughing together

Makes kids comfortable

Happily Ever Laughter

• Laughing releases the feel good hormone – endorphine- also a natural pain killer.

• Laughing lowers your blood pressure and heart rate.

• Laughing raises T-lymphocytes in your body.

• Increases your immune system .

• There is a 45 minutes residual chemical effect in your body after hearty laughter.

Laughter in the Classroom

• Increasing a feeling of hope --- taking the drudgery out of the time in class.

• Increasing retention

• Building rapport

• Relieving stress

How Humor Promotes RetentionHow Humor Promotes Retention

OxygenEndorphin Surge

Gets Attention!

Positive Climate

Increases Retention

Discipline

Mental Health

Function Junction

Function Junctionx f(x) Rule

• Demonstrate individual support for all students• Encourage and employ collaborative learning• Heighten student awareness about benefits of

nutrition, sleep, and fitness• Emphasize the importance of water for electrolytic

balance and hydration• Create opportunities for paired learning and peer

sharing • Provide experiences that target student interests

and concerns

Meet the intellectual, social, emotional, and physical developmental needs of

adolescents

•Tap prior knowledge to construct meaning

•Employ scaffolding strategies

•Teach study skills and learning how to learn

•Utilize both inductive and deductive reasoning

•Afford all students adequate processing time

Create atmosphere that is high in challenge and low in threat

• Provide choice of topics, ways of learning, and modes of expression

• Feature hands-on and touchable learning situations

• Increase motor activity, lab experiences, arts, music, and drama

• Build and nurture curiosity• Offer opportunities for self-assessment and

reflection • Give frequent and elaborative feedback

Emphasize an active approach to

instructional practice

• Seek patterns, relationships, and connections among the disciplines

• Reveal interconnectedness of concepts across multiple contexts

• Select essential concepts to investigate and explore deeply

• Plan and implement integrated units of study • Use project-based learning that connects

students’ effort with real life• Infuse the arts across the curriculum to build

and extend meaning

Adopt curricular models that support best practice

• Project-based and Authentic Learning Project-based and Authentic Learning OpportunitiesOpportunities

• Simulations and Role PlaysSimulations and Role Plays• Debates and Learner DiscourseDebates and Learner Discourse• Learning Strategies and Strategic Instruction Learning Strategies and Strategic Instruction

– Advance and Post organizersAdvance and Post organizers– Frequent checks for understandingFrequent checks for understanding– Elaboration and feedbackElaboration and feedback

Classroom Practices that Promote

Adolescent Learning

Content EnhancementsContent Enhancements• StorytellingStorytelling

• DrawingDrawing

• MusicMusic

• MnemonicsMnemonics• Concept maps; mind mappingConcept maps; mind mapping

Classroom Practices that Promote

Adolescent Learning

Batting Averages

Batting Averages – Middle School

Student teams will choose to follow one baseball team for ten games during the regular season. Each team will choose the most valuable member of that team for the season and be ready to defend the decision using appropriate statistics as evidence. The team will also be responsible for a broadcast in which they will report the analysis, categorization, and interpretation of the statistics. Team members will also create visual representations to demonstrate the results, including a Powerpoint presentation. In addition, they will submit individual journals in which each member has tracked the process of the broadcast development as well as daily team statistics.

Dealing with Uncertainty

Each student choose a partner, and together they take turns collecting and recording data.

The data recorder begins by guessing by guessing the sum of the last two digits of an imaginary zip code and writes the guess on data form.

Using the zip code page from a phone book, the other partner, with eyes closed randomly points to a zip code number on a page.

Dealing with Uncertainty Guess of sum of the last two digits________

Last two digits Sum of last two digits Matched the guess

Dealing with Uncertainty

The data collector then gives the actual sum of the last two digits of the number closest to his/her partner’s finger as well as the sum of the last two digits of the next number.

This is done for the next 13 consecutively listed numbers, bringing the total to 15 sums in all.

The recorder writes each of these sums and counts up and records the number of times his or her guess matched the sums.

How Do Genes Fit?

How Do Genes Fit? - Middle School

The goal of this unit, is to give the students hands-on experience in choosing appropriate strategies for problem solving. The students will find themselves drawing from past knowledge and experience as they progress in a logical and sequential manner toward their conclusions. They will begin to develop the critical thinking skills so vital today, skills necessary to create multiple strategies for multiple solutions.

Students will “marry” by picking matched numbers out of two baskets (one for girls and one for boys). They will organize and chart their hereditary history, and decide on the number of offspring they will have. Employing Mendel’s elementary probability models, they will attempt to predict the the probability of hair and eye color of these offspring. To do this, they must make their own probability models in a clear and easily understand manner.

Student Mother Father Sibling 1 Sibling 2 Sibling 3

Hair Color

Eye Color

In part 2, students with similar hair and eye color combinations will group together in sets of two pairs, and compare their model outcomes to see if similarities exist. They will then begin to look for any correlations, either positive or negative, to see if any outcomes are predictable. If a correlation is the extent to tow or more things are related to one another, would there be a positive or negative correlation between hair or eye color or parents and their off spring? Why?

Graphing

Graphing – Middle School

Students will work in groups (teams) of three to four. Each team will choose an original topic (name brand clothes) for use in the survey.

The teams will gather data from their sample populations, collate their data, and construct three graphs as a team; bar graph, a circle graph, and a pictograph, each using the identical set of data.

Graphing – Middle School

Each team will submit a written report describing the organization of their study, their data-gathering methods, and their conclusion.

The team will present their findings to the class in an oral report using visual supports (graph). The final oral presentation will also include an evaluation of the different graph types, listing positive and negative aspects as well as the appropriateness of each graph type in regard to the data.

Stock Market

Stock Market – Middle School

Students are each given a theoretical $500 to invest. They then pair up, “pool” their money, and select 6 or 7 stocks from a previously selected group of 20 choices.

These stocks are to be tracked over a fourteen week period on a spread sheet as well as a daily line graph (one graph per stock).

At the end of the four week period, students will combine the separate graphs into one long “multi-graph” showing the team’s total stock data.

Stock Market – Middle School

For the final graph, the teams will take the data directly from the spreadsheets so as to reduce the possibility of error due to carelessness.

Students as well as teacher will assess the final graphs as to their accuracy, readability, neatness, and ease of comprehension.

In addition, the students will draw inferences about their data.

Business Proposal

Student groups will determine the business they might like to own and operate.

They will research the typical costs of running the business and the typical income made with the business.

They will perform a break-even analysis to study the results.

They will present their findings to the class in the form of a bank proposal.

Business Proposal

Students will create appropriate graphs using the research date and will demonstrate how they will arrive at and/or pass the break-even point.

The proposal should be persuasive.

Students will also reflect on their own presentations in a post-project reflection and in journal entries.

Problem Solving

Activities for Learning Problem Solving

Activity Description Process

Brainstorming Group Problem-solving technique that involves the spontaneous contribution of ideas from all members of the group

Students seated in small groups speaking simultaneously yet listening to each other’s ideas without pre-judging.

Make It Simple Analyze the problem Students working on problems in order to break them down into their basic components

Using Logical Reasoning Inductive reasoning moves from particular examples to general principle

Deductive reasoning move from general principle to specific examples

Inductive reasoning: If every bowl of soup served you was hot, you would assume all soup is served hot.

Deductive reasoning: If soup is always served hot, and you are eating soup, then what you are eating must be hot.

Work Backwards Begin with the problem solution and work backwards to identify the original problem

Have students start with a problem solution and have them work to create an original problem with a result that will match the original

Make a Picture or a Diagram A picture or a diagram gives visual learners an opportunity to better understand the problem

While reading the problem, students (or the teacher) are (is) encouraged to diagram or illustrate the problem as if it were a story board

Make a Chart or a Table A chart or table helps to present information in an organized way so that students can better visualize and understand the given information

While reading the problem, students (or the teacher) are (is) encouraged to create a chart or table to help organize thinking

Make an Organized List An organized list divides the information into groupings that help students understand and process the problem’s information

While reading the problem, students (or the teacher) are (is) encouraged to create an organized list to better visualize the problem’s information

Look for a Pattern The innately seeks to reorganize large groupings of information into smaller groupings that repeat in a fixed sequence it can comprehend

While reading the problem, students (or the teacher) are (is) encouraged to look for smaller subsets of information that seem to repeat throughout the problem

Guess and Check This method probable is the first strategy the students used when they were younger

Students guess the problem’s solution, and then check to see if their guess is correct

Home Improvement

The class is divided into different teams for house painting.

Each team must submit a bid for painting several rooms in the principal’s home.

They must put together an estimate of what the job will run, both in labor and supplies as well as profit.

The job is to include painting the living room, dinning room, and family room walls, as well as the ceilings in all three areas.

A floor plan and elevation drawings are supplied.

Coaster Math Project

Coaster Math Project – High School

A large national amusement part is sponsoring a contest for design and construction of model roller coaster made from everyday, basic materials (e.g. toothpicks, straws, popsicle sticks, and metal tubing.) The coaster is to give the sensation of speed, acceleration, and thrill while keeping the ride safe. All of the completed models are to be functional so that designers will be able to demonstrate the capabilities of the various coaster models.

Data Analysis

Data Analysis – Grade 3 - 5

Have students discuss the number of brothers and sisters they have.

List the number in columns on the board.

Discuss that some students have same number or siblings and others have different numbers; some have more and some have less.

This activity introduces the concepts of range, mode, mean and median.

Truth – Truth – LieLike some of the others on this list you may have used this before. Remember that the bigger your repertoire the more

options you have “in the moment.” Have students in groups of three or more.

Each comes up with two truths and one lie. These can be personal or content

based. This is another way to check for understanding and review content. They

try to determine which is the lie.

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