Teaching and Teaching and Learning Learning MathematicsMathematics

How did we get to where we How did we get to where we are?are?

Sputnik -- 1957Sputnik -- 1957

Led to the Woods Hole Led to the Woods Hole ConferenceConference

Chaired by Jerome BrunerChaired by Jerome Bruner

Sooner is Better!!Sooner is Better!!

Clashed with PiagetClashed with Piaget

History after Woods History after Woods HoleHole 1960 – Meaningful Math (New Math)1960 – Meaningful Math (New Math)

Not only do we need to know Not only do we need to know math, we math, we need to be fluent math need to be fluent math theorists! theorists!

1980 – Back to the Basics1980 – Back to the Basics

Test scores have fallen, it’s a direct Test scores have fallen, it’s a direct result of a lack of understanding result of a lack of understanding

the the basicsbasics

History continuedHistory continued

1989 National Council of Teachers of 1989 National Council of Teachers of Mathematics (NCTM) StandardsMathematics (NCTM) StandardsTeaching, Curriculum, AssessmentTeaching, Curriculum, Assessment

Adopted ConstructivismAdopted Constructivism1.1. reasoning, reasoning, 2.2. problem solving, problem solving, 3.3. communication, communication, 4.4. representation representation

The Time Line of The Time Line of Mathematics Mathematics InstructionInstruction1900 1930 1900 1930 1960 1970 1980 1990 2000 1960 1970 1980 1990 2000

|________|________|________|_______|_____|________>|________|________|________|_______|_____|________>

<---Behaviorism--><-Bruner-><-Piaget---><Info <---Behaviorism--><-Bruner-><-Piaget---><Info Processing>Processing>

Drill & practice, Drill & practice, Meaningful New Meaningful New ConstructivismConstructivism

learning assoc-learning assoc- math math, math math,

iations iations Spiral Spiral

CurriculumCurriculum

Timss — Trends in Timss — Trends in International Math and International Math and

Science StudyScience Study 13-year-olds from the U.S. are scoring 13-year-olds from the U.S. are scoring

substantially lower in mathematics substantially lower in mathematics than students from Korea, Ireland, than students from Korea, Ireland, Spain, and the United KingdomSpain, and the United Kingdom

second International Assessment of second International Assessment of Education Progress -1991, U.S. Education Progress -1991, U.S. Students were outperformed by Students were outperformed by Korean, Swiss, and Taiwanese Korean, Swiss, and Taiwanese students in students in every areaevery area of mathematics of mathematics

TIMMS continuedTIMMS continued

U.S. students are outperformed U.S. students are outperformed by French and Hungarian by French and Hungarian students in four out of five areas students in four out of five areas tested. tested.

13-year-old American students 13-year-old American students outperformed only Luxembourg, outperformed only Luxembourg, Nigeria, and SwazilandNigeria, and Swaziland

2006 data – no change2006 data – no change

NAEP – National NAEP – National Assessment of Education Assessment of Education

Progress – Since 1969 Progress – Since 1969 1 in 5 4th and 8th Graders is 1 in 5 4th and 8th Graders is

proficient in mathematicsproficient in mathematics 1/3 of 4th graders are below basic 1/3 of 4th graders are below basic

(lowest level)(lowest level) 1% of 8th graders were proficient 1% of 8th graders were proficient

in Algebra, Geometry and basic in Algebra, Geometry and basic functionsfunctions

No Child Left BehindNo Child Left Behind

– 1) to institute high academic 1) to institute high academic standards for all students, and standards for all students, and

– 2) to insure that there are 'highly 2) to insure that there are 'highly qualified' teachers in every U.S. qualified' teachers in every U.S. classroomclassroom

NCLB cont.NCLB cont.

Content StandardsContent Standards. .

Annual TestingAnnual Testing. Ninety-five . Ninety-five percent of all students in grades 3 percent of all students in grades 3 – 8 must undergo annual testing – 8 must undergo annual testing in mathematics and reading. in mathematics and reading.

NCLB cont.NCLB cont.

Every Child’s Test ScoreEvery Child’s Test Score. NCLB . NCLB requires that every student be requires that every student be tested (only very minor exceptions tested (only very minor exceptions exist for severe mentally or exist for severe mentally or physically handicapped students) physically handicapped students) and that every child reach and that every child reach proficiency by 2014. (if subgroup proficiency by 2014. (if subgroup fails, the whole school fails) fails, the whole school fails)

NCLB cont.NCLB cont.

SanctionsSanctions. By 2014 . By 2014 everyevery American American student who is tested (100%) must student who is tested (100%) must demonstrate Adequate Yearly Progress demonstrate Adequate Yearly Progress (AYP) in reading and mathematics After (AYP) in reading and mathematics After five years of inadequate test score five years of inadequate test score gains, a school falls into the gains, a school falls into the “reconstitution” category. Such a fate “reconstitution” category. Such a fate results in dismissing the school’s results in dismissing the school’s teachers and administration and closing teachers and administration and closing the school. the school.

NCLB cont.NCLB cont.

Highly Qualified TeachersHighly Qualified Teachers

Licensed in the area they Licensed in the area they teachteach

Understand the contentUnderstand the content

Gifted teachersGifted teachers

What do we need to do in What do we need to do in order to compete in math order to compete in math

internationally?internationally? Look at mathematics differentlyLook at mathematics differently Teach it DifferentlyTeach it Differently Require students to solve Require students to solve

problems to learn algorithmsproblems to learn algorithms Focus on Problem solving not Focus on Problem solving not

mechanicsmechanics

NCTM 2000 Six Features NCTM 2000 Six Features of the of the NewNew Standards - Standards - 200020001.1. Equity – high expectations for Equity – high expectations for allall

students to study and learn students to study and learn mathematicsmathematics

2.2. Curriculum – coherent, well-organized Curriculum – coherent, well-organized learning that integrates mathematics learning that integrates mathematics ideasideas

3.3. Teaching – understanding what Teaching – understanding what students know and need to learn and students know and need to learn and using effective pedagogical strategiesusing effective pedagogical strategies

44. Learning – actively building . Learning – actively building conceptual understanding and conceptual understanding and proficiencyproficiency

55. Assessment – ongoing and routine . Assessment – ongoing and routine enhancement of student learning and enhancement of student learning and teacher instructionteacher instruction

66. Technology – normal and expected . Technology – normal and expected support for effective mathematics support for effective mathematics teaching and learningteaching and learning