Teaching and Learning Mathematics How did we get to where we are?

Sputnik Led to the Woods Hole Conference Led to the Woods Hole Conference Chaired by Jerome Bruner Chaired by Jerome Bruner Sooner is Better!! Clashed with Piaget

History after Woods Hole 1960 – Meaningful Math (New Math) 1960 – Meaningful Math (New Math) Not only do we need to know math, we need to be fluent math theorists! 1980 – Back to the Basics 1980 – Back to the Basics Test scores have fallen, it’s a direct result of a lack of understanding the basics

History continued 1989 National Council of Teachers of Mathematics (NCTM) Standards 1989 National Council of Teachers of Mathematics (NCTM) Standards Teaching, Curriculum, Assessment Adopted Constructivism Adopted Constructivism 1. reasoning, 2. problem solving, 3. communication, 4. representation

The Time Line of Mathematics Instruction |________|________|________|_______|_____|________> Drill & practice, Meaningful New Constructivism learning assoc- math math, iations Spiral Curriculum Curriculum

Timss — Trends in International Math and Science Study 13-year-olds from the U.S. are scoring substantially lower in mathematics than students from Korea, Ireland, Spain, and the United Kingdom 13-year-olds from the U.S. are scoring substantially lower in mathematics than students from Korea, Ireland, Spain, and the United Kingdom second International Assessment of Education Progress -1991, U.S. Students were outperformed by Korean, Swiss, and Taiwanese students in every area of mathematics second International Assessment of Education Progress -1991, U.S. Students were outperformed by Korean, Swiss, and Taiwanese students in every area of mathematics

TIMMS continued U.S. students are outperformed by French and Hungarian students in four out of five areas tested. U.S. students are outperformed by French and Hungarian students in four out of five areas tested. 13-year-old American students outperformed only Luxembourg, Nigeria, and Swaziland 13-year-old American students outperformed only Luxembourg, Nigeria, and Swaziland 2006 data – no change 2006 data – no change

NAEP – National Assessment of Education Progress – Since in 5 4th and 8th Graders is proficient in mathematics 1 in 5 4th and 8th Graders is proficient in mathematics 1/3 of 4th graders are below basic (lowest level) 1/3 of 4th graders are below basic (lowest level) 1% of 8th graders were proficient in Algebra, Geometry and basic functions 1% of 8th graders were proficient in Algebra, Geometry and basic functions

No Child Left Behind –1) to institute high academic standards for all students, and –2) to insure that there are 'highly qualified' teachers in every U.S. classroom

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

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

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

NCLB cont. Highly Qualified Teachers Highly Qualified Teachers Licensed in the area they teach Understand the content Gifted teachers

What do we need to do in order to compete in math internationally? Look at mathematics differently Look at mathematics differently Teach it Differently Teach it Differently Require students to solve problems to learn algorithms Require students to solve problems to learn algorithms Focus on Problem solving not mechanics Focus on Problem solving not mechanics

NCTM 2000 Six Features of the New Standards Equity – high expectations for all students to study and learn mathematics 2. Curriculum – coherent, well-organized learning that integrates mathematics ideas 3. Teaching – understanding what students know and need to learn and using effective pedagogical strategies

4. Learning – actively building conceptual understanding and proficiency 5. Assessment – ongoing and routine enhancement of student learning and teacher instruction 6. Technology – normal and expected support for effective mathematics teaching and learning