The National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics Dr. Robinson, EEX 4251, Spring 2008

The PSSM The Principles and Standards desire to set forth a “comprehensive and coherent set of goals for mathematics for all students from prekindergarten through grade 12” (NCTM, 2000). The Principles and Standards desire to set forth a “comprehensive and coherent set of goals for mathematics for all students from prekindergarten through grade 12” (NCTM, 2000).

Who was Involved? –Teachers –School administrators –Mathematics supervisors –University mathematicians –Mathematics educators –Researchers

Timeline 1951 Max Beberman – UICSM Project 1951 Max Beberman – UICSM Project 1957 SPUTNIK 1957 SPUTNIK 1960 “New Math” 1960 “New Math” 1963 FIMS – First International Mathematics Study 1963 FIMS – First International Mathematics Study 1969 NAEP – National Assessment of Ed Progress 1969 NAEP – National Assessment of Ed Progress 1973 Why Johnny Can’t Read – Morris Kline “Back to Basics” 1973 Why Johnny Can’t Read – Morris Kline “Back to Basics” 1975 NACOME 1975 NACOME 1980 Agenda For Action – NCTM “Pragmatic – Problem Solving” 1980 Agenda For Action – NCTM “Pragmatic – Problem Solving” 1982 SIMS – Second International Mathematics Study 1982 SIMS – Second International Mathematics Study 1983 A Nation at Risk 1983 A Nation at Risk 1987 J. R. Flanders analysis of textbooks – prior to algebra 1987 J. R. Flanders analysis of textbooks – prior to algebra

Timeline 1989 Curriculum Standards – NCTM 1989 Curriculum Standards – NCTM Everybody Counts – Lynn Steen & NRC Everybody Counts – Lynn Steen & NRC 1991 Teaching Standards – NCTM 1991 Teaching Standards – NCTM 1992 NSF-Funded Integrated Standards-Based Curriculums 1992 NSF-Funded Integrated Standards-Based Curriculums 1995 Assessment Standards – NCTM 1995 Assessment Standards – NCTM 1996 TIMSS – Third International Mathematics and 1996 TIMSS – Third International Mathematics and Science Study Science Study 1996 MAP 2000 – Mathematics Field Test 1996 MAP 2000 – Mathematics Field Test 1998 National High-Stakes Test Debate – California 1998 National High-Stakes Test Debate – California 2000 Principles & Standards for School Math – NCTM 2000 Principles & Standards for School Math – NCTM MAP & MSIP – Show-Me Standards, Curriculum MAP & MSIP – Show-Me Standards, Curriculum Frameworks, Grade-Level Expectations Frameworks, Grade-Level Expectations

The Principles The Principles highlight the basic characteristics of a high quality mathematics instructional program and provide guidance for making educational decisions. The Principles highlight the basic characteristics of a high quality mathematics instructional program and provide guidance for making educational decisions.

The Principles cont. Equity. Excellence in mathematics education requires equity—high expectations and strong support for all students. Equity. Excellence in mathematics education requires equity—high expectations and strong support for all students. Curriculum. A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades. Curriculum. A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades. Teaching. Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well. Teaching. Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.

The Principles cont. Learning. Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge. Learning. Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge. Assessment. Assessment should support the learning of important mathematics and furnish useful information to both teachers and students. Assessment. Assessment should support the learning of important mathematics and furnish useful information to both teachers and students. Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. Technology. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.

9 Standards 9 Number and Operations Algebra Geometry Measurement Data Analysis and Probability Problem Solving Reasoning and Proof Communication Connections Representation

The Standards Five Standards describe the mathematical content that students should learn to be successful Five Standards describe the mathematical content that students should learn to be successful

The Content Standards 1. Number and Operations 2. Algebra 3. Geometry 4. Measurement 5. Data Analysis and Probability

12 Content Standards Across the Grades Numb er Algebra Geometry Measurement Data Analysis and Probability Pre-K–23–56–89–12 Number and Operation

The Standards Five Standards highlight the mathematical processes that students draw on to acquire and use their content knowledge. Five Standards highlight the mathematical processes that students draw on to acquire and use their content knowledge.

The Process Standards 6. Problem Solving 7. Reasoning and Proof 8. Communication 9. Connections 10. Representation

The make up Each Standard is broken up into four grade-level bands: Each Standard is broken up into four grade-level bands: –Pre-K to 2 nd Grade –3 rd Grade to 5 th Grade –6 th Grade to 8 th Grade –9 th Grade to 12 th Grade Each of the Content Standards includes a set of expectations specific to that grade band. Each of the Content Standards includes a set of expectations specific to that grade band.

How were they made? NCTM was founded in NCTM was founded in In 1989 NCTM released Curriculum and Evaluation Standards for School Mathematics In 1989 NCTM released Curriculum and Evaluation Standards for School Mathematics Outlined extensive goals for teachers and policy makers for the school discipline. Outlined extensive goals for teachers and policy makers for the school discipline.

How were they made? In 1991, NCTM published the Professional Standards for Teaching Mathematics In 1991, NCTM published the Professional Standards for Teaching Mathematics Described the elements of effective mathematics teaching Described the elements of effective mathematics teaching In 1995 NCTM released the Assessment Standards for School Mathematics In 1995 NCTM released the Assessment Standards for School Mathematics Established objectives against which assessment practices can be measured Established objectives against which assessment practices can be measured

How were they made? From 1995 to 2000, NCTM rewrote and revised its three previous documents into one released in 2000: From 1995 to 2000, NCTM rewrote and revised its three previous documents into one released in 2000: The Principles and Standards for School Mathematics The Principles and Standards for School Mathematics A single resource that can be used to improve mathematics curricula, teaching, and assessment A single resource that can be used to improve mathematics curricula, teaching, and assessment

19 Principles 19 Describe particular features of high-quality mathematics programs Equity Curriculum Learning Teaching Assessment Technology

Statement of Principles The Equity Principle 20 Excellence in mathematics education requires equity– high expectations and strong support for all students. The Curriculum Principle A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the grades. The Teaching Principle Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.

Statement of Principles The Learning Principle 21 Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge. The Assessment Principle Assessment should support the learning of important mathematics and furnish useful information to both teachers and students. The Technology Principle Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.

22 School Mathematics Is Not Working Well Enough for Enough Students Internationally (TIMSS, ), our students are not mathematically competitive  4 th grade – average  8 th grade – below average  12 th grade – among lowest of 21  at 25 th percentile, like FIMS & SIMS  particularly poor in Geometry  better in creative constructed responses questions LOWER 7 countries LOWER 7 countries SAME 14 countries SAME 14 countries HIGHER 20 countries HIGHER 20 countries Source: US TIMSS Research Center, 1996–1998 US 8 th US 12 th US 4 th

23 Students Can Do Basics, % 73% Source: NAEP – 38 … But Students Cannot Solve Problems Ms. Yost’s class has read 174 books, and Mr. Smith’s class has read 90 books. How many more books do they need to read to reach the goal of reading 575 books? 33%

24 What Does Research Tell Us? 1 What we can’t expect from research …  Standards are not determined by research, but are instead statements of priorities and goals  What is “best” cannot be proven by research.  Research cannot imagine new ideas. What we can expect from research …  Research can influence the nature of the standard.  Research can document the current situation.  Research can document the effectiveness of new ideas.  Research can suggest explanations for success or failure. 1 Hiebert, J. (1999) Relationships between research and the NCTM Standards, Journal for Research in Mathematics Education, 30(1):3-19.

25 Do Skills Lead to Understanding? Can Drill Help Develop Increase Mathematical Reasoning? Can Calculators & Computers Increase Mathematical Reasoning? Steen, L.A. (1999). Twenty questions about mathematical reasoning. in L.V. Stiff & F.R. Curcio (Eds), Developing mathematical reasoning in grades K-12: 1999 Yearbook (pp ). Reston, VA : NCTM.