# Presentation: 360582

## Foundations for SuccessNational Mathematics Advisory Panel

- Final Report, March 2008

## Presidential Executive OrderApril 2006

**Presidential Executive Order*****April 2006***

- The Panel will advise the President and the Secretary of Education on the best use of scientifically based research to advance the teaching and learning of mathematics, with a specific focus on preparation for and success in algebra.

## What Concerns Led to the President’s Order?

**What Concerns Led to the President’s Order?**

- National prosperity and safety in international context
- - Role of mathematics in national well-being
*- Gathering Storm*
- Workforce of the future
- Options for individuals and families
- - College admission and graduation
- - Candidacy for technical workforce
- - Earning power
- - Adaptability

## Math Proficiency of U.S. Students

**Math Proficiency of U.S. Students**

- International comparisons
- Low fractions of proficiency on NAEP
- Falling proficiency at higher grades
- Heavy remedial demand upon entry into college
- Achievement gap
*Algebra as a gateway*

**Notes:**
- American students achieve in mathematics at a mediocre level by comparison to peers worldwide. 
Yet other results from NAEP are less positive: 32% of our students are at or above the “proficient” level in Grade 8, but only 23% are proficient at Grade 12. Consistent with these findings is the vast and growing demand for remedial mathematics education among arriving students in 4-year colleges and community colleges across the nation. 
On the TIMSS (Trends in International Mathematics and Science Study), U.S. students do less well in Grade 8 than grade 4. The performance is still poorer in Grade 12. 
In the PISA (Programme for International Student Assessment), U.S. 15-year-olds ranked 25th among 30 developed nations in math literacy and problem solving.
Even in elementary school, only 7% of U.S. 4th-graders scored at the advanced level in TIMSS, compared to 38% of 4th-graders in Singapore, a world leader in mathematics achievement

## Overview

**Overview**

- Task Groups
- - Conceptual Knowledge and Skills
- - Learning Processes
- - Instructional Practices
- - Teachers
- - Assessment
- Subcommittees
- - Standards of Evidence
- - Survey of Algebra Teachers
- Instructional Materials** **
- Reports
- - Final Report
- - 8 Task Group and Subcommittee Reports

**Notes:**
The U.S. Secretary of Education called upon known leaders in mathematics education—both educators, cognitive psychologists and mathematicians--who come from universities, research organizations, foundations, state government and classrooms.
19 members and 5 ex officio’s from different federal agencies

## Basis of the Panel’s work

**Basis of the Panel’s work**

- Review of 16,000 research studies and related documents.
- Public testimony gathered from 110 individuals.
- Review of written commentary from 160 organizations and individuals
- 12 public meetings held around the country
- Analysis of survey results from 743 Algebra I teachers

## Evidence Guidelines

**Evidence Guidelines**

- Executive Order
- - Marshal the “best available scientific evidence.”
- - Review “research relating to proven-effective and evidence-based mathematics instruction.”
- What is the best available scientific evidence?
- - 3 broad categories of quality.
- Highest quality = high internal and external validity.
- Promising or suggestive = has limitations.
- Opinion = values, impressions, or weak evidence.

## Two Major Themes

**Two Major Themes**

- “First Things First”
- 	 - Positive results can be achieved in a			reasonable time at accessible cost by             		   addressing clearly important things now.
- 		- A consistent, wise, community-wide effort will 		be required.
- “Learning as We Go Along”
- 	- In some areas, adequate research does not 	  exist.
- 	- The community will learn more later on the 	    	  basis of carefully evaluated practice and 		  research.
- 	- We should follow a disciplined model of 	  	  continuous improvement.

## Curricular Content

**Three Formal Products:*** *

- Major Topics of School Algebra
- Critical Foundations
- Benchmarks

## Curricular Content

**Curricular Content**

**Streamline the Mathematics Curriculum in Grades PreK-8:*** *

- Follow a Coherent Progression, with Emphasis on Mastery of Key Topics
- Focus on the Critical Foundations for Algebra
- - Proficiency with Whole Numbers
- - Proficiency with Fractions
-  Particular Aspects of Geometry and Measurement
- Avoid Any Approach that Continually Revisits Topics without Closure

**Notes:**
Difficulty with fractions (including decimals and percents) is pervasive and is a major obstacle to further progress in mathematics, including algebra. 
A nationally representative sample of teachers of Algebra I who were surveyed for the Panel rated students as having very poor preparation in “rational numbers and operations involving fractions and decimals.”
As with learning whole numbers, conceptual understanding of fractions and operational procedures for fractions and decimals reinforce one another. 

## Curricular Content

**Curricular Content**

**Benchmarks Should Guide:**
- Classroom Curricula
- Mathematics Instruction
- Textbook Development
- State Assessment

**Notes:**
Fluency with Whole Numbers
By the end of Grade 3: proficient with the addition and subtraction of whole numbers.  
By the end of Grade 5: proficient with multiplication and division of whole numbers.  
Fluency with Fractions
By the end of Grade 4: identify and represent fractions and decimals, and compare them on a number line 
By the end of Grade 5: proficient with comparing fractions and decimals and common percents, and with the addition and subtraction of fractions and decimals.  
By the end of Grade 6, students should be proficient with multiplication and division of fractions and decimals. 
By the end of Grade 6, students should be proficient with all operations involving positive and negative integers. 
By the end of Grade 7, students should be proficient with all operations involving positive and negative fractions.
By the end of Grade 7, solve problems involving percent, ratio, and rate, and extend this work to proportionality.  
Particular Aspects of Geometry and Measurement
By the end of Grade 5: solve problems involving perimeter and area of triangles, and all quadrilaterals having at least one pair of parallel sides (i.e., trapezoids).
By the end of Grade 6: analyze the properties of two dimensional shapes and solve problems involving perimeter and area. They should also be able to analyze the properties of three-dimensional shapes and solve problems involving surface area and volume.
By the end of Grade 7, students should understand relationships involving similar triangles. 

## Curricular Content

**Curricular Content**

**The Major Topics of School Algebra**
*Covering all of school algebra traditionally extending over two courses, Algebra I and Algebra II*
** **Symbols and Expressions
-  Linear Equations
-  Quadratic Equations
-  Functions
-  Algebra of Polynomials
-  Combinatorics and Finite Probability

## Curricular Content

**Curricular Content**

**An Authentic Algebra Course**
- All school districts:
- Should ensure that all prepared students have access to an authentic algebra course,  and
- Should prepare more students than at present to enroll in such a course by Grade 8.

## Curricular Content

**Curricular Content**

**What Mathematics Do Teachers Need to Know?**
- For early childhood teachers:
- Topics on whole numbers, fractions, and the appropriate geometry and measurement topics in the Critical Foundations of Algebra
- For elementary teachers:
- All topics in the Critical Foundations of Algebra and those topics typically covered in an introductory Algebra course
- For middle school teachers:
- -	The Critical Foundations of Algebra
- -	All of the Major Topics of School Algebra

## Learning Processes

**Learning Processes**

**Scientific Knowledge on Learning and Cognition Needs to be Applied to the Classroom to Improve Student Achievement:**
- Most children develop considerable knowledge of mathematics before they begin kindergarten.
- Children from families with low incomes, low levels of parental education, and single parents often have less mathematical knowledge when they begin school than do children from more advantaged backgrounds. This tends to hinder their learning for years to come.
- There are promising interventions to improve the mathematical knowledge of these young children before they enter kindergarten.

## Learning Processes

- To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, factual knowledge and problem solving skills.
- Limitations in the ability to keep many things in mind (working-memory) can hinder mathematics performance.
- Practice can offset  this through automatic recall, which results in less information to keep in mind and frees attention for new aspects of material at hand.
- Learning is most effective when practice is combined with instruction on related concepts.
- Conceptual understanding promotes transfer of learning to new problems and better long-term retention.

**Learning Processes**

## Learning Processes

**Learning Processes**

**Children’s goals and beliefs about learning are related to their mathematics performance.**
- Children’s beliefs about the relative importance of effort and ability can be changed.
- Experiential studies have demonstrated that changing children’s beliefs from a focus on ability to a focus on effort increases their engagement in mathematics learning, which in turn improves mathematics outcomes.

## Learning Processes

- Teachers and other educational leaders should consistently help students and parents understand that an increased emphasis on the importance of effort is related to improved mathematics grades.

**Learning Processes**

## Teachers and Teacher Education

**Mathematically Knowledgeable Classroom Teachers Have a Central Role in Mathematics Education.**
- Evidence shows that a substantial part of the variability in student achievement gains is due to the teacher.
- Less clear from the evidence is exactly what it is about particular teachers—what they know and do –that makes them more effective.
- The mathematics preparation of elementary and middle school teachers must be strengthened as one means for improving teacher effectiveness in the classroom

**Teachers and Teacher Education**

**Notes:**
Differences in teachers account for 12-14% of total variability in students’ mathematics achievement gains during an elementary school year

When teachers are ranked according to their ability to produce student achievement gains, there is a 10 percentile point difference across the course of a school year between achievement gains of students of top-quartile teachers versus bottom-quartile teachers.

## Teachers and Teacher Education

- Currently there are multiple pathways into teaching.
- Research indicates that differences in teachers’ knowledge and effectiveness between these pathways are small or non-significant compared to very large differences among the performance of teachers within each pathway.
- The Panel recommends that research be conducted on the use of full-time mathematics teachers in elementary schools, often called elementary math specialist teachers.

**Teachers and Teacher Education**

**Notes:**
Elementary math specialist teachers: 
Teachers with strong knowledge of mathematics who would teach mathematics full-time to several classrooms of students, rather than teaching many subjects to one class, as is typical in most elementary classrooms.

## Teachers and Teacher Education

**The Math Panel recommends policy initiatives that put in place and carefully evaluate the effects of:**
- Raising base salaries for teachers of mathematics to attract more mathematically qualified teachers into the workforce;
- Salary incentives for teachers of mathematics for working in locations that are difficult to staff; and
- Opportunities for teachers of mathematics to increase their base salaries substantially by demonstrable effectiveness in raising student achievement.

**Teachers and Teacher Education**

## Instructional Practices

**Instructional Practices**

- All-encompassing recommendations that instruction should be student-centered or teacher-directed are not supported by research.

**Instructional practice should be informed by high quality research, when available, and by the best professional judgment and experience of accomplished classroom teachers.**

## Instructional Practices 

**Instructional Practices**** **

**Formative assessment enhances mathematics achievement, particularly when:**
- Information is used to determine focus of instruction
- Expert teachers offer advice
- Computer-assisted instruction or peer tutoring is a component

## Instructional Practices 

- Explicit methods of instruction available on a regular basis
- Clear problem solving models
- Carefully orchestrated examples/ sequences of examples.
- Concrete objects to understand abstract representations and notation.
- Participatory thinking aloud by students and teachers.

**Instructional Practices**** **

**Use of technology shows promise when: **
- Computer-assisted instruction supports drill and practice
- Well designed tutorials are delivered through computer-assisted instruction
- Learning is supported by the careful, targeted application of computer programming
**More research is needed**

**Instructional Practices**** **

**Notes:**

Calculators: However, the Panel’s survey of the nation’s algebra teachers indicated that the use of calculators in prior grades was one of their concerns. The Panel cautions that to the degree that calculators impede the development of automaticity, fluency in computation will be adversely affected.

## Instructional Practices 

**Instructional Practices**** **

- A review of 11 studies that met the Panel’s rigorous criteria (only one study less than 20 years old) found limited or no impact of calculators on calculation skills, problem solving, or conceptual development over periods of up to one year.
- This finding is limited to the effect of calculators as used in the 11 studies and the Panel recommends more research.

- Mathematically precocious students with sufficient motivation appear to be able to learn mathematics successfully at a much higher rate than normally-paced students, with no harm to their learning.

## Instructional Materials

**Instructional Materials**

- U. S. mathematics textbooks are far too long -- often 700-1000 pages.  Mathematics textbooks are much smaller in many nations with higher mathematics achievement than the U.S.  Excessive length makes our books unnecessarily expensive and tends to undermine coherence and focus.
- Publishers must ensure the mathematical accuracy of their materials.

## Assessment

**Assessment**

- -	Are of the highest quality.
- -	Measure what is intended.
- -	Do not include design or wording problems that provide unintended sources of difficulties.

- NAEP and state tests must focus on the mathematics that students should learn, with scores reported and tracked over time.
- States and NAEP need to develop better quality control and oversight procedures to ensure that test items:

**Notes:**
- The Panel suggests that the NAEP strand on “Number Properties and Operations” be expanded and divided into two parts. 
The former should include a focus on whole numbers, including whole number operations (i.e., addition, subtraction, multiplication, division), at Grade 4, and on all integers (negative and positive) at Grade 8. 
The second content area involving number should focus on fractions.  At Grade 4, it should involve beginning work with fractions and decimals, including recognition, representation, and comparing and ordering.  The coverage should be expanded to include operations with fractions, decimals, and percent at Grade 8. 
- Similarly, the content of work with whole numbers and fractions on state tests should expand and cover these concepts and operations as they develop from year to year, particularly at Grades 5, 6, and 7, which are grade levels when the NAEP test is not offered.
The Panel recommends a more appropriate balance in how algebra is defined and assessed at both the Grade 4 and Grade 8 levels of the NAEP. The Panel strongly recommends that “algebra” problems involving patterns should be greatly reduced in these tests. The same consideration applies to state tests. 

## Research Policies and Mechanisms

**Research Policies and Mechanisms**

- It is essential to produce methodologically rigorous scientific research in crucial areas of national need, such as the teaching and learning of mathematics.* *
- More research is needed that identifies:
- -	Effective instructional practices, materials, and principles of 	instructional design,
- -	Mechanisms of learning,
- -	Ways to enhance teachers’ effectiveness, including teacher 	education, that are directly tied to objective measures of 	student achievement, and
- -	Item and test features that improve the assessment   of 	mathematical knowledge.

## 
The Panel recommends that governmental agencies that fund research give priority not only to increasing the supply of research that addresses mathematics education, but also to ensuring that such projects meet stringent methodological criteria. 

- The Panel recommends that governmental agencies that fund research give priority not only to increasing the supply of research that addresses mathematics education, but also to ensuring that such projects meet stringent methodological criteria.

- As in all fields of education, the large quantity of studies gathered in literature searches on important topics in mathematics education is reduced appreciably once contemporary criteria for rigor and generalizability are applied.

**Research Policies and Mechanisms**

**Notes:**
Notes
- Place an emphasis on the support of studies that incorporate randomized controlled designs (i.e., designs where students, classrooms, or schools are randomly assigned to conditions and studied under carefully controlled circumstances) or methodologically rigorous quasi-experimental designs. 
These studies must possess adequate statistical power, which will require substantial funding.
- Both smaller-scale experiments on the basic science of learning and larger-scale randomized experiments examining effective classroom practices are needed to ensure the coherent growth of research addressing important questions in mathematics education. 
- Highly relevant basic research can be carried out using rigorous methods, including randomized trials. 
Such methodologically rigorous research is underemphasized in current studies of mathematics education, but it is necessary for drawing clear causal conclusions about the effectiveness of educational practices.

- Leaders of graduate programs in education and related fields should ensure attention to research design, analysis, and interpretation for teachers and those entering academic and educational  leadership positions in order to increase the national capacity to conduct and utilize rigorous research.
- New funding should be provided to establish support mechanisms for career shifts (K, or career, awards from the NIH represent one example). Many accomplished researchers who study the basic components of mathematics learning are not directly engaged in relevant educational research.

**Research Policies and Mechanisms**

- Support should be provided to encourage the creation of cross-disciplinary research teams, including expertise in educational psychology, sociology, economics, cognitive development, mathematics, and mathematics education.
- PreK-12 schools should be provided with incentives and resources to provide venues for, and encourage collaboration in, educational research.
- Unnecessary barriers to research should be lowered.

**Research Policies and Mechanisms**

## Next Steps

**Next Steps**

- Release of the Final Report—March 13, 2008
- Publication of Final Report
- Publication of Task Group and Subcommittee Reports
- Expiration of the National Mathematics Advisory
- 	Panel—April 18, 2008
- National Forum

## For More Information

**For More Information**

- Please visit us online at:
- http://www.ed.gov/MathPanel