Big Foot Area Schools Association
REPORT OF FINDINGS AND RECOMMENDATIONS
Math Task Force A. 4
Task: Prepare a report of findings and recommendations based upon summary of the
background of the previous math study.
A. Findings
1. Teachers need extensive opportunities to acquire mathematical knowledge and expertise
in teaching mathematics.
2. Teachers should emphasize the interrelations of conceptual understanding of
mathematical operations, fluent execution of procedures, and fast access to number
combinations. (Five-strands, basic math facts, computation, etc…) These interrelations
jointly support effective and efficient problem solving.
3. Curriculum implementation and delivery needs to be based on external and internal
research and data.
4. In the BFASA Math Study June 2004, the analysis indicated that the vast majority of
recommendations have been fully implemented.
5. There are seven recommendations from the BFASA Math Study of 2004 that remain to
be addressed. (Analysis of BFASA Math Study 2004 – Table 4.1)
6. Permitting different schools to have different math programs and use of different
textbooks has its greatest negative impact on the development of all students.
B. Recommendations
1. Continue to offer opportunities for teachers to learn, observe models of effective practice,
and have access to expertise in mathematics teaching.
2. Continue to offer a curriculum that emphasizes the interrelations of conceptual
understanding of mathematical operations, fluent execution of procedures, and fast access
to number combinations.
3. Continue to implement and deliver curriculum based on external and internal research
and data. (i.e. WKCE, Terra Nova, audit forms, etc…)
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4. New recommendations should be implemented to the same degree of success as our 2004
math study recommendations. Continue to look for resources to assist us in completing
the remaining 2004 math study recommendations.
5. Develop action plans for the remaining seven recommendations for the BFASA Math
Study of 2004. (Analysis of BFASA Math Study 2004 – Table 4.1)
6. Continue to implement and deliver the current integrated, problem-solving, and
interactive based curriculum and follow its updated pacing guide and guidelines.
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Big Foot Area Schools Association
Math Task Force A. 4
Analysis of BFASA Math Study 2004
I. Overview: Math Study of June 2004
A. Three volumes
Volume I Executive Report
Volume II Demographic Report
Volume III Cohort and Individual Students Report, ACT Report,
Curriculum Report
B. The Executive Report is a compilation of all reports of findings and recommendations from
Volume II and Volume III.
C. Each district has a complete set of the Math Study of June 2004 for public review.
II. Review of Executive Summary: Volume I
1. Eight groups assigned to carry out the work of data collection, analysis, summaries of
findings and recommendations, and math study coordination and review.
a) Appendix A: Introduction
2. Discussion of historical development of math curriculum.
a) Appendix B: Overview and Plan of Action
3. Executive Summary of Findings and Recommendations from the Math Study Teams
a) Student Achievement as Reflected in Standardized Test Scores
b) Curriculum, Instruction, and Assessment, Evaluation and Accountability
c) Professional Development
d) Appendix C: Math Study Teams: Summary of Findings and Recommendations
4. Executive Summary of Findings and Recommendations from the Parent Advisory Team
a) Student Achievement, Student Learning, and Transitions
b) Curriculum, Instruction, and Assessment, Evaluation and Accountability
c) Professional Development
d) Appendix D: Parent Advisory Team: Summary of Findings and Recommendations
5. Summary Report of Board Goals
a) Identify strengths and weaknesses in the Consortium in regard to student demonstration
of math competencies using 4th, 8th, and 10th grade as our benchmarks.
b) Identify the factors that contribute the most significantly to these strengths and
weaknesses
c) Recommend plans to address weaknesses and build on strengths
d) Recommend an on-going evaluation plan to be used in the future years that would gather,
analyze, and report on the most pertinent data on a regular, prescribed basis.
e) Appendix E: Board Goals: Summary of Findings and Recommendations
6. Appendix with six sections.
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Analysis of the Executive Summaries from Each Math Study Team
I. Math Study Teams: Summary of Executive Recommendations and Status
Table 1.1 Student Achievement as Reflected in Standardized Test Scores
Recommendations Status
1. College bound students enroll in a fourth year Increasing: 2006-07 = 105 students
of mathematics 2009-2010 = 168 students
2. Complete junior year in Math prior to taking HS math instructors informing parents. Students
ACT taking it at the end of junior or the first part of senior
year. Despite findings in the Math Study, 2004,
some parents still encourage students to take the
ACT prior to completing three years of Mathematics.
3. Continue to offer ACT prep classes. Prep class offered. An online class is continuously
Advocate for increased parent/student available for student use both at home and at school.
accountability
Gather data on participation for ACT prep
classes.
4. Develop uniform assessment strategies and Common assessments identified on the JK-12 pacing
rubrics to identify JK-12 students at risk for guide. In the high school math department, common
not achieving proficient or higher on the assessments are developed for math courses.
WKCE 4, 8, & 10. Approved BFASA Math rubric on audit forms. Math
committee continues to work supporting teachers in
districts via math reps regarding assessment
strategies. BFASA approved math rubric which
serves as the basis for identifying students at risk for
not achieving. Audit form evaluations identify basic
and minimal students in each book.
Longitudinal Study identifies students with high
stanines of 7, 8, or 9.
Longitudinal Study identifies students with low
scales scores or stanines of 4, 3, 2, or 1
Pearson Success Net (Success Tracker): Pre & Post
Assessments
5. Target all students with enriched math Math committee approved resource materials in each
activities and problem solving to develop district
mathematical literacy for all. Learning centers required in each classroom
Provide full support in schools, especially for Staff development for all teachers JK – 12: MS
students at the minimal and basic levels Math Grant, Elementary Math Grant, Math Experts
including additional math time beyond Math tools and manipulatives in every classroom
recommended daily minutes. License for Geometer Sketchpad and Fathom
available in a computer lab in each district. Grade 5
– 12 teachers trained on both software programs.
Pearson Success Net (Success Tracker): Math
games, review, and reinforcement activities
Consortium recommendation: 15 minutes of
additional time for skill building and problem-
solving.
Math Title I resource teachers – varies by district
After school tutoring
Guided study halls
6. Consortium monitor student achievement by Common assessments identified on the JK-12 pacing
developing approved assessment aligned with guide.
curriculum, collect assessment data, and Annually the BFASA Math committee reviews Scale
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make interventions and decisions based on Score reports, index reports, and item analysis. This
data. information drives the set-up of the pacing guide,
targets math strands needing additional focus, and
guides curricular changes.
District interventions included suggested days of
pacing, key concepts for assessments, increasing
math minutes, and supporting professional
development. Classroom interventions include
Pearson Success Net (Success Tracker): Pre & Post,
individual and small group support, resource
teachers, parent communication, program letters for
each unit, math centers, and math committee
approved resources, cross-curricular integration,
cross-grade level projects, interactive software.
7. Monitor students who score minimal and Teachers use audit data to inform instruction and
basic on the audit forms for each book. provide differentiated learning activities for students
at all levels. Audits submitted to district
administrators for review and signature after each
book. District unit leaders and teams discuss student
concerns.
Table 1.2 Curriculum, Instruction, and Assessment
Recommendations Status
1. Continue to use and adjust JK – 12 pacing Reviewed and updated annually by math committee.
guide based on data. Administratively reviewed and BFASA board
approved. Adjusted during year if the committee
identifies.
Teachers request pacing guide in early August to
plan.
2. Administrators need to monitor JK – 3 Administration visit classrooms and review
classrooms to ensure pacing guide delivery. submitted audit forms.
3. Develop a uniform system of data collection Results of annual data review forwarded to
and dissemination for teachers and administrative team and reviewed by Area Board. In
administrators. Use information to inform addition the Area Board receives updated assessment
instructional strategies and curriculum data on a regular basis. Student achievement results
decisions. in the BFASA Curriculum Quarterly. Celebration
reports presented to consortium at BFASA Inservice
days.
4. Develop a uniform plan to assess transfer Teachers contact BFASA office and request
student placement and content delivery in assessment for student if they need to determine
mathematics and develop an instructional level. Assessments used may include the Terra
plan of action for transition. Nova, promotion assessment, elementary math
grades assessments, and selected program
assessments. Each district establishes plan of action
for the student.
5. Develop and implement best practice Members of BFASA Math Committee read and
strategies based on current research in review current research at each meeting. Grade level
instruction and assessment for diverse student meetings for math teachers to discuss instructional
populations JK – 12 practices and research best practice. Professional
journals provided in each district. Middle School
Math Grant and Elementary Math Grant training.
Robin Fogerty differentiated practice. Carol Otto led
JK-3 professional staff development. Kristin Klegg
led MS and HS professional development. Through
5
the MS and Elementary Math Grants schools were
visited and a lesson case study was developed.
Members of BFASA Math Committee attend
National and State Math Conferences and Green
Lake Math Conference. BFASA Math Committee
has also visited the following school sites and
discussed mathematics curriculum: Waunakee, WI
School District, Naperville, IL School District and
Wayzata School District in Minnesota.
Practices vary by school district and the requirements
6. Special education students (except the most of the student’s IEP. Accommodations identified
significant students with disabilities) must and implemented by IEP team and instruction staff.
experience the approved math program and
the IEP must address the Wisconsin math
standards (Math Processes, Number
Operation and Relationships, Geometry,
Measurement, Statistics and Probability,
Algebraic Relationships).
Identified gaps in curriculum offerings and
7. The BFASA Mathematics Committee needs proceeded to implement strategies for meeting these
to develop a plan of action to address the deficits. (At various grade levels some of the gaps
mathematical strands identified in the were number sense, geometry, time and money and
executive findings as needing further measurement). To meet the deficits updated and
analysis. improved textbooks, tools and manipulatives were
purchased. Expanded professional development was
offered.
This recommendation was considered and
8. Employ a math education specialist to assist investigated. It was the finding that this was not cost
with implementation of the recommendations effective. Additionally, the number of teachers
of this report. obtaining a master’s degree in mathematics and/or
the National Board Certification has increased, as
well as the leadership training provided by the JK-5
and Grade 5 – 8 MSP math grants. These teachers
serve in leadership roles and serve as mentors to
newly hired math teachers.
Table 1.3 Professional Development
Recommendations Status
1. Administration and BFASA Math Employed math experts to meet with teams of
Curriculum Committee need to develop a teachers during the school year to address findings.
comprehensive staff development plan to Middle School Math Grant and Elementary Math
address the findings and the Grant. BFASA Schools Inservices collegial
recommendations of this report. discussions.
2. Develop a plan of action to enhance the Committee members attend state and national
professional expertise of the BFASA Math conferences. Participate in math grants. Share
Curriculum Committee so further current research and discussion at meetings.
recommendations are grounded in the most
recent research and best practice.
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Table 1.4 Recommendation of Concurrence
Recommendations Status
1. The Investigations Math Program (K-5), the Investigations Math Program (K-5), the Connected
Connected Math Program (6-8), and the Core Math Program (6-8), and the Core Plus Mathematics
Plus Mathematics (9-12), curriculum should (9-12), are currently being implemented with the
be kept in place with the employment of the new second editions. In accordance with our
executive recommendations in this report. curriculum cycle, the mathematic committee
reviewed materials and chose the revised
Investigations Math Program for grades K-5, the
revised Connected Math Program for grades 6-8 and
the revised Core Plus Mathematics program for the
integrated pathway for grades 9-12. Executive
recommendations from the Math Study Teams have
been employed as reported.
II. Parent Advisory Team: Executive Summary of Recommendations and Status
Table 2.1 Student Achievement, Student Learning Supports and Transitions
Recommendations Status
1. A formal interactive evaluation process An evaluation process is in place using consortium
should be implemented for transfer and assessments, Terra Nova assessments, and other
transitional students involving teacher, parent available data to determine specific student needs in
and child and be tailored to the specific mathematics. Teachers may contact the Curriculum
student and math requirements for the Coordinator for assessments. At the district levels,
specific grade level. This is to aid in special teachers are available to meet with parents and
needs or curriculum adjustments for the support the transfer process to the math curriculum.
student in the transitional process.
2. Each district must develop a plan for District plans align with the BFASA formal
evaluating new students, monitoring, and evaluation process
placement, to be reviewed by the Parent
Advisory Team, and publicly available to
parents of all new students.
3. ACT/SAT workshops should continue to be Completed annually. High school funds through the
offered to Sophomores and Juniors. In Perkins Grant, the Plan and Explore tests for all 8 th
addition, parent and student notification of and 10th graders. Information to be used by parents
these and other ACT courses, available at and students in career planning and selection of
other locations, need to be enhanced through courses.
a variety of communication tools
(newspapers, websites, parent newsletters,
etc.).
4. Identify students scoring minimal and basic Identification completed annually. Current research
and provide immediate intervention. Follow is used. Intervention done in the classroom by the
up on current research and contact other teacher as needed. Response to Intervention ( RtI)
schools to see how they are supporting these programs available in each district. Contact with
students. other schools done at state and national leadership
conferences.
5. Guidance counselors must provide Annually completed. New Wisconsin Guidance
information to incoming freshman and Model will engage students and parents in planning a
parents including awareness that the current program of study to meet their post secondary
high school minimum requirement of two education and work force needs. Middle school
years of mathematics may be insufficient to mathematics teachers are also involved in assisting
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achieve adequate ACT/SAT scores and parents and students with course selection making
further reinforced through a map of needed recommendations based on student self-assessment
high school courses that will prepare them for regarding learning style.
their next level of education or intended
career. Counseling process needs to be
ongoing.
6. The BFASA must forward a report in Upon data review, all information is forwarded to the
October and May of each school year Administrative Team and Area Board in the fall.
detailing the progress and student The annual curriculum report presented in June
achievement levels, the progress on the addresses accomplishments, to do list, and
recommendations of this report, and other recommendations which guide the following
data on curriculum and professional curriculum year.
development to the Parent Advisory Team
and the Area Board for review.
Table 2.2 Curriculum, Instruction and Assessment, Evaluation and Accountability
Recommendations Status
1. The comprehensive pacing guide should Annually reviewed, updated, and approved by the
continue to ensure accountability and Area Board.
continuity of the proper implementation of
the math curriculum for all schools in the
district.
2. The minimum recommended instructional Current data from the 2008 – 09 audit forms indicate
minutes for the math curriculum needs to be work remains in this area in some districts.
implemented at all feeder schools.
3. BFASA Math Committee needs to continue The BFASA Math Committee has sponsored parent
to sponsor ongoing workshops for parents for workshops in the past. The committee needs to re-
the purpose of providing curriculum address this recommendation.
information and support.
4. The Investigations/Connected/Core Plus The programs are in place. The Consortium
mathematics curriculum should be kept in continues to consider the recommendations in this
place at the employment of the report.
recommendations in this report.
5. Provide accelerated math opportunities Each district provides opportunities for student
before school begins. acceleration for identified students. This can take
place during the school day, before or after school,
and during the summer.
6. Beginning in the 2005-06 school year, Student achievement from the audit forms completed
implement a more formal process to monitor on time provides data from the classroom that can be
the mathematics program closely. The used to inform instruction and notify the committee
process should continue to collect the data of required changes or major shifts. The committee
that can rapidly \identify major shifts in math also reviews and considers data from other
achievement in JK-12 and allow of ongoing, assessment tools including the WKCE, Terra Nova,
fact-based decisions. Explore, Plan and ACT testing.
7. Increase the minimum high school graduation Discussed at local and state level. No action taken at
requirement from two years to three years. this point.
8. Conduct a review of the 2/3 offering. Gather Review conducted of the 2/3 offering leading to its
qualitative and quantitative data to determine removal from the course guide. All students engage
if it is working. Conduct a comparative study in the approved universal curriculum at the high
with other schools using the Core Plus school. Support class added last year for incoming
Program to see how they structure math freshman in mathematics that provides review before
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offerings. going into the universal curriculum. All students
must complete two years of mathematics at the high
school. Pre-math classes do not count toward
graduation.
9. Demonstrate a commitment to mathematics On-going review and discussion. This change
by anchoring the high school block impacts other subject areas and staffing
scheduling system around mathematics and requirements. Every effort is made to provide
provide added flexibility by allowing math to students with a continuous mathematics sequence.
be taught in “skinnies”.
10. Using an external facilitator, interview all External evaluators and university partners have
those who are accountable to administer and been used to guide curriculum development and
deliver the math program to gain their professional development. MSP Grants, K-5 and 5-
perceptions on a) how the math program is 8, gathered data through exit surveys and journal
progressing, b) how student achievement is reflections.
progressing, and c) how staff development
needs are being met.
Table 2.3 Professional Development
Recommendations Status
1. The BFASA Math Committee must continue Meetings are held annually but not monthly due to
to hold monthly structure seminars in the time constraints and funding. During the MS and
instruction/delivery practice for the teachers Elementary Math grant periods this was most closely
and as a forum for the exchange of critical delivered.
issues and best practices. Priority should be
given to all math teachers in grades JK-12.
2. The BFASA Math Committee must continue Work in this area has been completed at the BFASA
to sponsor a math curriculum workshop at Inservice, curriculum meetings, and grade level
least three times each year, with mandatory meetings. MPS grants provided extensive time for
attendance by all district mathematics teachers to focus on pedagogical practices, best
teachers and be facilitated by an appropriate practice, and consistent delivery of program.
outside expert. The workshops should be Outside experts and teacher experts employed for
designed to be interactive with focus given to facilitation and training.
effective delivery techniques and improving
the program consistency and best practices
district wide.
3. Support materials should be purchased to This recommendation has been followed. Funding
enhance the teaching of current mathematics from MS Math Grant provided Geometer Sketchpad
curriculum and to supplement student skill and Fathom interactive software for JK – 12. The
development as warranted. These materials Elementary Grant provided Lego “Mind Storms” to
would include workbooks, and other develop critical thinking and technical writing
materials as selected. opportunities for students JK -5. Districts purchased
components of the Investigations, 2nd edition for all
classrooms.
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III. Board Goals: Summary of Recommendations and Status
Table 3.1 Summary of Board Goals
Recommendations Status
1. Identify strengths and weakness in the Annually completed by the BFASA Math Committee
consortium in regard to student and results reported to the Administrative Team and
demonstration of math competencies, using the BFASA Area Board. Analysis of trend and
4th, 8th, and 10th grade as our benchmarks. cohort data from the WKCE, Terra Nova, Math
audits.
2. Identify the factors that contribute the most Annually. All curriculum committees identify
significantly to these strengths and through the Annual Curriculum Report work
weaknesses. (refers to #1) accomplished in these areas and the following year’s
to-do list of work.
3. Recommend plans to address the weaknesses On-going. Teacher Leaders and members of the
and build on the strengths. curriculum committee identify plans for areas
needing strengthening.
4. Recommend an ongoing evaluation plan to Data retreats in the fall for each curriculum
be used in future years that would gather, committee with findings to the Administrative Team
analyze and report on the most pertinent data and Area board. Monthly curriculum reports from
on a regular, prescribed basis. the Curriculum Coordinator, Annual Curriculum
Report presented in June. Development of a BFASA
Curriculum Cycle and Assessment Program currently
under review by the Area Board.
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Task Force A.4
Analysis of Madison Math Study 2008
I. Overview
A. Introduction presents overview, resources, and revised focuses.
B. Award of $40,000 UW Baldwin Endowment, $16,000 MMSD
Scale 8 research funding. “The task force was on a forced hiatus until new resources
could be identified.” P. 15-16
C. Five Main Sections:
a. Learning from Curricula: Mitchell J. Nathan, UW-Madison
b. Instruction and Teacher Preparation: Eric Knuth, UW-Madison
c. Analysis of Student Achievement: Norman L. Webb, Wisconsin
d. Center for Education Research, UW-Madison
e. Survey of Students, Teachers, and Parents: Paula White, UW-Madison
f. Task Force Meeting Minutes
D. Each section facilitated by a different person.
E. Key Findings and Recommendations – Table 1.1
Table 1.1 Findings and Recommendations MMSD Math Study 2008
Findings
1. All students of Math should be taught by teachers that have been well prepared in the content of
mathematics and techniques of teaching mathematics.
2. Permitting different schools to have different math programs and use of different textbooks has its
greatest negative impact on the population that is already the hardest for the district to reach.
3. The district policy supporting the middle school curriculum of the connected math project is
laudable because (a) the curriculum has been adopted district wide; (b) the national research
available, though woefully incomplete, suggests that CMP is as good or better than other choices for
students overall; (c) CMP has strong support from teachers, as reflected in the teacher survey data;
and (d) the district-wide Web site has provided an outlet for teachers using CMP to organize and
share accommodations for struggling and advanced students, common assessments, and grading
practices.
4. Districts should pay special attention to the performance of high-achieving students, providing
supplemental materials as needed to ensure their success in mathematics.
5. Conceptual and procedural knowledge in mathematics should be developed in an integrated fashion
with basic skills being taught without sacrificing the development of conceptual understanding.
6. District should pursue a challenging, coherent, and focused K-12 mathematics curriculum that
includes core concepts of algebra and geometry early enough and with progressively increasing
depth.
7. National meta-analyses studies on the impact of curricula on student mathematics learning and
supporting both traditional and reform-oriented curricula found that Everyday Mathematics and
Investigations at the elementary grades, and CMP at the middle school grades were more likely to
support performance improvements among students in low-SES and to narrow the achievement gap
between Whites and historically lower performing groups such as Hispanics and African Americans.
8. A small number of studies found smaller performance gains for students already classified as high
achieving, for both the NSF-supported reform curricula and commercial curricula with a traditional
emphasis.
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9. Teacher’s knowledge of differentiating instruction adds to student success in mathematics.
10. Madison elementary school teachers identified the Math Investigations program as being too
difficult for many students.
11. Madison middle school teachers identified CMP doesn’t provide examples for parents to assist with
student homework.
12. In response to survey from teachers, parents, and students in the Madison School District,
recommendation was made to resist making frequent, unnecessary curriculum changes.
13. In response to survey from teachers, parents, and students in the Madison School District,
recommendation was made for mathematics teachers to have more time to communicate and
collaborate with each other.
Recommendations
1. Hire Math specialists in grades 5 – 8 within six years
2. Hire math specialists or teachers who commit to getting certification within three years.
3. Make a larger commitment to mathematics professional development than has been possible in
recent years
4. Partner with universities to provide coherent program that lead to a mathematics specialist
certification
5. Advocate to DPI and UW-Madison for a new middle school-level mathematics certification
6. Give serious consideration to selecting a single textbook for each grade level or course and re
requiring a common core sequence across all high schools.
7. The district should consider how best to reduce the large achievement gaps among subgroups of
students.
8. A value-added type of analysis of WKCE scores by district, school and grade level should be made
a standard part of district reporting.
9. More time should be provided for teacher collaboration for teachers to learn from each other,
analyze achievement data, meet needs of diverse learners, plan for instruction and ensure both
horizontal and vertical alignment of the curriculum.
10. Parents should be provided opportunities to learn about district mathematics instruction to be able to
assist and reinforce student learning a t home.
11. Instruction at all grade levels should focus on the integration of conceptual and procedural
knowledge; in particular, laying conceptual foundations for procedural and symbolic manipulation
skills.
12. Although the increase in the number of students taking and passing algebra is encouraging the large
number of failing grades is a serious concern. The district should investigate causes of the problem
and identify and implement research-based remedies.
13. The district should pursues a challenging, cohere, and focused K-12 mathematics curriculum that
includes core concepts of algebra and geometry early enough and with progressively increasing
depth so that the content covered in Integrated Math I and II or in traditional Algebra I and geometry
course is mastered by the end of grade 9.
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Math Task Force A.4
Analysis of Helping Children Learn Mathematics and NMAP 2008 Report
I. Key Findings from Helping Children Learn Mathematics
A. Philosophy
1. A greater understanding of mathematics is essential for the survival of this country.
2. All students mathematically proficient.
3. Close achievement gap among student groups.
4. Ensure that all students come to school with informal math concepts and skills: 1. play games, 2. experience natural counting opportunities,
3. sort objects, 4. identify shapes, details such as same, different, larger, smaller, and 5. experience math language in discussion.
5. Proficiency is much more likely to develop when the classroom is a community of learners rather than a collection of isolated individuals.
6. A significant amount of class time is spent developing mathematical ideas not just practicing mathematical skills.
7. Students should have opportunity to work independently of the teacher, individually, in pairs or groups.
8. Changes must be made to the educational system to realize the vision of all students mathematically proficient: changes in instruction,
materials that integrate the five stands of proficiency, assessments, teacher support, teacher understanding of the math content and how to
teach it to student.
9. Mathematical proficiency requires that everyone works together.
B. Mathematical Proficiency – “what it means to learn math successfully.”
1. There are five strands that are interwoven and interdependent. (P. 8)
2. The five strands: understanding, computing, applying, reasoning, engaging.
3. “Developing the strands of proficiency individually is much harder than learning them together. In fact, it is almost impossible to master
any one of the strands in isolation.” P. 17.
C. Teacher Development
1. Teachers much be proficient at a much deeper level than their students. (P. 31)
2. Provide time and resources for professional development.
3. Teachers need extensive opportunities to learn, observe models of effective practice, and have access to expertise in mathematics teaching.
It is not reasonable in the short term to expect teachers to acquire the knowledge needed for mathematical proficiency.
4. Undergraduate training: Future teachers need to continue their own mathematical proficiency, how to use that proficiency to guide
discussion, modify problems, and make decisions about to pursue in class.
D. Instruction
1. Math instruction cannot be effective if it is based on extreme positions. (P. 12)
2. Students become more proficient when they understand the underlying concepts of math and they understand the concepts more easily if
they are skilled at computational procedures.
3. Time and opportunity to learn are essentials. Suggested 60 minutes. This time is portioned so that all the strands receive adequate
attention.
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4. Textbooks and other instructional materials in the US need to support the learning of all five strands.
E. Assessment
1. Re-examine what assessments are measuring.
2. Formative assessment helps address instructional decisions.
3. Summative assessments helps track students’ progress and identify areas needing help.
4. Federal research group to analyze state and national math tests for the extent to which the test provides effective, reliable data.
F. System Approach
1. Everyone needs to work together to make the system changes.
2. Embrace the goal of mathematical proficiency for all.
3. Provide a math curriculum aligned with goal of math proficiency and align lessons to curriculum.
4. Hire math specialists for each elementary school.
5. Fund change initiatives.
6. Make available released time, stipends for sustained professional development.
7. Coherent, multi-year program – seamless curriculum.
G. System Support
1. Teachers need extensive opportunities to learn, observe models of effective practice, and have access to expertise in mathematics teaching.
It is not reasonable in the short term to expect teachers to acquire the knowledge needed for mathematical proficiency.
2. Instructional materials need to have teacher notes that support teacher’s understanding of mathematical concepts, student thinking, and
student errors, and effective pedagogical support and techniques.
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II. Key Findings from the NMAP 2008 Report
A. Background Executive Summary
1. Survival of the United States as an International nation.
2. Success in Mathematics Education for the well being of citizens and businesses.
3. Closing the disparity in Mathematics achievement between race and income.
B. Principal Messages
1. Panel identifies that the system of math education is broken and must be fixed.
2. “This is not a conclusion about any single element of the system. It is about how the many parts do not now work together to achieve a result
worthy of this country’s values and ambitions.” (Page xiii)
C. Six elements of the plan of action
1. Curriculum: Well defined, streamlined topics grades PreK-8
2. Application of research about how children learn: a) Children who come to school with strong mathematical experiences have an advantage
over other children. b) Students need to experience the mutually reinforcing benefits of conceptual understanding, procedural fluency and
automatic recall of facts. c) Student effort, not just inherent talent counts in mathematical achievement.
3. Citizens and educational leadership need to recognize that mathematically knowledgeable classroom teachers have a central role in
mathematics education. Citizens and educational leadership need to attract, evaluate, and retain effective teachers. Citizens and educational
leadership needs to support the appropriate preparation for prospective teachers.
4. Instructional Practices: a) High quality research b) informed by the best professional judgment and experience of accomplished classroom
teachers. “High-quality research does not support the contention that instruction should be either entirely student centered or teacher
directed.” (page xiv)
5. Assessments a) National and State assessments should be improved in quality b) National and State assessments should carry increased
emphasis on the most critical knowledge and skills leading to Algebra.
6. United States must support more rigorous research to inform public policy and instructional practice.
D. Leadership
1. This call to change mathematics education in this country requires time and money, and a community wide effort involving many people at
various levels.
2. The panel charges the US secretary of education to “take the lead in convening the forum initially, charge it to organize in a way that will
sustain an effective effort, and request a brief annual report on the mutual agenda adopted for the year ahead.” (page xiv)
E. Presidential Charge
1. Used the best available scientific research
2. Research evidence a) global considerations relating to standards of evidence. b) reviewed more than 16,000 publications and policy reports. c)
testimony from 110 individuals d) written commentary from 160 organizations and individuals e) survey results from 743 active teachers of
algebra. Panel worked for over 20 months
3. Panel defined many concrete steps that can be taken toward improving mathematics education and views them as the start in a long process.
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4. The presidential charge contains many explicit elements with an emphasis on the preparation of students for entry into algebra.
F. Main findings and recommendations = 45
1. Curricular content: recommendation #1-7
Proficiency defined in recommendation one and aligned with the five attributes associated with the concept of proficiency – 1) conceptual
understanding, 2) procedural fluency (computing), 3)strategic competence (applying), 4) adaptive reasoning, 5) productive disposition
(engaging.) Adding It Up (National Research Council, 2001, p. 116)
2. Learning processes: recommendation #8-15
Algebra preparation #10: To prepare the students for Algebra, the curriculum must simultaneously develop conceptual understanding,
computational fluency, and problem solving skills. Debates regarding the relative importance of these aspects of mathematical knowledge are
misguided. These capabilities are mutually supportive, each facilitating learning of the others. Teachers should emphasize these interrelations;
taken together, conceptual understanding of mathematical operations, fluent execution of procedures and fast access to number combinations
jointly support effective and efficient problem solving. (xix)
3. Teachers and Teacher education: recommendation #16-22
Teacher mathematical knowledge #17: Research on the relationship between teachers’ mathematical knowledge and students’ achievement
confirms the importance of teachers’ content knowledge…More precise measures are needed to specify in greater detail the relationship among
elementary and middle school teachers’ mathematical knowledge, their instructional skill, and students’ learning. (xxi)
4. Instructional Practices: recommendation #23-30
Approaches to Instruction: # 23, 24, 26:
#23 – Use both “student centered” and “teacher directed” approaches.
#24 - Team assisted individualization to improve student computation skills.
#26 – Use real-world context to introduce mathematical ideas.
5. Instructional Materials: recommendation #31 – 33
Materials: #31, #32
#31 – Shorter, more focused text books
#32 – Strive for great agreement regarding topics to be used.
6. Assessment: recommendation #34 – 38
Recommendation # 34
NAEP and state tests for students through Grade 8 should focus on and adequately represent the Panel’s Critical Foundations of Algebra.
Student achievement on this critical mathematics content should be reported and tracked over time.
7. Research Policies and Mechanisms: recommendation #39 – 45
Recommendation #39
It is essential to produce methodologically rigorous scientific research in crucial areas of national need, such as the teaching and learning of
mathematics. (page xxvi)
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