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Improving K-12 Mathematics Education: Challenges & Opportunities . Barbara J. Reys University of Missouri - Columbia. 2011 MEA-MFT Educators' Conference October 20-21, Missoula Barbara Reys University of Missouri Center for the Study of Mathematics Curriculum. About this Session.
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Barbara J. Reys
University of Missouri - Columbia
2011 MEA-MFT Educators' Conference October 20-21, Missoula
University of Missouri
Center for the Study of Mathematics Curriculum
5 Challengesand1 Opportunity (CCSS)
Widespread perception that mathematics is a set of facts, rules, and procedures to be mastered.
Many current textbooks reinforce the perception of mathematics as a set of rules, procedures.
Lack of student interest in and motivation to learn mathematics.
There is no coherent system for improving teaching practices ( professional development).
U.S. teachers spend about 80 percent of their total working time engaged in classroom instruction, as compared to about 60 percent for teachers in many other nations.
Professional Learning in the Learning Profession (2009)
National Staff Development Council
Annual high-stakes assessments are currently the primary tool for gauging school/teacher success (accountability).
Common Core State Standards Initiative
National Governor’s Association
Council of Chief State School Officers
1 – Nothing (except the last slide), that’s why I’m here.
2 – A little (I know what “CCSSM” stands for and I’ve been introduced to it).
3 – Some – I’ve read/reviewed some or all of it.
4 – A lot, I’ve thought about implications for my classroom/work.
5 – A whole lot – I could facilitate this session.
The 2011 Montana draft standards are the CCSSM with the addition of embedded Indian Education statements.
Are/were state standards alike or different (many were based on the NCTM Standards of 2000)?
4th grade mathematics standards
10 largest states.
- 108 “unique” standards
(4 of 108 learning goals)
(28 of 108 learning goals)
The differences across state standards (and related assessments) regarding what to teach and when to teach particular mathematics topics practically guarantees curriculum materials that are “a mile wide and an inch deep.”
Standards for Mathematical Practice
Standards for Mathematical Content
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Use of precise mathematical language to convey learning goals.
Increased emphasis on some models
Some content moved to earlier grades
Less emphasis on data analysis and probability in K-5
More emphasis on transformational geometry in high school.
Little attention to or acknowledgement of technology as a tool for doing or learning mathematics
At high school level, standards are listed by “conceptual category” - not by course.
Topic: Fluency with basic facts for multiplication and division.
Current MT standard:
Recall basic multiplication facts to products up to 100 and related division facts. (Grade 4)
By the end of Grade 3, know from memory all products of two one-digit numbers. (Grade 3)
Grade 3: “Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.”
“Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.”
“Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.”
Emphasis on particular models
(e.g., number line)
Use models to identify equivalent symbolic representations of improper fractions and mixed numbers. (Gr. 4)
Compare and order fractions using area, set, and linear models. (Gr. 5)
Montana Standards (2009)
Teachers need many opportunities to study, discuss, and plan for the changes in approach, sequence or intended models in the Common Core State Standards.
The Standards must be partnered with a content-rich curriculum, focused professional development and robust assessments aligned to the Standards.
31 states, including MO
Washington – lead state
“SBAC will create state-of-the-art adaptive online exams, using “open source” technology. The online system will provide accurate assessment information to teachers and others on the progress of all students, including those with disabilities, English language learners and low- and high-performing students. The system will include:
Partnership for Assessment of Readiness for College and Careers (PARCC) Consortia:
Florida – Lead state
“The proposed assessment system will be computer-based and will measure student progress at key times during the school year, rather than on one test at the end, to allow for instructional adjustment and extra support to students who need it.”
The next generation of curriculum materials
Set of activities/tasks/problems that illustrate the type of mathematical work that students will experience in a faithful implementation of the Common Core State Standards.
Set of mathematics curriculum analysis tools that allow K–12 textbook adoption committees, school administrators, and K–12 teachers to analyze mathematics curriculum materials with regard to their alignment to the Common Core