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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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improving k 12 mathematics education challenges opportunities

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
About this Session

5 Challengesand1 Opportunity (CCSS)


Challenge #1:

Widespread perception that mathematics is a set of facts, rules, and procedures to be mastered.

  • This perception leads to:
  • teaching that focuses on presentation rather than student engagement.
  • a general public which values math but doesn’t like it or feel comfortable using it.

Challenge #2:

Many current textbooks reinforce the perception of mathematics as a set of rules, procedures.

  • They don’t offer teachers good guidance for engaging students.

Challenge #3:

Lack of student interest in and motivation to learn mathematics.

  • Many students don’t think that learning mathematics is important.
  • Some students are not willing to work hard to learn mathematics.

Challenge #4:

There is no coherent system for improving teaching practices ( professional development).

  • The teacher work day lacks “space” for continual professional development OR for serious collaboration with colleagues.

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


Challenge #5:

Annual high-stakes assessments are currently the primary tool for gauging school/teacher success (accountability).

an opportunity to focus on improvement
An opportunity to focus on improvement:

Common Core State Standards Initiative

common core state standards ccssm
Common Core State Standards (CCSSM)

Initiated by:

National Governor’s Association


Council of Chief State School Officers

how much do you know about ccssm
How much do you know about CCSSM?

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.


Common Core State Standards Initiative

  • State consensus on learning goals (standards) for mathematics, K-12
  • State collaboration to develop and use improved assessments to monitor student learning

Common Core State Standards (Math)

Adopted by all but 6 states (as of 9/20/11)


The 2011 Montana draft standards are the CCSSM with the addition of embedded Indian Education statements.

  • Public Hearing: Oct. 24, 2011
  • Action on Adoption (Montana Board of Public Education): Nov. 4, 2011

Common Core State Standards (Math)

Adopted by all but 6 states (as of 9/20/11)


Why a common core curriculum?

  • Potential to increase the quality of …
  • instructional materials
  • high stakes assessments
  • Common standards address one cause of the U.S. “mile-wide, inch-deep” curriculum.


4th grade mathematics standards

10 largest states.

- 108 “unique” standards

gr 4 mathematics standards common across 10 largest states in 2006
Gr. 4 mathematics standards common across 10 largest states in 2006:
  • Read, write, compare, and order whole numbers.
  • Read, write, compare and order decimals.
  • Add and subtract decimals.
  • Solve problems involving whole number multiplication and division.

(4 of 108 learning goals)

gr 4 standards unique to only one of ten state s examples
Gr. 4 standards unique to only one of ten states (examples):
  • Use concrete materials and symbolic notation to represent numbers in bases other than base ten, such as base five.
  • Compare decimal number system to the Roman numeral system (using the Roman numerals I, V, X, L, C, D, and M.)
  • Use models to identify perfect squares to 100.

(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.”


What are the CCSS and how are they organized?

  • How are they different from current state standards?

The standards are not intended to define HOW to teach.

Standards for Mathematical Practice

  • Carry across all grade levels
  • Describe habits of mind of a mathematically expert student

Standards for Mathematical Content

  • K-8 standards presented by grade level
    • Organized into domains that progress over several grades
    • Grade introductions give 2–4 focal points at each grade level
  • High school standards presented by conceptual themes (two “pathways” included in Appendix – single subject and integrated)
standards for mathematical practice
Standards for Mathematical Practice

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.

opportunity of common core
Opportunity of Common Core

The standards:

  • Attention to mathematical practices/processes
  • Focus on understanding
  • Some attention to learning progressions

More generally:

  • Energy and activity focused on same learning goals:
    • Curriculum development
    • Professional development
    • Assessments (high stake)
how is the common core different from previous state standards
How is the Common Core different from previous state Standards?

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.


Example of grade level shift

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)

CCSSM standard:

By the end of Grade 3, know from memory all products of two one-digit numbers. (Grade 3)

use of precise mathematical language
Use of precise mathematical language

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.”

Grade 3:

“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 represent equivalent fractions. Represent fractions using an area model, and/or parts of a set model and locate points on a number line model. (Gr. 3)

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.

standards important but not sufficient
Standards: Important but not sufficient

The Standards must be partnered with a content-rich curriculum, focused professional development and robust assessments aligned to the Standards.


SMARTER Balanced Assessment Consortia (SBAC)

$160 million

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:

  • the required summative exams (offered twice each school year);
  • optional formative, or benchmark, exams; and
  • a variety of tools, processes and practices that teachers may use in planning and implementing informal, ongoing assessment.”

Partnership for Assessment of Readiness for College and Careers (PARCC) Consortia:

$170 million

26 states

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


Gates Foundation Project

  • Provided $3 million to support a joint effort with Pearson Foundation to develop curriculum centered on Common Core
  • Instructional system of 24 online courses covering K-12 English/language arts and K-10 math.
  • One course for each grade level.
  • Four of the courses - two in each subject area in the early to middle high school grade levels - will be contributed as free and open resources.

Illustrative Mathematics Project

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.


CCSSM Curriculum Analysis Tool

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



Inside Mathematics


Barbara J. Reys