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Making Proficiency in Math. Soar to Greater Heights November 2, 2006 Claudia Ahlstrom. Agenda. Look at the data Review released NMSBA item Look at NM Math Standards Standards-based classroom Implementing connections Instructional materials Cognitive demand Resources . Difficulty

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making proficiency in math

Making Proficiency in Math

Soar to Greater Heights

November 2, 2006

Claudia Ahlstrom

  • Look at the data
  • Review released NMSBA item
  • Look at NM Math Standards
  • Standards-based classroom
  • Implementing connections
  • Instructional materials
  • Cognitive demand
  • Resources
math grade 4 ascending items

Type of item


Item number

Proficiency levels

Math Grade 4 – ascending items
grade 4 math oe
Grade 4 Math OE

Points 0 1 2 3 4

Total % 16 16 27 30 10

Hi 1 4 20 48 28

Mid 9 17 34 32 7

Low 50 25 15 4 0

4th grade item
4th grade item

Do this problem and be thinking about:

What students need to know & be able to do to be successful on this type of task.

nm math standards
NM Math Standards

Number & Operations




Data Analysis & Probability

process standards
Process Standards
  • Problem Solving
  • Reasoning & Proof
  • Communication
  • Connections
  • Representations
classroom experiences
Classroom Experiences
  • What types of classroom experiences do students need to be prepared for NMSBA?
  • What should curriculum & instruction look like to support this type of learning?
  • What might a standards-based classroom look like?
  • What kind of support will teachers need to implement this type of curriculum?
improving mathematics teaching
Improving Mathematics Teaching
  • James Stigler & James Hiebert
  • Cultural Nature of Teaching
  • Making connections v. using procedures
  • Implementating connections problems
instructional materials
Instructional Materials
  • What are the characteristics of the kinds of instructional materials that would best support content & process standards-based instruction?
mc rationale for program recommendations
MC² Rationale for Program Recommendations

Math Content:

Problem Solving


Communication & Representation

Reasoning & Proof

Comprehensive & Standards Based

Instructional Design and Student Experiences:

Clear Goals & Deep Understanding

Active Learners

Explore Math using Manipulatives & Technology

Teacher Role:

Tasks and Lessons for Students

Sense Making & Facilitating Learning


Integrated into Instructional Program

category 1 mathematics content processes
Category 1 – Mathematics Content Processes
  • Reflects problem solving nature of mathematics & thinking that mathematicians use.
  • Makes connections within mathematics and between disciplines.
  • Incorporates mathematics as communication and representation into the program.
  • Incorporates mathematics as reasoning and proof into the program.
  • Is comprehensive & includes math content emphasized in NM Standards and Benchmarks at each grade level.
category 2 instructional design
Category 2 – Instructional Design

1. States learning goals clearly and explicitly and students are asked to work on

worthwhile mathematical tasks.

2. Is coherent and attends to students’ prior knowledge.

3. Provides extensive use of open-ended, free response, questions.

4. Incorporates calculators, computers and/or other technology into the program as

tools for students to use to do mathematics.

5. Is appropriate for all students.

6. Provides differentiated instructional strategies to address diverse learning needs

(i.e., ELL and SPED).

7. Supports learning at home.

category 3 student experiences
Category 3 – Student Experiences

1. Designed so students are active learners.

2. Designed for students to construct their own understanding of mathematics.

3. Asks students to engage in mathematical discourse.

4. Provides manipulatives and/or technology to explore mathematical ideas, model mathematical situations, analyze data, calculate numerical results and solve problems.

5. Expects students to determine when they need to calculate in a problem and whether they require an exact or approximate answer.

6. Expects students to reflect on, make judgments about, and report on their own thought process, problem solving attempts, and performance.

7. Providesuser-friendly students’ materials

category 4 teacher role instructional materials
Category 4 – Teacher Role: Instructional Materials

1. Provide suggestions to teachers so that in tasks and lessons teachers can help students.

2. Provide suggestions for teachers in initiating and orchestrating mathematical discourse.

3. Provide assistance to teachers to facilitate learning by all students.

4. Provide suggestions to teachers for establishing a student centered classroom learning environment.

5. Provide suggestions to teachers to help them reflect on what happened in the classroom so that they can adjust or adapt their teaching plans.

category 5 assessment
Category 5 – Assessment

1. Integrates content and process standards into the instructional program

2. Uses multiple means of assessment, informal as well as formal

3. Includes assessment tasks making connections between mathematical ideas.

4. Assesses conceptual understanding and procedural knowledge frequently through tasks that ask students to apply information about a given concept in novel situations.

cognitive demand
Cognitive Demand
  • Memorization Tasks
  • Procedures without Connections Tasks
  • Procedures with Connections Tasks
  • Doing Mathematics Tasks

Tasks: NAEP, BAM

Instructional Materials: MC², NCREL, TERC,