Transcript Making Proficiency in Math - New Mexico State University

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
Math Grade 4 – ascending
items
• Difficulty
• Type of item
• Score
• Item number
• Proficiency levels
Grade 4 Math OE
Points
Total %
0
16
1
16
2
27
3
30
4
10
Hi
Mid
Low
1
9
50
4
17
25
20
34
15
48
32
4
28
7
0
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
Number & Operations
Algebra
Geometry
Measurement
Data Analysis & Probability
Process Standards
• Problem Solving
• Reasoning & Proof
• Communication
• Connections
• Representations
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
• James Stigler & James Hiebert
• Cultural Nature of Teaching
• Making connections v. using procedures
• Implementating connections problems
Instructional Materials
• What are the characteristics of the kinds
of instructional materials that would best
support content & process standardsbased instruction?
MC² Rationale for Program
Recommendations
Math Content:
Problem Solving
Connections
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
Assessment:
Integrated into Instructional Program
Category 1 – Mathematics
Content Processes
1. Reflects problem solving nature of mathematics
2.
3.
4.
5.
& 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
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
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. Provides user-friendly students’ 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
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
• Memorization Tasks
• Procedures without Connections Tasks
• Procedures with Connections Tasks
• Doing Mathematics Tasks
Resources
Tasks: NAEP, BAM
Instructional Materials: MC², NCREL, TERC,