1. Four Features of a Productive Classroom Culture
1. Ideas are the currency of the classroom 2. Students have autonomy with respect to the methods used to solve problems. 3. The classroom culture exhibits an appreciation for mistakes as opportunities to learn. 4. The authority for reasonability and correctness lies in the logic and structure of the subject, rather than in the social status of the participants.
. Ideas, expressed by any
participant, have the potential to
contribute to everyone’s learning and
consequently warrant respect and
response.
Students must respect the
need for everyone to understand their
own methods and must recognize that
there are often a variety of methods
that will lead to a solution.
Copyright © 2010 by Pearson Education, Inc. All rights reserved.

2. Learning Theory: Implications for Instruction
1. Build new knowledge from prior knowledge
2. Provide opportunities to talk about mathematics
3. Build in opportunities for reflection
4. Encourage multiple approaches
5. Treat errors as opportunities for learning
6. Scaffold new content
7. Honor diversity

3. Mathematics Proficiency
The five “strands” of mathematics proficiency (NRC, 2001):
Conceptual Understanding – comprehension of mathematical concepts, operations, and relations
Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
Strategic Competence – ability to formulate, represent, and solve mathematical problems
Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification
Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy
The five process standards (NCTM, 2000):
Problem Solving
Reasoning and Proof
Communication
Connections
Representations

4. Diversity in the Math Classroom

5. Ways to Ensure Equitable Teaching
Highly qualified teacher
Examining achievement gaps vs. instructional or expectation gaps
“[H]igh expectations, respect, understanding, and strong support for all students” (NCTM, 2008)
Copyright © Allyn and Bacon 2010

6. Creating Equitable Instruction
It is not enough to provide equal opportunity for all students to learn math
It is being sensitive to individual differences
It is treating students fairly and impartially
It is examining your beliefs about students’ abilities to learn (especially those in poverty)
Copyright © Allyn and Bacon 2010

7. Mathematics for All Children (Diversity in Today’s Classroom)
Diversity includes students who are:
Identified as having a specific learning disability
From different cultural backgrounds
English language learners
Mathematically gifted
Copyright © Allyn and Bacon 2010

8. Mathematics for All Children (Tracking and Flexible Grouping)
Is responsible for lower expectations for students in the “slow” track
Frequently denies students access to challenging materials
For “slower” tracks is often remedial drill
Exaggerates differences instead of bridging them
Makes it almost impossible to move to a higher track
Does not benefit higher-achieving students
Copyright © Allyn and Bacon 2010

9. Copyright © Allyn and Bacon 2010
Mathematics for All Children (Instructional Principles for Diverse Learners)
Learning with understanding is based on connecting and organizing knowledge around big conceptual ideas
Learning builds on what students already know
Instruction in school takes advantage of the children’s informal knowledge of mathematics
Don’t forget about accommodations and modifications
Copyright © Allyn and Bacon 2010

10. Copyright © Allyn and Bacon 2010
Providing for Students with Special Needs Response to Intervention (RTI)
Source: Scott, T., and Lane, H. (2001). Multi-Tiered Interventions in Academic and Social Contexts. Unpublished manuscript, University of Florida, Gainesville.
Copyright © Allyn and Bacon 2010

11. RTI: Common Features Across All Tiers
Research-based practices
Data-driven
Instructional
Context-specific
Copyright © Allyn and Bacon 2010

12. Students with Mild Disabilities
Students in Tier 3 May Have Difficulty with:
Memory
General strategy use
Attention
Ability to speak or express ideas
Perception of auditory, visual, or written information
Integration of abstract ideas
Copyright © Allyn and Bacon 2010

13. Research-Based Strategies (to Be Used with Tier 3 Students)
Explicit strategy instruction
Peer-assisted learning
Student think-alouds
Copyright © Allyn and Bacon 2010

14. Modifications and Accommodations (for Tier 3 Students)
Before
Structure the environment
Identify potential barriers
During
Provide clarity
After
Consider alternative assessments
Emphasize practice and summary
Copyright © Allyn and Bacon 2010

15. Students with Significant Disabilities
Students are expected to learn the mathematical content based on the NCTM standards
Students need the content connected to real-life skills and possible features of jobs
Not all facts must be mastered before progressing further in the curriculum
Copyright © Allyn and Bacon 2010

16. Copyright © Allyn and Bacon 2010
Additional Strategies for Supporting Students with Moderate and Severe Disabilities
Systematic instruction
Visual supports
Response prompts
Task chaining
Problem solving
Self-determination and independent self-directed learning
Copyright © Allyn and Bacon 2010

17. Strategies for Teaching Mathematics for ELLs
Write and state the content and language objectives
Build background
Encourage use of native language
Comprehensible input
Explicitly teach vocabulary
Plan cooperative/interdependent groups to support language
Create partnerships with families
Copyright © Allyn and Bacon 2010

18. Working Toward Gender Equity
Although there is no discrepancy in boys’ and girls’ math scores, we need to be aware of and address gender equity in the classroom
Many more males enter into graduate-level fields with a heavy emphasis on math than do females
Copyright © Allyn and Bacon 2010

19. Copyright © Allyn and Bacon 2010
Gender Inequity
Possible Causes
Belief systems related to gender
Teacher interactions and gender
Possible Solutions
Awareness
Involve all students
Copyright © Allyn and Bacon 2010

20. Reducing Resistance and Building Resilience
Give children choices and capitalize on their unique strengths
Nurture traits of resilience
Demonstrate an ethic of caring
Make mathematics irresistible
Give students some leadership in their own learning
Copyright © Allyn and Bacon 2010

21. Providing for Students Who Are Mathematically Gifted
Strategies to Avoid
More of the same
Allowing free time when they complete their work
Routinely assigning them to teach other students
Strategies to Incorporate
Acceleration
Enrichment
Sophistication
Novelty
Copyright © Allyn and Bacon 2010

22. Copyright © Allyn and Bacon 2010
Final Thoughts
Identify current knowledge and build upon it
Push students to high-level thinking
Maintain high expectations
Use a multicultural approach
Recognize, value, explore, and incorporate the home culture
Use alternative assessments
Measure progress over time
Promote the importance of effort and resilience
Copyright © Allyn and Bacon 2010

23. Integrating Assessment into Instruction
Assessment should enhance student learning
Assessment is a valuable tool for making instructional decisions
Copyright © Allyn and Bacon 2010

24. Copyright © Allyn and Bacon 2010
Why Do We Assess?
To monitor student progress
To make instructional decisions
To evaluate student achievement
To evaluate programs
Source: Adapted from NCTM, Assessment Standards for School Mathematics, 1995, p. 25. Used with permission.
Copyright © Allyn and Bacon 2010

25. Thoughts about Assessment Tasks
In some instances, the real value of the task will come in the discussion that follows
Explanations need to be a regular practice in every classroom
Copyright © Allyn and Bacon 2010

26. Rubrics and Performance Indicators
Scoring: Comparing students’ work to criteria or to rubrics that describe what we expect the work to be
Grading: The result of accumulating scores and other information about students’ work for the purpose of summarizing and communicating to others
Rubric: A framework that can be designed or adapted by the teacher for a particular group of students or particular math task, using a three- to six-point scale to rate performance
Copyright © Allyn and Bacon 2010

27. Copyright © Allyn and Bacon 2010

28. Copyright © Allyn and Bacon 2010
Observation Tools
Anecdotal notes
Observation rubric
Checklists for individuals
Checklists for full class
Copyright © Allyn and Bacon 2010

29. Copyright © Allyn and Bacon 2010
Tests
Will always be a part of assessment
Do not have to test low-level skills
Can be designed to assess understanding of concepts
Should go beyond just knowing how to perform an algorithm
Should allow and require a student to demonstrate a conceptual basis for the process
Copyright © Allyn and Bacon 2010