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.

Four Features of a Productive

Classroom Culture1. Ideas are the currency of the classroom2. 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.

Copyright © 2010 by Pearson Education, Inc. All rights reserved.

Learning Theory:Implications for

Instruction1. Build new knowledge from prior knowledge2. Provide opportunities to talk about mathematics3. Build in opportunities for reflection4. Encourage multiple approaches5. Treat errors as opportunities for learning6. Scaffold new content7. Honor diversity

Mathematics Proficiency

The five process standards (NCTM, 2000):

• Problem Solving

• Reasoning and Proof

• Communication

• Connections

• Representations

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

Diversity in the Math Classroom

Copyright © Allyn and Bacon 2010

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)


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)


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


Mathematics for All Children(Tracking and Flexible Grouping)

Tracking

• 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


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


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.


RTI: Common Features Across All Tiers

• Research-based practices• Data-driven• Instructional • Context-specific


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


Research-Based Strategies (to Be Used with Tier 3 Students)

• Explicit strategy instruction• Peer-assisted learning• Student think-alouds


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


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


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


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


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


Gender Inequity

Possible Causes

• Belief systems related to gender

• Teacher interactions and gender

Possible Solutions

• Awareness

• Involve all students


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


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


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


Integrating Assessment into Instruction

• Assessment should enhance student learning

• Assessment is a valuable tool for making instructional decisions


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.


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


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



• Anecdotal notes• Observation rubric• Checklists for individuals• Checklists for full class

Observation Tools


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

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.

Documents

students nctm

copyright allyn

students access

students abilities

math classroom slide

gifted slide

efficacy slide

poverty slide