1. Elementary and Middle School Mathematics Chapter Reflections: 1,2,3,5,6
By: Amy Howland

2. Teaching Mathematics in the 21st Century
Chapter 1
Teaching Mathematics in the 21st Century

3. The Six Principles 6 Major Components of the Mathematics Classroom
Equity- high expectations for all students
Curriculum- “big ideas”
Teaching- Teachers understand concepts, understand how students learn math, and select meaningful instructional tasks
Learning- Learning math with understanding is essential and students can learn math with understanding
Assessment-Ongoing observations and feedback
Technology- Essential tools for enhancing learning
6 Major Components of the Mathematics Classroom
Creating and equal opportunity environment
Focusing on a balance of conceptual understanding and procedural fluency
Active engagement in the NCTM process standards
Using technology to enhance learning
Incorporating multiple assessments
Helping students recognize the power of sound reasoning and mathematical integrity

4. Exploring What It Means to Know and Do Mathematics
Chapter 2
Exploring What It Means to Know and Do Mathematics
What, Why and How of teaching mathematics

5. Implications for Teaching Mathematics
Doing Mathematics: Students begin to take math ideas to the next level by connecting to previous material and responding with information beyond the required response and predicting.
Implications for Teaching Mathematics
Build new knowledge from prior knowledge
Provide opportunities to talk about math
Build in opportunities for reflective thought
Encourage multiple approaches
Engage students in productive struggle
Treat errors as opportunities for learning
Scaffold new content
Honor diversity
Constructivism: The notion that learners are not blank slates but rather creators of their own learning.
We use existing knowledge and build upon it creating a network of connections, the more connections, the better we understand!

6. Teaching Through Problem Solving
Chapter 3
Teaching Through Problem Solving

7. Four-Step Problem Solving Process
Low-Level Cognitive Demand: -Memorization tasks -Procedures without connections tasks High-Level Cognitive Demand: -Procedures with connections tasks -Doing mathematics tasks
Four-Step Problem Solving Process
Understanding the problem
Devising a plan
Carrying out the plan
Looking Back
Tasks should have multiple exit points or various ways that students can demonstrate understanding of the learning goal.
Children's literature (and other resources/links to other disciplines) can help students learn and work through math problems
The teacher’s role is to understand student thinking(not to lead students to the correct answer).
3 Phase lesson plan: before (into), during(through) and after(beyond)
Problem-Solving Strategies:
Draw a picture, act it out, use a model
Look for a pattern
Guess and check
Make a table or chart
Try a simpler form
Make a list

8. Building Assessment into Instruction
Chapter 5
Building Assessment into Instruction

9. Ways of Assessing Students Rubrics
Purposes of Assessment
Evaluating Programs
Modify Program
Evaluating student achievement
Recognize Accomplishment
Monitoring student progress
Promote growth
Making instructional decisions
Improve Instruction
Ways of Assessing Students
Rubrics
Writing and Journals (I think the answer is… or What did you still have questions about?)
Student self-assessment
Tests
Diagnostic Interviews
Observations
Anecdotal notes
Checklists (individual or whole class)

10. Teaching Mathematics Equitably to All Children
Chapter 6
Teaching Mathematics Equitably to All Children

11. Math for all: - students who are identified as struggling or having a disability - students from different cultural backgrounds - students who are mathematically gifted - students who are unmotivated or need to build resilience
Strategies to promote diversity:
Identify children’s current knowledge bade and build instruction around that
Push all students to high-level thinking
Maintain high expectations
Use a multicultural approach
Recognize, value, explore, and incorporate the home culture
Use alternative assesments
Measure progress over time
Promote the importance of effort
Instructional Principles:
Learning with understanding is based on connecting and organizing knowledge around big conceptual ideas
Learning builds on what students already know
Instruction in school should take advantage of students’ informal knowledge of mathematics