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

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

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

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

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!

Teaching Through Problem Solving Chapter 3 Teaching Through Problem Solving

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

Building Assessment into Instruction Chapter 5 Building Assessment into Instruction

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)

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

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