Text Reflection 1, 2, 3, 5, 6

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Text Reflection 1, 2, 3, 5, 6

Chapter 2 HighlightsKnowing how to do math is more than just being able to do a procedure.-Math is more than completing exercises and mimicking processes.-Math is the science of pattern and order.-Math language matters, utilize verbs that engage students in doing math.-Classroom environment- engaging in productive struggle helps students learn math.-Provides opportunities to do math with various activities.-Learners are not blank slates, but rather creators. Constructivism (Piaget)-Sociocultural theory (Vygotsky)-Discussions based on student ideas and interests, and solutions is fundamental to learning.-Buld new knowledge from prior knowledge (scaffolding)-Honor diversity in the classroom.-Redefine "helping", rather than showing students how to do something. -Understadning Mathematics- five different representations of ideas.-Ineffective use of tools and manipulatives such as "do as I do". -Math proficiency (Conceptual, Procedural).-Teaching math proficiency requires a lot of effort, and takes time.-Benfits of proficiency (less to remember, increased retention/recall, enhanced problem solving, improved attitude/beliefs).Chapter 6-teaching math equitably to all students-placing students or tracking creates inequities in learning math.-achieving higher level perforamance requires an approach called RtI.-A tiered student support system. -monitor student progress.-directed teaching format prescribes the use of manipulatives, and a model prompt practice sequence.-peer assisted learning-think alouds instructional strategies.-examples of activities for those with moderate to severe disabilities. -simplifying the concepts only lowers the chance of learning content. -connect concepts meaningfully to other content.-allow students to see themselves in math, incorporate their identities. -value diversity in language and heritage. -use comprehensible input, make sure your message is understood. -make teaching math vocabulary explicit. play games, use concept maps, word walls, etc. -be aware of and avoid math steroetypes in gender abilities. girls who believe in these will avoid harder math classes.-Give students choices, reduce resistance and build resilience. -Nurture traits such as social competence, problem solving, autonomy, and a sense of purpose and future.

Chapter Reflections

-1, 2, 3, 5, 6_

Teaching Mathematics in the 21st Century

Chptr 1

-Teachers must be aware of some of the forces that effect change in the mathematics classroom. - Standards based movement (Common Core)-The six principles (equity, curriculum, teaching, learning, assessment, and technology).-The five content standards (Number and operations, algebra, geometry, measurement, data analysis and probability).-The 5 process standards (Problem solving, reasoning and proof, communication, connections, representations).specific "targets" for each grade level (coherence).Professional Standards for tecaching math.-Research suggests that the U.S. still has disappointing levels of math competency.-discovered that we need more depth rather than trying to do a little of everything.-The U.S. approach to teaching math has been essentially unchanged for over 100 years. -Textbooks influence teaching. -Mathematics ability is not inherited, anyone can learn mathematics.-We need to treat math just as we do reading, we are all readers, so we can all be mathematicians. -Thinking and talking about math is more important that the "one right answer".-Math teacher qualities include (persistence, positive attitude, readiness for change, reflective disposition).

Chapter 3 Highlights-Teaching for problem solving-Four step problem solving process-It is important to select worthwhile tasks, cognitively demanding. low level vs. high level.-Include problems for different levels and abilities (entry and exit points. -Context is key, hook them into being interested in the task.-Children's literature is a rich source for all levels, not just primary.-Find links to other contexts-standards based instruction-We need to ask students questions, if you do not ask, they will not think.-Informations can and should be shared as long as you dont give the answer away. -Writing used in the math classroom.-problem based lessons are taught in 3 phases.

Make Math Fun!

Chapter 5-Integrating assessment into instruction-assessment should happen everyday-the purpose of assessment is to evaluate programs, monitor progress, evaluate achievement, make instructional decisions. -When is assessment appropriate.Performance tasks are linked to problem solving.-scoring with a 4 point rubric -writing is both an assessment tool and learning opportunity.-tests- always be apart of assessment, but not a collection of low level skills exercises.-through observation, teachers learn useful bits of info about students everyday.-Anecdotal notes is a system for recording observations both during or following a lesson.Diagnostic interviews-summative assessments-



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