best practices- math & science
Published on Nov 20, 2015
Accompanying visual for presentation on Chps. 5 & 6 of Best Practice: Bringing Standards to Life in America's Classroom
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PRESENTATION OUTLINE
realization that math is...
- dynamic
- coherent
- interconnected
Helping all students understand that mathematics is a dynamic, coherent, interconnected set of ideas-
• Requires a paradigm shift in methodology.
• Math is the science of patterns.
• Emphasis on reasoning and understanding concepts, rather than on separate, seemingly unrelated topics.
• Requires a paradigm shift in methodology.
• Math is the science of patterns.
• Emphasis on reasoning and understanding concepts, rather than on separate, seemingly unrelated topics.
Photo by TheAlieness GiselaGiardino²³
powerful use of mathematical concepts
Support all students to understand and use mathematical concepts powerfully.
• Mathematical thinking is a normal part of everyone’s mental ability.
• Not just for math people.
• Social constructivism is crucial-Japan vs. US, p. 169. We have a national deficit of connection making and cooperative learning.
• Mathematical thinking is a normal part of everyone’s mental ability.
• Not just for math people.
• Social constructivism is crucial-Japan vs. US, p. 169. We have a national deficit of connection making and cooperative learning.
Photo by tj.blackwell
critical cognitive processes
- make connections
- solve problems
- represent processes
- communicate mathematical ideas
Focus instruction on enabling students to successfully engage in critical cognitive processes.
• Making connections-the balance between examples and explanations. Reasoning is a habit that has to be developed.
• Problem solving-grappling with a problem and learning as they go, rather than pre-loading the process. Have students analyze their progress and their approach to the process.
• Representational strategies-different mental models--discussions, manipulative, acting it out, create a visual (or pictorial representation), make a list or a table
• Communicating mathematical ideas-Creating a safe space where students feel free to discuss, write about, read about, and listen to mathematical concepts.
• Making connections-the balance between examples and explanations. Reasoning is a habit that has to be developed.
• Problem solving-grappling with a problem and learning as they go, rather than pre-loading the process. Have students analyze their progress and their approach to the process.
• Representational strategies-different mental models--discussions, manipulative, acting it out, create a visual (or pictorial representation), make a list or a table
• Communicating mathematical ideas-Creating a safe space where students feel free to discuss, write about, read about, and listen to mathematical concepts.
Photo by CERDEC
strong foundation in...
- counting strategies
- number concepts
- operations
- computational procedures
Helping students understand and use counting strategies, number concepts, operations, and computational procedures.
• Whole number counting, relationships, decomposing and recomposing quantities, structuring numbers in base ten, conceptual understanding of the four operations, and strategies for working with them
• When gaps arise in these foundations, they must be filled as soon as possible.
• Whole number counting, relationships, decomposing and recomposing quantities, structuring numbers in base ten, conceptual understanding of the four operations, and strategies for working with them
• When gaps arise in these foundations, they must be filled as soon as possible.
Photo by ansik
algebra & algebraic reasoning K-12
Give all students opportunities to engage in doing algebra and reasoning algebraically throughout their K-12 years.
• Supports the idea of moving into the conceptual, earlier
• Pre-algebraic thinking within rich contexts develops students’ understanding of change, variables, equality and equations, function, rate of change, linearity and nonlinearity, etc.
• Supports the idea of moving into the conceptual, earlier
• Pre-algebraic thinking within rich contexts develops students’ understanding of change, variables, equality and equations, function, rate of change, linearity and nonlinearity, etc.
Photo by ddluong_
meaningful contexts
- real-world
- realistic
- authentic
Build understanding of mathematical concepts in geometry, measurement, data, statistics, and probability, use real-world, realistic, authentic contexts that are inherently meaningful to students.
• Relevance and access to the content, prior to direct teach of vocab and formulas, create engagement.
• Multiple entry-points to attributes being measured, creating a deep understanding.
• Students asked to design, defend, collect, organize, reflect, and model
• Relevance and access to the content, prior to direct teach of vocab and formulas, create engagement.
• Multiple entry-points to attributes being measured, creating a deep understanding.
• Students asked to design, defend, collect, organize, reflect, and model
Photo by Ѕolo
formative assessment
Use assessment that provides an understanding of what students know and guides meaningful decisions about teaching and learning activities.
• How do we know what they know…
• How do we know what they know…
Photo by Institut-Escola Les Vinyes
building on student curiosity
Photo by NASA Goddard Space Flight Center
knowledge, use, and interpretation of scientific explanations
Photo by Steve took it
generation & evaluation of scientific evidence & explanations
Photo by Green Map System
understanding of the nature & development of scientific knowledge
Photo by Amy M. Youngs
participation in scientific practices & discourse
Photo by Clint Hamada
integration of
engineering & science
Photo by NASA HQ PHOTO
knowledge and use of students' prior knowledge
Photo by Anthony Shemmans
self-directed learning
Photo by Barrett.Discovery
authentic assessment
Photo by Old Shoe Woman
