Math Methods Midterm

common core state standards

college & career readiness

CCSS founding organizations

1. Council of Chief State School Officers

2. National Governor’s Association

CCSS design

backward designed starting with 12th grade down to kindergarten, where at each grade level students reengage with previous knowledge to build understanding.

benefits of sharing and discussing computation strategies

1. clarify their own thinking

2. test other strategies to see if they are logical.

3. investigate and apply mathematical relationships

4. build a repertoire of efficient strategies.

5. make decisions about choosing specific strategies for particular problems.

CCSS connection to TN standards

TN adopted CCSS in 2010, but revised it beginning in 2015 to change the pacing and add in more problem-solving components.

significance of instructional materials being aligned to standards

• consistency in learning objectives

• quality and effectiveness

• equitable education

• assessment preparation for students

• focused instruction

  • support for student success

focus

greater focus on fewer topics. great depth on major work in each grades

coherence

linking topics and thinking across grades to build a coherent progression of understanding

rigor

pursue conceptual understanding, procedural skills and fluency, and application with equal intensity

conceptual understanding

understanding of mathematical concepts, operations, and relations. why an idea is an important.

procedural fluency

the ability to apply procedures accurately, efficiently, and flexibly

mathematical reasoning

process of thinking logically and systematically to understand, analyze, and solve math problems

application

practicing skills in a relevant, meaningful way. students develop problem-solving skills, reasoning, and critical thinking skills.

what are SMP

“Habits of mind'“ or approaches and practices that allow students to develop fluency, procedural skills, and conceptual understanding.

8 SMP

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with math.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

   1. Look for and express regularity in repeated reasoning.

literacy skills in math

1. use multiple reading strategies

2. understand and use correct math vocab

3. discuss and articulate math ideas.

   1. write math arguments.

importance of children’s literature in math

• spark student imagination

• boost confidence of those who are “math-wary”

• think and reason mathematically

• teach basic concepts

mindset

self-perception that people have about themselves

growth mindset

people believe that your abilities can be improved with dedication and hard work

fixed mindset

people believe their basic abilities have been pre-determined and are unchangeable.

mathematical mindset

similar to productive disposition, where students view math as sensible, useful, and worthwhile. students believe they can do math efficiently and achieve the highest level of math.

How do we develop mathematical mindsets?

• believe everyone can learn at the highest levels

• visual math and “open” math (creative and different)

• curious and wondrous learning environment

  • communication, connections, and mistakes are valued

number sense

thinking about different sized quantities and use numbers and relationships in multiple ways to estimate and solve problems.

number core

quantity, counting, and knowing how many. Ability to subitize (see numbers and not have to count).

relations core

more than, less than, and equal to. construct sets and make comparisons.

operations core

addition and subtraction are connected as multiplication and division are connected. models can be used to represent operations.

number talks

relatively short routines that provide students with opportunities to change their view of mathematics, develop number sense, and engage them in create, open math.

addition and subtraction strategies

• making 10s

• counting on

  • break apart

structure of a math task

• private think time for 5 min

• group work for 15 min, where students ask clarifying questions, explain their thinking, and conduct peer assessments.

• whole-group discussion where students share their ideas, students ask questions, construct arguments, and defend their reasoning.

• independent exit ticket

• laying out norms for discussion beforehand, like how to listen and ask questions

HQIM

high-quality instructional materials. targets grade-level mathematical standards to the full depth of the standard.

lesson internalization

steps a teacher takes to intellectually prepare for a unit/lesson. analyzing components to support learning goal and achieve the full depth of the standard.

standards and why they are important

particular facts and concepts that a school should teach. guide instruction in a focused and deep manner.

multiple reading strategies

predict, infer, visualize, ask questions, draw conclusions.

activities: before, during, after reading strategies

mathematical vocabulary

guided notes, writing activities, interactive word walls, vocab notebooks

discuss and articulate math ideas

paraphrasing, summarizing, think-pair-share, stem starters, accountable talk, etc

writing math arguments

journals, poems, word problems, entrance/exit tickets, support conclusions with evidence.