Access and Equity

high expectations for ALL students

Curriculum

coherent, focused, and well-articulated across grade levels

Teaching and Learning

deep understanding of content and of how students learn mathematics; selection of appropriate instructional tasks; new knowledge is built through connections with prior knowledge and appropriate experiences

Assessment

should support the learning of mathematics and guide instructional decisions

Tools and Technology

enhances student learning; allows for more/deeper mathematics to be taught

Professionalism

this is only the beginning; life-long learning is necessary to be successful; take advantage of professional development opportunities

List the 5 NCTM Content Standards

-Algebra -Geometry -Number & Operations -Measurement -Data Analysis & Probability

5 NCTM Process Standards- Problem Solving

Apply and adapt to a variety of appropriate strategies to solve problems that arise in mathematics and other context. Students can build a new mathematical knowledge through problem solving.

5 NCTM Process Standards- Representation

Mathematical concepts can be represented through real-life context, written symbols, manipulative models/physical tools, oral/written language, and graphs, tables and diagrams.

5 NCTM Process Standards- Reasoning & Proof

the logical thinking that tells us if and why our answers make sense and are correct

5 NCTM Process Standards- Communication

We communicate through speaking, writing, critical listening, and reading. We can organize and consolidate our mathematical thinking through communication.

5 NCTM Process Standards- Connection

making mathematical connections between either mathematics and the real world, mathematics and another subject, within one content strand (multiplication to addition- number & operations), or between two content strands (expressing probability as a fraction- data analysis & probability and number & operations)

8 Mathematical Practice Standards

-Make sense of problems and persevere in solving them -Reason abstractly and quantitatively -Construct viable arguments and critique the reasoning of others -Model with mathematics -Use appropriate tools strategically -Attend to precision -Look for and make use of structure -Look for and express regularity in repeated reasoning

Describe the structure of the Common Core State Standards for Mathematics Content and be able to define domain, standard and cluster.

The structure of the Common Core State Standards for Mathematics Content starts with the domain which is the overall category like Geometry or Number and Operations. The domains have clusters inside of them which are a set of standards group together based on relatedness, and inside of the clusters are the individual standards which are explicit statements of what the students in that specific grade should know and be able to do.

What is Constructivism?

Constructivism is the belief that students must be an active participant in the development of their own learning. Constructivism states that students are not blank slates and do not absorb ideas, they construct their knowledge through reflective thought.

What is a problem and what are the 3 features of a problem for learning math?

A problem is any task or activity for which the students have no prescribed or memorized rules or methods to use to solve it, nor is there a perception by students that there is a specific “correct” solution method. The 3 features of a problem are it must begin where students are, the problem or engaging aspect of the task must be due to the mathematics that the students are to learn, and it must require justifications and explanations for answers and methods.

What is taught when teaching through problem solving?

Number & Operations, Algebra, Geometry, Measurement, Data Analysis & Probability

What is taught when teaching about problem solving?

Problem Solving Strategies

What are the 3 types of information teachers should provide to students?

1. Mathematical conventions- symbols, terminology, definitions, labels; but only after student’s “need” them 2. Alternative methods- more efficient recording procedures; but only as “suggestions” 3. Clarification or formalization of students’ methods- to focus attention on the main ideas of the lesson

What is a drill?

Repetitive exercises used to improve skills/procedures already acquired.

What is practice?

Multiple task that focus on the same concept or procedure, occurring over multiple class periods.

What are the actions of a teacher in the Before Problem Solving phase of a lesson?

activates the student’s prior knowledge, make sure that the task is understood, and establish clear expectations

What are the actions of a teacher in the During Problem Solving phase of a lesson?

use flexible grouping, let go (GRR), notice students mathematical thinking, provide appropriate support (through questioning), and differentiate.

What are the actions of a teacher in the After Problem Solving phase of a lesson?

promote a mathematical community of learners, listen actively without evaluation, summarize main ideas and identify future tasks, and formally assess.

How can you plan for diverse learners? What are specific things teachers can do to attend to diverse learners?

To plan for diverse learners, provide open questions and multiple entry point and exit point problems. Specific things the teacher can do to attend to diverse learners are to plan differentiated task, learning centers, tiered lessons, using flexible grouping, and making accommodations or modifications as needed for individual student needs.

What is a Multiple Entry Point problem, and what is an example of one?

A problem that can be solved using several different methods or approaches. One example of this kind of problem would be “what is one way we can make the number 10?”

What are best practices regarding math homework?

-Help parents/caregivers know how to help -Limit low-level practice -Use projects -Use a distributed content approach

What is assessment?

Assessment is the process of gathering evidence about a student’s knowledge of, ability to use, and disposition toward mathematics and of making inferences from that evidence for a variety of purposes. Assessment is also a way of understanding a child in order to make informed decisions about the child.

What are the 4 purposes of assessment?

1. To monitor student progress 2. To make instructional decisions 3. To evaluate student achievement 4. To evaluate programs

What three areas of mathematics education should be assessed?

1. Conceptual understanding & procedural fluency 2. Strategic competence & adaptive reasoning 3. Productive disposition

Scoring

comparing students work to correct answers or specific criteria that describe what we expect the work to be. Through scoring, we determine what is correct or not and assign a score to the work

Grading

the result of accumulating scores and other information about a students work for the purpose of summarizing and communicating to others

Rubrics

used when you want to know how well students can do a particular skill rather than IF they can do it or not

Performance Indicators

task-specific statements that describe what performance looks like at each level of the rubric and in doing so establish criteria for acceptable performance

What are ways to use writing in the mathematics classroom?

-Journal writing/ writing with prompts -Problem solving -Explaining an idea- concepts and processes -Reflective writing- productive dispositions -Student self-assessments

What are ways of addressing Gender Bias/ways of promoting Gender Equity?

-Provide equal opportunities and respect differences -Ensure that girls and boys have the same experiences -Attempt to compensate for gender differences in society

What are strategies for Teaching Multilingual Learners?

-Honor the use of native language -Explicitly teach vocabulary -Select culturally relevant contexts -Use comprehensible input -Plan partnerships to support language development -Engage students in discourse that reflects language needs

What are the types of Virtual Manipulatives?

Static and Dynamic

What does equitable mathematics instruction take into consideration?

-Content -Relationships -Cultural knowledge -Flexibility in approaches -Use of familiar or interesting learning context -A responsive learning community -Working in cross-cultural partnerships

Mathematics Identity

sense of themselves as a doer of mathematics and includes their disposition toward mathematics and sense of competences as a learner and contributor in the mathematics classroom

Mathematics Agency

behavioral side of a person’s mathematics identity or their identity-in-action

What is the difference between accommodations and modifications?

Accommodations- adjustments made based on the needs of the environment or learner; do NOT change the task in any way. Modifications- change made to a task to make it accessible to a particular student, eventually students will be led back to the original task.

What are some strategies for teaching and assessing students with learning disabilities?

-Structure the environment -Identify and remove potential barriers -Provide clarity -Consider alternative assessments -Emphasize practice and summary

What are strategies that should be avoided as “enrichment”?

-Assigning more of the same work -Giving free time to early finishers -Assigning gifted students to help struggling students -Providing gifted pull-out opportunities -Offering independent enrichment on the computer