NCTM AND STATE STANDARDS
List the 5 NCTM Content Standards
1) Number and Operations
2) Algebra
3) Geometry
4) Measurement
5) Data analysis and probability
what is constructivism?
At the heart of constructivism is the notion that learners are not blank slates but rather creators or constructions of their own learning.
What is drill?
To be completed quickly and accurately, to assess ability to implement knowledge already acquired, not intended to teach new material.
what is assessment?
The process of gathering evidence about a student’s knowledge of, ability to use, and disposition towards mathematics and of making inferences from that evidence for a variety of purpose.
what are ways of addressing gender bias/ ways of promoting gender equality:
-Provide equal opportunities and respect the differences in learning style and
ability between all students
- Ensure that male and female students are provided the same learning
experiences and opportunities
-Use language with your students that rejects the modern societal gender roles
and norms
- Heterogenous grouping for collaborative practice
Remember there is no perfect solution—just do your best to provide equitable
learning opportunities for ALL your students.
What NCTM process standard is missing?
Problem solving, reasoning and proof, connections, and representation
What is a problem? what are the three features of a problem?
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 student’s that there is a specific “correct” solution method.
1. It must begin where students are
2. The problematic and engaging aspect of the task must be due to the
mathematics that students are about to learn.
3. It must require justification and explanation for both answers and methods.
what is practice?
Multiple tasks that focus on the same concept or procedure, occurs over multiple class periods.
Conceptual understanding and procedural understanding
Strategic competence and adaptive reasoning
3. Productive disposition.
what are strategies for teaching mathematics to ELLs?
-Using open questions and multiple entry point and exit point problems-questions
and problems that can be approached in several different ways depending on the
ability of the student
-Plan and implement differentiated tasks (content, process, product); learning
centers, tiered lessons
-Use parallel tasks
-Use flexible, heterogenous grouping with individual accountability and shared
responsibility; avoid ability grouping
-Make accommodations and modifications as needed for individual students'
needs
28. What are the types of Virtual Manipulatives (from article reading)?
-static images of representations -computer-manipulated images or representations -Virtual manipulative websites
29. What is difference between accommodations and modifications?
Accommodation: is a response to the needs of the environment or the learner; it does not alter the task.
Ex: you may write down directions for a student instead of just saying them or printing the task in larger font.
Modification: changes the task, making it more accessible to the student.
Ex: suppose the task begins with finding the area of a compound shape, you may decide instead to decompose the shape into two rectangles and ask the student to find the area of each chape and combine.
-Explicitly teach vocabulary
-Discussion
-Think-pair-share
-Concrete models
-Build on/ use students' prior experiences
- Don't diminish the challenge
Utilize visual aids
Describe the structure of the common core standards for mathematics content. and define each
Domain (largest) – largest most broad group of related standards. Cluster- smaller group of related standards within domains
Standard (smallest)- define what students should understand and be able to do by the end of instruction or the end of the year
what are the three types of information teachers should provide to students?
mathematical conventions- symbols, terminology, definitions, labels, etc.—but only after student’s “need” them.
Alternative methods- more efficient recording procedures but only as “suggestions”
Clarification or formalization of student’s methods- to focus attention on the main ideas of the lesson.
what is multiple entry point problem and an example?
Multiple entry point- a problem which can be approached in several different ways and may be solved by more than one “correct” answer.
Ex: “delivering the mail” “sir multiple and princess prime”
differentiate between scoring and grading.:
Scoring- teacher compares the student’s’ work to correct answers or specific criteria that describe what the work is expected to be (85/100)
Grading- the result of accumulating scores and other information about a student’s work for the purpose summarizing and communicating to others (90% or A)
what are types of virtual manipulatives:
-static images of representations
-computer-manipulated images or representations
-Virtual manipulative websites
List 3 of the 6 NCTM principles for teach mathematics:
teaching and learning, access and equity, curriculum, tools and technology, assessment, professionalism.
what is taught when teaching through problem solving and what is taught when teaching about problem solving?
through:
Teaching specific mathematical content guided by the content standards.
about:
Teaching actual strategies for approaching/solving problems.
List some things you never need to have in a math objective:
-unobservable behavior
-Teacher-oriented instruction implied
- stating the actual activity
-Ambiguity in skill/concept being taught
-ambiguity in condition and /or degree of student’s understanding.
differentiate between performance indicators and rubrics:
Rubrics- a framework that can be designed or adjusted by the teacher for a particular group of student’s or mathematical task to score it ( 4-3-2-1, analytic rubric)
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 (different leveled requirements hat students meet within a rubric.)
what is accommodation and an example:
Accommodation: is a response to the needs of the environment or the learner; it does not alter the task.
Ex: you may write down directions for a student instead of just saying them or printing the task in larger font.
name 5 of the 8 standards for mathematical practice
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 or structure
Look for and express regularity in repeated reasoning.
what are the actions of teachers before during and after problem solving?
BF:
Teachers should--- activate prior knowledge.
- Be sure the task is understood.
- Establish clear expectations.
Teacher should---- let go- release responsibility for learning, listen actively asking appropriate guiding/higher order thinking questions and scaffolding, when necessary, provide appropriate hints and suggestions, encouraging testing of ideas, and provide worthwhile extension/enrichment activities for students who finish quickly.
after:
Teachers should--- promote a mathematical community of learners, listen actively without evolution, listen actively without evaluation, summarize main ideas, and identify future problems.
:
What are best practices regarding math homework?
- given frequently but not overly time consuming, should reflect the goals and objectives set for each student, should mirror/resemble instruction and practice in class, directions should be explicitly explained in class to all students, confirm students understand what I expected of them.
what are ways to sue writing in the mathematics classroom?
By: -math related journal prompts or reflect on their thought processes rather than just solving practice problems.
- Have students explain an idea or concept in their own words in a written response
- Asking students to explain why they solved a problem the way they did (just not how they solved it)
what is modification and an example:
Modification: changes the task, making it more accessible to the student.
Ex: suppose the task begins with finding the area of a compound shape, you may decide instead to decompose the shape into two rectangles and ask the student to find the area of each chape and combine.