Math Midterm

Conceptual understanding

A flexible web of connections and relationships within and between ideas, interpretations, and images of mathematical concepts- a relational understanding.

What is productive struggle?

A question that produces some struggle from students, but they can answer with some support. It requires teachers to scaffold their students to arrive to the answer.

Accommodation

A response to the needs of the environment or the learner. It does NOT alter the task.

Which of the following is an example of a statement spoken in the language of doing mathematics? "Memorize these steps," "Compute this answer," "Explain how you solved the problem," or "Copy down these steps into your notebooks" explain your choice.

An example of a statement spoken in language of doing math is "explain how you solved the problem" because of the higher level of bloom's taxonomy we want students to have. Higher order thinking.

Who can repeat

Asking students to repeat someone else's idea or to add onto one's idea and make connections.

The NCTM Principles and Standards stress two main ideas of integrating assessment into instruction, what are they?

Assessment should enhance students learning and assessment is a valuable tool for making instructional decisions.

What is culturally responsive mathematics instruction?

Attention to mathematical thinking, language, and culture, not just for recent immigrant but for all students including from different ethnic groups and socioeconomic status.

Modification

CHANGES the task to make it more accessible to the student.

What are Common Core State Standards and what standards are used in Texas? What is the fundamental reason for creating the Common Core State Standards?

Common core state standards are grade level specific standards and the reason for creating these is to know what to teach. It is what students should know and be able to do at each grade level.

What theory(s) allow a classroom culture to access prior knowledge, use tools to build knowledge?

Constructivist

What are the three critical elements that you can differentiate across?

Content (what you want each student to know) Process (how you will engage the students in thinking about the content) Product (what students will show to prove they are mastering the content)

What are the lesson types you should use in this course?

Cooperative learning, manipulative, literature, multiple intelligences, technology

One of the statements below represents a method for developing the Reasoning and proof process standard.

Create opportunities for students to evaluate conjectures.

What is differentiating instruction?

Differentiating instruction: a teacher's lesson plan includes strategies to support the range of academic backgrounds found in classrooms that are academically, culturally, and linguistically diverse.

While teaching his class, Mr. Diaz asks Rebecca, a first grader, to answer a math question. After about 10 seconds, Rebecca answers the question correctly. Mr. Diaz has done a good job of.

Employing a wait time strategy

Semi- Concrete

Encourage learning through movement or action with manipulatives

What is the difference between formative and summative assessment?

Formative Assessment is during instructional activities and is checking the status of students development. Summative assessment is cumulative evaluations that take place after instruction is complete.

Understanding exists along a continuum from a what understanding to a what understanding?

From an instrumental (no connections) to a relational (create their own problems)

Wait time

Giving students time to think about an answer to a posed question and giving students time to think about what other students have said.

What are the characteristics of tasks that promote problem solving?

Guess and check, pictures, high-level thinking, cognitive demanding, multiple entry and exit points.

What teaching methods you should use in this course?

Guided Instruction, direct, inquiry, experiential, problem based.

Partner Talk

Having students talk to their next-door neighbor and share their ideas with one another.

Doing mathematics begins with posing worthwhile tasks. What are some verbs that align with activities that lead to higher-level thinking? Lower-level thinking?

Higher- level thinking verbs include: investigate, construct and formulate. Lower- level thinking verbs include: memorize, drill, practice, listen, copy, recall, calculate

Differentiation of instruction in mathematics lessons is needed to support and challenge the learning for all students. One statement below is an example of a differentiating process.. Single choice.

Identify what thinking will engage students in the mathematical content.

What is an IEP?

Individualized Educational Plan: for students with disabilities. It ensures that the student is attending an educational institution while receiving special services to help with their learning.

Doing mathematics begins with posing worthwhile tasks. Which verbs align with activities that lead to higher-level thinking?

Investigate, construct, and formulate

Procedural fluency

Involves developing conceptual understanding and making connections among mathematical ideas. Four components: Efficiency, flexibility, accuracy, strategy selection

Why is flexible grouping important?

It allows students to collaborate on tasks and provides support and challenges, increasing their change to communicate about mathematics and build understanding.

Which statement best reflects the approach of teaching for problem solving?

It frequently results in the instructor explaining a skill and providing practice and application of the skill.

What are the characteristics, habit of thought, skills, and dispositions that must be continuously cultivated to reach success as an effective teacher of mathematics?

Knowledge of mathematics, persistence, positive disposition, readiness for change, willingness to be a team player, lifelong learning, make time to be self- aware and reflective.

Which choice reflects two factors that influence the teaching of Mathematics effectively?

Knowledge of standards and practices

Teaching for problem solving

Learning the abstract concept and then moving to solving problems to apply the learned skills. Ex: students learn algorithm for adding fractions and then once mastered solve story problems. This is the most common approach. INSTRUCTOR EXPLAINING A SKILL AND PROVIDING PRACTICE AND APPLICATION OF THE SKILL.

Concrete

Models that support explicit instruction

What is NCTM?

National Council of Teachers of Mathematics

What are the six content standards?

Numbers and operations, Algebra, Geometry, Measurement, data analysis and probability, financial literacy

Ms. Jimenez plans to have her second graders work in cooperative groups during a unit they are solving one digit addition story problems. What is the best way to organize her students into groups?

Organize heterogeneous groups of three or four students and announce the groups to the students.

What is constructivism?

Piaget. Learners are creators of their own learning. Allows a classroom culture to access prior knowledge, use tools to build knowledge.

Checklists

Place for comments that should concentrate ideas and conceptual understanding

What are the five process standards from Principles and Standards for School Mathematics?

Problem solving, reasoning and proof, communication, connections, representation.

What are the five teaching talk actions?

Revoicing, wait time, partner talk, say more, and who can repeat?

Teaching and Learning

Select focused mathematical goals, use meaningful instructional tasks that develop reasoning, encourage productive struggle, generate ways for students to provide evidence, ask essential questions.

What is a tiered lesson?

Set of similar problems focused on the same mathematical goal, but adapted to meet the range of learners, with different groups of students working on different tasks.

Say more

Sometimes students say 2-3 words so you can ask for them to elaborate more.

The mathematical needs in society have changed and are influencing what should be taught in pre-K-8 mathematics classrooms. What are some key factors promoting the change?

Sputnik and public or political pressure

How are the TEKS organized?

Strand, Content, Rigor, and Specificity

What is the zone of proximal development?

Student's range of knowledge that may be out of reach for a student to learn on his/her own but is accessible if the learner has support from peers.

Teaching through problem solving

Students learn through inquiry, explore real contexts, problems, and situations. Focuses on student's attention on ideas and sense making. Is the exact opposite of teaching for problem solving.

Teaching about problem solving

Students need guidance on how to problem solve. Ex: drawing a picture. Four step problem solving: understand the problem, devise a plan, carry out the plan, look back.

What is a parallel task?

Students working on different tasks all focused on the same learning goal. The focus is on choice which gives students motivation.

What is student self-assessment?

Students' abilities to self-regulate as active participants in their own learning. Should be a record of how students perceive their strengths and weaknesses as they begin to take responsibility for their learning.

Diagnostic interview

Teacher listens to students descriptions of their strategies and probe their understanding with the purpose of discovering both strength and gaps.

What are the three approaches to problem solving that are used in classrooms?

Teaching for problem solving, teaching through problem solving, teaching about problem solving

Write an instructional objective

The student will be able to

Revoicing

The teacher restates a statement or question to clarify what a student said.

What did the National Assessment of Educational Progress reveal about grades 4 and 8 achievement in 2015? How did the U.S. students perform at the International?

They said that performance of students were below average

What are the tiers to RTI?

Tier 1: represents a level of instruction with corresponding monitoring of results and outcomes. Tier 2: represents students who did not reach the level of achievement expected during tier 1 instruction.

Which one of the following types of lessons would be MOST beneficial for a student who is a kinesthetic leaner?

Using algebraic tiles for algebraic functioning

Rigor

Verbs

What is sociocultural theory?

Vygotsky. Active meaning- seeking on part of the learner. Way in which information is internalized or learned depends on whether it was within a learner's zone of proximal development.

Content

What is it going to be about?

Specificity

What we are looking at specifically

RTI

a multitiered student support system that is often represented in a triangular format, what are tiers and how are they used to meet students' needs?

Curriculum

build connections across mathematics topics, look for both horizontal and vertical alignment to build coherence

Access and equity

establish high expectations, provide support, develop all student's confidence, enhance learning of all.

Interviews

help steer instruction system by getting in depth information about a particular concept, procedure, or process.

Explicit strategy instruction

highly structured teacher-led instruction on a specific strategy

ThinkAloud

how you might accomplish a task while verbalizing the thinking and reasoning that accompany the actions

Tools and Technology

include an array of technological tools and manipulatives, explore connections to how technology links to career readiness.

Observations

learning bits of information from your students by watching them. Listening to students during an organized plan for gathering data or evidence while observing.

Assessment

move beyond test results, consider multiple assessments, teach students how to check their own work.

Strand

numbers and operations, algebra, geometry, measurement, data analysis

Anecdotal notes

process where the teacher observes learners through a focus on three phases: attending, interpreting, and deciding.

Questions

provides useful data and insight that could inform instruction. Four types: information gathering, student thinking, mathematical structures, reflection and justification

Which of the following is NOT a good example of helping students make connections between the real world and mathematics?

reviewing major mathematical theorems on a regular basis

Task specific rubrics

should include specific statements also known as performance indicators that describe what students' work should look like at each rubric level.

Tests should always match what?

the objective and the goals of your instruction