Final Exam - EDE 3523

7 headers in the procedure section of a math lesson plan

Mangement Introduction Before During After Assessment Closure

What is taught when teaching through problem solving

Math content- five strands: Number & Operations, Algebra, Geometry, Measurement, Data Analysis & Probability Actually teaching math

Be able to list the 3 types of information teachers should provide to students (During and after problem solving)

Mathematical conventions - symbols, terminology, definitions, labels; but only after students "need" them Alternative methods - more efficient recording procedures; but only as "suggestions" Clarification of students' methods - to focus attention on the main ideas of the lesson

What assessment is

the process of gathering evidence about a student's knowledge of, ability to use, and disposition toward mathematics and of making inference from that evidence.

The Structure of the Common Core State Standards for Mathematics Content and be able to define domain, standard and cluster

- Content: broken down, changes each year, what math content students should know by the year (Actual math skills that we are teaching) Domains: are the larger group of related standards. They are the headers on a page; in a tree they would be a tree/trunk Clusters: are the subheadings, a group of related standards, in a tree they would be the limbs of a tree. Standards: they are the math content/skills the students should learn, which are broken into pieces in the tree example they are the leaves. Practice: same every grade level, you practice to understand and learn content (things we do to help them learn it)

The 8 Standards for Mathematical Practice

- Make sense of problems and persevere in solving them Be able to explain the meaning of a problem, describe approaches, consider similar problems Explain what the problem is asking Describe possible approaches to a solution Consider similar problems to gain insight Use concrete objects or drawings to think about and solve problems Monitor and evaluate their progress and change strategies if needed Check their answers using a different method - Reason abstractly and quantitatively Explain relationship between quantities in problem situations, represent situations using symbols, create representations, use flexibilities in properties of operations and objects Explain the relationships between quantities in problem situations Represent situations using symbols (writing expressions or equations) Create representations that fit the problem Use flexibly the different properties of operations and objects - Construct viable arguments and critique reasoning of others Should understand and use assumptions, definitions, and previous results to justify solutions. Justify in way that is understandable for everyone, and compare strengths and weaknesses Understand and use assumptions, definitions, and previous results to explain or justify solutions Make conjectures by building a logical set of statements Analyze situations and use examples and counterexamples Justify conclusions in a way that is understandable to teachers and peers - Model with mathematics Apply mathematics to solve problems in everyday life Apply mathematics to solve problem in everyday life Make assumptions and approximations to simplify a problem Identify important quantities and use tools to connect their relationships Reflect on the reasonableness of their answers based on the context of the problem Problems in context Simply a problem Identify quantities Reflect on reasonableness - Use appropriate tools strategically Consider a variety of tools Consider a variety of tools and choose the appropriate tool to support their problem solving Use estimation to detect possible errors and establish a reasonable range of answers Use technology to help visualize, explore, and compare information Variety of tools Estimation techology - Attend to precision Communicate precisely, using clear definitions and appropriate math language Communicate precisely using clear definitions and appropriate mathematical language State accurately the meaningful language -Look for and make use of structure -Look for and express regularity in repeated reasoning

Connections

- Recognize and use connections among mathematical ideas - Understand how mathematical ideas interconnect and build on one another to produce a produce a coherent whole - Recognize and apply mathematics in contexts outside of mathematics ex. Connections within math Across same strands Across different strands Connections between math and other subjects Connections between math and real world ex. Delivering the mail Pattern block

What a problem is and the 3 features of a problem for learning math (on a slide- day 4?)

-A problem is any task or activity that poses a question 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 3 features -It must begin where the students are. - The problematic or engaging aspect of the task must be due to the mathematics that the students are to learn. - It must require justifications and explanations for answers and methods.

Representation

-Create and use representations to organize, record, and communicate mathematical ideas - Select, apply, and translate among mathematical representations to solve problems - Use representations to model and interpret physical, social, and mathematical phenomena ex. Pictures, written symbols, oral language, charts,manipulative models, real world situations, graphs, diagrams ex. Delivering the mail Fraction blocks

The types of Virtual Manipulatives (from article reading)

1. Static mostly pictures - similar to concrete images but cannot be flipped or turned 2. Dynamic objects - can be flipped and turned

The benefits of using calculators (according to your textbook)

1. can be used to develop concepts and enhance problem solving 2. can be used for practicing basic facts 3. can improve student attitudes and motivation 4. commonly used in society

What should be assessed - the three areas of mathematics education that should be assessed (LISTING)

1. conceptual understanding & procedural fluency 2. strategic competence & adaptive reasoning 3. productive disposition

Ways to use writing in the mathematics classroom

1. journal writing of conceptual understandings, attitudes, fears, confidences, etc. 2. problem solving 3. explaining an idea 4. reflecting on a problem

The 6 Assessment Standards and what each means (page number on powerpoint for each)

1. mathematics standard - base assessments on the essential concepts and skills as defined by state or local standards. Develop assessments that encourage the application of mathematics to real-world situations. Focus on significant and meaningful mathematics. 2. learning standard - Incorporate assessment as an integral part of instruction and not an isolated singular event at the end of a unit of study. Inform students about important content by emphasizing those ideas in your instruction. Base future instruction on evidence of students' strengths or gaps of understanding. 3. equity standard - Respect the unique qualities, experiences, and expertise of all students. Maintain high expectations for students while recognizing their individual needs. Incorporate multiple assessment approaches, including accommodations and modifications for students with disabilities. 4. openness standard - Establish with students the expectations for their performance. Give attention not only to answers but also to the thinking process students used. Provide examples of responses that do and do not meet expectations for student discussion. 5. inferences standard - Reflect on what students are revealing about what they know. Use multiple assessments (e.g. observations, interviews, tasks, tests) to draw conclusions about students' performance. Establish a rubric that describes the evidence needed and the value of each component used for scoring. 6. coherence standard - Match your assessments with both the objectives of your instruction and the methods and models used in your instruction. Ensure that assessments are a reflection of the desired expectations. Develop a feedback loop that allows you to use the assessment results to inform your instruction.

The 4 purposes of assessment

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

How to plan for diverse learners; specific things teachers can do to attend to diverse learners (Multiple Choice)

2 activities to implement to diverse learners -Enrichment - Remediation Struggling students stay with the objective, but revert to a different teaching method (lower numbers, more guidance) Advanced students extend the lesson for them so they can think more deeply about it

Know the actions of a teacher in the Before, During and After Problem Solving phases of a lesson (textbook chapter 3 or 4)

Before - activate prior knowledge During - provide appropriate hints and worthwhile extensions After - be certain students have understanding and summarize main ideas of lesson

Ways of addressing Gender Bias/Ways of promoting Gender Equity

Differentiate between a modification and an accommodation. Describe the components of a multitiered system of support for struggling students and identify successful components of interventions for students with disabilities. Apply knowledge of working with students who are gifted and talented mathematically. Detail ways to implement a gender-friendly classroom.

Drill and Practice - what each is, what each provides, and when each is appropriate (multiple choice)

Drill repetitive exercises used to improve skills/procedures already acquired Can sometimes not show what students really know, they might pick up on a pattern What is seen most in the classroom But, It's only memorization\ Should not be prominent Practice multiple tasks that focus on the same concept or procedure, occurring over multiple class periods Helps practice a skill we learned, but also shows us how to see when a skill should be applied Mardi Gras Mask activity- Different tasks but same concepts being worked on

The Six Principles & what each means (Excellent Teams Average Chocolate Logs Together)

Equity: high expectations and support for ALL students Curriculum: more than just a collection of activities: it must be coherent, focused on important mathematics across grade levels . Teaching: selection of appropriate task, deep understanding of content and how students learn. Understanding what student know and need to learn and then challenging and supporting them to learn it well. Learning: Students must learn math with understanding, actively building new knowledge from experience and prior knowledge. New knowledge built through precious knowledge Assessment: support of learning of mathematics and guided instructional tasks. Support the learning of important math and furnish useful information to both teachers and students Technology: enhances learning; essential in teaching and learning: influences the math student learning

Strategies for Teaching Mathematics to ELLs

Explain characteristics of culturally responsive instruction, including how to focus on developing academic vocabulary during mathematics instruction. Illustrate approaches that are used to develop students' resilience and reduce resistance in learning mathematics.

How to write a daily instructional objective, given a CCSSM objective or an incorrect objective

Most likely will not have a condition- do not include the actual activity- the objective is for the students to know/use forevermore Degree = Accuracy - MUST HAVE THIS FOR MATHEMATICS - make sure there is a percent ALWAYS HAVE TSW AND ONE VERB AND EXACTLY WHAT THEY ARE GOING TO DO Make it clear, concise, and to the point 75%-80% is the best to use Our goal should never deal with just memorization Example: CCSS.MATH.CONTENT.5.MD.A.1: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Objective: -TSW convert among different-sized standard measurement within a given measurement system with 80% accuracy. -TSW use conversions within a given measurement system in solving multi-step real world problems with 80% accuracy.

The Five Content Standards (Never Oppose Angry Men Going On Dates Against People)

Number and operations (foundation for all the others) Geometry Measurement Algebra Data analysis and probability

Communication

Organize and consolidate their mathematical thinking through communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others Analyze and evaluate their mathematical arguments and proofs Use the language of mathematics to express mathematical ideas precisely. ex. Delivering the mail Four fours Perimeter and areas

What is taught when teaching about problem solving

Problem Solving Strategies How might we solve it

The Five Process Standards

Problem solving representation connections communication reasoning and proof

Reasoning and proof

Recognize reasoning and proof as fundamental aspects of mathematics Make and investigate mathematical conjectures Develop and evaluate mathematical arguments and proofs Select and use various types of reasoning and methods of proof ex. Delivering the mail, mardi gras mask

Scoring, Grading, Rubrics, & Performance Indicators - what each is

Scoring comparing students' work to correct answers or specific criteria Grading is the result of accumulating scores and other information about a student's work for the purpose of summarizing and communicating to others Rubrics a framework that can be designed or adjusted by the teacher for a particular group of students or a specific mathematical task

What Constructivism is (Definition type question)

Students must be active participants in the development of their own understanding; i.e. in the "construction" of their understanding. To construct and understand a new idea, students make connections between old ideas and the new one. Students are not "blank slates"; they do not absorb ideas. Constructing knowledge requires reflective thought - actively thinking about an idea, sifting through existing ideas.

Problem Solving

build mathematical knowledge through PS solve problems that arise in math and other contexts apply and adapt a variety of appropriate strategies to solve problems. Monitor and reflect on process of math problem-solving. ex. Delivering the mail Value of a name

What a Multiple Entry Point problem is & an example of one

can be extremely extended; there are several ways to start and stop it; these types of problems are flexible Ex. sir multiple and princess prime - it can continually be extended- allows for someone with no knowledge of the content to engage in the problem

Homework

communicates the importance of conceptual understanding to both students and parents; it is the parent's' window into your classroom Mimic the during problem solving stage Distributive content approach Send some things home that have already been learned, done in class that day, and sometimes in the future