next generation math standards

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Next Generation Math StandardsElementary School Version

West Virginia RESAs 3 and 7Charleston and Morgantown, WV

Math Tools for Unpacking & Addressing the West Virginia

April, 2013

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Essential Workshop Questions

1. What is the relationship between the Common Core Standards an the Next Generation Math Standards, and why were they developed?

2. How are the Next Generation Math Standards organized?

3. What are the Six Instructional Shifts and the Eight Mathematical Practices; What are their role in the Next Generation Standards?

4. What processes are useful for unpacking the standards?

5. What are the implications of the Standards on the way we approach the teaching and learning of mathematics?

CCSS WV Institute 4 3 2 1

VKR

Standards for Mathematical Practices

Content Standards

etc.

VKR Math Vocabulary Activity

• Assess your Vocabulary Knowledge Rating (VKR) of personal knowledge of these important workshop words.

• Consider each word and check the appropriate column. Check #4 column, if you could explain and teach others. Check #3 column if you know the term well, but would not want to teach others. Check #2 column if you have heard of the term. Check #1 column if the word is new to you.

VKR Math Vocabulary Activity

Common Core Standards

Next Generation Standards

Standard

Cluster

Objective

Teaching Strategy

Student Engagement Activity

Five Stages of T&L Math

Six Instructional Shifts

Eight Mathematical Practices

1 2 3 4

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What’s the connection between the Common Core Standards and the Next Generation Standards, and why were

these standards developed?

What are the Common Core Standards?

The Common Core Standards are a product of a U.S. education initiative that seeks to bring diverse state curricula into alignment with each other by following the principles of standards-based education reform. The initiative is sponsored by the National Governors Association (NGA) and the Council of Chief State School Officers (CCSSO). At this time, 45 U.S. States are committed to implementing the Common Core Standards.

http://en.wikipedia.org/wiki/Standards-based_education_reform

http://en.wikipedia.org/wiki/National_Governors_Association

http://en.wikipedia.org/wiki/Council_of_Chief_State_School_Officers

What are the Next Generation Standards?

The Next Generation Standards are West Virginia’s education standards. These standards parallel the Common Core Standards, and contain modifications that meet the specific needs of West Virginia. The Next Generation Standards represent the next logical step in the progression of the statewide movement called EducateWV: Enhancing Learning. For Now. For the Future.

http://wvde.state.wv.us/educatewv/

http://wvde.state.wv.us/educatewv/

Why were the new Standards developed?

The Next Generation Standards were developed to:

• provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. • be robust and relevant to the real world

• reflect the knowledge and skills that our young people need for success in college and careers



• be sure that American students are fully prepared for success in the global economy

• help teachers zero in on the most important knowledge and skills

• establish shared goals among students, parents, and teachers



• help states and districts assess the effectiveness of schools and classrooms and give all students an equal opportunity for high achievement

• help solve the problem of discrepancies between State’s test results and International test results

• replace the discrepant array of curriculums that existed across the country

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How are the Next Generation Standards organized?

Common Core and Next Generation Organization Terminology

Common Core Standards (CCS)

Next Generation Standards (NGS)

Domain (CCS only)

Standards (CCS and NGS)

Cluster (CCS and NGS)

Objective (NGS only)

Common Core Organization/Terminology

In the Common Core Standards, the terms domain, standard, and cluster have the following meanings.

domain: used for the broad math strand or category name

standard: more specific math category name (next level beyond domain)

cluster: group of specific learning objectives that connect with the standard

Grade 5 Standard: Operations and Algebraic Thinking

Write and interpret numerical expressions

M.5.OA.1 Use parentheses, brackets or braces in

numerical expressions, and evaluate expressions with these symbols.

M.5.OA.2 Write simple expressions that record

calculations with numbers.

Common Core Standards for Math;Example of how they are organized

Domain

Standard

Clu

ste

r

Next Generation Organization/Terminology

In the Next Generation Standards, the terms standard, cluster, and objective have the following meanings.

standard: used for the broad math strand or category name (replaces the CC word domain)

cluster: more specific math category name (next level beyond standard, replaces the CC word standard)

objectives: specific things that students should learn and be able to do (listed in each cluster)


Write and interpret numerical expressions

M.5.OA.1 Use parentheses, brackets or braces in

numerical expressions, and evaluate expressions with these symbols.

M.5.OA.2 Write simple expressions that record

calculations with numbers.

How are the Next GenerationMath Standards organized?

Standard

Cluster

Ob

jecti

ves

The next five slides show the standards (broad math categories or strands) for grades K-5. Note the similarities and differences among the grade levels.

The Next Generation Math Standards for Grades K-5

Kindergarten Standards

Counting and CardinalityQuestions and Algebraic ThinkingNumbers and Operations in Base TenMeasurement and DataGeometry


First Grade Standards

Operations and Algebraic ThinkingNumbers and Operations in Base TenMeasurement and DataGeometry


Second Grade Standards

Operations and Algebraic ThinkingNumbers and Operations in Base TenMeasurement and DataGeometry


Third Grade Standards

Operations and Algebraic ThinkingNumbers and Operations in Base TenNumbers and Operations with FractionsMeasurement and DataGeometry


Fourth Grade Standards



Fifth Grade Standards



The next five slides show the breakdown of the common Operations and Algebraic Thinking (Questions and Algebraic Thinking for Kindergarten) standard for grades K-5. Each slide shows the clusters for the standard, and the number of objectives associated with each cluster.


Take note of the standard, cluster, and number of objectives for each cluster. Work with a partner from your grade level, and see if you can guess what the objectives are for your grade-level clusters.


Kindergarten Standard and Cluster

Questions and Algebraic Thinking• Understand addition as putting together and adding to, and

understand subtraction as taking apart and taking from (5 objectives)

How are the Next Generation Math Standards organized?

First Grade Standard and Cluster

Operations and Algebraic Thinking•Represent and Solve Problems Involving Addition and Subtraction- (2 objectives)• Understand and Apply Properties of Operations and the Relationship between Addition and Subtraction- (2 objectives)• Add and Subtract within 20- (2 objectives)• Work with Addition and Subtraction Equations- (2 objectives)


Second Grade Standard and Cluster

Operations and Algebraic Thinking• Represent and Solve Problems Involving Addition and Subtraction- (1 objective)• Add and Subtract within 20- (1 objective)• Work with Equal Groups of Objects to Gain Foundations for Multiplication- (2 objectives)


Third Grade Standard and Cluster

Operations and Algebraic Thinking• Represent and Solve Problems Involving Multiplication and Division- (4 objectives)• Understand Properties of Multiplication and the Relationship between Multiplication and Division- (2 objectives)• Multiply and Divide within 100- (1 objective)• Solve Problems Involving the Four Operations and Identify and Explain Patterns in Arithmetic- (2 objectives)


Fourth Grade Standard and Cluster

Operations and Algebraic Thinking• Use the Four Operations with Whole Numbers to Solve Problems- (3 objectives)• Gain Familiarity with Factors and Multiples- (1 objective)• Generate and Analyze- (1 objective)


Fifth Grade Standard and Cluster

Operations and Algebraic Thinking• Write and Interpret Numerical Expressions- (2 objectives)• Analyze Patterns and Relationships- (1 objective)


After guessing what the objectives are for each cluster, work in grade-level teams and read the objectives for each cluster identified in this activity. For each objective, work together to create a math problem that captures the essence of the objective. The standard, clusters, objectives and sample problems will be share with the entire group to provide a K-5 vertical view of the teaching and learning progressions associated with the K-5 math program.


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Six Instructional Shifts Associated with West Virginia’s Next Generation

Math Standards

Six Instructional Shifts in Math

New Points of Emphasis for Teaching the Next Generation Standards

Focus Coherence Fluency

Applications Dual Intensity Understanding

Kelly L. Watts, RESA 3

Instructional ShiftsInstructional Shifts within the common core are needed

for students to attain the standards.


6 Shifts in MathematicsFocus

Coherence

Fluency

Deep Understanding

Applications

Dual Intensity


FocusIn reference to the TIMMS study, there is power

of the eraser and a gift of time. The Core is asking us to prioritize student and teacher time, to excise out much of what is currently being taught so that we can put an end to the mile wide, inch deep phenomenon that is American Math education and create opportunities for students to dive deeply into the central and critical math concepts. We are asking teachers to focus their time and energy so that the students are able to do the same.


FocusStudents

Spend more time thinking and working on fewer concepts

Being able to understand concepts as well as processes. (algorithms)

Teachers

Make conscious decisions about what to excise from the curriculum and what to focus on

Pay more attention to high leverage content and invest the appropriate time for all students to learn before moving onto the next topic

Think about how the concepts connect to one another

Build knowledge, fluency, and understanding of why and how we do certain math concepts.


CoherenceWe need to ask ourselves –

• How does the work I’m doing affect work at the next grade level? • Coherence is about the scope and sequence of those

priority standards across grade bands.

• How does multiplication get addressed across grades 3-5?

• How do linear equations get handled between 8 and 9?

• What must students know when they arrive, what will they know when they leave a certain grade level?


CoherenceStudents

Build on knowledge from year to year, in a coherent learning progression

Teachers

Connect the threads of math focus areas across grade levels

Think deeply about what you’re focusing on and the ways in which those focus areas connect to the way it was taught the year before and the years after


FluencyFluency is the quick mathematical content; what you

should quickly know. It should be recalled very quickly. It allows students to get to application much faster and get to deeper understanding. We need to create contests in our schools around these fluencies. This can be a fun project. Deeper understanding is a result of fluency. Students are able to articulate their mathematical reasoning, they are able to access their answers through a couple of different vantage points; it’s not just getting the answer but knowing why. Students and teachers need to have a very deep understanding of the priority math concepts in order to manipulate them, articulate them, and come at them from different directions.


FluencyStudents

Spend time practicing, with intensity, skills (in high volume)

Teacher

Push students to know basic skills at a greater level of fluency

Focus on the listed fluencies by grade level

Create high quality worksheets, problem sets, in high volume


Deep Understanding The Common Core is built on the assumption that only through

deep conceptual understanding can students build their math skills over time and arrive at college and career readiness by the time they leave high school. The assumption here is that students who have deep conceptual understanding can:

• Find “answers” through a number of different routes

• Articulate their mathematical reasoning

• Be fluent in the necessary baseline functions in math, so that they are able to spend their thinking and processing time unpacking mathematical facts and make meaning out of them.

• Rely on their teachers’ deep conceptual understanding and intimacy with the math concepts


Deep UnderstandingStudents

Show, through numerous ways, mastery of material at a deep level

Use mathematical practices to demonstrate understanding of different material and concepts

Teacher

Ask yourself what mastery/proficiency really looks like and means

Plan for progressions of levels of understanding

Spend the time to gain the depth of the understanding

Become flexible and comfortable in own depth of content knowledge


ApplicationsThe Common Core demands that all students

engage in real world application of math concepts. Through applications, teachers teach and measure students’ ability to determine which math is appropriate and how their reasoning should be used to solve complex problems. In college and career, students will need to solve math problems on a regular basis without being prompted to do so.


ApplicationsStudents

Apply math in other content areas and situations, as relevant

Choose the right math concept to solve a problem when not necessarily prompted to do so

Teachers

Apply math in areas where its not directly required (i.e. science)

Provide students with real world experiences and opportunities to apply what they have learned


Dual IntensityThis is an end to the false dichotomy of the

“math wars.” It is really about dual intensity; the need to be able to practice and do the application. Both things are critical.


Dual IntensityStudents

Practice math skills with a intensity that results in fluency

Practice math concepts with an intensity that forces application in novel situations

Teacher

Find the dual intensity between understanding and practice within different periods or different units

Be ambitious in demands for fluency and practices, as well as the range of application

The next six slides show the six instructional shifts and short instructional scenarios that each connect with one of the shifts. Read each scenario and determine the instructional shift that it represents.



Mrs. Johnson, a fifth-grade teacher, delivered two informational lessons on the concept of parentheses, brackets, braces, and numeric expressions. After two days of paper/pencil practice, she decided to teach her students the 550 Game (demonstrated in the Corwin/Silver Strong workshop) and to let them compete in pairs. Her goal was to help her 5th graders to sharpen their proficiency with numeric expressions and math symbols, and to mentally process numbers faster.

Fluency Focus Coherence

Applications

Dual Intensity

Understanding


Focus Coherence

Fluency

Applications

Dual Intensity

Understanding

In planning a unit on Place Value, Mrs. Smith used the Five Stages planning tool (demonstrated in the Corwin/Silver Strong workshop) to ensure that she would design lessons and student engagement activities that would help her students to develop a strong knowledge base, understanding of concepts, proficiency of skills, and the ability to solve a variety of related problems.


Dual Intensity

Focus Coherence

Fluency

Applications

Understanding

Principal Joe visited several math classes and noticed that the lessons all emphasized procedures, skills, and practice. Joe met with the teachers and complimented them on their thorough approach to skill development. Joe also encouraged them to work together and to devise a plan to show students how those math skills are used in the real world. The goal would be to continue to strengthen students’ skills, and to teach students how to use those skills in problem solving.


Coherence

Focus Fluency

Applications

Dual Intensity

Understanding

Several math teachers and administrators from participated in a joint exercise where they investigated several Next Generation math objectives from grades levels K-5. The participants developed sample math problems that aligned with the K-5 objectives and shared their work with each other, so they could all understand how the curriculum pieces fit together.


Focus Coherence

Fluency

Applications

Dual Intensity

Understanding

Prior to learning the rules associated with operations on fractions and mixed numbers, students participated in the Fraction Paper Cutting Activity (demonstrated in the Corwin/Silver Strong workshop). The student-centered activity allowed students to cut paper, form fraction pieces, and use their paper pieces to model and investigate a variety of fraction problems.


Applications

Focus Coherence

Fluency

Dual Intensity

Understanding

Mr. Williams noticed that his fourth-grade science curriculum presented a number of opportunities to integrate math into several science lessons, and vice versa. Mr. Williams decided to create a simple correlation of science concepts with math concepts that featured common math concepts and skills, so they can be taught together.

Can you remember the Six Instructional Shifts? The Great Coverup Strategy, shown on the next slide, will challenge you to see how many shifts you can recall and recite.

The Six Instructional Shifts

Dual Intensity

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Six Instructional Shifts

Focus

Coherence

Fluency

Understanding

Application

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Standards for the Eight Mathematical Practices

Making a case . . .

Work individually and investigate the result of adding two even whole numbers. Is the sum always, sometimes, or never even? Create a sensible rule for adding two even whole numbers and the expected result. Explain why your rule works.

Continue to work individually and investigate the result of adding two odd whole numbers. Is the sum always, sometimes, or never odd? Create a sensible rule for adding two odd whole numbers and the expected result. Explain why your rule works.Share your findings, rules, and explanations with a learning partner. Will your rules always work? Be sure to critique your partner’s argument.

Making a case . . .

In the preceding activity, participants had opportunities to think about math, investigate math, draw conclusions, communicate their findings to other participants, and critique each others’ thinking. This kind of math engagement satisfies one of the 8 Mathematical Practices shown below.

Mathematical Practice #3: Construct viable arguments and critique the reasoning of others

The Eight Mathematical Practice are shown on the next slide.

The 8 Mathematical Practices

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 mathematics.

5. Use appropriate tool strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Building insights about meaning, and learning how to communicate those insights


Cluster: Write and interpret numerical expressionsM.5.OA.1 Use parentheses, brackets or braces in numerical

expressions, and evaluate expressions with these symbols.

M.5.OA.2 Write simple expressions that record calculations

with numbers.

Eight Mathematical Practices Applied to a Real Standard

Review the list of Eight Mathematical Practices. How can they be applied to the standard and objectives

below?

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Unpacking the Standards

Many organization templates and tools exist and can be used to unpack math standards. One such tool is the Five Stages Unpacking Tool for Math Standards. This tool is aligned with the Five Stages of Teaching and Learning Mathematics. The next three slides provide an explanation of the Five Stages of Teaching and Learning Math.

Unpacking the Standards

Try this . . .

(n – 2)1801. Write the numerical expression for the sum of the interior angles of a polygon with n sides.

2. Explain why this formula works.

3. Use the formula to calculate the sum of the interior angles of an octagon.

(8 – 2)180 = 6(180) = 600 + 480 = 1080 degrees

4. Knowing that 3 interior angles of home plate are right angles, find the measures of the other two.

Try this . . .

(n – 2)180

4. Knowing that 3 interior angles of home plate are right angles, find the measures of the other two.

(5 – 2)180=

(3)180=

540=

540 – 270= 270

270 ÷ 2= 135o

Try this . . .

(n – 2)1801. Write the numerical expression for the sum of the interior angles of a polygon with n sides.

2. Explain why this formula works.

3. Use the formula to calculate the sum of the interior angles of an octagon.(8 – 2)180 = 1080

degrees

4. Knowing that 3 interior angles of home plate are right angles, find the measures of the other two.Each angle = 135 degrees

5. Now that you know how to solve this kind of problem, what will help you to remember how to solve the problem for future applications?

Knowledge

Understanding

Proficiency of Skills

Applications

Retention

Success or failure associated with solving an arbitrary math problem comes down to five questions. 1. Did the student know the math vocabulary, terms, formulas, and number facts associated with the problem?2. Did the student understand the math concepts, hidden questions, and math connections in the problem?3. Was the student fluent with respect to the math procedures and skills needed to solve the problem?4. Was the student able to apply the knowledge, understanding, and skills in relation to the real-world context of the problem?5. Was the student able to retain or remember important math facts, skills, and concepts needed to solve the problem?

The Five Stages of Teaching and Learning Mathematics

The Five Stages of Teaching and Learning Mathematics is a helpful framework for planning, teaching, and assessing a math lesson or unit.

The Five Stages of Teaching and Learning Mathematics can also serve as a model for unpacking a math standard.


The Five Stages of Teaching and Learning Math

Great Considerations for Unpacking a Math Standard

Knowledge Understanding Proficiency of Skills

Applications Retention

The next three slides provide an example of how the Five Stages of Teaching and Learning Math can be used to unpack a math objective. A sample objective is shown below.

Grade 4: M.4.NF4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.


Unpacking Grade4: M.4.NF4

Grade 4: M.4.NF4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.Knowledge • product- answer to multiplication

problem• The fractional equivalent to a whole number n is n/1.• 1 times any number is the number itself.• 0 times any number is zero• n x a/b = na/b• how to simplify an improper fractionUnderstanding

• For any fraction a/b, ‘a’ is the number of times that 1/b occurs• If n >1, then n x a/b is greater than a/b.• The concept of n x a/b expresses the idea of ‘bringing the amount a/b to the table n times.• improper fraction and proper fraction equivalencies

Teaching Strategies

Teaching Strategies • The hands-on/multiplication

component of the Fraction Paper Cutting Activity

• Mental Math Strings that feature these facts• The Great Cover Up• Convergence Mastery• Proceduralizing


Grade 4: M.4.NF4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.Proficiency of Skills • Multiply any whole number n times

any of the common fractions a/b where b= 1, 2, 3, 4, 5, 6, 8, 10, and 12.• Simplify problems of the type: n x a/b n x a/b + m and n x a/b + c/b

Applications • Work with Tangram pieces

• Solve problems involving fractional pieces of Hershey’s chocolate bars• Solve two-step word problems• Solve problems involving fractional parts of time and money

Teaching Strategies

Teaching Strategies • Task Rotation applied to

problem solving• Graduated Difficulty• Modeling and Experimentation

• Mental Math Strings that feature these facts• The Great Cover Up• Algebra War Games (modified)• Timed Challenges (for fractions)• Convergence Mastery


Grade 4: M.4.NF4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.Retention • General Math Facts

• Measurement Equivalencies• Properties of Fractions• Patterns

8 Math Practices that apply1. Make sense of problems and persevere in solving them. (All problems and

experiences)2. Reason abstractly and quantitatively. (Fraction Paper Cutting Activity)3. Construct viable arguments and critique the reasoning of others (Is nxa/b always > a/b?)4. Model with mathematics. (Fraction Paper Cutting Activity, Tangrams, Candy bars)5. Use appropriate tool strategically.6. Attend to precision. (Computing exact answers, not estimates)7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning. (n x a/b always equals na/b.)

Teaching Strategies • Review math facts using Timed Challenges• Incorporate measurement equivalencies in fraction problems• Create patterns based on whole numbers x fractions

The next two slides provide a sample objective for grades K-5. Work with a grade level partner. Unpack the objective using the Five Stages Unpacking Tool. Make connections between the Eight Mathematical Practices and the things that students will learn and experience as they learn the math associated with the objective.


Unpacking the Common Core Math Standards

Knowledge

Understanding

Proficiency of SkillsApplications

Retention


Grade K: Solve addition and subtraction word problems, by adding and subtracting within 10, by using objects or drawings

Grade 1: Apply properties of operations as strategies to add and subtract within 20

Grade 2: Use addition and subtraction within 100 to solve one and two-step word problems

Work with a partner, choose a standard, and unpack the standard using the Five Stages tool.

Unpacking the Next Generation Math Standards

Knowledge

Understanding

Proficiency of SkillsApplications

Retention


Grade 3: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division

Grade 4: Solve multi-step word problems, posed with whole numbers, using the four operations

Grade 5: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols

Work with a partner, choose a standard, and unpack the standard using the Five Stages tool.

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Instructional ConsiderationsThe 3- 4- 5- Math Instructional Model

The 3- 4- 5- Math Instructional Model

RVD

The Four Learning Styles and Task Rotation


3

4

5

Repetition, Variation of Context, Depth of Study

The next slides provide important information about• The RVD Instructional Model,• The Four Learning Styles of students, and • The Five Stages of Teaching and Learning Math

Each of these have important roles in the teaching and learning of mathematics.

Teaching math associated with the Next Generation Standards Mathematics

R - V - DRVD provides teachers with three important ideas

that can be applied to the teaching and learning process. Repetition reminds us that practice is an essential tool for developing fluency and proficiency with math skills and procedures. Variation reminds us that students need to experience math in more than one context. Different instructional and application contexts give students opportunities to make important connections and deepen their understanding of math. Depth reminds us that students need to learn and experience all aspects of a math concept and not superficially engage in exercises that only scratch the surface.

Introduction to the Four Learning Styles

Mastery Learner

Understanding Learner

Self-Expressive Learner

Interpersonal Learner


Mastery Learners

• Want to learn practical information and procedures

• Like math problems that are algorithmic

• Approach problem solving in a step by step manner

• Experience difficulty when math becomes abstract

• Are not comfortable with non-routine problems

• Want a math teacher who models new skills, allows time for practice, and builds in feedback and coaching sessions


Interpersonal Learners

• Want to learn math through dialogue and collaboration

• Like math problems that focus on real world applications

• Approach problem solving as an open discussion among a community of problem solvers

• Experience difficulty when instruction focuses on independent seatwork

• Want a math teacher who pays attention to their successes and struggles in math

• Want a math teacher who pays attention to their successes and

struggles in math


Understanding Learners


• Want to understand why the math they learn works

• Like math problems that ask them to explain or prove

• Approach problem solving by looking for patterns and identifying hidden questions

• Experience difficulty when there is a focus on the social environment of the classroom

• Want a math teacher who challenges them to think and who lets them explain their thinking


Self-Expressive Learners


• Want to use their imagination to explore math

• Like math problems that are non-routine

• Approach problem solving by visualizing the problem, generating possible solutions and explaining alternatives

• Experience difficulty when instruction focuses on drill and practice and rote problem solving

• Want a math teacher who invites imagination and creative problem solving into the math classroom

The Four Learning Styles

Research shows that student learn in different ways. The Four Learning Styles provide the basis for a teaching and learning framework that addresses the different ways students learn. By providing rich learning experiences that reflect the different learning styles, teachers can lead more students to success in math.

The Task Rotation Teaching Strategy provides four tasks, one for each type of learner. Students who study math through the contexts of different learning styles will increase their levels of success in math.


Great Considerations for Planning, Teaching, and Assessing a Math Lesson

Knowledge Understanding Proficiency of Skills

Applications Retention

Success or failure associated with solving a math problem comes down to five questions. 1. Did the student know the math terms, formulas, and number facts associated with the problem?2. Did the student understand the math concepts, hidden questions, and math connections in the problem?3. Was the student fluent with respect to the math procedures and skills needed to solve the problem?4. Was the student able to apply the knowledge, understanding, and skills in the context of the problem?5. Was the student able to retain or remember important math facts, skills, and concepts needed to solve the problem.


Cooperative Planning Activity

Work together and talk about how you will use the information and strategies, featured in this workshop, to improve math instruction and achievement in your classroom(s).

Workshop Reflections

Specific facts and ideas that I learned today

Why the things I learned will help my students to learn math

Things I learned that will really help me in my classroom

Creative modifications and extentions to the things I learned today

next generation math standards

Documents

new standards

principles of standards

important knowledge

appropriate column

stages of tl math

education initiative

west virginiaapril

american students