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# 6th-8th Math Teacher Leaders

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Tweet## Jason Braddock

on 3 October 2012#### Transcript of 6th-8th Math Teacher Leaders

Common Core State Standards 6th-8th Teacher Leaders Jason Braddock

MS/HS Mathematics Instructional Consultant Introduction and Overview Why? We are doing well, why change? Mathematical Practices Literacy Across the Hall

“I teach Math, why should I teach the literacy standards?” Literacy Standards Critical Areas of Focus Comparative Analysis, Model Curriculum, etc... Tools PARCC Assessment Documents, Rich Problems, etc... Resources To provide opportunities for Ohio educators to develop an understanding of the revised standards and model curricula in Mathematics. Session Goal Developing a clear picture of the Common Core State Standards by:

Using rich problems to understand the Standards for Mathematical Practice

Digging into the content standards through the Critical Areas of Focus

in order to create instruction based upon the CCSSM and develop a foundation for curriculum revision. MP + CAF + Standards = Instruction In order to design instruction that meets the rigor and expectations of the CCSSM, understanding the Mathematical Practices and Critical Areas of Focus are essential. Overview *A Look Inside the CCSSM 6- 8

*Digging Deeper

*Incorporating Literacy Standards and 21st Century *Skills

*Using Rich Problems

*Model Curriculum

*Progressions

*Resources

*What Should Districts Be Doing Now? Focus

- Identifies key ideas, understandings and skills for each grade or course

- Stresses deep learning, which means applying concepts and skills within the same grade or course

- The PARCC Assessment will focus strongly where the Standards focus Coherence

- Articulates a progression of topics across grades and connects to other topics

- Vertical growth that reflects the nature of the discipline Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application. Shift #1 – Focus: The PARCC assessments will focus strongly where the Standards focus

Advance: PARCC assessments will focus strongly where the Standards focus (70% or more on the major work in grades 3-8).

- Focus allows for a variety of problem types to get at concept in multiple ways.

- Students will have more time to master concepts at a deeper level. Shift #2 - Coherence: Think across grades, and link to major topics within grades

Advance: The assessment design is informed by multi-grade progressions in the Standards and the Model Content Frameworks.

- Key beginnings are stressed (e.g., ratio concepts in grade 6), as are key endpoints and - takeaway skills (e.g., fluency with the multiplication table in grade 3). Shift #3 - Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application

Advance: PARCC assessments will reach the rigor in the Standards through innovations in technology and item design… Shift #2 - Coherence: Think across grades, and link to major topics within grades

Advance: Integrative tasks draw on multiple standards to ensure students are making important connections.

The Standards are not treated as a checklist. 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 Activity 1: Standards for Mathematical Practice - Read the assigned Standard for Mathematical Practice

Think – Write – Pair – Share

- What is the meaning of the practice?

- How will the practice look at my grade level?

- Group Sharing Grade 7 Sample Illustrative Item: Speed

Task Type I: Tasks assessing concepts, skills and procedures

Alignment: Most Relevant Content Standard(s)

7.RP.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

In addition, see 7.RP.2d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and

(1, r) where r is the unit rate. (The “explain” portion is not required in the task, but the task involves some of the concepts detailed here.)

Alignment: Most Relevant Mathematical Practice(s)

MP.2 enters (Reason abstractly and quantitatively), as students must relate the graphs and tables to each other via the unit rate and then to the context at hand. Grade 7 Sample Illustrative Item Key Features and Assessment Advances

- The PARCC assessment will seek to preserve the focus of the Standards by thoroughly exploring the major work of the grade.

- In this case, a multi-point problem is devoted to a single standard about proportional relationships, which are a major focus in grades 6 and 7.

- Unlike traditional multiple choice, it is difficult to guess the correct answer or use a choice elimination strategy.

- Variants of the task could probe understanding of unit rates and representations of proportional relationships by showing different scales on the two graphs, and/or by presenting the data in tables C and D with the ordered pairs not equally spaced in time. High School Sample Illustrative Item: Seeing Structure in a Quadratic Equation

Task Type I: Tasks assessing concepts, skills and procedures

Alignment: Most Relevant Content Standard(s)

A-REI.4. Solve quadratic equations in one variable.

a.) Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form.

b.) Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a +- bi for real numbers a and b.

Alignment: Most Relevant Mathematical Practice(s)

Students taking a brute-force approach to this task will need considerable symbolic fluency to obtain the solutions. In this sense, the task rewards looking for and making use of structure (MP.7). The Common Core State Standards in English language arts/literacy and mathematics were created by educators around the nation. Nearly every state in the nation is working individually and collectively to improve its instruction and assessments to ensure students graduate with the knowledge and skills most demanded by college and careers. Things you could do for next time.... a.k.a. Homework. - Listen to the PARCC webinar on the Content Frameworks

- Read the PARCC Content Frameworks

http://www.parcconline.org/parcc-content-frameworks

- Reflect on the reading

- Discuss with grade level/course teams/PLCs K-3 Diagnostics (Mathematics K-2 only)

- Realigned to CCSS

- Minor modifications to fill gaps

- Ready for use in 2012-13

OAA (Mathematics Grades 3-8)

- Continue to be administered through 2013-14

- Assessing the 2001 Ohio Academic Content Standards

OGT

- Continues after 2014 for additional opportunities for passage Review current and potential resources for alignment to the CCSSM

- Use Resource filter (soon to be posted on the ODE Mathematics webpage) - Identify “rich” mathematical problems

- Make sure to cite the source of the problem*

- Align this “rich” problem to:

- Grade level

- Critical Area of Focus

- Mathematical Practice(s)

- Share with colleagues Next Steps: Mathematical Practices - Use K-8 Comparative Analysis to:

- Choose new or modified content

- Select the relevant mathematical practice(s)

- Read the related Model Curriculum to find instructional ideas and resources

- Determine appropriate rich tasks, materials and strategies for instruction CCSSO

http://www.ccsso.org

Achieve

http://www.achieve.org

NCTM

http://www.Nctm.org

Center for K-12 Assessment & Performance Management at ETS

http://www.k12center.org

YouTube Video Vignettes explaining the CCSS

http://www.Youtube.com/user/TheHuntInstitute#P/a Pod Casts

- Common Core State Standards – 101

- Ohio’s CCSS Model Curriculum – 102

- Standards for Mathematical Practice and the

Critical Areas of Focus – 103

Resource Alignment Tool

Eye of Integration CCSS Support Materials - Future Development - Mathematics Common Core State Standards and Model Curriculum

- K-8 Comparative Analysis

- Standards Progressions View

- K-8 Critical Areas of Focus

- Crosswalks: Cluster to Benchmark Comparison

- What should districts be doing?

- FAQ Rich Task Sources Ohio Resource Center

http://www.OhioRC.org

Inside Mathematics

http://www.insidemathematics.org

Balanced Assessment (MARS tasks)

http://balancedassessment.concord.org

NCTM Illuminations

http://illuminations.nctm.org/ Activity:Task Analysis with the Standards for Mathematical Practice - Individually work MARS task #1

- Identify Standards for Mathematical Practice

- Individually work MARS task #3

- Identify Standards for Mathematical Practice

Share with a partner:

*Solution(s)

*Determine, support 1-2 Mathematical Practices What do you know about rich problems? Significant mathematics

Mathematical Practices

Multiple layers of complexity

Multiple entry points

Multiple solutions and/or strategies

Leads to discussion or other questions

Students are the workers and the decision makers What are essential characteristics of rich problems? Brian ran a 5 km run in 18.4 minutes. How fast did he run?

Factor the trinomial 21x² – 50x – 16

Multiply 14 times 2.5.

The angles of a quadrilateral have measures 90°, 90°, 100° and n°. Find the value of n. How would you enrich these? Problem Exercise The answer is not immediately known

Requires persistence

Engaging

Feasible

Valued Computation “problem”

Solution process is recognizable

Routine

Contextual but not engaging Activity:

Read a 6-8 grade level’s Critical Areas of Focus

What are the concepts?

What are the skills and procedures?

What relationships are students to make? Critical Areas of Focus inform instruction by describing the mathematical connections and relationships students develop in the progression at this point. Change of Emphasis Grades 6-8

- Beginning of Data Analysis and Probability

- Introduction of Integers, Coordinate Graphing

- Focus on Linear Algebra: numerically, graphically and symbolically

- Completion of Operations with fractions and decimals Problems worth doing: Multi-step problems, conceptual questions, applications, and substantial procedures will be common, as in an excellent classroom.

Better Standards Demand Better Questions: Instead of reusing existing items, PARCC will develop custom items to the Standards.

Fidelity to the Standards (now in Teacher’s hands): PARCC evidences are rooted in the language of the Standards so that expectations remain the same in both instructional and assessment settings. 21st Century Skills Creativity and innovation

Critical thinking and problem solving

Communication and collaboration

Information, media and technology literacy

Personal management

Productivity and accountability

Leadership and responsibility

Interdisciplinary and project-based learning Technology enhancements supporting accessibility (e.g., the ability to hover over a word to see and/or hear its definition, etc.)

Transformative formats making possible what can not be done with traditional paper-pencil assessments (e.g., simulations to improve a model, game-like environments, drawing/constructing diagrams or visual models, etc.)

Getting beyond the bubble and avoiding drawbacks of traditional selected response such as guessing or choice elimination. Highlight the phrases that refer to

- citing evidence or

- communication (writing, talking)

Be prepared to justify your choices

- Why

- Literacy Standards links Capturing complex student responses through a device interface (e.g., using drawing tools, symbol palettes, etc.)

Machine scorable multi-step tasks are more efficient to administer and score. What does literacy look like in the mathematics classroom? Learning to read mathematical text

Communicating using correct mathematical terminology

Reading, discussing and applying the mathematics found in literature

Researching mathematics topics or related problems

Reading appropriate text providing explanations for mathematical concepts,

reasoning or procedures

Applying readings as citing for mathematical reasoning

Listening and critiquing peer explanations

Justifying orally and in writing mathematical reasoning

Representing and interpreting data Informational Text Text Dependent Questions Sources

Textbooks

Internet

Reference books The Rocket Problem Math ≠ ELA Mathematics - Right to Left

- Decimals

- Symbols Change

- Key Idea at End (problems) ELA - Left to Right

- Periods

- Symbols are Static

- Key Idea in Beginning

- Beginning Middle End Note Taking Abbreviate

- Use the first few letters of the word

- vocabulary – vocab

- Leave out the vowels

- book= bk;

- Use the first letter of each syllable

- notebook = nb; without = w/o

Use symbols: #, %, $, &, =, +,?, ∆

- traditional or your own Note Taking - Notes are for the user

- Paraphrase

- Single words

- Pictures

- Choose a format that works for the topic and YOU

- Bulleted list

- T-chart

- Web

- 4 square Summarizing “Restating the essence of text or an experience in as few words as possible or in a new, yet efficient, manner.”

Rick Wormeli Take many forms:

Orally

Visually

Physically

Musically

Writing

In groups or

Individually Graphic Organizers Provide visual representation of facts and concepts and their relationships helping students to:

- Organize ideas

- Represent abstract ideas more concretely

- Illustrate the relationships among facts and concepts

- Store and recall information - Explain the purpose and benefits

- Importance of organization

- Assists in comprehension and recall

- For each organizer :

- Explain purpose and form

- Model with familiar information

- Model with new information

- Let students apply to familiar information

- Let students apply to new information Word Splash - A three to five minute writing

- Specific Focus

- Required words are written at the top of the page (limit)

- Required words are familiar key vocabulary words or concepts

- Words splash words are spelled correctly

- Word splash words are used correctly

- Graded Thinking and talking about experiences not only helps to make sense of the past, but also changes the likelihood of subsequent remembering.

Daniel Schacter

The Seven Sins of Memory

Full transcriptMS/HS Mathematics Instructional Consultant Introduction and Overview Why? We are doing well, why change? Mathematical Practices Literacy Across the Hall

“I teach Math, why should I teach the literacy standards?” Literacy Standards Critical Areas of Focus Comparative Analysis, Model Curriculum, etc... Tools PARCC Assessment Documents, Rich Problems, etc... Resources To provide opportunities for Ohio educators to develop an understanding of the revised standards and model curricula in Mathematics. Session Goal Developing a clear picture of the Common Core State Standards by:

Using rich problems to understand the Standards for Mathematical Practice

Digging into the content standards through the Critical Areas of Focus

in order to create instruction based upon the CCSSM and develop a foundation for curriculum revision. MP + CAF + Standards = Instruction In order to design instruction that meets the rigor and expectations of the CCSSM, understanding the Mathematical Practices and Critical Areas of Focus are essential. Overview *A Look Inside the CCSSM 6- 8

*Digging Deeper

*Incorporating Literacy Standards and 21st Century *Skills

*Using Rich Problems

*Model Curriculum

*Progressions

*Resources

*What Should Districts Be Doing Now? Focus

- Identifies key ideas, understandings and skills for each grade or course

- Stresses deep learning, which means applying concepts and skills within the same grade or course

- The PARCC Assessment will focus strongly where the Standards focus Coherence

- Articulates a progression of topics across grades and connects to other topics

- Vertical growth that reflects the nature of the discipline Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application. Shift #1 – Focus: The PARCC assessments will focus strongly where the Standards focus

Advance: PARCC assessments will focus strongly where the Standards focus (70% or more on the major work in grades 3-8).

- Focus allows for a variety of problem types to get at concept in multiple ways.

- Students will have more time to master concepts at a deeper level. Shift #2 - Coherence: Think across grades, and link to major topics within grades

Advance: The assessment design is informed by multi-grade progressions in the Standards and the Model Content Frameworks.

- Key beginnings are stressed (e.g., ratio concepts in grade 6), as are key endpoints and - takeaway skills (e.g., fluency with the multiplication table in grade 3). Shift #3 - Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application

Advance: PARCC assessments will reach the rigor in the Standards through innovations in technology and item design… Shift #2 - Coherence: Think across grades, and link to major topics within grades

Advance: Integrative tasks draw on multiple standards to ensure students are making important connections.

The Standards are not treated as a checklist. 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 Activity 1: Standards for Mathematical Practice - Read the assigned Standard for Mathematical Practice

Think – Write – Pair – Share

- What is the meaning of the practice?

- How will the practice look at my grade level?

- Group Sharing Grade 7 Sample Illustrative Item: Speed

Task Type I: Tasks assessing concepts, skills and procedures

Alignment: Most Relevant Content Standard(s)

7.RP.2b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

In addition, see 7.RP.2d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and

(1, r) where r is the unit rate. (The “explain” portion is not required in the task, but the task involves some of the concepts detailed here.)

Alignment: Most Relevant Mathematical Practice(s)

MP.2 enters (Reason abstractly and quantitatively), as students must relate the graphs and tables to each other via the unit rate and then to the context at hand. Grade 7 Sample Illustrative Item Key Features and Assessment Advances

- The PARCC assessment will seek to preserve the focus of the Standards by thoroughly exploring the major work of the grade.

- In this case, a multi-point problem is devoted to a single standard about proportional relationships, which are a major focus in grades 6 and 7.

- Unlike traditional multiple choice, it is difficult to guess the correct answer or use a choice elimination strategy.

- Variants of the task could probe understanding of unit rates and representations of proportional relationships by showing different scales on the two graphs, and/or by presenting the data in tables C and D with the ordered pairs not equally spaced in time. High School Sample Illustrative Item: Seeing Structure in a Quadratic Equation

Task Type I: Tasks assessing concepts, skills and procedures

Alignment: Most Relevant Content Standard(s)

A-REI.4. Solve quadratic equations in one variable.

a.) Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)^2 = q that has the same solutions. Derive the quadratic formula from this form.

b.) Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a +- bi for real numbers a and b.

Alignment: Most Relevant Mathematical Practice(s)

Students taking a brute-force approach to this task will need considerable symbolic fluency to obtain the solutions. In this sense, the task rewards looking for and making use of structure (MP.7). The Common Core State Standards in English language arts/literacy and mathematics were created by educators around the nation. Nearly every state in the nation is working individually and collectively to improve its instruction and assessments to ensure students graduate with the knowledge and skills most demanded by college and careers. Things you could do for next time.... a.k.a. Homework. - Listen to the PARCC webinar on the Content Frameworks

- Read the PARCC Content Frameworks

http://www.parcconline.org/parcc-content-frameworks

- Reflect on the reading

- Discuss with grade level/course teams/PLCs K-3 Diagnostics (Mathematics K-2 only)

- Realigned to CCSS

- Minor modifications to fill gaps

- Ready for use in 2012-13

OAA (Mathematics Grades 3-8)

- Continue to be administered through 2013-14

- Assessing the 2001 Ohio Academic Content Standards

OGT

- Continues after 2014 for additional opportunities for passage Review current and potential resources for alignment to the CCSSM

- Use Resource filter (soon to be posted on the ODE Mathematics webpage) - Identify “rich” mathematical problems

- Make sure to cite the source of the problem*

- Align this “rich” problem to:

- Grade level

- Critical Area of Focus

- Mathematical Practice(s)

- Share with colleagues Next Steps: Mathematical Practices - Use K-8 Comparative Analysis to:

- Choose new or modified content

- Select the relevant mathematical practice(s)

- Read the related Model Curriculum to find instructional ideas and resources

- Determine appropriate rich tasks, materials and strategies for instruction CCSSO

http://www.ccsso.org

Achieve

http://www.achieve.org

NCTM

http://www.Nctm.org

Center for K-12 Assessment & Performance Management at ETS

http://www.k12center.org

YouTube Video Vignettes explaining the CCSS

http://www.Youtube.com/user/TheHuntInstitute#P/a Pod Casts

- Common Core State Standards – 101

- Ohio’s CCSS Model Curriculum – 102

- Standards for Mathematical Practice and the

Critical Areas of Focus – 103

Resource Alignment Tool

Eye of Integration CCSS Support Materials - Future Development - Mathematics Common Core State Standards and Model Curriculum

- K-8 Comparative Analysis

- Standards Progressions View

- K-8 Critical Areas of Focus

- Crosswalks: Cluster to Benchmark Comparison

- What should districts be doing?

- FAQ Rich Task Sources Ohio Resource Center

http://www.OhioRC.org

Inside Mathematics

http://www.insidemathematics.org

Balanced Assessment (MARS tasks)

http://balancedassessment.concord.org

NCTM Illuminations

http://illuminations.nctm.org/ Activity:Task Analysis with the Standards for Mathematical Practice - Individually work MARS task #1

- Identify Standards for Mathematical Practice

- Individually work MARS task #3

- Identify Standards for Mathematical Practice

Share with a partner:

*Solution(s)

*Determine, support 1-2 Mathematical Practices What do you know about rich problems? Significant mathematics

Mathematical Practices

Multiple layers of complexity

Multiple entry points

Multiple solutions and/or strategies

Leads to discussion or other questions

Students are the workers and the decision makers What are essential characteristics of rich problems? Brian ran a 5 km run in 18.4 minutes. How fast did he run?

Factor the trinomial 21x² – 50x – 16

Multiply 14 times 2.5.

The angles of a quadrilateral have measures 90°, 90°, 100° and n°. Find the value of n. How would you enrich these? Problem Exercise The answer is not immediately known

Requires persistence

Engaging

Feasible

Valued Computation “problem”

Solution process is recognizable

Routine

Contextual but not engaging Activity:

Read a 6-8 grade level’s Critical Areas of Focus

What are the concepts?

What are the skills and procedures?

What relationships are students to make? Critical Areas of Focus inform instruction by describing the mathematical connections and relationships students develop in the progression at this point. Change of Emphasis Grades 6-8

- Beginning of Data Analysis and Probability

- Introduction of Integers, Coordinate Graphing

- Focus on Linear Algebra: numerically, graphically and symbolically

- Completion of Operations with fractions and decimals Problems worth doing: Multi-step problems, conceptual questions, applications, and substantial procedures will be common, as in an excellent classroom.

Better Standards Demand Better Questions: Instead of reusing existing items, PARCC will develop custom items to the Standards.

Fidelity to the Standards (now in Teacher’s hands): PARCC evidences are rooted in the language of the Standards so that expectations remain the same in both instructional and assessment settings. 21st Century Skills Creativity and innovation

Critical thinking and problem solving

Communication and collaboration

Information, media and technology literacy

Personal management

Productivity and accountability

Leadership and responsibility

Interdisciplinary and project-based learning Technology enhancements supporting accessibility (e.g., the ability to hover over a word to see and/or hear its definition, etc.)

Transformative formats making possible what can not be done with traditional paper-pencil assessments (e.g., simulations to improve a model, game-like environments, drawing/constructing diagrams or visual models, etc.)

Getting beyond the bubble and avoiding drawbacks of traditional selected response such as guessing or choice elimination. Highlight the phrases that refer to

- citing evidence or

- communication (writing, talking)

Be prepared to justify your choices

- Why

- Literacy Standards links Capturing complex student responses through a device interface (e.g., using drawing tools, symbol palettes, etc.)

Machine scorable multi-step tasks are more efficient to administer and score. What does literacy look like in the mathematics classroom? Learning to read mathematical text

Communicating using correct mathematical terminology

Reading, discussing and applying the mathematics found in literature

Researching mathematics topics or related problems

Reading appropriate text providing explanations for mathematical concepts,

reasoning or procedures

Applying readings as citing for mathematical reasoning

Listening and critiquing peer explanations

Justifying orally and in writing mathematical reasoning

Representing and interpreting data Informational Text Text Dependent Questions Sources

Textbooks

Internet

Reference books The Rocket Problem Math ≠ ELA Mathematics - Right to Left

- Decimals

- Symbols Change

- Key Idea at End (problems) ELA - Left to Right

- Periods

- Symbols are Static

- Key Idea in Beginning

- Beginning Middle End Note Taking Abbreviate

- Use the first few letters of the word

- vocabulary – vocab

- Leave out the vowels

- book= bk;

- Use the first letter of each syllable

- notebook = nb; without = w/o

Use symbols: #, %, $, &, =, +,?, ∆

- traditional or your own Note Taking - Notes are for the user

- Paraphrase

- Single words

- Pictures

- Choose a format that works for the topic and YOU

- Bulleted list

- T-chart

- Web

- 4 square Summarizing “Restating the essence of text or an experience in as few words as possible or in a new, yet efficient, manner.”

Rick Wormeli Take many forms:

Orally

Visually

Physically

Musically

Writing

In groups or

Individually Graphic Organizers Provide visual representation of facts and concepts and their relationships helping students to:

- Organize ideas

- Represent abstract ideas more concretely

- Illustrate the relationships among facts and concepts

- Store and recall information - Explain the purpose and benefits

- Importance of organization

- Assists in comprehension and recall

- For each organizer :

- Explain purpose and form

- Model with familiar information

- Model with new information

- Let students apply to familiar information

- Let students apply to new information Word Splash - A three to five minute writing

- Specific Focus

- Required words are written at the top of the page (limit)

- Required words are familiar key vocabulary words or concepts

- Words splash words are spelled correctly

- Word splash words are used correctly

- Graded Thinking and talking about experiences not only helps to make sense of the past, but also changes the likelihood of subsequent remembering.

Daniel Schacter

The Seven Sins of Memory