The Math Diet: An Instructional Framework To Grow .
The Math Diet:An Instructional Frameworkto Grow MathematiciansKateri Thunder, Ph.D.katerithunder@gmail.comPreK-4 Lead Math TeacherPreK TeacherCharlottesville City SchoolsAlisha Demchak, M.Ed.and3u@virginia.eduPreK-4 Lead Literacy TeacherInstructional CoachCharlottesville City SchoolsVirginia Council of Mathematics Specialists ConferenceCulpeper, VASeptember 30, 2016Thunder & Demchak, www.mathplusliteracy.com
By the end of the session,you should be able to: Describe the five components of the MathDiet and explain why each component isimportant to mathematical learning.Explain how to use the Math Diet to plan amath unit and a math lesson.Walk away with instructional strategiesand activities to share with educators asthey implement the Math Diet.Thunder & Demchak, www.mathplusliteracy.com
Our Agenda What is a “diet”?The 5 components of the Math Diet throughthe lens of a sample math unit and a samplemath lesson.Questions & AnswersThunder & Demchak, www.mathplusliteracy.com
What is a “diet”? An instructional framework based on the metaphor of a dietIn a balanced diet, the components work together to give students multiplecontexts to practice and transfer their understanding, knowledge, andskills.A bridge bet ween literacy and math. Teachers are typically familiar withthe literacy diet: Developing Word Recognition (2014) by Latisha Hayes and KevinFlanaganThe Balanced Literacy Diet: ood Groups/index.htmlNational Reading Panel: /nrp.aspxThe goal of the Math Diet is to develop mathematical proficiency (NRC, 2001).Thunder & Demchak, www.mathplusliteracy.com
Important Math Diet Terms High-Leverage Content (Ball et al., 2009) High-Leverage Practices (Ball et al., 2009) Cognitive Demand (Stein et al., 2000)Thunder & Demchak, www.mathplusliteracy.com
Important Math Diet Language High-Leverage Content (Ball et al., 2009): content withthe highest mathematical significant acrossmath content areas and gradesHigh-Leverage Practices (Ball et al., 2009): practiceswith the highest effectiveness for studentlearning across content areas and contextsCognitive Demand (Stein et al., 2000): the complexity ofmental processing required to solve a problemThunder & Demchak, www.mathplusliteracy.com
Cognitive DemandThunder & Demchak, www.mathplusliteracy.com
Sample Unit2nd Grade FractionsWhat are the three stages of Backwards Design?(Wiggins & McTighe, 2005)Thunder & Demchak, www.mathplusliteracy.com
Sample Unit2nd Grade FractionsThunder & Demchak, www.mathplusliteracy.com
Sample Unit2nd Grade FractionsThunder & Demchak, www.mathplusliteracy.com
The Math DietThunder & Demchak, www.mathplusliteracy.com
Conceptual Understanding What? Comprehending the why ofmathematical concepts.Why? Develops a deep understanding of themeaning and structure of mathematicsWhen? Daily for the majority of instructionaltime To begin a unitHow? High cognitive demand tasks,contextualized problems, truly problematicsituations, literacy comprehension strategiesThunder & Demchak, www.mathplusliteracy.com
What is conceptual understanding?Thunder & Demchak, www.mathplusliteracy.com
What is conceptual understanding?Thunder & Demchak, www.mathplusliteracy.com
High-Leverage Practicesfor DevelopingConceptual Understanding High Cognitive Demand Tasks (Stein et al., 2000) Truly Problematic Situations (Fosnot & Dolk, 2001) Contextualized Problems witha low mathematical floor and a highmathematical ceiling (Boaler, 2014) Literacy Comprehension Strategies (Duke &Pearson, 2001)Thunder & Demchak, www.mathplusliteracy.com
ImplementingConceptual Understandingin a Unit What task(s) willengage students inthinking about andunpacking the bigideas?What sequence shouldthose tasks go in?Thunder & Demchak, www.mathplusliteracy.com
ImplementingConceptual Understandingin a UnitThunder & Demchak, www.mathplusliteracy.com
Strategic Competence What? Knowing the how of mathematicalconceptsWhy? Develops strategies to applyconceptual understanding to problem solveWhen? Daily for the majority of instructionaltime After building conceptual understanding(for the majority of the unit)How? High Cognitive Demand Tasks, NumberTalks, Anchor Charts, Think AloudsThunder & Demchak, www.mathplusliteracy.com
What is strategic competence?Thunder & Demchak, www.mathplusliteracy.com
What is strategic competence?Thunder & Demchak, www.mathplusliteracy.com
High-Leverage Practicesfor DevelopingStrategic Competence Number Talks (Parrish, 2014) (Humphreys & Parker, 2015) Anchor Charts (Newman, 2010) Think Alouds (Hart et al., 2004) High Cognitive Demand Tasks (Stein et al., 2000)Thunder & Demchak, www.mathplusliteracy.com
ImplementingStrategic Competencein a Unit What strategies do theyneed to learn to meet the doobjectives?What task(s) will engagestudents in exploring andevaluating these strategies?What sequence should thosetasks go in?Thunder & Demchak, www.mathplusliteracy.com
ImplementingStrategic Competencein a UnitThunder & Demchak, www.mathplusliteracy.com
ImplementingStrategic Competencein a UnitThunder & Demchak, www.mathplusliteracy.com
Procedural Fluency What? Flexibility, Accuracy, Efficiency(Russell, 2000)Why? Helps reduce cognitive load whileproblem solvingWhen? Regularly, frequently, for shortperiods of time, in multiple contexts To conclude and review the unitHow? Basic fact games, goal setting,number talks, low cognitive demandtasks, math vocabulary gamesThunder & Demchak, www.mathplusliteracy.com
What is procedural fluency?Thunder & Demchak, www.mathplusliteracy.com
High-Leverage Practicesfor DevelopingProcedural Fluency Effective Basic Fact Practice Games (Van deWalle et al., 2014) Number Talks (Parrish, 2014) (Humphreys & Parker, 2015) Goal Setting and Self-Evaluation (Van de Walleet al., 2014; Hattie, 2010) Vocabulary Games (Beck, McKeown, & Kucan, 2013) Low Cognitive Demand Tasks (Stein et al., 2000)Thunder & Demchak, www.mathplusliteracy.com
ImplementingProcedural Fluencyin a Unit What skills/vocabularydo they need to practice?What task(s) will engagestudents in effective,deliberate practice?What sequence shouldthose tasks go in?Thunder & Demchak, www.mathplusliteracy.com
ImplementingProcedural Fluencyin a UnitThunder & Demchak, www.mathplusliteracy.com
Counting What? The five counting principlesWhy? Foundation of number sense for wholenumbers, decimals, and fractionsWhen? Regularly, frequently, for short periods oftime, in multiple contexts Daily/Weekly Routines Throughout the unitHow? Counting games, counting collections,reading & writing counting booksThunder & Demchak, www.mathplusliteracy.com
5 Counting Principles(Gelman & Gallistel, 1978) one-thirdThunder & Demchak, www.mathplusliteracy.com
5 Counting Principles(Gelman & Gallistel, 1978) one-thirdThunder & Demchak, www.mathplusliteracy.com
5 Counting Principles(Gelman & Gallistel, 1978) one-thirdThunder & Demchak, www.mathplusliteracy.com
5 Counting Principles(Gelman & Gallistel, 1978) one-thirdThunder & Demchak, www.mathplusliteracy.com
5 Counting Principles(Gelman & Gallistel, 1978) one-thirdThunder & Demchak, www.mathplusliteracy.com
High-Leverage Practicesfor Counting Counting Games (NRC, 2009) Counting Songs (NRC, 2009) Counting Collections (Schwerdtfeger & Chan, 2007) Counting on Number Charts, NumberLines, Game Boards (NRC, 2009) Reading and Writing Counting Books(NRC, 2009)Thunder & Demchak, www.mathplusliteracy.com
Implementing Countingin a Unit What type of number willstudents count?What task(s) will engagestudents in counting?Which counting tasks helpprepare students to workon which other tasks?Thunder & Demchak, www.mathplusliteracy.com
Implementing Countingin a UnitThunder & Demchak, www.mathplusliteracy.com
Subitizing What? Quick recognition of a quantity of objectswithout countingWhy? Develops number sense, spatial reasoning, andmental math strategiesWhen? Regularly, frequently, for short periods of time, inmultiple contexts Daily/Weekly Routines Throughout the unitHow? Quick Images, reading & writing books forvisualizing quantitiesThunder & Demchak, www.mathplusliteracy.com
High-Leverage Practicesfor Subitizing Build, Draw, Describe Quick Images (NRC,2009) Reading and Writing Books forVisualizing Images (NRC, 2009)Thunder & Demchak, www.mathplusliteracy.com
Implementing Subitizingin a Unit What type of number willstudents subitize?What task(s) will engagestudents in subitizing?Which subitizing taskshelp prepare students towork on which othertasks?Thunder & Demchak, www.mathplusliteracy.com
Implementing Subitizingin a UnitThunder & Demchak, www.mathplusliteracy.com
SubitizingSamples of Student Workfrom Fraction Quick Images - DescribeThunder & Demchak, www.mathplusliteracy.com
The Math DietThunder & Demchak, www.mathplusliteracy.com
ImplementingThe Math Diet in a LessonThunder & Demchak, www.mathplusliteracy.com
ImplementingThe Math Diet in a LessonThunder & Demchak, www.mathplusliteracy.com
ImplementingThe Math Diet in a LessonThunder & Demchak, www.mathplusliteracy.com
ImplementingThe Math Diet in a LessonThunder & Demchak, www.mathplusliteracy.com
The Math DietThunder & Demchak, www.mathplusliteracy.com
By the end of the session,you should be able to: Describe the five components of the MathDiet and explain why each component isimportant to mathematical learning.Explain how to use the Math Diet to plan amath unit and a math lesson.Walk away with instructional strategiesand activities to share with educators asthey implement the Math Diet.Thunder & Demchak, www.mathplusliteracy.com
The Math Diet:An Instructional Frameworkto Grow MathematiciansKateri Thunder, Ph.D.katerithunder@gmail.comPreK-4 Lead Math TeacherPreK TeacherCharlottesville City SchoolsAlisha Demchak, M.Ed.and3u@virginia.eduPreK-4 Lead Literacy TeacherInstructional CoachCharlottesville City SchoolsVirginia Council of Mathematics Specialists ConferenceCulpeper, VASeptember 30, 2016Thunder & Demchak, www.mathplusliteracy.com
What is a “diet”? An instructional framework based on the metaphor of a diet In a balanced diet, the components work together to give students multiple contexts to practice and transfer their understanding, knowledge, and skills. A bridge between literac
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