SLIDE 1 Core e In Instruction n (Tie ier r One) ) in in Mathematics s
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WELCOME!
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SLIDE 4 Principle #1: Increases in student learning occur
improvements in the level
knowledge and skill, and student engagement.
Richard Elmore, Ph.D., Harvard Graduate School of Education
Principle #2: If you change
instructional core, you have to change the other two.
The In Instructional Core
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General Shif ifts in in Mathematics s
Focus: focus strongly where the standards focus Co Coherence: think across grades, and link to major topics in each grade Rig igor: in major topics, pursue with equal intensity – conceptual understanding, – procedural skill and fluency, and – applications
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Shift One: Focus
SLIDE 7 K 12 Number and Operations Measurement and Geometry Algebra and Functions Statistics and Probability
Traditional U.S .S. Approach
SLIDE 8 Focusing Attention Wit ithin Number and Operations
Operations and Algebraic Thinking Expressions and Equations Algebra → → Number and Operations—Base Ten → The Number System → Number and Operations— Fractions → K 1 2 3 4 5 6 7 8 High School
SLIDE 9 HS S Alg lgebra a Resources s as s an n Example e
the Core Grade Two Overview (http:// //www.achievethecore.org/)
t a Gla lance (Y (YAG)
Sequenced Unit its (http:// //www.utdanacenter.org/) /) (R (Reference Documents)
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Shift Two: : C Coherence
SLIDE 11 Th The Why: : Sh Shift Two
Coherence ac across grades, an and lin link to maj ajor topics wit ithin grades (th thinking in interdependently)
Carefu full lly connect th the lea learn rnin ing with ithin in and across grades so so that students can build ild new understandin ing
ions buil ilt in in previ vious years.
Begin in to count t on so soli lid conceptual l understandin ing of core content and buil ild on it.
is not a new event, but t an ext xtensio ion of f previ vious lea learn rnin ing.
SLIDE 12 Coherence: : Thin ink Across Grades
Fraction example: “The coh
- herence and sequential nature of mathematics dictate
the foundational skills that are necessary for the learning of
- algebra. The most important foundational skill not presently
developed appears to be proficiency with fractions (including decimals, percents, and negative fractions). Th The teachin ing of
fractions must be ackn acknowle ledged as as crit criticall lly im important an and im improved before an an in incr crease in in stu tudent ach achie ievement in in alg algebra can an be expected.”
Final Report of the National Mathematics Advisory Panel (2008, p. 18)
SLIDE 13 In Instructional l Content t (F (Focus) and (C (Coherence- th thin inkin ing in interdependentl tly across grade le levels ls) Potential l St Startin ting Poin int
Learning Targets ali lign wit ithin grade-levels and across grade-levels focus*1
Identify fy major clu lusters, supporting clu lusters, and additional clu lusters
- Summative assessments are selected pri
rior to teaching
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TRANSITION: : Swit itching Gears Your Turn
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Reminder fr from the In Instit itute: Technical Problems and Adaptive Chall llenges
Sharon Dalo loz Parks, in in the book Leadership Can be Taught (2005)notes that: “technical pro roblems (even though they y may y be complex) can be solv lved wit ith knowle ledge and procedures alr lready in in hand. . In In contrast, , adaptiv ive ch challe lenges requir ire new le learnin ing, g, in innovation, and new patterns of behavio ior.
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The Pra ractice of Adaptive Leadership: T Tools and Tactics for r Changing Your Org rganization and the World (2009) by y Heif ifetz, , Grashow, , and Lin insky “But t auth thoritie ies cannot t solv lve an adaptiv tive chall llenge by y is issuin ing a dir irectiv tive or brin ingin ing togeth ther a group of f exp xperts ts, , because th the solu luti tions to th the adaptiv ive proble lems lie lie in in th the new attit titudes, , competencies, and coordination of f th the people with ith th the proble lem its itself lf”(p 73).
SLIDE 17 Fir irst Two Shif ifts: F Focus and Coherence
eacher: How mig ight I I tak akes steps to mas aster th the math content knowledge for th the ar area of f focus I I am am teaching? (T (Technical Problem an and/or Adaptive Challenge- es especiall lly coherence ac across grades)
istrict Lea eadership: What steps mig ight we e take to ad address th the al alig ignment an and coherence of f math cu curriculum, , text xtbooks, an and materials wit ith th the Id Idaho Core Standards? (T (Technical Problem)
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Shift Three: : R Rig igor
SLIDE 19 Rig igor: In In majo jor topics, pursue wit ith equal in intensity
(a (addressing student mis isconceptions)
ill and fl fluency
(Depth of f Knowledge- DOK Levels 1-4) 4)
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Rig igor: Pursue wit ith equal in intensity
Th The challenge of “rigor” is fin findin ing th the bala lance betw tween conceptual l understandin ing, procedural flu fluency, and appli licatio ion. Many of f us s wil ill l need to lea learn rn new knowle ledge, str trategie ies, and sk skil ills ls in in order r to fin find th the bala lance. We have organized the implementation of “rigor” into th three areas: : D Deliv livery ry of f In Instr tructio ion, , In Instructio ional Activ tivit itie ies, , and Materia ials ls.
SLIDE 21 Several modes of f Deli livery of f In Instruction wil ill be needed for r conceptual knowledge, procedural skil ill, and application
Structure e and d pacing options considered d (p (poss ssible e adaptive e chall llenge)
, procedu dures, , and d in instructional group uping
g and d Depth h of f Knowledge
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TRANSITION: : Swit itchin ing Gears
SLIDE 23 In Instructional l Activ ivities s
e ass ssessment t practices guid ide decisions s to
just t and d dif ifferentiate
Stud udent t th thin ink-aloud uds
l Practices are e uti tilized d
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TRANSITION: : Swit itchin ing Gears
SLIDE 25 Overarching Habits of f Min ind: Persistence and Effort
“The Secret to Raising Smart Kids” in Scientific American Mind: By Carol S. Dweck; Dec2007/Jan2008, Vol. 18 Issue 6, pp. 36-43 More than three decades of research shows that a focus on effort—not on intelligence or ability—is key to success in school and in life World Economic Forum, Panel Discussion, December 2013: ANDREAS SCHLEICHER, THE OECD'S SPECIAL ADVISER ON EDUCATION POLICY, ON THE RESULTS OF THE PISA TEST (PROGRAMME FOR INTERNATIONAL STUDENT ASSESSMENT) NOTES: "IN SHANGHAI OVER 30% OF STUDENTS CAN CONCEPTUALIZE, GENERALIZE AND USE ADVANCED MATH IN CREATIVE WAYS.” “HE ARGUES THAT EAST ASIA'S RESULT IS THANKS TO A BELIEF IN THE VALUE OF HARD WORK AND PERSISTENCE RATHER THAN INHERENT ABILITY.”
SLIDE 26 Grouping of f Mathematical Practices
Reasoning and Explaining
- 2. Reason abstractly and quantitatively
- 3. Construct viable arguments and critique the reasoning of others
Modeling and Using Tools
- 4. Model with mathematics
- 5. Use appropriate tools strategically
Seeing Structure and Generalizing
- 7. Look for and make use of structure
- 8. Look for and express regularity in repeated reasoning
Overarching Habits of Mind of a Productive Mathematical Thinker
- 1. Make sense of problems and persevere in solving them
- 6. Attend to precision
Adapted from (McCallum, 2011)
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TRANSITION: : Swit itchin ing Gears
SLIDE 28 M Materials s
lign wit ith in instructional content for grade- le level focus
isual and graphic depictions of f problems
items to detect (d (dia iagnosis) ) and address common stu tudent misconceptions*6
SLIDE 29 Mathematics: Understanding the Score (2008); Office for Standards in Education, Children’s Services and Skills kills (Ofsted), p. . 6-in in the U.K .K.
- “Satisfactory lessons were […]ch
characterised by th the teacher doing most t of f th the talk lking, g, emphasising rule les and procedures rath ther th than concepts or lin links with ith oth ther parts
f mathematics.”
- “In the most effective lessons […] teachers listened to
pupils carefully and observ rved th their work th throughout th the le lesson. . They aim imed to id identify fy any potential mis isconceptions or barriers to understanding key concepts, and responded accordingly.”
SLIDE 30 Question: D Detecting a Mis isconception
In In whic ich of f th these rig ight t tr tria iangles is is a2 + b2 = c2
2 ?
A a c b C b c a E c b a B a b c D b a c F c a b
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Addressing Mis isconceptions
Misc isconceptio ions by lan Samson & David Burghes http://www.cimt.plymouth.ac.uk/resources/help/misco n.htm
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TRANSITION: Switching Gears
SLIDE 33 Three More Potential Start rting Poin ints
Reviewing th the Remaining Th Three Areas on th the Core In Instruction Math th Graphic:
ry of f In Instruction
Instructional Acti tivities
Th The th three topics above require professional development and are present adaptive challenges for r many ele lementary teachers
SLIDE 34 Where
e might t you u begin? ? Id Idaho
e Mathematics s Stand ndards s Overview w AND D Core e In Instruction n Math h Graph phic c
SLIDE 35 Shif ift Three: : R Rig igor
eacher: Where mig ight I I beg egin lea learning new ways s in in conceptual understanding, g, procedural flu fluency, , an and application to en enhance th the le learning for r my students? (Ad (Adaptive Challenges)
istrict Lea eadership: What act ctions mig ight we e take to su support new lea learning for our r teachers in in conceptual understanding, g, procedural flu fluency, , an and application in in mathematics in instruction? (Technical Problems)
SLIDE 36 Resource: : Mathematical Thin inking for r In Instruction (M (MTI) I) at BSU
tices embedded in in th the Bu Buil ildin ing Mathematic ical l Understandin ing fr framework rk; takin ing students' id ideas se serio riously ly, , focusi sing on the stru ructure of mathematic ics, , addressin ing misc isconceptio ions, pressin ing stu tudents' conceptuall lly, and encouragin ing multip ltiple le strategie ies and models.” http:// //dmt.bois isestate.edu/proje jects/mti
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Resource: Research Bri rief
Effectiv ive Stra rategies for r Teaching Students wit ith Dif ifficulties in in Mathematics Based upon two meta-analyses of 50 studie ies Produced by: : National Council il of Teachers of Mathematics
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Clo losing
