Upgrading the Six Instructional Shifts in MATHShift 1: FOCUS

Teacher Student Principal

● Decide what to cut from the curriculum / content in order to go deeper.

● Focus instructional time on priority concepts

● Give students the gift of time● “Uncovers” the curriculum rather than

trying to “cover” everything.

● Spend more time on fewer concepts.

● Mastery of conceptual understanding aids in mastery of process.

● Observes depth and rigor in lessons● Discusses priority content in pre-

observation conferences● Observes students discussing /

sharing multiple ways to solve problems

Modern Lens

● Give opportunities to contextualize information. (5 + 7 = 12…12 what?)● Math practice #3: construct viable arguments and critique the reasoning of others.● Math Emphases document from EngageNY: http://www.engageny.org/sites/default/files/resource/attachments/nys-math-

emphases-k-hs.pdf

Shift 2: COHERENCE

Teacher Student Principal

● Connect the threads of math foci / priorities across grade levels

● Connect to the way content was taught the year before and the years after

● Focus on priority progressions

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

Make connections from previous learning to new material

Observes connections to previous learning being made in instruction.

Observes math being taught in a logical progression

Discusses previous grade level’s learning and subsequent grade level’s learning as a situational perspective during pre-observation conferences

Modern Lens

● Explore the Math Dependency Chart: http://jeffbaumes.github.io/standards/● Priority progressions: http://ime.math.arizona.edu/progressions/

Shift 3: FLUENCY*

Teacher Student Principal

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

● Focus on the listed fluencies by grade level

● Use high quality problem sets, in high volume

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

Practices solving problems where priority skills are fluent so that deep thinking occurs with new material.

Observes fluency practice in action, often

Observes engagement of basic skills as a foundation for solving more complex problems

Discusses focus on required fluencies during pre-observation conferences

Modern Lens

● Mental Models / Modeling WITH Math, not necessarily manipulatives / Modeling Apps on Digital Devices● Classroom procedures in place for practice time and fluency development● Math Fact Fluency presentation: http://www.loganschools.org/curriculum/2010NCTM/mathfactfluency.pdf● Digital Resources – Web apps, device apps, Virtual Centers, etc.

Michael Fisher – Orleans Niagara BOCES JULY 2013

Shift 4: DEEP UNDERSTANDING

Teacher Student Principal

● Create opportunities for students to understand the answer from variety of access points

● Ensures that every student “gets it” before moving on

● Increase level of content knowledge that may involve concepts above and below current grade level

Show mastery of material at a deep level in numerous ways

Articulate mathematical reasoning

Demonstrate deep conceptual understanding of priority concepts

Observes student-centered work and student-led discussions of solutions

Discusses content knowledge with teacher during pre-conferences and how that impacts pedagogy

Observes flexibility in the classroom for Socratic-type discussions and high levels of critical thinking opportunities

Modern Lens

● Communication and collaboration lead to non-linear and multi-faceted ways to solve problems. (Comes through student discussion and debrief – constructing viable arguments and critiquing the reasoning of others.)

● Solution Fluency: In order to solve problems, students need a toolbox of resources and variable processes to pull from.● Students need to look for and make use of structure, persevere in solving problems, and reason abstractly & quantitatively.

Shift 5: APPLICATION

Teacher Student Principal

● Apply math in areas or situations where it’s not directly required (i.e. in science)

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

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.

See math as a toolbox full of tools to solve problems in any subject

Observes authenticity in classwork. Observes this shift in other relevant

classrooms

Modern Lens

● Opportunities for authentic application of conceptual knowledge and processes.● Construct viable arguments and critique the reasoning of others.

Shift 6: DUAL INTENSITY

Teacher Student Principal

● Be ambitious in demands for fluency and practice

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

Practice Math Skills with an intensity that results in fluency

Practice Math Concepts with an intensity that forces application in novel situations.

Observes fluency practice often with follow up application opportunities

Discusses opportunities for Dual Intensity in pre-conference conversations

Observes automaticity of basic skills while students solve higher level and/or multi-step problems.

Modern Lens

● Sprints: Check out samples here: http://rooseveltufsd.schoolwires.net/Page/560● Debriefs with students around reasoning strategies and multiple problem solving methods.

*Priorities in Support of Rich Instruction and Expectations ofFluency / Conceptual Understanding

K-2 Addition and subtraction, measurement using whole number quantities

4 Add / Subtract within 1,000,000

K Add / Subtract within 5 5 Multi-Digit Multiplication1 Add / Subtract within 10 6 Ratios and proportional reasoning; early expressions

and equations; multi-digit division; multi-digit decimal operations

2 Add / Subtract within 20Add / Subtract within 100 (pencil and paper)

7 Ratios and proportional reasoning; arithmetic of rational numbers; solve px + q = r & p(x + q) = r

3-5 Multiplication and division of whole numbers and fractions

8 Linear Algebra; Solve simple 2X2 systems by inspection

3 Multiply / Divide within 100Add / Subtract within 1000