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Mathematics Educators to the Career and College Ready Conference

A Quick Look at Critical Topics in Mathematics

Reform from Past Academies

Reduce Side Chatter

Involve Yourself in the Process

Give Your Thoughts & Ideas

Open Your Mind on how You Can Change Instruction

Remember to Silence Electronic Devices

Reflect on how the Standards for Mathematical Practice will be infused into daily instruction.

Become familiar with the Maryland's College and Career-Ready Standards.

Analyze the instructional SHIFTS

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others.4. Model with Mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure.8. Look for and express regularity in reasoning

Apply to every Mathematics Unit in every grade/course

SMP Placemat Activity

Behavior Cards

Placemat

Conceptual Categories for High School:

•Number and Quantity•Algebra•Functions•Geometry•Modeling •Probability and Statistics

Algebra IArithmetic with Polynomials and Rational

Functions

Perform arithmetic operations on polynomials

Understand the relationship between zeros and factors of polynomials

Use polynomial identities to solve problems

Rewrite rational expressions

FocusCoherenceRigorConceptual Understanding

Procedural SkillModeling/Application

FOCUS

FOCUS is largely built into the CCSSM curriculum. The charge for the classroom teacher is to take opportunities to revisit major content frequently and make connections between the major and supporting and additional content.

New Learning Pr

ior

Lear

ning

COHERENCE

Shift #2

Connects to

Pythagorean Theorem Distance Formula

Pythagorean Trig Identities

Connects to

Progression

Documents

Instruction in the mathematics classroom of the future must take advantage of every opportunity to make connections between topics both within a course and from course to course if the SHIFT toward COHERENCE is to be a achieved.

COHERENCE

“Rigor is the goal of helping students develop the capacity to understand content that is complex, ambiguous, provocative, and personally or emotionally challenging.”Shift #3

Rigorous Learning Experiences Challenge students Require effort and tenacity Focus on quality Have multiple paths Not always “tidy” Connect ideas in

mathematics Develop strategic, flexible

thinking Encourage reasoning and

sense-making Actively involve students

Non-rigorous Learning Experiences

Awkward, difficult values Minimal effort required Focus on quantity,

repetition Scripted, includes pathway

to the solution No links to other

mathematics Routine, rote procedures Memorized rules without

understanding Teachers do the work

while students observe

What are some characteristics of RIGOROUS learning experiences?

PARCC Model Content Framework documents includeFluency Recommendations

A.Drag into the box exactly three unique items whose sum is less than 10.

B.Drag into the box exactly three unique items whose sum is between 10 and 20.

C.Drag into the box exactly three unique items whose sum is greater than 20.

A. Three unique items whose sum is less than 10

B. Three unique items whose sum is between 10 and 20

C. Three unique items whose sum is greater than 20

8

6

1--2 2

13

5 7

13

33

20- 20

4

8

Items

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

Standard A-REI.10

Conceptual Category: Algebra Domain: Reasoning with Equations and InequalitiesCluster: Represent and solve equations graphically

To help students develop conceptual understanding provide learning experiences that :

•see connections between the mathematics they are learning and what they already know.

•use manipulatives to model concepts, and then verbalize their results.

•show different representations of the same mathematical situation.

What does it mean to MODELwith mathematics?

• SMP #4:Model with mathematics• Conceptual Category :Modeling• Modeling Standards: A.CED.1

 Tasks assessing modeling / applications •call for modeling/application in a real-world context or scenario (MP.4) and can also involve other mathematical practice standards.

•tasks may include a mix of innovative, machine scored and hand scored responses.

•will be included on the PBA component and generate evidence for measuring mathematical modeling/application with connections to content.

Report

Modeling CycleProblem

Compute ValidateFormulate

Interpret

Report

Modeling CycleProblem

Compute

ValidateFormulate

Interpret

Procedural Skill

Modeling/Application

Conceptual Understanding

Illustrative Math https://www.illustrativemathematics.org/

• Bill McCullum, CCSS lead writer• Sample Lessons that illustrate specific standards Achieve The Core https://achievethecore.org

• Jason Zimba, CCSS lead writer• Multiple Resources – e.g. Lesson Plans, Assessments,

Professional Development courses, Grade-at-a-GlancePARCC http://parcconline.org

• Information about PARCC Assessments• Sample Lessons• Practice Tests

Annie Fetter

http://www.youtube.com/watch?v=WFvYZDR4OeY

The greatest danger for most of us is not that our aim is too high and we

miss it….

But that it is too low and we

reach it.--

Michelangelo