Investigations in Number, Data, and Space K-5

1National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Getting Started with the Practices

Investigations in Number, Data, and Space K-5

“In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures. Mathematical competence opens doors to productive futures. A lack of mathematical competence keeps those doors closed….All students should have the opportunity and the support necessary to learn significant mathematics with depth and understanding.”

NCTM (2000, p.50)

2National Council of Supervisors of MathematicsIllustrating the Standards for Mathematical Practice: Getting Started with the Practices2

Underlying Frameworks

National Council of Teachers of Mathematics

The 6 Principles• Equity• Curriculum• Teaching• Learning• Assessment• Technology

NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author.




Equity

“Excellence in mathematics educationrequires equity – high expectations andstrong support for all students.”

(NCTM, 2000, p.12)





Curriculum

“A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics,and well articulated across the grades.”

(NCTM, 2000, p.14)





Teaching

“Effective mathematics teaching requires understanding what students know and need to learn and then challengingand supporting them to learn it well.”

(NCTM, 2000, p.16)





Learning

“Students must learn mathematics withunderstanding, actively building new knowledge from experience and priorknowledge.”

(NCTM, 2000, p.20)



Underlying Frameworks National Council of Teachers of Mathematics

Assessment

“Assessment should support the learningof important mathematics and furnishuseful information to both teachers andstudents…Assessment should not merely be done to students: rather, it should also be done for students, to guide andenhance their learning.”

(NCTM, 2000, p.22) NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author.




Technology

“Technology is essential in teaching andlearning mathematics; it influences the mathematics that is taught and enhances students’ learning.”

(NCTM, 2000, p.24)



Standards for Mathematical Practice

“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.” (CCSS, 2010)




5 Process Standards• Problem Solving• Reasoning and Proof• Communication• Connections• Representations




Strands of Mathematical Proficiency

Strategic Competence

Adaptive Reasoning

Conceptual Understanding

Productive Disposition

Procedural Fluency

NRC (2001). Adding It Up. Washington, D.C.: National Academies Press.


Strands of Mathematical Proficiency

• Conceptual Understanding – comprehension of mathematical concepts, operations, and relations

• Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately

• Strategic Competence – ability to formulate, represent, and solve mathematical problems

• Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification

• Productive Disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.


Standards for Mathematical Practice and PARCC

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the

reasoning of others.4. Model with mathematics. 5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated

reasoning.


Construction of Ideas


Problem-Based or Inquiry Approach

When students explore a problem and the mathematical ideas are later connected to that experience.

It is through inquiry that students are activating their own knowledge and trying to make new knowledge (meaning). This builds conceptual understanding.


Procedural Fluency

Knowledge and use of rules and procedures used in carrying out mathematical processes and also the symbolism used to represent mathematics.

The ineffective practice of teaching procedures in the absence of conceptual understanding results in a lack of retention and increased errors.


Six Components of Mathematics Classrooms

1. Creating an environment that offers all students an equal opportunity to learn

2. Focusing on a balance of conceptual understanding and procedural fluency

3. Ensuring active student engagement in the mathematical practices

4. Using technology to enhance understanding5. Incorporating multiple assessments aligned with

instructional goals and mathematical practices6. Helping students recognize the power of sound

reasoning and mathematical integrity


What Teachers Think

What part(s) of the Investigations program has had a strong impact on student learning?

•Deeper thinking and understanding•Students show work with pictures, numbers and words•Students can now decompose numbers•Mathematical reasoning has improved•Hands-on learning is motivating•Students are able to think flexibly•Closely aligned with the common core state standards•The program is completely student-centered•Mental math skills have improved•Less math concepts in more depth


Jean C. RichardsonMath Specialist K-8

Mayfield City School [email protected]

440-995-7879

mailto:[email protected]

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Investigations in Number, Data, and Space K-5

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