1. The National Council of Supervisors of Mathematics
The Common Core State Standards
Illustrating the Standards for Mathematical Practice:
Getting Started with the Practices
Facilitators will need to have the following resources for each participant:
A copy of the PPT (formatted with two slides per page)
A copy of the participant handouts (see Introduction Handout and Resources PDF)
- Common Core Content Standards for Mathematics
- Bulleted version of the Common Core State Standards for Mathematical Practice (If you can, it is nice to have these Standards printed on card stock and laminated!)
3. Other materials as needed such as chart paper and markers, highlighters or pens for participants, blank journals to record their thinking.

2. “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)

3. What’s different about these standards?
Accountability
Communication
New Definition of proficient
Accountability for both the content and practice standards! These new standards will be assesses using a national assessment. State assessment programs for mathematics and ELA is generally drop away in the states where the standards have been adopted.

4. Integration of Standards for Mathematical Practice
Not “Problem Solving Fridays”
Not “enrichment” for advanced students
Most lie in the process of arriving at an answer, not necessarily in the answer itself
Every lesson should seek to build student expertise in Content and Practice standards

5. 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)
The new Standards for Mathematical Practice were based on the NCTM Process Standards and the National Research Council’s (NRC) Stands of Mathematical Proficiency.
The next four slides describe the connections between the new Standards for Mathematical Practice and their predecessors… the NCTM Process Standards and the NRC’s Stands of Mathematical Proficiency. Review each of the slides and ask for any questions from participants.

6. Underlying Frameworks
National Council of Teachers of Mathematics
5 Process Standards
Problem Solving
Reasoning and Proof
Communication
Connections
Representations
Participants may or may not be familiar with the Process Standards. Either way, the purpose of this slide is to establish history so don’t spend too much time here.
NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

7. Underlying Frameworks
Strands of Mathematical Proficiency
Strategic Competence
Adaptive Reasoning
Conceptual Understanding
Productive Disposition
Procedural Fluency
Some participants are likely to be unfamiliar with NRC Adding it Up. Mention that these build upon and expand NCTM Process Standards. Briefly mention inter-related nature of these proficiencies, then move to next slide that defines each of these proficiencies.
Adding It Up:Helping Children Learn Mathematics
National Research Council
NRC (2001). Adding It Up. Washington, D.C.: National Academies Press.

8. 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.
Facilitators won’t need to read this slide aloud, but suggest that participants do so if they are not familiar with the Strands of Mathematical Proficiency.
Consider doing turn and talk—how are these different from NCTM process Standards.
e.g., strategic competence includes formulating, representing and solving problems.
Be sure to draw attention to productive disposition—since that is different than what is explicitly in NCTM Process Standards and is very important for practices.
Many educators are continuing to use both the Strands of Mathematical Proficiency and the NCTM Process Standards with the CCSS Standards for Mathematical Practice since each adds depth and dimension to our understanding of mathematical fluency.

9. Standards for Mathematical Practice
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
For the next activity refer participants to the handout with the description of the CCSS Standards for Mathematical Practices in bulleted form.

10. The Standards for Mathematical Practice
Take a moment to examine the first three words of each of the eight mathematical practices… what do you notice?
Mathematically proficient students…
Do activity on slide . . .

11. The Standards for Mathematical Practice
What are the verbs that illustrate the student actions for your chosen mathematical practice?
Circle, highlight or underline them for your assigned practice…
Discuss with a partner: How does this practice compare to your current practice?
Assign teachers in each section of the room or at a table a number from 1 to 8. Their number identifies their assigned practice.
Then ask participants to individually read and highlight the verbs in their assigned practice.
Next, have participants turn and talk with a partner, or in table groups (if sitting at table).

12. The Standards for Mathematical Practice
#1: Explain and make conjectures…
#2: Make sense of…
#3: Understand and use…
#4: Apply and interpret…
#5: Consider and detect…
#6: Communicate precisely to others…
#7: Discern and recognize…
#8: Notice and pay attention to…
This just highlights some of the verbs . Quickly show and move on to next slide

13. The Standards for Mathematical Practice
On a scale of 1 (low) to 6 (high), to what extent are you or your school/district promoting all students’ proficiency in the practice you discussed?
What evidence might you site for your rating?
Asking for a rating gets participants into a deeper discussion of their current practice compared to what is called for in the Standards. Depending on the nature of your session, you might want to spend more/less time on this.
Consider asking for a brief show of hands re: ratings of 6, Etc. to get an idea of where participants think they are.
Equally important to a productive discussion will be to push participants to share what they consider evidence for their rating. This portion of the discussion will add to what teachers understand about what the practices intend for students and classroom practice.

14. Standards for Mathematical Practice
On one hand, the Standards for Mathematical Practice describe mathematical content students need to learn.
SP1. Make sense of problems
“… students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.”
The Standards for Mathematical Practice have a dual nature. On one hand, they are meant to describe additional content that students need to know. The intent is for students to develop proficiency in the Standards while they are learning content—not intended to be separate . . .
On the other hand, the Practices also suggest the types of mathematical activities students will need to engage in to learn mathematics content. We will see an example of both today.

15. Standards for Mathematical Practice
On the other hand, they describe the nature of the learning experiences, thinking processes, habits of mind, and dispositions that students need to develop a deep, flexible, and enduring understanding of mathematics; in this sense they are also a means to an end.
SP1. Make sense of problems
“….they [students] analyze givens, constraints, relationships and goals. ….they monitor and evaluate their progress and change course if necessary. …. and they continually ask themselves “Does this make sense?”
Help participants to understand that the Practices are dense statements that describe both the content and thinking processes/habits of mind that students need to develop.

16. Structuring the Practices
This organization of the Standards for Mathematical Proficiency was developed by one of the principal authors of the Common Core State Standards for Mathematics, Dr. William McCallum, University of Arizona. His rationale for this organization given at the website below is as follows:
“In the progressions project, we’ve been discussing how best to represent the Standards for mathematical practice. The practices are signposted throughout the documents, but we’ve also been thinking about how to provide some structure for the practice Standards that will help people avoid fruitless tagging exercises in their efforts to integrate the practice Standards into the content Standards. If you think about it long enough you can associate just about any practice standard with any content standard, but this sort of matrix thinking can lead to a dilution of the force of the practice Standards—if you try to do everything all the time, you end up doing nothing. This diagram is an attempt to provide some higher order structure to the practice Standards, just as the clusters and domains provide higher order structure to the content Standards.”

17. Standards for Mathematical Practice
The eight Standards for Mathematical Practice place an emphasis on students doing mathematics and demonstrating learning.
Equitable achievement will begin with an understanding of how the selection of tasks, the assessment of tasks, and the student learning environment can support or undermine equity in our schools.
One last idea before we close this session. Access to the type of tasks that let students engage in the practices, that is in doing mathematics, can be an equity issue. Offering all students the opportunity to demonstrate their learning, explore new ideas, use a variety of tools including technology based tools, and struggle on challenging tasks is not intended for just a few students, but for all students AND will require changes in the way we teach mathematics in order to enable all students to participate successfully.
Central to this shift in practice are the tasks we choose to use each day in our classrooms.

18. Resources for the practice standards