One of the unique features of the Common Core Standards for
Mathematics is the focus on

*Content*standards and*Process*standards. These*process*standards (there are 8 of them) are not a checklist of teacher to-dos, but rather they are*proficiencies*for students to experience and demonstrate as they master the content standards.
Each of the eight Standards for Mathematical Practice begins
with three words—

*Mathematically proficient students*. This language establishes an expectation for evidence of student growth toward proficiency in each of these eight practices as part of the K–12 mathematics learning experience.
And

The Standards for

*Mathematical Practice*describe what*students*are*doing*as they engage in learning the CCSS for mathematics content standards. How should students engage with mathematics tasks and interact with their fellow students? How well do teachers develop students’ engagement in mathematics reflecting the CCSS Mathematical Practices?
One of the fundamental shifts of the Common Core for
Mathematics is that

**how**students learn the mathematics, is now as important as**what**students learn. And, as a school leader, you need to both support (celebrate) and hold accountable teacher lesson planning design and implementation that intentionally plans for these student proficiencies.
Over the next few blogs, I will outline ideas for each of
the eight mathematical practices around two critical questions:

1. What is the intent of each Mathematical practice?

2. How will you ensure each collaborative team addresses the
CCSS Mathematical practice on a unit-by-unit basis?

It is up to you and your teachers to shift instruction and provide
evidence that students are actually developing each

*practice.***Mathematical Practice 1: Make Sense of Problems and Persevere in Solving Them**

Mathematical Practice 1, “Make sense of problems and
persevere in solving them

**,”**refers to the ability of students to explain to themselves (and others) the meaning of a mathematical task or problem and look for entry points to its solution (NGA & CCSSO, 2010, p. 5).

*What Is the Intent of Mathematical Practice 1?*
Problem solving is one of the hallmarks of mathematics
and is the essence of doing mathematics (NCTM, 1989). When students are engaged
in problem solving, it means they are drawing on their understanding of
mathematical concepts and procedures with the goal to reach a successful
response to the problem.

As you study the expectations for Mathematical Practice
1, you will notice several areas for student proficiency including:

1. Students
make conjectures about the meaning of a solution and plan a solution pathway.

2. Students
try special cases or simpler forms to gain insight (they hypothesize and test
conjectures).

3. Students
monitor and evaluate their progress and discuss with others.

4. Students
understand multiple approaches and ask the question, “Does this solution make
sense?”

5. Students
explain correspondences between equations, tables, graphs, verbal descriptions,
and data and search for regularity, patterns, or trends.

Successful problem solving does not mean that students
will always conclude with the correct response to a problem, but rather that
students will undertake a genuine

**to engage in the problem-solving process, drawing on learning resources described in the other practices such as appropriate tools, using their prior knowledge, engaging in mathematical discourse with other students, and asking questions to make progress in the problem solving process. Successful problem solvers also recognize that powerful learning can be experienced even when an appropriate answer to a problem ultimately evades the student.***effort***How Can Collaborative Teams Address Mathematical Practice 1?**

Teachers play the important role in supporting students’
ability to make sense of problems and persevere in solving them. The first of
these roles is the presentation of appropriate problems or tasks for students
to solve. While it seems that

*appropriate*is subjective, there are six questions you can present to teachers for discussion within their collaborative teams when planning lessons to assess the quality of problem solving within a common or shared mathematical task.
As we develop common tasks and problems to be used
during the unit, we should consider:

1. Is the problem interesting to students?

2. Does the problem involve meaningful mathematics?

3. Does the problem provide an opportunity for
students to apply and extend mathematics?

4. Is the problem challenging for students? Does it
apply a complexity of reasoning at the DOK level 3 or 4?

5. Does the problem support the use of multiple
strategies or solution pathways?

6. Will students’ interactions with the problem and
peers reveal information about their mathematics understanding?

Observing students’ interactions with a mathematical task
(for example, students’ work, discourse, tools, and representations) will
provide information about how their thinking is hindered or evolving by
interaction with the problem or task selected. This list of questions is not
exhaustive, but it is a beginning step toward examining problems for the
potential benefit they can provide for advancing students’ mathematical problem
solving and learning.

Your leadership role is to ensure teachers work in collaborative
teams to discuss how to help students understand that the answer is not the
final step in the problem-solving process. A great deal of mathematical
learning can happen when students are guided to explain and justify processes
and check the reasonableness of the solution. After teaching lessons within the
unit, teachers on the team should ask:

*“Is there evidence that students are learning other ways of solving the problem? Is there evidence that students are making and learning mathematical connections to other problems and mathematical connections as they persevere in solving the problem?”*

As a school leader, you must focus deliberate attention on implementing
the CCSS Mathematical Practices, part of your challenge will be to envision and
teach what the practices "look and sound" like in the classroom as part of instruction.

The student tasks teachers design, the questions they ask in
the classroom, and the discourse in which students participate will all combine
to advance students’ abilities to

*engage*with peers in the Mathematical Practices.
I'd argue that the first consideration (Is the problem interesting to students?) for creating common tasks and problems is the most important and one that we as educators sometimes fail to meet, putting the cart before the horse. Getting students to buy-in is a necessity. Providing interesting tasks is a necessity for students to be curious. When we neglect this component we perpetuate the student perception that math is used to solve contrived problems of little significance.

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