Perseverance

With the transition to the Common Core and a recent session at the IMPACT Center at Plymouth State University, perseverance has come into the fore front of my teaching and planning.  What does it mean for students to persevere in the math classroom? How can we teach this to students?  How can our lessons, activities, instruction and curriculum encompass this idea of perseverance?

The quick and easy answer here is problem solving.  Ask teachers how to challenge students and the likely response will include problem solving.  Check in with directors of mathematical instruction and surely problem solving will arise as a focus or solution in one way or another.  However, problem solving does not appear to be a simple answer for developing and promoting perseverance in our students.  In reality problem solving is what makes our students throw their hands in the air. One could say problem solving is the anti-perseverance.

Engaging students in the problem solving process can be described as exploring, examining, applying, testing, reflecting and developing conjectures. Students are given mathematical problem upon problem with the dream that consistent exposure will develop student understanding and mathematical skills needed for the real-world. The emphasis becomes cooperative learning, active participation and investigations that build new knowledge. Again, where does the habit of perseverance come into play? It is expected but how is it taught?

Perseverance is commitment, hard work, patience and endurance. Perseverance is a willingness to try and try again.  Check Webster’s online dictionary and you will see perseverance defined as a “continued effort to do or achieve something despite difficulties, failure, or opposition: the action or condition or an instance of persevering.”  How do we incorporate this into our mathematical classrooms?  We expect it and want students to develop this as one of their very own habits of mind but as teachers we need to teach this.

There is not a quick and simple answer to teaching perseverance.  It is not going to magically happen in one class or even in one year. As educators we can only model, expose and encourage this habit regularly and regularly.  Here are some suggestions on how to develop perseverance:

• Give students non-routine problems which may appear impossible.
• Let students wonder and inquire for extended times. Refrain from giving out the correct answer.  Prolong the awe and wonderment for classes, days and even weeks.
• Allow students to share observations and build off one another’s reasoning.  Let students support and argue the findings of another. 
• Ask questions and expect students to prove themselves.  Expect convincing arguments.
• Let students experience failure.  It is okay for students to take a risk and find out that was the wrong route to take.
• Work with students and show them that you don’t have all the answers.  Model the process of learning together.

Perseverance….the habit of mind which teachers are expected to teach must persevere to perfect.

The Common Core State Standards are Coming: What’s Your Problem?

            Lingering in the air are the Common Core State Standards.  Administrators, teachers, specialists, and entire districts are in a state of wonder and insecurity.  How are we going to transition from the GLEs to the CCSS with ease?  How are we going to transition to the CCSS without leaving gaps in student understanding? How can teachers efficiently and effectively transition to the CCSS without affecting student learning? 

            The CCSS stress the mathematical habits of mind, the inclusion of mathematical practices and mathematical processes.

·      Make sense of problems and persevere

·      Attend to precision

·      Reason abstractly and quantitatively

·      Construct viable arguments and critique the reasoning of others

·      Model with mathematics

·      Use appropriate tolls strategically

·      Look for and make use of structure

·      Look for and express regularity in repeated reasoning

           Embedded in our current practices are these very same habits, practices and processes.  Currently we push students beyond the everyday “drill and kill” into the higher levels of thought through modes of instruction, classroom activities, applications and assessment.  When we narrow down where and when we are asking students to perform beyond the basic skills we can certainly look at one’s mathematical competence in problem solving.

            Assessing students’ problem solving abilities gives educators a peek inside the mathematical mind of the learner.  Given a rich problem, students can show the mathematical knowledge, skill, understanding and any misconceptions they may have. To proficiently problem solve students must have a deeper knowledge base than the application of algorithms and procedural knowledge. When given a rich problem, students must have an understanding of the mathematics; how to justify, apply, explain, use appropriate tools and engage in the mathematical practices.  The key here is providing rich problems where students are given the opportunity apply the skills and habits we need to assess; the proficiencies and practices proposed by the CCSS.

             Look through those file cabinets, memory sticks and internet resources for your favorite problem solving task. Adapt this problem to make it one which is asks students to apply pattern building, conjecturing, generalizations and mathematical justifications.  Ask students to explain what they are thinking, how it can be solved or modeled another way, how they know that something is true or if something always works.  Give students the opportunity to show their skills in adaptive reasoning, conceptual understanding, productive disposition, strategic competence and procedural fluency. You have made this problem your own and adaptable to the CCSS. Connect it to a standard and you are one step closer to a smooth transition. This is your “problem.”

The CCSS are not asking educational systems to get rid of what works.  In reading a draft of the Content Specifications with Content Mapping for the Summative Assessment of the CCSS, there are four claims which put the goals of the CCSS in perspective.

·      Explain and apply mathematical concepts and procedures with precisions and fluency

·      Construct viable arguments to support their reasoning and critique the reasoning of others

·      Analyze complex, real-world scenarios and use mathematical models to interpret and solve problems

·      Frame and solve a range of complex problems in pure and applied mathematics

The CCSS are asking educators to continue working with what they know works with a clearer national focus to develop a cohesion that has been lacking in the mathematical arena. This is the time for educators to reflect on their instruction and determine what connections can be made to the CCSS.  Start with problem solving. No need to reinvent the wheel; just refine it. Think to yourself…The Common Core State Standards are coming. What’s my problem?