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?

Mathematical Discourse

Mathematical Discourse

            Mathematical discussion in the classroom is not a new idea or concept in education. Educators utilize this as one of the most powerful tools in the development and assessment of student learning. How is the level of mathematical discourse in your classroom?

Connolly and Smith (2002) studied classroom discussion and “the way it should be.” They found student and teacher viewpoints differed in terms of the teacher’s role within small group discussion, competition versus collaboration, familiarity with the discussion topic and comfort within small group settings. As a result of their studies, Connolly and Smith stated the importance of teachers “talking about talk.”  Students not only benefit from knowing the teachers expectations for discussions but also benefit from the definition of norms pertaining to who gets to speak, in what manner, about what, and in what format. 

            Cohen (1992) addressed the value of focusing on the concepts and the type of interaction desired by the teacher. Teachers should not base the value of a discussion solely on the frequency of the student interactions. Instead, teachers must turn their focus on the fact that if students are not taught differently, they will tend to operate at the most concrete level. Exposure to deliberate skill building or motivation techniques can enrich what is happening in the classroom. This means creating tasks which are resource and goal interdependent, individual and group rewards, role assignments and constructive controversy; tasks which require teacher direction. The teacher’s role should be delegating authority to the students and fostering conceptual and elaborate discussions by teaching specific and relevant behaviors.  

Discussing the various roles individual students can take and assigning students these various roles can have a direct affect on the quality of the mathematical discussions. Defining the components of quality discussions and the roles that individuals play within discussions can clear student misconceptions and provide the necessary tools needed to meet teacher expectations. Providing students with role assignments and on-task tools are simple ways to increase student responsibility, bring ownership to the individuals, increase participation and enhance the quality of the discussion.

          Engaging in a quality mathematical discussion is as a complex task. Despite the exposure during the elementary years, teachers must have an awareness of student dependence on teachers as models for communicating with peers and take an active role in establishing expectations. Focus on how students contribute to mathematical discussions over time and the role of the teacher in this process.  Focus on the student’s ability to construct useful or useable concepts to take part in the society of the classroom. Pay special attention to the elements of student discourse including patterns of discourse, levels of response, teacher and student roles, norms and classroom practices. Bring the level of mathematical discourse in the classroom to a new level.

        

Somethin' Fishy

This is one of my favorite activities to do with students.  Modify it for by using any candy, item or special day.

Playground Designs

Playground Designs

Provide groups of students with the CurrentPlayground Design.

Have students take turns identifying the fractional parts of each area of the playground. Direct students to record the fractional areas onto their individual Current Playground Design. 

Note:  Students may ask whether or not the fractions should be written as a fraction of the section or of the whole playground.  This is an opportune time to lead a discussion. Allow students to discuss their question and come to a consensus as a group or as a class based on this discussion.

Give each group a copy of the FuturePlayground Design Guidelines (see attached). Have groups of students follow the Future Playground Design Guidelines to create the new playground design onto graph paper.  Although students are working as a group, each student should create a new playground design.

Note:  Students will be asking many clarifying questions.  Allow the students to ask the whole class for clarification. Allow students to discuss their views and understanding.  You may decide the whole class will need to come to a consensus or allow individual groups to develop their own.  However, students should be prepared to discuss support their reasoning in their written explanations in addition to clarifying any assumptions they have made.

Students should then follow-up the design process by individually responding to the questions found at the bottom of the FuturePlayground Design Guidelines.

Display the completed playground designs and rationales. 

Have students examine the solutions of the groups. As students are looking at the works of their peers, ask them to provide feedback to their peers in the form of guiding questions.  In other words, students should be writing questions that guide the playground designer to consider the accuracy of their work based on a given guideline.   

Have students review the questions asked by their peers. Ask students to reflect on the playground development process including the feedback received by their peers. 

Based on the Playground Problem developed by the Virginia Department of Education 2004

Mathematics Standards of Learning Enhanced Scope and Sequence. (2004). Retrieved from http://www.doe.virginia.gov

Inspiration

“There are many ways to organize curricula. The challenge, now rarely met, is to avoid those that distort mathematics and turn off students.” - Steen, 2007

            Those individuals who attended NCTM Denver in April 2013 could not have felt anything less than inspired.  Inspired by the energy, enthusiasm, research and knowledge shared by the professionals who swarmed the city.  In the hotels, restaurants, walkways, buses and throughout the convention center, there was a constant hum of those who were energized by the mathematics present at this annual meeting and exposition.

                  In one session, Picture Yourself Having Fun at Math, Mary A. Robertson shared how photography can be used to incorporate real-world situations into the math classroom. The use of pictures can be used to reinforce concepts involving geometric shapes, areas, volumes, similar figures, transformations and so much more. I found myself reflecting on how the simple task of incorporating photography into the math classroom can be used inspire a student to look at mathematics through a different lens (which happened to be one of the hashtags used throughout the week).

Who has heard of mARTh?   The basic idea of mARTh is to connect mathematical concepts in a visual, kinesthetic way to make math fun, hands-on and beautiful. The presenter noted the goal of mARTh is to use creative expression to connect students to mathematical concepts.  This is a teacher whose goal is to help students make a personal, physical and visual connection with mathematics. 

            In another session, Making Cents of CCSS, Doug Tyson and Jason Molesk addressed ways to make inferences and justify conclusions from sample surveys, experiments and observational studies through spinning pennies and simulations.  The presenters shared ways to lead students in a statistical significance test in a way that non-stats teachers can implement…even at the middle school level. Did you know there are pennies from the 1960’s that will land nearly 100% of the time on heads when spun on its side? 

David Masunaga’s Geometry on a Shoestring Budget was described as “the most profound, interactive and dynamic activities that don’t require expensive technologies” and that is exactly what it was.  Masunaga kept the audience captivated and yearning for more with cheap and nontraditional geometric manipulatives that could be used to reason and prove various geometric concepts.  Every person in the room was engaged and inspired by Masunaga; the power of one.

Jo Boaler made a valid and strong point in Using Research to Make a Difference where she clearly noted that producing research knowledge is not enough to make changes in the math classroom.   How do K-8 Teachers Change Their Practices after Learning More Mathematics?  shed light on the aspects of teaching practices connecting a teacher’s knowledge and beliefs which led directly to Ritual:  A Category for Understanding Persistent Practices in Math Education; a theoretical study on the persistence of practices in math classrooms which contributed to a theory of rituals in math education. 

            With so much happening in Denver it is impossible to share every ounce of awe and amazement one experienced throughout the week.  During the opening session, The Power of Just One Teacher, Mayim Bialik shared a mission which all teachers should consider encompassing into their rituals, beliefs, practices and everyday practices: to inspire students to pursue STEM education.  This is not to say that we should expect every student make the maths and sciences the end all of education but as educators we should make it our mission to ignite a spark in every student.  As educators we have the immense and immeasurable power to inspire our students to develop a love for mathematics in some way, shape or form.  Every lesson, activity, assessment and mathematical discussion keep the common core and the mathematical practices in mind.  However, do not forget to inspire, engage and help students to develop an appreciation for mathematics that permeates beyond the classroom; you have the power to make an inspirational difference.

I look forward to another inspirational NCTM conference in New Orleans.